List of integer sequences with links to LODA programs.

  • A100005 (program): Bisection of A001414.
  • A100006 (program): Integer log of 2n: sum of primes dividing 2n (with repetition).
  • A100007 (program): Number of unitary divisors of 2n-1 (d such that d divides 2n-1, GCD(d,(2n-1)/d)=1). Bisection of A034444.
  • A100008 (program): Number of unitary divisors of 2n.
  • A100019 (program): a(n) = n^4 + n^3 + n^2.
  • A100021 (program): Numbers of the form 3prime(n) - prime(n+1) - 3.
  • A100029 (program): Bisection of A008472.
  • A100030 (program): Bisection of A008472.
  • A100031 (program): Bisection of A005384.
  • A100032 (program): Bisection of A005384.
  • A100033 (program): Bisection of A001700.
  • A100036 (program): a(n) = smallest m such that A100035(m) = n.
  • A100037 (program): Positions of occurrences of the natural numbers as a second subsequence in A100035.
  • A100038 (program): Positions of occurrences of the natural numbers as third subsequence in A100035.
  • A100039 (program): Positions of occurrences of the natural numbers as fourth subsequence in A100035.
  • A100040 (program): a(n) = 2*n^2 + n - 5.
  • A100041 (program): a(n) = 2*n^2 + n - 7.
  • A100042 (program): a(n) = prime(n)*2^prime(n).
  • A100043 (program): a(n) = (3*n-1)!.
  • A100044 (program): Decimal expansion of Pi^2/9.
  • A100047 (program): A Chebyshev transform of the Fibonacci numbers.
  • A100048 (program): A Chebyshev transform of the Pell numbers.
  • A100049 (program): A Chebyshev transform of the Padovan numbers.
  • A100050 (program): A Chebyshev transform of n.
  • A100051 (program): A Chebyshev transform of 1,1,1,…
  • A100052 (program): A Chebyshev transform of the odd numbers.
  • A100053 (program): Maximum run of white (or OFF) cells in generation n of the Rule 30 elementary cellular automaton.
  • A100057 (program): Sum of absolute differences of p(n) defined in A054065, oriented around a clock.
  • A100058 (program): Expansion of 1 / (1 - 3x - x^2 + 2x^3).
  • A100059 (program): First differences of A052911.
  • A100061 (program): Numerator of the probability that an integer n occurs in the cumulative sums of the decimal digits of a random real number between 0 and 1.
  • A100062 (program): Denominator of the probability that an integer n occurs in the cumulative sums of the decimal digits of a random real number between 0 and 1.
  • A100063 (program): A Chebyshev transform of Jacobsthal numbers.
  • A100066 (program): Expansion of x/((1-x)sqrt(1-4x^2)).
  • A100067 (program): a(n) = Sum_{k=0..floor(n/2)} binomial(n,k)*2^(n-2*k).
  • A100068 (program): a(n) = Sum_{k=0..floor(n/2)} binomial(n,k)*3^(n-2*k).
  • A100069 (program): a(n) = Sum_{k=0..floor(n/2)} binomial(n,k)*4^(n-2*k).
  • A100070 (program): Number a(n) of forests with two components in the complete bipartite graph K_{n,n}.
  • A100071 (program): a(n) = n * binomial(n-1, floor((n-1)/2)) = n * max_{i=0..n} binomial(n-1, i).
  • A100073 (program): Number of representations of n as the difference of two positive squares.
  • A100087 (program): Expansion of x/(sqrt(1-4*x^2) + x - 1).
  • A100088 (program): Expansion of (1-x^2)/((1-2*x)*(1+x^2)).
  • A100089 (program): a(n) = (3*n+1)!.
  • A100095 (program): An inverse Chebyshev transform of the Fibonacci numbers.
  • A100096 (program): An inverse Chebyshev transform of the Jacobsthal numbers.
  • A100097 (program): An inverse Chebyshev transform of the Pell numbers.
  • A100098 (program): An inverse Chebyshev transform of (1-x)/(1-2x).
  • A100099 (program): An inverse Chebyshev transform of x/(1-2x).
  • A100100 (program): Triangle T(n,k) = binomial(2*n-k-1, n-k) read by rows.
  • A100101 (program): Bell(2n)*(2n-1)!!, where Bell are the Bell numbers A000110.
  • A100102 (program): a(n) = 2^(2*n)-(2*n-1).
  • A100103 (program): a(n) = 2^(2*n) - 2*n.
  • A100104 (program): a(n) = n^3 - n^2 + 1.
  • A100105 (program): a(n) = 2^prime(n)-prime(n).
  • A100107 (program): Inverse Moebius transform of Lucas numbers (A000032) 1,3,4,7,11,..
  • A100109 (program): a(n) = n^3 - 2*n^2 + 2.
  • A100111 (program): a(n) = Sum_{k >= 0} prime(n-4k).
  • A100112 (program): If n is the k-th squarefree number then a(n) = k, otherwise a(n) = 0.
  • A100118 (program): Numbers whose sum of prime factors is prime (counted with multiplicity).
  • A100119 (program): a(n) = n-th centered n-gonal number.
  • A100130 (program): Expansion of (eta(q) * eta(q^4) / eta(q^2)^2)^24 in powers of q.
  • A100131 (program): a(n) = Sum_{k=0..floor(n/4)} binomial(n-2k, 2k)*2^(n-4k).
  • A100132 (program): a(n) = Sum_{k=0..floor(n/4)} C(n-2k,2k) * 2^(n-3k).
  • A100133 (program): a(n) = Sum_{k=0..floor(n/4)} C(n-2k,2k) * 3^k * 2^(n-4k).
  • A100134 (program): a(n) = Sum_{k=0..floor(n/6)} binomial(n-3k,3k).
  • A100135 (program): a(n) = Sum_{k=0..floor(n/6)} C(n-3k,3k) * 2^k.
  • A100136 (program): a(n) = Sum_{k=0..floor(n/6)} C(n-3k,3k) * 3^k.
  • A100137 (program): a(n) = Sum_{k=0..floor(n/6)} C(n-3k,3k) * 2^(n-6k).
  • A100138 (program): a(n) = Sum_{k=0..floor(n/6)} C(n-3k,3k) * 2^(n-5k).
  • A100139 (program): a(n) = Sum_{k=0..floor(n/6)} C(n-3k,3k) * 3^k * 2^(n-6k).
  • A100143 (program): Unique sequence with a(1)=1 where each a(n) occurs in the same order a(n) times consecutively in its sequence of first differences which contains no other terms.
  • A100144 (program): First differences of A100143.
  • A100145 (program): Structured great rhombicosidodecahedral numbers.
  • A100146 (program): Structured great rhombicubeoctahedral numbers.
  • A100147 (program): Structured icosidodecahedral numbers.
  • A100148 (program): Structured small rhombicosidodecahedral numbers.
  • A100149 (program): Structured small rhombicubeoctahedral numbers.
  • A100150 (program): Structured snub cubic numbers.
  • A100151 (program): Structured snub dodecahedral numbers.
  • A100152 (program): Structured truncated cubic numbers.
  • A100153 (program): Structured truncated dodecahedral numbers.
  • A100154 (program): Structured truncated icosahedral numbers.
  • A100155 (program): Structured truncated octahedral numbers.
  • A100156 (program): Structured truncated tetrahedral numbers.
  • A100157 (program): Structured rhombic dodecahedral numbers (vertex structure 9).
  • A100158 (program): Structured disdyakis triacontahedral numbers (vertex structure 11).
  • A100159 (program): Structured disdyakis triacontahedral numbers (vertex structure 7).
  • A100160 (program): Structured disdyakis triacontahedral numbers (vertex structure 5).
  • A100161 (program): Structured disdyakis dodecahedral numbers (vertex structure 9).
  • A100162 (program): Structured disdyakis dodecahedral numbers (vertex structure 7).
  • A100163 (program): Structured disdyakis dodecahedral numbers (vertex structure 5).
  • A100164 (program): Structured rhombic triacontahedral numbers (vertex structure 11).
  • A100165 (program): Structured rhombic triacontahedral numbers (vertex structure 7).
  • A100166 (program): Structured deltoidal hexacontahedral numbers (vertex structure 9).
  • A100167 (program): Structured pentagonal icositetrahedral numbers (vertex structure 13).
  • A100168 (program): Structured pentagonal icositetrahedral numbers (vertex structure 10).
  • A100169 (program): Structured pentagonal hexacontahedral numbers (vertex structure 16).
  • A100170 (program): Structured pentagonal hexacontahedral numbers (vertex structure 10).
  • A100171 (program): Structured triakis octahedral numbers (vertex structure 4).
  • A100172 (program): Structured triakis icosahedral numbers (vertex structure 4).
  • A100173 (program): Structured pentakis dodecahedral numbers (vertex structure 6).
  • A100174 (program): Structured tetrakis hexahedral numbers (vertex structure 5).
  • A100175 (program): Structured triakis tetrahedral numbers (vertex structure 4).
  • A100176 (program): Structured octagonal prism numbers.
  • A100177 (program): Structured meta-prism numbers, the n-th number from a structured n-gonal prism number sequence.
  • A100178 (program): Structured hexagonal diamond numbers (vertex structure 5).
  • A100179 (program): Structured heptagonal diamond numbers (vertex structure 5).
  • A100181 (program): Odd terms in A120070.
  • A100182 (program): Structured tetragonal anti-prism numbers.
  • A100183 (program): Structured hexagonal anti-prism numbers.
  • A100184 (program): Structured octagonal anti-prism numbers.
  • A100185 (program): Structured meta-anti-prism numbers, the n-th number from a structured n-gonal anti-prism number sequence.
  • A100186 (program): Structured heptagonal anti-diamond numbers (vertex structure 7).
  • A100187 (program): Structured octagonal anti-diamond numbers (vertex structure 7).
  • A100188 (program): Polar structured meta-anti-diamond numbers, the n-th number from a polar structured n-gonal anti-diamond number sequence.
  • A100189 (program): Equatorial structured meta-anti-diamond numbers, the n-th number from an equatorial structured n-gonal anti-diamond number sequence.
  • A100190 (program): The (4,1)-entry in the 4 X 4 matrix M^n, where M = [1,0,0,0 / 3,3,0,0 / 3,6,3,0 / 1,3,3,1].
  • A100191 (program): The (1,1)-entry in the 3 X 3 matrix M^n, where M = [1,2,1 / 2,2,0 / 1,0,0].
  • A100192 (program): a(n) = Sum_{k=0..n} binomial(2n,n+k)*2^k.
  • A100193 (program): a(n) = Sum_{k=0..n} binomial(2n,n+k)*3^k.
  • A100196 (program): Numbers of positive integer cubes <= n^2.
  • A100197 (program): Numbers of squares in the range [n^3, (n+1)^3].
  • A100198 (program): Let f(0) = -1, f(n) = Moebius(n) = A008683(n) for n>0. Sequence gives partial sums a(n) = Sum_{ 0 <= i <= n} f(i).
  • A100201 (program): Primes of the form 23n+3.
  • A100202 (program): Primes of the form 13*k + 3.
  • A100203 (program): Primes of the form 37n+3.
  • A100204 (program): Numbers of cubes in the range [n^2, (n+1)^2].
  • A100206 (program): Row sums of Clark’s triangle A046902.
  • A100207 (program): a(n) = 4 + 8*n + 10*n^2 + 4*n^3.
  • A100212 (program): Expansion of (x^5 + 2*x^4)/(1/2*x^2 - 2*x^6 + 2*x^5 - x^4 - 1/2*x + 1/4).
  • A100213 (program): G.f. x* (4-7*x+2*x^2-8*x^4+16*x^5-16*x^6) / ((2*x-1) * (2*x^2-1) * (2*x^2-2*x+1) * (2*x^2+1)).
  • A100214 (program): a(n) = 4*n^3 + 4.
  • A100215 (program): Expansion of (4 - 7*x + 2*x^2)/((1-2*x)*(1 - 2*x + 2*x^2)).
  • A100216 (program): Relates row sums of Pascal’s triangle to expansion of cos(x)/exp(x).
  • A100217 (program): Diagonal sums of a binomial number triangle.
  • A100218 (program): Riordan array ((1-2x)/(1-x), (1-x)).
  • A100219 (program): Expansion of (1-2*x)/((1-x)*(1-x+x^2)).
  • A100223 (program): G.f. A(x) satisfies: 2^n - 1 = Sum_{k=0..n} [x^k]A(x)^n and also satisfies: (2+z)^n - (1+z)^n + z^n = Sum_{k=0..n} x^k^n for all z, where [x^k]A(x)^n denotes the coefficient of x^k in A(x)^n.
  • A100224 (program): Triangle, read by rows, of the coefficients of [x^k] in G100224(x)^n such that the row sums are 2^n-1 for n>0, where G100224(x) is the g.f. of A100224.
  • A100225 (program): G.f. A(x) satisfies: 3^n - 1 = Sum_{k=0..n} [x^k]A(x)^n and also satisfies: (3+z)^n - (1+z)^n + z^n = Sum_{k=0..n} x^k^n for all z, where [x^k]A(x)^n denotes the coefficient of x^k in A(x)^n.
  • A100226 (program): Triangle, read by rows, of the coefficients of [x^k] in G100225(x)^n such that the row sums are 3^n-1 for n>0, where G100225(x) is the g.f. of A100225.
  • A100227 (program): Main diagonal of triangle A100226.
  • A100230 (program): Main diagonal of triangle A100229.
  • A100233 (program): a(n) = Lucas(3*n) - 1.
  • A100236 (program): Main diagonal of triangle A100235.
  • A100237 (program): Secondary diagonal of triangle A100235 divided by row number: a(n) = A100235(n+1,n)/(n+1) for n >= 0.
  • A100238 (program): G.f. A(x) satisfies: 2^n + 1 = Sum_{k=0..n} [x^k] A(x)^n for n>=1.
  • A100239 (program): G.f. A(x) satisfies: 3^n + 1 = Sum_{k=0..n} [x^k]A(x)^n and also satisfies: (3+z)^n + (1+z)^n - z^n = Sum_{k=0..n} x^k^n for all z, where [x^k]A(x)^n denotes the coefficient of x^k in A(x)^n.
  • A100240 (program): G.f. A(x) satisfies: 4^n/2 = Sum_{k=0..n} [x^k]A(x)^n and also satisfies: ((4+z)^n + z^n)/2 = Sum_{k=0..n} x^k^n for all z, where [x^k]A(x)^n denotes the coefficient of x^k in A(x)^n.
  • A100242 (program): a(n) = n^5 - n^2*(n^2 - 1)/2.
  • A100244 (program): a(n) = smallest positive integer such that {1 + product{k=1 to n} a(k)} is coprime to n.
  • A100247 (program): Slanted Catalan convolution table, read by rows of 2*n+1 terms in row n, where T(n,k) = C(n+2*k-[k/2],k)*(n-[k/2])/(n+2*k-[k/2]).
  • A100248 (program): Row sums of the slanted Catalan convolution table A100247.
  • A100249 (program): Antidiagonal sums of the slanted Catalan convolution table A100247.
  • A100250 (program): Positions where values change in A100144.
  • A100255 (program): Squares of pentagonal numbers: a(n) = (1/4)*n^2*(3*n-1)^2.
  • A100256 (program): Squares of second pentagonal numbers: (1/4) n^2(3n+1)^2.
  • A100257 (program): Triangle of expansions of 2^(k-1)*x^k in terms of T(n,x), in descending degrees n of T, with T the Chebyshev polynomials.
  • A100259 (program): Coefficient of x^2 in 2n-th normalized Legendre polynomial.
  • A100260 (program): Fixed point of morphism 0 -> 01, 1 -> 02, 2 -> 31, 3 -> 32.
  • A100262 (program): Expansion of A(x)^2, where A(x) = o.g.f. of n^n (A000312).
  • A100279 (program): a(n) = A100107(A000032(n)).
  • A100280 (program): Inverse permutation to A099896.
  • A100282 (program): a(n) = A100280(A100280(n)).
  • A100283 (program): a(n) = floor(p*(n+1)) - floor(p*(n)) - 1 where p = Padovan plastic number = 1.324718… (cf. A060006).
  • A100284 (program): Expansion of (1-4x-x^2)/((1-x)(1-4x-5x^2)).
  • A100285 (program): Expansion of (1+5x^2)/(1-x+x^2-x^3).
  • A100286 (program): Expansion of (1+2x^2-2x^3+2x^4)/(1-x+x^2-x^3+x^4-x^5).
  • A100287 (program): First occurrence of n in A100002; the least k such that A100002(k) = n.
  • A100290 (program): Numbers divisible by smallest number with same number of 1’s in its binary expansion. That is, A038573(a(n)) divides a(n).
  • A100295 (program): Simple recursive sequence generated from a symmetric matrix.
  • A100296 (program): Sequence generated from a symmetric matrix.
  • A100299 (program): Number of dissections of a convex n-gon by nonintersecting diagonals into an even number of regions.
  • A100300 (program): Number of dissections of a convex n-gon by nonintersecting diagonals into an odd number of regions.
  • A100302 (program): Expansion of (1 - x - 6*x^2)/((1 - x)*(1 - x - 8*x^2)).
  • A100303 (program): Expansion of (1 - x - 4*x^2)/(1 - x - 8*x^2).
  • A100304 (program): Expansion of (1 - x - 6*x^2)/(1 - x - 8*x^2).
  • A100305 (program): Expansion of (1 - x - 4*x^2)/(1 - 2*x - 7*x^2 + 8*x^3).
  • A100307 (program): Modulo 2 binomial transform of 3^n.
  • A100308 (program): Modulo 2 binomial transform of 5^n.
  • A100309 (program): Modulo 2 binomial transform of 6^n.
  • A100310 (program): Modulo 2 binomial transform of 7^n.
  • A100311 (program): Modulo 2 binomial transform of 8^n.
  • A100312 (program): Number of 3 X n binary matrices avoiding simultaneously the right angled numbered polyomino patterns (ranpp) (10;0) and (01;1).
  • A100313 (program): Number of 4 X n binary matrices avoiding simultaneously the right angled numbered polyomino patterns (ranpp) (10;0) and (01;1).
  • A100314 (program): Number of 2 X n 0-1 matrices avoiding simultaneously the right angled numbered polyomino patterns (ranpp) (00;1), (01;0), (10;0) and (01;1).
  • A100315 (program): Number of 3 X n 0-1 matrices avoiding simultaneously the right angled numbered polyomino patterns (ranpp) (00;1), (01;0), (10;0) and (01;1).
  • A100316 (program): Number of 4 X n 0-1 matrices avoiding simultaneously the right angled numbered polyomino patterns (ranpp) (00;1), (01;0), (10;0) and (01;1).
  • A100317 (program): Numbers k such that exactly one of k - 1 and k + 1 is prime.
  • A100318 (program): Numbers n such that at least one of n-1 and n+1 is composite.
  • A100319 (program): Even numbers m such that at least one of m-1 and m+1 is composite.
  • A100320 (program): A Catalan transform of (1 + 2*x)/(1 - 2*x).
  • A100321 (program): The trinomial transform (A027907) gives powers of 2, while the trinomial transform of this sequence shift one place left gives powers of 3.
  • A100326 (program): Triangle, read by rows, where row n equals the inverse binomial of column n of square array A100324, which lists the self-convolutions of SHIFT(A003169).
  • A100327 (program): Row sums of triangle A100326, in which row n equals the inverse binomial of column n of square array A100324.
  • A100328 (program): Column 1 of triangle A100326, in which row n equals the inverse binomial of column n of square array A100324, with leading zero omitted.
  • A100329 (program): a(n) = -a(n-1)-a(n-2)-a(n-3)+a(n-4), a(0)=0, a(1)=1, a(2)=-1, a(3)=0.
  • A100334 (program): An inverse Catalan transform of F(2n).
  • A100335 (program): An inverse Catalan transform of J(2n).
  • A100336 (program): Arshon’s sequence with a different start: start from 2 and replace the letters in odd positions using 1 -> 123, 2 -> 231, 3 -> 312 and the letters in even positions using 1 -> 321, 2-> 132, 3 -> 213.
  • A100337 (program): Arshon’s sequence with a different start: start from 3 and replace the letters in odd positions using 1 -> 123, 2 -> 231, 3 -> 312 and the letters in even positions using 1 -> 321, 2-> 132, 3 -> 213.
  • A100340 (program): Numerators of the convergents in the continued fraction expansion for the constant given by A100338, where the partial quotients equal A006519 (greatest power of 2 dividing n).
  • A100341 (program): Denominators of the convergents in the continued fraction expansion for the constant given by A100338, where the partial quotients equal A006519 (greatest power of 2 dividing n).
  • A100342 (program): Numerators of the convergents in the continued fraction expansion for twice the constant given by A100338, where the partial quotients equal A006519 (greatest power of 2 dividing n) interleaved with 2’s.
  • A100343 (program): Denominators of the convergents in the continued fraction expansion for twice the constant given by A100338, where the partial quotients equal A006519 (greatest power of 2 dividing n) interleaved with 2’s.
  • A100345 (program): Triangle read by rows: T(n,k) = n*(n+k), 0<=k<=n.
  • A100367 (program): Even numbers with two prime factors, not counting multiplicity.
  • A100368 (program): Numbers of the form 2^k * p where k > 0 and p is an odd prime.
  • A100371 (program): a(n) = 2^phi(n) - 1 = A066781(n) - 1.
  • A100374 (program): Largest power of 2 dividing prime(n+1) - prime(n), the n-th consecutive prime difference.
  • A100375 (program): a(n) is the n-th consecutive prime difference divided by the largest power of 2 which divides it.
  • A100376 (program): a(n) is the largest number x such that for m=n to n+x-1, A006530(m) increases.
  • A100381 (program): a(n) = 2^n*binomial(n,2).
  • A100387 (program): a(n) is the largest number x such that for m=n to n+x-1, A006530(m) decreases.
  • A100388 (program): a(n) = Bell(n) + Fibonacci(n).
  • A100389 (program): a(n) = Bell(n) - Fibonacci(n).
  • A100390 (program): Numbers n where A006530 has a local minimum.
  • A100392 (program): Numbers k such that A006530(k-1) < A006530(k) > A006530(k+1).
  • A100394 (program): a(n) is the subscript of the greatest prime factor of (2*prime(n) + 1).
  • A100396 (program): Bell(n-1) + Fibonacci(n).
  • A100397 (program): Bell(n-1) - Fibonacci(n).
  • A100399 (program): a(n) = Fibonacci(n)^n.
  • A100400 (program): Triangle read by rows: T(n,k) is the number of nonroot nodes of outdegree k (0<=k<=n-1) in all non-crossing trees with n edges.
  • A100401 (program): Digital root of 3^n.
  • A100402 (program): Digital root of 4^n.
  • A100403 (program): Digital root of 6^n.
  • A100404 (program): a(n) = L(n) * n! where L(n) are the Lucas numbers.
  • A100412 (program): a(n) = 8*10^n - 7.
  • A100413 (program): Numbers n such that n is reversal(n)-th even composite number (n is A004086(n)-th even composite number).
  • A100428 (program): Bisection of Kolakoski sequence A000002.
  • A100429 (program): Bisection of Kolakoski sequence A000002.
  • A100430 (program): Bisection of A002417.
  • A100431 (program): Bisection of A002417.
  • A100432 (program): Bisection of A005349.
  • A100433 (program): Bisection of A005349.
  • A100434 (program): G.f.: (1+x)*(3+x)/(1+6*x^2+x^4).
  • A100441 (program): a(n) is the denominator of f(n) where f(1) = 2 and f(n+1) is the solution of x + Sum_{i=1..n} f(i) = x * Product_{i=1..n} f(i).
  • A100442 (program): Binomial transform of A003418.
  • A100443 (program): Inverse binomial transform of A003418.
  • A100444 (program): Bisection of A000255.
  • A100445 (program): Bisection of A000255.
  • A100446 (program): Bisection of A000031.
  • A100447 (program): Bisection of A000031.
  • A100448 (program): Number of triples (i,j,k) with 1 <= i <= j < k <= n and gcd{i,j,k} = 1.
  • A100449 (program): Number of ordered pairs (i,j) with |i| + |j| <= n and gcd(i,j) <= 1.
  • A100450 (program): Number of ordered triples (i,j,k) with |i| + |j| + |k| <= n and gcd(i,j,k) <= 1.
  • A100451 (program): a(n) = 0 for n <= 2; for n >= 3, a(n) = (n-2)*floor((n^2-2)/(n-2)).
  • A100454 (program): a(n) = sum of n-th column in array in A100452.
  • A100455 (program): a(n) = 2^n + sin(n*Pi/2).
  • A100462 (program): Leading diagonal of array in A100461.
  • A100463 (program): a(n) = 2^(n-1) - A100462(n).
  • A100466 (program): Semiprimes of special form: sum of an integer k and the k-th semiprime.
  • A100470 (program): n appears A055642(n) times (appearances equal number of decimal digits).
  • A100472 (program): Inverse modulo 2 modulo transform of 9^n.
  • A100477 (program): a(n) = 3*a(n-1)+2*a(n-2)+a(n-3) if n>=3 else a(n) = n.
  • A100479 (program): Prime(2n-1) + prime(2n).
  • A100481 (program): Greatest prime factor in A095117(n) = greatest prime factor in n + pi(n) where pi(n) is the prime counting function = greatest prime factor in n + A000720(n).
  • A100484 (program): The primes doubled.
  • A100486 (program): a(n) = pi(n) + n-th prime, where pi(n) = A000720(n) is the prime counting function.
  • A100490 (program): Odd numbers ending in {1,3,7,9} that are not primes.
  • A100493 (program): a(n) = n + n-th semiprime.
  • A100494 (program): Primes of the form 47n+3.
  • A100500 (program): a(n) = prime(3n-2) + prime(3n-1) + prime(3n).
  • A100503 (program): Bisection of A000125.
  • A100504 (program): a(n) = (4*n^3 + 6*n^2 + 8*n + 6)/3.
  • A100510 (program): Bisection of A005425.
  • A100511 (program): a(n) = Sum_{j=0..n} Sum_{k=0..n} binomial(n,j)*binomial(n,k)*max(j,k).
  • A100512 (program): Numerator of Sum_{k=0..n} 1/C(2n,2k).
  • A100513 (program): Denominator of Sum_{k=0..n} 1/C(2n,2k).
  • A100516 (program): Numerator of Sum_{k=0..n} 1/binomial(n,k)^2.
  • A100517 (program): Denominator of Sum_{k=0..n} 1/binomial(n,k)^2.
  • A100518 (program): Numerator of Sum_{k=0..n} 1/binomial(n,k)^3.
  • A100519 (program): Denominator of Sum_{k=0..n} 1/binomial(n,k)^3.
  • A100520 (program): Numerator of Sum_{k=0..2*n} (-1)^k/binomial(2*n, k)^2.
  • A100521 (program): Denominator of Sum_{k=0..2*n} (-1)^k/binomial(2*n, k)^2.
  • A100525 (program): Bisection of A048654.
  • A100526 (program): Number of local binary search trees (i.e., labeled binary trees such that every left child has a smaller label than its parent and every right child has a larger label than its parent) with n vertices such that the root has only one child.
  • A100528 (program): a(0) = 1, a(n+1) = a(n)^2 + 1 - floor(log_2(a(n))).
  • A100530 (program): Numbers == 0,2,5,9 modulo 10.
  • A100531 (program): a(n) = a(n-1) + (2*n - 1) mod 8 + 1 with a(0)=1.
  • A100532 (program): The first four numbers of this sequence are the primes 2,3,5,7. The other terms are calculated by adding the previous four terms.
  • A100534 (program): Number of partitions of 2*n into parts of two kinds.
  • A100535 (program): Number of partitions of 2*n + 1 into parts of two kinds.
  • A100536 (program): a(n) = 3*n^2 - 2.
  • A100537 (program): Triangle read by rows: T(n,k) is the number of Dyck n-paths whose first descent has length k.
  • A100538 (program): Volume of the 3-dimensional box of sides of length equal to consecutive Padovan numbers (A000931). These boxes form a spiral in three dimensions similar to the spiral of Fibonacci boxes in two dimensions.
  • A100542 (program): Two-color Rado numbers R(0,n).
  • A100545 (program): Expansion of (7-2*x) / (1-3*x+x^2).
  • A100546 (program): Difference between the smallest semiperimeter (see A063655) and its integer log (A001414) equals 1.
  • A100549 (program): Let n = 2^e_2 * 3^e_ * 5^e_ * … be the prime factorization of n; then a(n) = largest prime <= 1 + max{e_2, e_3, e_5, …}; a(1) = 1 by convention.
  • A100550 (program): If n>3 a(n)=a(n-1)+2*a(n-2)+3*a(n-3) else a(n)=n
  • A100551 (program): Coefficient list of ChebyshevU(k,1-x).
  • A100555 (program): Smallest square that is equal to the sum of n not-necessarily-distinct primes plus 1.
  • A100560 (program): Numerator of Sum_{k=0..[n/2]} 1/binomial(n,k).
  • A100561 (program): Denominator of Sum_{k=0..[n/2]} 1/binomial(n,k).
  • A100565 (program): a(n) = Card{(x,y,z) : x <= y <= z, x|n, y|n, z|n, gcd(x,y)=1, gcd(x,z)=1, gcd(y,z)=1}.
  • A100566 (program): 2*a(n) = prime(prime(n)) + prime(prime(2n)).
  • A100567 (program): Prime-indexed primes as n runs through the integers congruent to 0 or 1 mod 3.
  • A100571 (program): Cubes m^3 such that m^3 is the sum of m-1 consecutive primes plus a larger prime.
  • A100575 (program): Half the number of permutations of 0..n with exactly two maxima.
  • A100577 (program): Number of sets of divisors of n with an odd sum.
  • A100583 (program): Number of triangles in an n X n grid of squares with diagonals.
  • A100585 (program): a(n+1) = a(n)+floor(a(n)/3), a(1) = 3.
  • A100586 (program): Write down the numbers from 3 to infinity. Take next number, M say, that has not been crossed off. Counting through the numbers that have not yet been crossed off after that M, cross off every 5th term. Repeat, always crossing off every 5th term of those that remain. The numbers that are left form the sequence.
  • A100587 (program): Number of nonempty subsets of divisors of n.
  • A100606 (program): a(n) = n^4 + n^3 + n.
  • A100612 (program): a(n) = (0! + 1! + … + (p-1)!) mod p, where p = prime(n).
  • A100613 (program): Number of elements in the set {(x,y): 1 <= x,y <= n, gcd(x,y) > 1}.
  • A100617 (program): There are n people in a room. The first half (i.e., floor(n/2)) of them leave, then 1/3 (i.e., floor of 1/3) of those remaining leave, then 1/4, then 1/5, etc.; sequence gives number who remain at the end.
  • A100618 (program): Initially there are n people in a room. At each step, if there are currently M people in the room, [M/k^2] of them leave, for k = 2, 3, … Sequence gives number who are left at the end.
  • A100619 (program): Fixed point of the morphism 1 -> 12, 2 -> 31, 3 -> 1, starting from a(1) = 1.
  • A100622 (program): Expansion of e.g.f. exp( (1+2*x-sqrt(1-4*x))/4).
  • A100626 (program): Numbers of the form 2^(2p+1) where p is prime.
  • A100627 (program): 3^(2p + 1) where p is prime.
  • A100628 (program): a(n) = 2^(3*prime(n) + 1).
  • A100629 (program): a(n) = 2^(5*prime(n) + 1).
  • A100630 (program): Array read by antidiagonals: T(m,n) = Sum(1<=i<=m) [ i*(n-1+i)! ]
  • A100634 (program): a(n) is the decimal equivalent of the binary number whose k-th least significant bit is 1 iff k is a prime number and k <= n.
  • A100635 (program): Number of 2 X 2 matrices with elements in {1,2,…,n} such that LCMs of rows and columns are n.
  • A100637 (program): Trisection of A000720.
  • A100638 (program): Successive powers of the matrix A=[1,2;3,4] written by rows in groups of 4.
  • A100656 (program): a(n)=1 if a hexagonal number is a prime, otherwise 0.
  • A100659 (program): Floor of measure (in degrees) of the internal angles of a regular polygon with n sides.
  • A100661 (program): Quet transform of A006519 (see A101387 for definition). Also, least k such that n+k has at most k ones in its binary representation.
  • A100662 (program): Primes of the form n^3 + (n+1)^2.
  • A100665 (program): a(n) = round(F(n)^(1/2)) where F(n) is the n-th Fibonacci number (A000045).
  • A100670 (program): Number of two-card Baccarat hands of point n.
  • A100671 (program): A Graham-Pollak-like sequence with multiplier 3 instead of 2.
  • A100672 (program): Second least-significant bit in the binary expansion of the n-th prime.
  • A100675 (program): a(1) = 1; for n >= 1, a(n+1) = Sum_{k=1..n} gcd(k, a(n)).
  • A100679 (program): Floor of cube root of tetrahedral numbers.
  • A100683 (program): a(n) = a(n-1) + a(n-2) + a(n-3); a(0) = -1, a(1) = 2, a(2) = 2.
  • A100688 (program): a(n) = prime(n) * 3^prime(n) - 1.
  • A100689 (program): a(n) = prime(n) * 4^prime(n) - 1.
  • A100690 (program): a(n) = p * 5^p - 1 where p=prime(n).
  • A100691 (program): Number of self-avoiding paths with n steps on a triangular lattice in the strip Z x {0,1}.
  • A100698 (program): Primes of the form n^3 - n + 1.
  • A100699 (program): Number of ways to partition n into two squarefree numbers that are not prime.
  • A100700 (program): n-th Fibonacci number minus n-th prime number.
  • A100701 (program): a(n) = a(n-1) + a(n-2) + a(n-1)*a(n-2) for n>=2; a(0)=2, a(1)=3.
  • A100702 (program): Number of layers of dough separated by butter in successive foldings of croissant dough.
  • A100703 (program): (T(n-1) + T(n-2)) + T(n-1)*T(n-2) where T(0)=3, T(1)=5 and n >= 2.
  • A100705 (program): a(n) = n^3 + (n+1)^2.
  • A100706 (program): Bisection of A002275.
  • A100709 (program): Trajectory of 1001 under “3x+1” map.
  • A100710 (program): Characterized by a(n) XOR (a(n) + 1) = a(n) - n.
  • A100714 (program): Number of runs in binary expansion of A000040(n) (the n-th prime number) for n > 0.
  • A100716 (program): Numbers k such that p^p divides k for some prime p.
  • A100720 (program): Expansion of g.f.: (3+x+2*x^2-2*x^3)/((1-2*x)*(1+x^2)).
  • A100722 (program): Prime numbers whose binary representations are split into exactly five runs.
  • A100723 (program): Prime numbers whose binary representations are split into exactly seven runs.
  • A100726 (program): Prime numbers whose binary representations are split into a maximum of 7 runs.
  • A100727 (program): Continued fraction expansion of (1/2) [tan(1) + sec(1)].
  • A100732 (program): a(n) = (3*n)!.
  • A100733 (program): a(n) = (4*n)!.
  • A100735 (program): Inverse modulo 2 binomial transform of 2^n.
  • A100736 (program): Inverse modulo 2 binomial transform of 3^n.
  • A100737 (program): Inverse modulo 2 binomial transform of 4^n.
  • A100738 (program): Inverse modulo 2 binomial transform of 5^n.
  • A100740 (program): Inverse modulo 2 binomial transform of 7^n.
  • A100744 (program): Inverse modulo 2 binomial transform of (-2)^n.
  • A100745 (program): Modulo 2 binomial transform of the Jacobsthal numbers J(n).
  • A100746 (program): Inverse modulo 2 binomial transform of Jacobsthal numbers J(n).
  • A100747 (program): A modular recurrence.
  • A100749 (program): Triangle read by rows: T(n,k)=number of 231- and 312-avoiding permutations of [n] having k fixed points.
  • A100752 (program): a(n) is the number of positive integers <= 10^n that are divisible by no prime exceeding 3.
  • A100760 (program): Primes of the form 47n+5.
  • A100762 (program): Let n = 2^e_2 * 3^e_3 * 5^e_5 * … be the prime factorization of n and let P(n) = A100549(n); then a(n) = Product_{ q <= P(n) } q^e_q; a(1) = 1 by convention.
  • A100764 (program): a(1) = 1, a(2) = 2, a(3) = 3, a(n) = least number not the sum of three or fewer previous terms.
  • A100768 (program): a(n) = p * (n^p) - 1 where p = prime(n).
  • A100774 (program): a(n) = 2*(3^n - 1).
  • A100775 (program): a(n) = 97*n + 101.
  • A100776 (program): a(n) = 997 * n + 1009.
  • A100777 (program): Square-factorial numbers: a(1) = 1, a(n+1) = a(n) * largest square divisor of (n+1).
  • A100779 (program): Expansion of (1+t^2+4*t^3+2*t^4+t^5+3*t^6)/((1-t)^2*(1-t^2)*(1-t^3)^2).
  • A100789 (program): First differences of A000543.
  • A100790 (program): First differences of A047780.
  • A100791 (program): Group the natural numbers so that the n-th group contains n(n+1)/2 = T(n) terms: (1), (2,3,4), (5,6,7,8,9,10), (11,12,13,14,15,16,17,18,19,20),(21,22,23,24,25,26,27,28,29,30,31,32,33,34,35),… The n-th row of the following triangle is formed from the sum of first n terms, next n-1 terms,next n-2 terms … of the n-th group; e.g. third row is (5+6+7), (8+9), (10) or 18,17,10. Sequence contains the triangle read by rows.
  • A100792 (program): Group the natural numbers so that the n-th group contains n(n+1)/2 = T(n) terms: (1), (2,3,4), (5,6,7,8,9,10), (11,12,13,14,15,16,17,18,19,20),(21,22,23,24,25,26,27,28,29,30,31,32,33,34,35),… The r-th term of the n-th row of the following triangle is the sum of the next r terms of the n-th group, e.g. third row is (5),(6+7), (8+9+10) or 5,13,27. Sequence contains the triangle read by rows.
  • A100795 (program): n occurs n times, as early as possible subject to the constraint that no two successive terms are identical.
  • A100802 (program): a(n) = least k >= 0 such that (n+k)/2 is prime.
  • A100803 (program): A100802(m) where A100802(m) > A100802(m-1).
  • A100808 (program): Quet transform (see A101387 for definition) of Kolakoski sequence A000002.
  • A100810 (program): a(n) = 0 if prime(n) + 2 = prime(n+1), otherwise 1.
  • A100814 (program): Digits 9 to 0 are written in order with increasing number of digits for each member of the sequence. Leading zeros are counted, but are not written down.
  • A100817 (program): Product of the digits of n, each doubled.
  • A100818 (program): For a given unrestricted partition pi, let P(pi)=lambda(pi), if mu(pi)=0. If mu(pi)>0 then let P(pi)=nu(pi), where nu(pi) is the number of parts of pi greater than mu(pi), mu(pi) is the number of ones in pi and lambda(pi) is the largest part of pi.
  • A100820 (program): Number of odd numbers between prime(n) and prime(n+1).
  • A100821 (program): a(n) = 1 if prime(n) + 2 = prime(n+1), otherwise 0.
  • A100822 (program): Triangle read by rows: T(n,k) is the number of deco polyominoes of height n with k cells in the first column. (A deco polyomino is a directed column-convex polyomino in which the height, measured along the diagonal, is attained only in the last column).
  • A100824 (program): Number of partitions of n with at most one odd part.
  • A100828 (program): Expansion of (1+2*x-2*x^3-3*x^2)/((x-1)*(x+1)*(x^2+2*x-1)).
  • A100830 (program): Smallest number with same digital root as n but distinct from n and all earlier occurrences.
  • A100832 (program): Amenable numbers: n such that there exists a multiset of integers (s(1), …, s(n)) whose size, sum and product are all n.
  • A100833 (program): Smallest positive palindrome-free and squarefree sequence.
  • A100836 (program): a(n) is the smallest value k > 1 such that k^2 - 1 is divisible by n^2.
  • A100843 (program): F(P(n)) where P(n) is the unrestricted partition number of n and F(n) is the Fibonacci number.
  • A100845 (program): a(n) = L(P(n)), where P = A000041 (partition numbers) and L = A000032 (Lucas numbers).
  • A100851 (program): Triangle read by rows: T(n,k) = 2^n * 3^k, 0<=k<=n.
  • A100852 (program): Triangle read by rows: T(n,k) = 2^k * 3^n, 0 <= k <= n.
  • A100855 (program): n*(n^3-n^2+n+1)/2.
  • A100856 (program): a(n) = (prime(n) - 1)! + prime(n).
  • A100859 (program): Beginning with 3, increasing primes such that no two adjacent terms are congruent mod 4.
  • A100860 (program): Lesser of two consecutive primes of forms 4k+3 and 4k+1 respectively.
  • A100861 (program): Triangle of Bessel numbers read by rows: T(n,k) is the number of k-matchings of the complete graph K(n).
  • A100862 (program): Triangle read by rows: T(n,k) is the number of k-matchings of the corona K’(n) of the complete graph K(n) and the complete graph K(1); in other words, K’(n) is the graph constructed from K(n) by adding for each vertex v a new vertex v’ and the edge vv’.
  • A100868 (program): a(n) = Sum_{k>0} k^(2n-1)/phi^(2k) where phi = (1+sqrt(5))/2 = A001622.
  • A100872 (program): a(n) = (1/sqrt(5)) * Sum_{k>0} k^(2n)/phi^(2k) where phi = (1+sqrt(5))/2 = A001622.
  • A100876 (program): Least number of squares that sum to prime(n).
  • A100877 (program): Greater of two consecutive primes of form 4k+3 and 4k+1 respectively.
  • A100879 (program): a(n) = n^sigma(n).
  • A100886 (program): Expansion of x*(1+3*x+2*x^2)/((1+x+x^2)*(1-x-x^2)).
  • A100887 (program): Expansion of (-1+2x+2x^2)/((1+x+x^2)(1-x-x^2)).
  • A100888 (program): Expansion of (3+x-x^2)/((1+x+x^2)(1-x-x^2)).
  • A100892 (program): a(n) = (2*n-1) XOR (2*n+1), bitwise.
  • A100898 (program): Triangle read by rows: T(n,k) is the number of k-matchings of the fan graph on n+1 vertices (i.e., the join of the path graph on n vertices with one extra vertex).
  • A100915 (program): Numbers n such that n plus n-th semiprime is semiprime.
  • A100916 (program): Sum of a semiprime and its semiprime index is a new semiprime.
  • A100921 (program): n appears A023416(n) times (appearances equal number of 0-bits).
  • A100922 (program): n appears A000120(n) times (appearances equal number of 1-bits).
  • A100923 (program): a(n) = 1 iff 6*n+1 and 6*n-1 are both prime numbers (0 otherwise).
  • A100930 (program): Semiprimes of the form (2*p+1)*(p-1)/2, p prime.
  • A100937 (program): Main diagonal of symmetric square array A100936.
  • A100938 (program): Self-convolution of A092684.
  • A100948 (program): Irregular triangle with T(n,1) = floor(n!/3), T(n,2) = n!/2, T(n,3) = n!, read by rows.
  • A100954 (program): Decimal expansion of 7/2 - sqrt(2)/4.
  • A100959 (program): Non-semiprimes.
  • A100963 (program): a(1)=1. a(n) = a(n-1) + sum of the triangular numbers which are among the first (n-1) terms of the sequence.
  • A100990 (program): a(n) = n^21 mod 100.
  • A100992 (program): Indices k of Fibonacci numbers F(k) (A000045) that are divisible by k+1.
  • A100993 (program): Indices k of Fibonacci numbers F(k) (A000045) that are divisible by k-1.
  • A100994 (program): If n is a prime power p^m, m >= 1, then n, otherwise 1.
  • A100995 (program): If n is a prime power p^m, m >= 1, then m, otherwise 0.
  • A101000 (program): Periodic sequence with period 3.
  • A101028 (program): Numerator of partial sums of a certain series. First member (m = 2) of a family.
  • A101029 (program): Denominator of partial sums of a certain series.
  • A101030 (program): Triangle read by rows: T(n,k) = number of functions from an n-element set into but not onto a k-element set.
  • A101031 (program): Triangle read by rows: T(n,k) = (1/k) times the number of functions from an n-element set into but not onto a k-element set.
  • A101035 (program): Dirichlet inverse of the gcd-sum function (A018804).
  • A101037 (program): Triangle read by rows: T(n,1) = T(n,n) = n and for 1<k<n: T(n,k) = floor((T(n-1,k-1)+T(n-1,k))/2).
  • A101038 (program): Inverse to sequence matrix for odd numbers.
  • A101040 (program): If n has one or two prime-factors then 1 else 0.
  • A101041 (program): Number of numbers not greater than n having no more than two prime factors.
  • A101048 (program): Number of partitions of n into semiprimes (a(0) = 1 by convention).
  • A101052 (program): Number of preferential arrangements of n labeled elements when only k <= 3 ranks are allowed.
  • A101053 (program): a(n) = n! * Sum_{k=0..n} Bell(k)/k! (cf. A000110).
  • A101054 (program): E.g.f.: exp(exp(x)-1)/(1-x)^2.
  • A101055 (program): E.g.f.: exp(exp(x)-1)/(1-x)^3.
  • A101080 (program): Table of Hamming distances between binary vectors representing i and j, for i >= 0, j >= 0, read by antidiagonals.
  • A101082 (program): Numbers n such that binary representation contains bit strings “10” and “01” (possibly overlapping).
  • A101084 (program): Numbers k such that 97*k + 101 is a prime.
  • A101086 (program): Numbers k for which 997*k + 1009 is prime.
  • A101089 (program): Second partial sums of fourth powers (A000583).
  • A101090 (program): Third partial sums of fourth powers (A000583).
  • A101091 (program): Fourth partial sums of fourth powers (A000583).
  • A101092 (program): Second partial sums of fifth powers (A000584).
  • A101093 (program): Second partial sums of sixth powers (A001014).
  • A101094 (program): a(n) = n*(n+1)*(n+2)*(n+3)*(1+3*n+n^2)/120.
  • A101095 (program): Fourth difference of fifth powers (A000584).
  • A101096 (program): Third differences of fifth powers (A000584).
  • A101097 (program): a(n) = n*(n+1)*(n+2)*(n+3)*(n+4)*(2 + 4*n + n^2)/840.
  • A101098 (program): a(1)=1; thereafter, a(n+1) = 20*n^3 + 10*n.
  • A101099 (program): Third partial sums of fifth powers (A000584).
  • A101100 (program): The first summation of row 5 of Euler’s triangle - a row that will recursively accumulate to the power of 5.
  • A101101 (program): a(1)=1, a(2)=5, and a(n)=6 for n>=3.
  • A101102 (program): Fifth partial sums of cubes (A000578).
  • A101103 (program): Partial sums of A101104. First differences of A005914.
  • A101104 (program): a(1)=1, a(2)=12, a(3)=23, and a(n)=24 for n>=4.
  • A101105 (program): Row sums of triangle A101224, which is related to the Flavius sieve (A000960).
  • A101107 (program): Sorted and uniqued list of class numbers (number of conjugacy classes) of all non-Abelian simple groups.
  • A101109 (program): Number of sets of lists (sequences) of n labeled elements with k=3 elements per list.
  • A101119 (program): Nonzero differences of A006519 (highest power of 2 dividing n) and A003484 (Radon function).
  • A101120 (program): Records in A101119, which forms the nonzero differences of A006519 and A003484.
  • A101123 (program): Numbers n for which 7*n + 11 is prime.
  • A101124 (program): Number triangle associated to Chebyshev polynomials of first kind.
  • A101125 (program): Row sums of a Chebyshev number triangle.
  • A101127 (program): McKay-Thompson series of class 12D for the Monster group.
  • A101135 (program): a(1)=1. a(n) = a(n-1) + sum of the squares which are among the first (n-1) terms of the sequence.
  • A101156 (program): a(n) = 2*Fibonacci(n) + 8*Fibonacci(n-5).
  • A101157 (program): Let j be the smallest integer for which n+(n+1)+…+(n+j) is a square, say k^2; then a(n)=k.
  • A101158 (program): Let j be the smallest integer for which n+(n+1)+…+(n+j) is a square; sequence gives the squares.
  • A101159 (program): Let j be the smallest integer for which n+(n+1)+…+(n+j) is a square; then a(n) = n+j.
  • A101160 (program): a(n) is the smallest integer j for which n+(n+1)+…+(n+j) is a square.
  • A101161 (program): A number triangle associated with the Chebyshev polynomials of the first kind.
  • A101162 (program): Row sums of a Chebyshev number triangle.
  • A101164 (program): Triangle read by rows: Delannoy numbers minus binomial coefficients.
  • A101165 (program): a(n) = (7*n^3 + 6*n^2 + 5*n) / 6.
  • A101166 (program): a(n) = (15*n^4 + 22*n^3 + 45*n^2 + 14*n) / 24.
  • A101168 (program): Lengths of successive words (starting with a) under the substitution: {a -> aab, b -> aac, c -> a}.
  • A101169 (program): Lengths of successive words (starting with a) under the substitution: {a -> aab, b -> aac, c -> ab}.
  • A101184 (program): a(n) = n + pi(n) + pi(pi(n)) + pi(pi(pi(n))) + pi(pi(pi(pi(n)))) + …
  • A101195 (program): Expansion of psi(x^3) / psi(x) in powers of x where psi() is a Ramanujan theta function.
  • A101197 (program): Lengths of successive words (starting with a) under the substitution: {a -> aab, b -> aac, c -> b}.
  • A101201 (program): Maximal number of kings in the toroidal king’s graph on an n X n board such that each king is attacking no more than four other kings.
  • A101202 (program): Multiples of 142857.
  • A101203 (program): a(n) = sum of nonprimes <= n.
  • A101207 (program): For each prime power n, a(n) is the number of positive integers that have n as their greatest prime power.
  • A101213 (program): a(n) = n * (n+1)^2 * (n+2)^3.
  • A101214 (program): a(n) = n * (n+1)^2 * (n+2)^3 * (n+3)^4.
  • A101220 (program): a(n) = Sum_{k=0..n} Fibonacci(n-k)*n^k.
  • A101230 (program): Number of partitions of 2n in which both odd parts and parts that are multiples of 3 occur with even multiplicities. There is no restriction on the other even parts.
  • A101243 (program): Slowest increasing sequence where the absolute difference between the last digit of a(n) and the first digit of a(n+1) equals 9.
  • A101256 (program): Sum of composites <= n.
  • A101257 (program): Remainder when the least divisor of n greater than or equal to the square root of n (A033677(n)) is divided by the greatest divisor of n less than or equal to the square root of n (A033676(n)).
  • A101263 (program): Decimal expansion of sqrt(2 - sqrt(3)), edge length of a regular dodecagon with circumradius 1.
  • A101264 (program): a(n) = 1 if 2*n + 1 is prime, otherwise a(n) = 0.
  • A101265 (program): a(1) = 1, a(2) = 2, a(3) = 6; a(n) = 5*a(n-1) - 5*a(n-2) + a(n-3) for n>3.
  • A101266 (program): First differences of A101402.
  • A101269 (program): a(1)=0, a(2)=1 a(n+2)=(8*n^2+2*n+1)*a(n+1)-2*n*(2*n-1)^3*a(n).
  • A101271 (program): Number of partitions of n into 3 distinct and relatively prime parts.
  • A101272 (program): a(n)=n, n <=6; a(n)=6, n > 6.
  • A101279 (program): a(1) = 1; a(2k) = a(k), a(2k+1) = k.
  • A101289 (program): Inverse Moebius transform of 5-simplex numbers A000389.
  • A101291 (program): Sum of all numbers with n digits.
  • A101292 (program): a(n) = n! + Sum_{i=1..n} i.
  • A101296 (program): n has the a(n)-th distinct prime signature.
  • A101297 (program): Bisection of A001622 (decimal expansion of the golden ratio).
  • A101299 (program): Numbers n such that -1 + Sum_{x=1..n} phi(x) is a prime number.
  • A101300 (program): Second-smallest prime larger than n.
  • A101301 (program): The sum of the first n primes, minus n.
  • A101304 (program): a(n) = 2^(prime(n) + 1) + 1.
  • A101305 (program): Begin with 0 and at each successive iteration append the next power of 10.
  • A101306 (program): a(n) = Sum_{i=1..n} {last digit of prime(i)}.
  • A101309 (program): Matrix logarithm of A047999 (Pascal’s triangle mod 2).
  • A101310 (program): Sum((prime(k)*10^(k),k=1..n))).
  • A101321 (program): Table T(n,m) = 1 + n*m*(m+1)/2 read by antidiagonals: centered polygonal numbers.
  • A101322 (program): a(n) = n - (least divisor of n greater than the square root of n) + (greatest divisor of n less than the square root of n) = n + A033676(n) - A033677(n).
  • A101324 (program): Primes p such that p+1=C(q)=q-th composite and q is prime.
  • A101328 (program): Recurring numbers in the count of consecutive composite numbers between balanced primes and their lower or upper prime neighbors.
  • A101332 (program): a(n) = Knuth’s Fibonacci (or circle) square “n o n”.
  • A101333 (program): A081254-A072762.
  • A101334 (program): a(n) = n^n - (n+1)^(n-1).
  • A101338 (program): Antidiagonal sums in A101321.
  • A101339 (program): Prime(n)^prime(n)-prime(n).
  • A101340 (program): a(n) = prime(n)^prime(n)+prime(n).
  • A101342 (program): Fibonacci-Mersenne numbers.
  • A101344 (program): Number of primes between prime(n) and 3prime(n).
  • A101345 (program): a(n) = Knuth’s Fibonacci (or circle) product “2 o n”.
  • A101346 (program): a(n) = binomial(2^n, n-1).
  • A101348 (program): Arises from a particular cyclic transformation of the floretion - .5’i - .5i’ - .5’ij’ - .5’ik’ + .5’ji’ + .5’ki’.
  • A101349 (program): Numbers of cubes between prime(n) and prime(n+1).
  • A101351 (program): a(n) = 2^n-1 + Fibonacci(n).
  • A101352 (program): Partial sums of A101351.
  • A101353 (program): a(n) = Sum_{k=0..n} (2^k + Fibonacci(k)).
  • A101356 (program): Binomial( 2*binomial(2*n,n-1),n-1).
  • A101357 (program): Partial sums of A060354.
  • A101361 (program): a(1) = a(2) = 1; for n > 2, a(n) = Knuth’s Fibonacci (or circle) product “a(n-1) o a(n-2)”.
  • A101362 (program): a(n) = (n+1)*n^4.
  • A101368 (program): The sequence solves the following problem: find all the pairs (i,j) such that i divides 1+j+j^2 and j divides 1+i+i^2. In fact, the pairs (a(n),a(n+1)), n>0, are all the solutions.
  • A101369 (program): a(2n-1) = the smallest positive integer not occurring earlier in the sequence. a(2n) = the a(2n-1)th smallest positive integer among those not occurring earlier in the sequence.
  • A101374 (program): a(n) = n*(n^3 - n + 2)/2.
  • A101375 (program): a(n) = n*(n+1)*(n^2-2*n+2)/2.
  • A101376 (program): a(n) = n^2*(n^3 - n^2 + n + 1)/2.
  • A101377 (program): a(n) = n^2*(n^3-n+2)/2.
  • A101378 (program): a(n) = n^2*(n^3+1)/2.
  • A101381 (program): a(n) = n^2*(n+1)^2*(4*n^2 - 5*n + 4)/12.
  • A101382 (program): a(n) = n*(n+1)*(2*n^3 - n^2 + 2)^2/6.
  • A101383 (program): a(n) = n*(n+1)*(2*n^3 - n^2 + 2)/6.
  • A101384 (program): a(n) = n*(n-1)^3*(n^2-n-1)/2.
  • A101386 (program): Expansion of g.f.: (5 - 3*x)/(1 - 6*x + x^2).
  • A101399 (program): a(0) = 1, a(1) = 2, a(2) = 5; for n >= 3, a(n) = a(n-1) + 2*a(n-2) + a(n-3).
  • A101400 (program): a(n) = a(n-1) + 2*a(n-2) + a(n-3) - a(n-4).
  • A101401 (program): Triangle read by rows: T(n,k) is the number of noncrossing trees with n edges in which the leftmost child of the root has degree k.
  • A101402 (program): a(0)=0, a(1)=1; for n>=2, let k = smallest power of 2 that is >= n, then a(n) = a(k/2) + a(n-1-k/2).
  • A101403 (program): Number of times that n occurs in A101402.
  • A101404 (program): a(n) = n*A101403(n).
  • A101405 (program): a(n) = n^(pi(n-1)).
  • A101417 (program): Number of partitions of n into parts without powers of 2.
  • A101418 (program): Floor of the area of a lens constructed using circular arcs of radius n.
  • A101421 (program): Numbers which are the sum of two positive cubes and divisible by 7.
  • A101423 (program): Number of different cuboids with volume p^3 * q^n, where p,q are distinct prime numbers.
  • A101424 (program): Number of different cuboids with volume p^4 * q^n, where p,q are distinct prime numbers.
  • A101425 (program): Number of different cuboids with volume p^5 X q^n, where p,q are distinct prime numbers.
  • A101426 (program): Number of different cuboids with volume p^6 * q^n, where p,q are distinct prime numbers.
  • A101427 (program): Number of different cuboids with volume (pq)^n, where p,q are distinct prime numbers.
  • A101428 (program): Number of ways to write n as an ordered sum of a triangular number (A000217) and a square (A000290).
  • A101432 (program): Each term is the number of letters in the Spanish name of the previous term.
  • A101433 (program): Partial sums of A101402.
  • A101435 (program): Dimension of a certain space of modular forms of weight 2 and level p^2, where p runs through the primes > 3 that are == 3 mod 4. See reference for precise definition.
  • A101441 (program): n^prime(n+1).
  • A101442 (program): a(n) = 9973*n + 10007.
  • A101443 (program): Continued fraction expansion of (I_0(1/2)/I_1(1/2)-1)/2 = 1.56185896… (where I_n is the modified Bessel function of the first kind).
  • A101444 (program): Numbers k such that (9973*k + 10007) is a prime.
  • A101447 (program): Triangle read by rows: T(n,k) = (2*k+1)*(n+1-k), 0 <= k < n.
  • A101448 (program): Nonnegative numbers k such that 2k + 11 is prime.
  • A101455 (program): a(n) = 0 for even n, a(n) = (-1)^((n-1)/2) for odd n. Periodic sequence 1,0,-1,0,…
  • A101457 (program): Prime digits in the decimal expansion of golden ratio phi (or tau) = (1 + sqrt 5 )/2.
  • A101461 (program): Row maximum of Catalan triangle with zeros (A053121), i.e., maximum value of (m+1)*binomial(n+1,(n-m)/2)/(n+1) for given n with m same parity as n.
  • A101463 (program): G.f.: (x^3+x^2+2*x+1)/(x^4+5*x^2+1).
  • A101464 (program): Decimal expansion of sqrt(2-sqrt(2)), edge length of a regular octagon with circumradius 1.
  • A101465 (program): Decimal expansion of 2-sqrt(2), square of the edge length of a regular octagon with circumradius 1.
  • A101468 (program): Triangle read by rows: T(n,k)=(n+1-k)*(3*k+1).
  • A101471 (program): Numbers n such that the number n11 is prime.
  • A101472 (program): Numbers n such that the number n33 is prime.
  • A101473 (program): Boustrophedon transform of the Jacobsthal numbers.
  • A101474 (program): Boustrophedon transform of the signed Jacobsthal numbers.
  • A101478 (program): G.f. satisfies A(x) = x*(1+A)^4/(1+A^2).
  • A101485 (program): a(n) = (4n)! / ( 4^n * (2n)! ).
  • A101488 (program): Number of naturally embedded binary trees with n nodes that have no label greater than 0.
  • A101490 (program): G.f. satisfies A(x) = x*(1+A^2)^2/(1-A+A^2).
  • A101492 (program): Triangle read by rows: T(n,k) = (n-k+1)*(4*k+1).
  • A101493 (program): Triangle read by rows: T(n,k) = (n+1)*(2*(n+1)-1) - k*(2*k-1).
  • A101495 (program): Column 1 of triangle A101494.
  • A101496 (program): Expansion of (1-x^2)/(1-x-x^2+x^3+x^4).
  • A101497 (program): Expansion of (1-x^2)/(1-2x+2x^3+x^4).
  • A101498 (program): Expansion of (1-x^2)/(1-3x+x^2+3x^3+x^4).
  • A101499 (program): A Chebyshev transform of the Catalan numbers.
  • A101500 (program): A Chebyshev transform of the central binomial numbers.
  • A101501 (program): Number of walks between adjacent nodes on C_5 tensor J_2.
  • A101502 (program): Number of closed walks on C_5 tensor J_2.
  • A101503 (program): Numbers n such that 11*n + 101 is prime.
  • A101505 (program): Smallest m such that A101504(m) = n.
  • A101508 (program): Product of binomial matrix and the Mobius matrix A051731.
  • A101509 (program): Binomial transform of tau(n) (see A000005).
  • A101514 (program): Shifts one place left under the square binomial transform (A008459): a(0) = 1, a(n) = Sum_{k=0..n-1} C(n-1,k)^2*a(k).
  • A101550 (program): Lopsided (or biased) numbers: numbers n such that the largest prime factor of n is > 2*sqrt(n).
  • A101551 (program): C(n-2,2)+C(n-5,5)+…+C(n-(3*floor((n-3)/3)+2),3*floor((n-3)/3)+2).
  • A101552 (program): C(n-3,3)+C(n-7,7)+…+C(n-(4*floor((n-4)/4)+3),4*floor((n-4)/4)+3).
  • A101553 (program): A modular recurrence.
  • A101554 (program): Second inverse mod 2 binomial transform of 2^n.
  • A101555 (program): Convolution of A010060 and A000244.
  • A101556 (program): A Thue-Morse convolution.
  • A101557 (program): Numbers k such that 101*k + 1009 is prime.
  • A101561 (program): a(n)=(-1)^n*coefficient of x^n in sum{k>=1,x^(k-1)/(1+3x^k)}.
  • A101562 (program): a(n)=(-1)^n*coefficient of x^n in sum{k>=1,x^(k-1)/(1+4x^k)}.
  • A101563 (program): a(n)=(-1)^n*coefficient of x^n in sum{k>=1,x^(k-1)/(1+10x^k)}.
  • A101566 (program): Binary partition sequence matrix.
  • A101596 (program): G.f.: c(2*x)^4, where c(x) is the g.f. of A000108.
  • A101600 (program): G.f.: c(3x)^2, c(x) the g.f. of A000108.
  • A101601 (program): G.f.: c(3x)^3, c(x) the g.f. of A000108.
  • A101602 (program): G.f.: c(3x)^4, c(x) the g.f. of A000108.
  • A101603 (program): Riordan array (1/(1-x^2), x(1+x)/(1-x)).
  • A101604 (program): a(n) = 2*a(n-1) + 5*a(n-2) + 2*a(n-3).
  • A101605 (program): a(n) = 1 if n is a product of exactly 3 (not necessarily distinct) primes, otherwise 0.
  • A101606 (program): a(n) = number of divisors of n that have exactly three (not necessarily distinct) prime factors.
  • A101607 (program): a(2n) = 7 - a(n), a(2n+1) = (n-1 mod 3) + 1.
  • A101608 (program): Solution to Tower of Hanoi puzzle encoded in pairs with the moves (1,2),(2,3),(3,1),(2,1),(3,2),(1,3). The disks are moved from peg 1 to 2. For a tower of k disks use the first 2^k-1 number pairs.
  • A101609 (program): a(n) = n! * Sum_{k=1..floor(n/2)} 1/k.
  • A101610 (program): n! * Sum[k=1..ceiling(n/2), 1/k].
  • A101611 (program): a(n) = n! * Sum_{k=ceiling(n/2)..n} 1/k.
  • A101613 (program): (2n)! * Sum[k=n..2n, 1/k].
  • A101614 (program): Fixed point of morphism 0 -> 01, 1 -> 02, 2 -> 10.
  • A101615 (program): Number of representations of n as a sum of the Jacobsthal numbers A078008 (2 is allowed twice as a part).
  • A101616 (program): Partial sums of a Jacobsthal representation sequence.
  • A101617 (program): The trinomial transform (A027907) gives powers of 3, while the trinomial transform of this sequence shift one place left gives powers of 5.
  • A101621 (program): Initial decimal digit of n^11.
  • A101622 (program): A Horadam-Jacobsthal sequence.
  • A101623 (program): Modular binomial transform of 10^n.
  • A101624 (program): Stern-Jacobsthal numbers.
  • A101625 (program): A bisection of the Stern-Jacobsthal numbers.
  • A101626 (program): Initial decimal digit of n^12.
  • A101627 (program): Numerator of partial sums of a certain series.
  • A101628 (program): Denominator of partial sums of a certain series.
  • A101630 (program): Denominator of partial sums of a certain series.
  • A101631 (program): Numerator of partial sums of a certain series.
  • A101632 (program): Denominator of partial sums of a certain series.
  • A101634 (program): Subtract 1, multiply by 1, subtract 2, multiply by 2, etc.
  • A101635 (program): Increasing primes of alternating congruences modulo 6.
  • A101637 (program): a(n) = 1 if n is a 4-almost prime, that is a product of exactly four (not necessarily distinct) primes, 0 otherwise.
  • A101642 (program): a(n) = Knuth’s Fibonacci (or circle) product “3 o n”.
  • A101643 (program): First row of array in A101385.
  • A101645 (program): Third row of array in A101385.
  • A101650 (program): A Thue-Morse-Stern sequence.
  • A101651 (program): a(n)=Product{k=0..n, 1+0^A010060(k)}/2.
  • A101652 (program): a(n)=Product{k=0..n, 1+2^A010060(k)}/2.
  • A101653 (program): a(n)=Product{k=0..n, 1+3^A010060(k)}/2.
  • A101654 (program): a(n)=Product{k=0..n, 1+4^A010060(k)}/2.
  • A101655 (program): a(n)=Product{k=0..n, 1+9^A010060(k)}/2.
  • A101659 (program): Fixed point of morphism 0 -> 01, 1 -> 02, 2 -> 11.
  • A101660 (program): Fixed point of morphism 0 -> 01, 1 -> 02, 2 -> 12.
  • A101661 (program): Fixed point of morphism 0 -> 01, 1 -> 02, 2 -> 20.
  • A101662 (program): Fixed point of morphism 0 -> 01, 1 -> 02, 2 -> 21.
  • A101663 (program): Fixed point of morphism 0 -> 01, 1 -> 02, 2 -> 22.
  • A101664 (program): Fixed point of morphism 0 -> 01, 1 -> 12, 2 -> 00.
  • A101665 (program): Fixed point of morphism 0 -> 01, 1 -> 12, 2 -> 02.
  • A101666 (program): Fixed point of morphism 0 -> 01, 1 -> 12, 2 -> 10, starting with 0.
  • A101668 (program): Fixed point of morphism 0 -> 01, 1 -> 20, 2 -> 00.
  • A101669 (program): Fixed point of morphism 0 -> 01, 1 -> 20, 2 -> 01.
  • A101670 (program): Fixed point of morphism 0 -> 01, 1 -> 20, 2 -> 02.
  • A101671 (program): Fixed point of morphism 0 -> 01, 1 -> 20, 2 -> 10.
  • A101672 (program): Fixed point of morphism 0 -> 01, 1 -> 20, 2 -> 11.
  • A101673 (program): Fixed point of morphism 0 -> 01, 1 -> 20, 2 -> 20.
  • A101674 (program): Fixed point of morphism 0 -> 01, 1 -> 20, 2 -> 21.
  • A101675 (program): Expansion of (1 - x - x^2)/(1 + x^2 + x^4).
  • A101676 (program): a(n) = a(n-1) - a(n-2) + a(n-3) - a(n-4) + a(n-5) with initial terms 1,0,-2,-1,0.
  • A101677 (program): a(n) = a(n-1) - 2*a(n-2) + 2*a(n-3) - 2*a(n-4) + 2*a(n-5) - a(n-6).
  • A101680 (program): A modular binomial transform of 10^n.
  • A101682 (program): Expansion of 2 - exp(-1 + sqrt(1-4x)).
  • A101683 (program): Write exp(sqrt(1+x)-1) = Sum c(n) x^n/n!; then a(n) = numerator of c(n).
  • A101686 (program): a(n) = Product_{i=1..n} (i^2 + 1).
  • A101687 (program): a(n) = Sum_{k=1..n} floor(binomial(n,k)/k).
  • A101688 (program): Once 1, once 0, repeat, twice 1, twice 0, repeat, thrice 1, thrice 0… and so on.
  • A101691 (program): A modular binomial sum sequence.
  • A101692 (program): A modular binomial sum transform of 2^n.
  • A101693 (program): A modular binomial sum transform of 2^n.
  • A101695 (program): a(n) = n-th n-almost prime.
  • A101705 (program): Numbers n such that n = 12*reversal(n).
  • A101711 (program): Main diagonal of A101646.
  • A101741 (program): 4th row of A101646.
  • A101744 (program): Triangular numbers which are 10-almost primes.
  • A101745 (program): Indices of triangular numbers which are 10-almost primes. Indices of A101744.
  • A101776 (program): Smallest k such that k^2 is equal to the sum of n not-necessarily-distinct primes plus 1.
  • A101780 (program): Primes of the form 100*n + 3.
  • A101785 (program): G.f. satisfies: A(x) = 1 + x*A(x)/(1 - x^2*A(x)^2).
  • A101786 (program): G.f. satisfies: A(x) = 1 + x*A(x)/(1 - 2*x^2*A(x)^2).
  • A101787 (program): |S(n)| where S(n) = {i : 1 <= i <= n and 4n-1 and 8n-1 are primes}.
  • A101788 (program): n - A101787.
  • A101789 (program): 8n-1 such that 4n-1 and 8n-1 are primes.
  • A101790 (program): Numbers n such that 4n-1, 8n-1 and 16n-1 are primes.
  • A101791 (program): 4n-1 such that 4n-1, 8n-1 and 16n-1 are primes.
  • A101792 (program): Primes of the form 8*k-1 such that 4*k-1 and 16*k-1 are primes.
  • A101793 (program): 16k-1 such that 4k-1, 8k-1 and 16k-1 are primes.
  • A101803 (program): Nearest integer to n*(phi-1), where phi is golden ratio 1.618033988749895… (A001622).
  • A101808 (program): Number of primes between two consecutive even numbers.
  • A101810 (program): Number of compositions (ordered partitions) of the n-th prime into n nonnegative integers.
  • A101813 (program): Odd Niven (or Harshad) numbers: odd numbers that are divisible by the sum of their digits.
  • A101814 (program): Even Niven (or Harshad) numbers: even numbers that are divisible by the sum of their digits.
  • A101817 (program): Triangle read by rows: T(n,h) = number of functions f:{1,2,…,n}->{1,2,…,n} such that |Image(f)|=h; h=1,2,…,n, n=1,2,3,… . Essentially A090657, but without zeros.
  • A101818 (program): Triangle read by rows: (1/n)*T(n,h), where T(n,h) is the array in A101817.
  • A101822 (program): Expansion of 1/(1-x-2*x^2-3*x^3).
  • A101825 (program): G.f.: x*(1+x)^2/(1-x^3).
  • A101850 (program): A Catalan transform of Pell(n+1).
  • A101851 (program): a(n) = Sum_{k=0..n} (-1)^(n-k)*k*Stirling2(n,k).
  • A101853 (program): a(n) = n*(20 + 15*n + n^2)/6.
  • A101854 (program): a(n) = n*(n+1)*(n^2 + 21*n + 50)/24.
  • A101855 (program): a(n) = n*(n+1)*(n+2)*(n+4)*(n+23)/120.
  • A101859 (program): a(n) = 11 + (23*n)/2 + n^2/2.
  • A101860 (program): a(n) = (3+n)*(2 + 33*n + n^2)/6.
  • A101861 (program): n*(n+5)*(50+45*n+n^2)/24.
  • A101862 (program): a(n) = n*(n+1)*(n+7)*(122+57*n+n^2)/120.
  • A101863 (program): Main diagonal of A101858.
  • A101864 (program): Wythoff BB numbers.
  • A101865 (program): Third row of A101858.
  • A101867 (program): Main diagonal of A101866.
  • A101868 (program): a(n) = n + 2*ceiling(phi n), where phi = (1 + sqrt(5))/2. Row 1 of A101866.
  • A101869 (program): Row 2 of A101866.
  • A101870 (program): Row 3 of A101866.
  • A101871 (program): Number of Abelian groups of order 2n+1.
  • A101873 (program): Number of Abelian groups of order 4n+1.
  • A101874 (program): Number of Abelian groups of order 4n+3.
  • A101875 (program): Number of Abelian groups of order 4n+2.
  • A101878 (program): Expansion of -LambertW(LambertW(-x))/x.
  • A101879 (program): a(0) = 1, a(1) = 1, a(2) = 2; for n > 2, a(n) = 5*a(n-1) - 5*a(n-2) + a(n-3).
  • A101881 (program): Write two numbers, skip one, write two, skip two, write two, skip three … and so on.
  • A101882 (program): Write three numbers, skip one, write three, skip two, write three, skip three… and so on.
  • A101883 (program): Write four numbers, skip one, write four, skip two, write four, skip three… and so on.
  • A101890 (program): Sum C(n,2k)F(k), k=0..floor(n/2).
  • A101891 (program): Sum C(n,2k)F(k+1), k=0..floor(n/2).
  • A101892 (program): Sum C(n,2k)J(k), k=0..floor(n/2).
  • A101893 (program): a(n) = sum_{k=0..floor(n/2)} C(n,2k)*Pell(k).
  • A101904 (program): Number of leg-hypotenuse twin Pythagorean triples < 10^n.
  • A101907 (program): Numbers n-1 such that the arithmetic mean of the first n Fibonacci numbers (beginning with F(0)) is an integer.
  • A101909 (program): Number of primes between 2n and 4n.
  • A101917 (program): G.f. satisfies: A(x) = 1/(1 + x*A(x^7)) and also the continued fraction: 1 + x*A(x^8) = [1; 1/x, 1/x^7, 1/x^49, 1/x^343, …, 1/x^(7^(n-1)), …].
  • A101921 (program): a(2n) = a(n) + 2n - 1, a(2n+1) = 4n.
  • A101925 (program): a(n) = A005187(n) + 1.
  • A101926 (program): a(n) = 2^A101925(n).
  • A101927 (program): E.g.f. of sin(arcsinh(x)) (odd powers only).
  • A101928 (program): E.g.f. cos(arcsinh(x)) = sin(arccosh(x)) (even powers only).
  • A101942 (program): Sequence f[n,4], where f[n,b] is as defined below.
  • A101943 (program): Sequence f[n, 5], where f[n, b] is described in A101942.
  • A101945 (program): a(n) = 6*2^n - n - 5.
  • A101946 (program): a(n) = 6*2^n - 3*n - 5.
  • A101950 (program): Product of A049310 and A007318 as lower triangular matrices.
  • A101979 (program): Antidiagonal sums of A101309, which is the matrix logarithm of A047999 (Pascal’s triangle mod 2).
  • A101986 (program): Maximum sum of products of successive pairs in a permutation of order n+1.
  • A101987 (program): Product of nonzero digits of n-th prime.
  • A101990 (program): a(1) = a(2) = 1, a(3) = 9; for n > 3, a(n) = 3*a(n-1) - 3*a(n-2) + 9*a(n-3).
  • A102000 (program): Sequence generated from a lattice packing matrix.
  • A102001 (program): A weighted tribonacci, (1,2,4).
  • A102002 (program): Weighted tribonacci (1,2,4), companion to A102001.
  • A102005 (program): Fixed point of the morphism 1 -> 12, 2 -> 111.
  • A102026 (program): Number of n-bit strings that contain no more than 4 zeros and no more than 2 leading and 2 trailing zeros.
  • A102036 (program): Triangle, read by rows, where the terms are generated by the rule: T(n,k) = T(n-1,k) + T(n-1,k-1) + T(n-2,k-1) + T(n-3,k-1), with T(0,0)=1.
  • A102037 (program): Triangle of BitAnd(BitNot(n), k).
  • A102038 (program): a(n+1) = n*a(n) + a(n-1), a(1)=1, a(2)=2.
  • A102039 (program): a(n) = a(n-1) + last digit of a(n-1), starting at 1.
  • A102040 (program): a(n) = a(n-1) + last digit of a(n-1), starting at 3.
  • A102041 (program): a(n) = a(n-1) + last digit of a(n-1), starting at 7.
  • A102042 (program): a(n) = a(n-1) + last digit of a(n-1), starting at 9.
  • A102047 (program): Decimal expansion of -1/4 + log(2)/2.
  • A102048 (program): Exponent of A046021(n) (least inverse of Kempner function A002034) when written as a power of A006530(n) (largest prime dividing n), with a(1) = 1.
  • A102052 (program): Column 1 of triangle A102051, which is the matrix inverse of triangle A101275 (number of Schroeder paths).
  • A102055 (program): Column 1 of A102054, the matrix inverse of A060083 (Euler polynomials).
  • A102058 (program): Expansion of e.g.f. sin(arctanh(x)), odd powers only.
  • A102059 (program): Expansion of e.g.f. cos(arctanh(x)), even powers only.
  • A102066 (program): Sum of the first n primes, mod 6.
  • A102068 (program): a(n) = P(n)!, where P(n) is the largest prime factor of n (with a(1) = 1).
  • A102069 (program): Analogous to the oblong (promic or heteromecic) sequence formed but with reversal digits of factors multiplied.
  • A102071 (program): Pairwise sums of general ballot numbers (A002026).
  • A102080 (program): Number of matchings in the C_n X P_2 (n-prism) graph.
  • A102083 (program): a(n) = 8*n^2 + 4*n + 1.
  • A102084 (program): a(1) = 0; for n>0, write 2n=p+q (p, q prime), p*q maximal; then a(n)=p*q (see A073046).
  • A102091 (program): Number of perfect matchings in the C_{2n} X P_3 graph (C_{2n} is the cycle graph on 2n vertices and P_3 is the path graph on 3 vertices).
  • A102092 (program): a(n)< a(n+1) and: each digit is the absolute difference of the previous two; each digit is the absolute difference of the next two; each digit is the absolute difference of its two neighbors.
  • A102094 (program): a(n) = (2*n-1)*(2*n+1)^2.
  • A102105 (program): a(n) = (19*5^n - 16*3^n + 1) / 4.
  • A102108 (program): Numbers of partitions of 2n into n primes.
  • A102110 (program): Iterations during which LQTL cellular automaton passes through the origin. Iteration 4 8 32 64 416 and 832 result in completed Barbour-Chapman squares (see A094867).
  • A102111 (program): Iccanobirt numbers (1 of 15): a(n) = a(n-1) + a(n-2) + R(a(n-3)), where R is the digit reversal function A004086.
  • A102112 (program): Iccanobirt numbers (2 of 15): a(n) = a(n-1) + R(a(n-2)) + a(n-3), where R is the digit reversal function A004086.
  • A102113 (program): Iccanobirt numbers (3 of 15): a(n) = a(n-1) + R(a(n-2)) + R(a(n-3)), where R is the digit reversal function A004086.
  • A102114 (program): Iccanobirt numbers (4 of 15): a(n) = R(a(n-1)) + a(n-2) + a(n-3), where R is the digit reversal function A004086.
  • A102115 (program): Iccanobirt numbers (5 of 15): a(n) = R(a(n-1)) + a(n-2) + R(a(n-3)), where R is the digit reversal function A004086.
  • A102116 (program): Iccanobirt numbers (6 of 15): a(n) = R(a(n-1)) + R(a(n-2)) + a(n-3), where R is the digit reversal function A004086.
  • A102117 (program): Iccanobirt numbers (7 of 15): a(n) = R(a(n-1)) + R(a(n-2)) + R(a(n-3)), where R is the digit reversal function A004086.
  • A102118 (program): Iccanobirt numbers (8 of 15): a(n) = R(a(n-1) + a(n-2) + a(n-3)), where R is the digit reversal function A004086.
  • A102126 (program): Minimum number of pieces needed to dissect a square into n smaller squares (not necessarily of the same size).
  • A102129 (program): Expansion of (1 - x)*(1 + 2*x) / ((1 + x)*(1 - 4*x - x^2)).
  • A102130 (program): Primes of the form 8*n^2 + 4*n + 1.
  • A102147 (program): Second Eulerian transform of 1, 2, 3, 4, 5, … (A000027).
  • A102148 (program): Numbers k such that 101*k + 11 is prime.
  • A102166 (program): Numbers n such that 2*n^2 + 11*n + 101 is prime.
  • A102188 (program): a(n) = Sum_{m=0..n} (-1)^m * binomial(n,m)*(1*3*5*…*(4m-1)).
  • A102190 (program): Irregular triangle read by rows: coefficients of cycle index polynomial for the cyclic group C_n, Z(C_n,x), multiplied by n.
  • A102206 (program): a(0) = 3, a(1) = 8, a(n+2) = 4*a(n+1) - a(n) - 2.
  • A102207 (program): a(n) = 5a(n-1) - 5a(n-2) + a(n-3) with a(0) = 4, a(1) = 17, a(2) = 65.
  • A102208 (program): Decimal expansion of the volume of an icosahedron with unit edge length.
  • A102209 (program): Decimal expansion of ratio of both the surface area and the volume of an icosahedron to a dodecahedron with the same inradius.
  • A102214 (program): Expansion of (1 + 4*x + 4*x^2)/((1+x)*(1-x)^3).
  • A102217 (program): 3-Suzanne numbers.
  • A102219 (program): 3-Monica numbers.
  • A102221 (program): Column 0 of triangular matrix A102220, which equals [2*I - A008459]^(-1).
  • A102230 (program): Triangle, read by rows, where each column equals the convolution of A032349 with the prior column, starting with column 0 equal to A032349 shift right.
  • A102232 (program): Number of preferential arrangements of n labeled elements when at least k=three ranks are required.
  • A102233 (program): Number of preferential arrangements of n labeled elements when at least k=3 elements per rank are required.
  • A102237 (program): Smallest number equal to the product of n primes which is also equal to the sum of n distinct primes.
  • A102239 (program): a(n) = (Sum_{i=0..n} 5^i) + 1 - (Sum_{i=0..n} 5^i) mod 2.
  • A102244 (program): a(n) = exp(-1) * (n+1)! * Sum_{i>j>=0} j^n/i!.
  • A102248 (program): Numbers n such that n111 is prime.
  • A102249 (program): Numbers k such that k1111 is prime.
  • A102250 (program): Indices of semiprime Haüy rhombic dodecahedral numbers.
  • A102261 (program): a(n) = A002144(n) - A002145(n).
  • A102269 (program): Primes p such that Q(sqrt(-21p)) has genus characters chi_{-3} = +1, chi_{-7} = +1.
  • A102276 (program): a(n) = (a(n-1) * a(n-5) + a(n-3)^2) / a(n-6) with a(0) = … = a(5) = 1, a(n) = a(5-n) for all n in Z.
  • A102283 (program): Period 3: repeat [0, 1, -1].
  • A102285 (program): G.f. (1-x)/(7*x^2-6*x+1).
  • A102286 (program): Total number of odd blocks in all partitions of n-set.
  • A102287 (program): Total number of even blocks in all partitions of n-set.
  • A102289 (program): Total number of odd lists in all sets of lists, cf. A000262.
  • A102290 (program): Total number of even lists in all sets of lists, cf. A000262.
  • A102291 (program): Total number of prime parts in all compositions of n.
  • A102294 (program): Number of prime divisors (with multiplicity) of icosahedral numbers.
  • A102296 (program): a(n) = (1/6)*(n+1)*(10*n^2 + 17*n + 12).
  • A102297 (program): Number of distinct divisors of n+1 where n and n+1 are composite or twin composite numbers.
  • A102298 (program): Number of prime divisors with multiplicity of n+1 where n and n+1 are composite or twin composite numbers.
  • A102299 (program): Number of prime divisors with multiplicity of n where n and n+1 are composite or twin composite numbers.
  • A102300 (program): Number of distinct prime divisors of n where n and n+1 are composite or twin composite numbers.
  • A102301 (program): a(n) = ((3*n + 1)*2^(n+3) + 9 + (-1)^n)/18.
  • A102302 (program): Largest number < n/2 coprime to n.
  • A102303 (program): a(n) = (1/6) * (7^(n+1) - 3*(-1)^n + 2).
  • A102304 (program): Sum of factors of numbers having exactly three prime factors.
  • A102305 (program): a(n) = n^2 + 2*n + 3.
  • A102307 (program): a(n) = Fibonacci(2n+1) * binomial(2n,n).
  • A102309 (program): a(n) = Sum_{d divides n} moebius(d) * C(n/d,2).
  • A102310 (program): Square array read by antidiagonals: Fibonacci(k*n).
  • A102311 (program): Sum_{k=1..n} Fibonacci(k*(n-k)).
  • A102312 (program): a(n) = Fibonacci(5*n).
  • A102318 (program): A mean binomial transform of the Catalan numbers.
  • A102319 (program): A mean binomial transform of the central binomial numbers.
  • A102338 (program): Numbers n such that 10n+3 is prime.
  • A102339 (program): Numbers k such that k*10^3 + 333 is prime.
  • A102341 (program): Areas of ‘close-to-equilateral’ integer triangles.
  • A102342 (program): Numbers k such that 10k + 7 is prime.
  • A102343 (program): Numbers k such that k*10^3 + 777 is prime.
  • A102344 (program): Numbers n such that the Diophantine equation (x+2)^3-x^3=2*n^2 has solutions.
  • A102345 (program): a(n) = 3^n + (-1)^n.
  • A102348 (program): Decimated primes: every 10th prime has been omitted.
  • A102350 (program): Prime(144*n).
  • A102352 (program): Numbers n such that n^3 can be partitioned into n primes such that n-1 are consecutive primes and the remaining prime is larger than the sum of the n-1 consecutive primes.
  • A102354 (program): a(n) is the number of ways n can be written as k^2 * j, 0 < j <= k.
  • A102362 (program): This finite sequence describes itself completely: there is 1 “0” in it, 1 “3”, 1 “4”, …, 2 “2” and 11 “1”.
  • A102363 (program): Triangle read by rows, constructed by a Pascal-like rule with left edge = 2^k, right edge = 2^(k+1)-1 (k >= 0).
  • A102364 (program): Number of terms in Fibonacci sequence less than n not used in Zeckendorf representation of n (the Zeckendorf representation of n is a sum of non-consecutive distinct Fibonacci numbers).
  • A102366 (program): Number of subsets of {1,2,…,n} in which exactly half of the elements are less than or equal to sqrt(n).
  • A102368 (program): Smallest k>0 such that n^k + 1 is not prime.
  • A102370 (program): “Sloping binary numbers”: write numbers in binary under each other (right-justified), read diagonals in upward direction, convert to decimal.
  • A102371 (program): Numbers missing from A102370.
  • A102376 (program): a(n) = 4^A000120(n).
  • A102377 (program): Gould’s sequence A001316 in binary.
  • A102378 (program): a(n) = a(n-1) + a([n/2]) + 1, a(1) = 1.
  • A102379 (program): a(n) is the minimal number of nodes in a binary tree of height n.
  • A102386 (program): Numbers k such that k99999 is prime.
  • A102389 (program): An evil count.
  • A102390 (program): An odious count.
  • A102391 (program): Evil numbers in evil places.
  • A102392 (program): Odious numbers in odious places.
  • A102393 (program): A wicked evil sequence.
  • A102394 (program): A wicked odious sequence.
  • A102395 (program): A mod 2 related Jacobsthal sequence.
  • A102396 (program): A mod 2 related Jacobsthal sequence.
  • A102397 (program): a(n) = concatenation of first n elements of Thue-Morse sequence A010059.
  • A102403 (program): Number of Dyck paths of semilength n having no ascents of length 2.
  • A102414 (program): Smallest semiprime greater than n-th prime.
  • A102421 (program): To get a(n), start with 2n+1, multiply by 3 and add 1 and divide out any power of 2; then multiply by 3 and subtract 1 and divide out any power of 2.
  • A102426 (program): Triangle read by rows giving coefficients of polynomials defined by F(0,x)=0, F(1,x)=1, F(n,x) = F(n-1,x) + x*F(n-2,x).
  • A102427 (program): Triangle based on downward diagonals of A102426.
  • A102428 (program): Central column of triangle A102427.
  • A102429 (program): Row sums of A102427.
  • A102436 (program): Number of matchings of the corona L’(n) of the ladder graph L(n)=P_2 X P_n. and the complete graph K(1); in other words, L’(n) is the graph constructed from L(n) by adding for each vertex v a new vertex v’ and the edge vv’.
  • A102438 (program): a(n) = 100*n + 44.
  • A102439 (program): a(n) = 100*n + 4.
  • A102446 (program): a(n) = a(n-1) + 4*a(n-2) for n>1, a(0) = a(1) = 2.
  • A102460 (program): a(n) = 1 if n is a Lucas number, else a(n) = 0.
  • A102466 (program): Numbers such that the number of divisors is the sum of numbers of prime factors with and without repetitions.
  • A102467 (program): Positive integers k, such that d(k) <> Omega(k) + omega(k), where d = A000005, Omega = A001222 and omega = A001221.
  • A102470 (program): Numbers n such that denominator of Sum_{k=0 to n} 1/k! is n!.
  • A102471 (program): Numbers n such that the denominator of Sum_{k=0 to 2n} 1/k! is (2n)!.
  • A102472 (program): Triangle read by rows. Let S(k) be the sequence defined by F(0)=0, F(1)=1, F(n-1) + (n+k)*F(n) = F(n+1). E.g. S(0) = 0, 1, 1, 3, 10, 43, 225, 1393, 9976, 81201, … Then S(0), S(1), S(2), … are written vertically, next to each other, with the initial term of each on the next row down.
  • A102473 (program): Triangle read by rows. Let S(k) be the sequence defined by F(0)=0, F(1)=1, F(n-1) + (n+k)*F(n) = F(n+1). E.g. S(0) = 0,1,1,3,10,43,225,1393,9976,81201, … Then S(0), S(1), S(2), … are written next to each other, vertically, with the initial term of each on the next row down. The order of the terms in the rows are then reversed.
  • A102476 (program): Least modulus with 2^n square roots of 1.
  • A102479 (program): Triangle read by rows: row n contains the numbers C(n,k)^(k-1) for 0 <= k <= n-1, n >= 1.
  • A102480 (program): Triangle read by rows: row n contains the numbers C(n,k)^(k-1) for 0 <= k <= n, n >= 0.
  • A102485 (program): a(n) = 5*3^n - 4*2^n.
  • A102486 (program): a(n) = 4*a(n-1) - 5*a(n-2).
  • A102487 (program): Numbers in base-12 representation that can be written with decimal digits.
  • A102488 (program): Numbers in base-12 representation that cannot be written with decimal digits.
  • A102489 (program): Take the decimal representation of n and read it as if it were written in hexadecimal.
  • A102490 (program): Numbers in base-16 representation that cannot be written with decimal digits.
  • A102508 (program): Suppose there are equally spaced chairs around a round table. Then a(n) is the maximal number of chairs for which there exists a seating arrangement of n people around the table such that if a waiter puts two glasses (randomly) on the table in front of two (different) chairs, it is always possible to turn the table so that the two glasses end up in front of two seated persons.
  • A102511 (program): Sum(A008683(A102510(k)): k<=n).
  • A102515 (program): a(n) = floor(1 + sqrt(2n + 1)).
  • A102516 (program): Sum C(n-3k,3k+1), k=0..floor(n/6).
  • A102517 (program): Expansion of (1+x^2)/((1-x+x^2)(1+2x^2)).
  • A102518 (program): a(n) = Sum_{k=0..n} binomial(n, k) * Sum_{j=0..k} binomial(3k, 3j).
  • A102519 (program): Decimal expansion of 1-(3*sqrt(3))/(4*Pi).
  • A102520 (program): Decimal expansion of 1-(9*sqrt(3))/(8*Pi).
  • A102526 (program): Antidiagonal sums of Losanitsch’s triangle (A034851).
  • A102528 (program): a(n)=least positive integer not a(k) or a(k)+floor(k/2) for any k<n.
  • A102529 (program): Complement of A102528.
  • A102537 (program): Triangle T(n,k) read by rows: (1/n) * C(2n+k,k-1) * C(n,k).
  • A102545 (program): Numbers k such that k999999 is prime.
  • A102546 (program): Numbers t such that t1 is prime and t is a multiple of 10.
  • A102547 (program): Triangle read by rows, formed from antidiagonals of the antidiagonals (A011973) of Pascal’s triangle (A007318).
  • A102548 (program): Number of positive integers <= n that are expressible in the form u^2+v^2, with u and v integers.
  • A102551 (program): a(n) = [prime(n)/(prime(n+1)-prime(n))], where [x] means the integer part of x.
  • A102552 (program): a(n) = prime(n)-(prime(n+1)+prime(n-1))/2.
  • A102554 (program): Numbers n such that p <> (n AND p) for at least one prime-factor p.
  • A102556 (program): Numerator of the probability that 2n-dimensional Gaussian random triangle has an obtuse angle.
  • A102557 (program): Denominator of the probability that 2n-dimensional Gaussian random triangle has an obtuse angle.
  • A102558 (program): Numerator of the probability that (2n+1)-dimensional Gaussian random triangle has an obtuse angle.
  • A102559 (program): Denominator of the probability that (2n+1)-dimensional Gaussian random triangle has an obtuse angle.
  • A102560 (program): Expansion of (1-x^3)/(1-x^4).
  • A102561 (program): a(n) = 2^floor(n/2)*((-1)^floor(n/2) + (-1)^n)/2.
  • A102563 (program): A000120(A001045(n))-A001045(A000120(n)).
  • A102564 (program): A000120(A078008(n))-A078008(A000120(n)).
  • A102565 (program): a(n) = A102563(n) - A102564(n).
  • A102566 (program): a(n) = {minimal k such that f^k(prime(n)) = 1} where f(m) = (m+1)/2^r, 2^r is the highest power of two dividing m+1.
  • A102572 (program): a(n) = floor(log_4(n)).
  • A102574 (program): a(n) is the sum of the distinct norms of the divisors of n over the Gaussian integers.
  • A102584 (program): a(n) = 1/2 times the cancellation factor in reducing Sum_{k=0 to 2n+1} 1/k! to lowest terms.
  • A102587 (program): T(n, k) = (-1)^n*2*[x^k] ChebyshevT(n, (1 - x)/2) with T(0,0) = 1, for 0 <= k <= n, triangle read by rows.
  • A102590 (program): Inverse Boustrophedon transform of 2^n.
  • A102591 (program): a(n) = Sum_{k=0..n} binomial(2n+1, 2k)*3^(n-k).
  • A102592 (program): a(n) = Sum_{k=0..n} binomial(2n+1, 2k)*5^(n-k).
  • A102594 (program): Number of noncrossing trees with n edges in which no border edges emanate from the root.
  • A102603 (program): 24n + 21.
  • A102611 (program): Numbers n such that the number n77 is prime.
  • A102613 (program): Numerator of the reduced fractions of the ratios of the number of primes less than n over the number of composites less than n.
  • A102614 (program): Denominators of the reduced fractions of the ratios of the number of primes less than n over the number of composites less than n.
  • A102615 (program): Nonprime numbers of order 2.
  • A102616 (program): Nonprime numbers of order 3.
  • A102617 (program): Primes p(n) such that n is a second-order nonprime number.
  • A102619 (program): Numbers which are the sum of two positive cubes and divisible by 19.
  • A102620 (program): Number of legal Go positions on a 1 X n board (for which 3^n is a trivial upper bound).
  • A102622 (program): Nonprime numbers n concatenated n times.
  • A102624 (program): Numbers k such that the number k23 is prime.
  • A102625 (program): Triangle read by rows: T(n,k) is the sum of the weights of all vertices labeled k at depth n in the Catalan tree (1 <= k <= n+1, n >= 0).
  • A102631 (program): a(n) = n^2 / (squarefree kernel of n).
  • A102649 (program): Numbers n such that 11*n^2 + 11*n + 3 is prime.
  • A102650 (program): a(n) = 4 * floor(28*2^n/15).
  • A102651 (program): a(n) = 4 * floor(23*2^n/15).
  • A102652 (program): a(n) = 4 * floor(24*2^n/15) = 4*A077854(n).
  • A102653 (program): a(n) = 4 * floor(27*2^n/15).
  • A102655 (program): Numbers that are the arithmetic mean of four successive primes.
  • A102656 (program): Numbers n such that 11*n + 1 is prime.
  • A102657 (program): Numbers n such that 11n^2 + 11n + 1 is prime.
  • A102662 (program): Triangle read by rows: T(1,1)=1,T(2,1)=1,T(2,2)=3, T(k-1,r-1)+T(k-1,r)+T(k-2,r-1).
  • A102669 (program): Number of digits >= 2 in decimal representation of n.
  • A102670 (program): Number of digits >= 2 in the decimal representations of all integers from 0 to n.
  • A102671 (program): Number of digits >= 3 in decimal representation of n.
  • A102672 (program): Number of digits >= 3 in the decimal representations of all integers from 0 to n.
  • A102673 (program): Number of digits >= 4 in decimal representation of n.
  • A102674 (program): Number of digits >= 4 in the decimal representations of all integers from 0 to n.
  • A102675 (program): Number of digits >= 5 in decimal representation of n.
  • A102676 (program): Number of digits >= 5 in the decimal representations of all integers from 0 to n.
  • A102677 (program): Number of digits >= 6 in decimal representation of n.
  • A102678 (program): Number of digits >= 6 in the decimal representations of all integers from 0 to n.
  • A102679 (program): Number of digits >= 7 in decimal representation of n.
  • A102680 (program): Number of digits >= 7 in the decimal representations of all integers from 0 to n.
  • A102681 (program): Number of digits >= 8 in decimal representation of n.
  • A102682 (program): Number of digits >= 8 in the decimal representations of all integers from 0 to n.
  • A102683 (program): Number of digits 9 in decimal representation of n.
  • A102684 (program): Number of times the digit 9 appears in the decimal representations of all integers from 0 to n.
  • A102685 (program): Partial sums of A055640.
  • A102686 (program): Numbers k such that 11*k + 3 is prime.
  • A102688 (program): a(n) = (1/n)*Sum_{k=1..n} k*2^gcd(n,k).
  • A102689 (program): a(n) = 10000*n + 2468.
  • A102690 (program): Number of n-expodigital numbers (i.e., numbers m such that m^n has exactly n decimal digits).
  • A102691 (program): Least n-expodigital number (i.e., numbers m such that m^n has exactly n decimal digits).
  • A102693 (program): a(n) is the number of digraphs (not allowing loops) with vertices 1,2,…,n that have a unique Eulerian tour (up to cyclic shift).
  • A102699 (program): Number of strings of length n, using as symbols numbers from the set {1, 2, …, n}, in which consecutive symbols differ by exactly 1.
  • A102700 (program): Numbers k such that 10*k + 9 is prime.
  • A102701 (program): Non-“Ding!Bong!” numbers: positive numbers which are not a positive linear combination of 5’s and 7’s.
  • A102702 (program): Expansion of (2-x-2*x^2-x^3)/(1-x-x^2)^2.
  • A102703 (program): Numbers k such that 100*k+99 is prime.
  • A102704 (program): Numbers k such that k999 is prime.
  • A102705 (program): Numbers not of the form 7x + 9y with nonnegative x and y.
  • A102710 (program): a(1) = 2, a(2) = 3, a(n+2) = a(n)*(a(n)+a(n+1)) - a(n+1).
  • A102711 (program): Numbers k such that 11*k + 7 is prime.
  • A102713 (program): Total sum of odd parts in all compositions of n.
  • A102714 (program): Expansion of (x+2) / ((x+1)*(x^2-3*x+1)).
  • A102715 (program): Triangle read by rows: T(n,k) is phi(binomial(n,k)), where phi is Euler’s totient function (0 <= k <= n).
  • A102716 (program): Triangle read by rows: T(n,k) = sigma(binomial(n,k)) (0 <= k <= n), where sigma(m) is the sum of the positive divisors of m.
  • A102721 (program): Numbers n such that 11*n + 13 is prime.
  • A102724 (program): Sum of the first n pairs of consecutive primes (for example, a(3) = (2+3) + (3+5) + (5+7) = 25).
  • A102728 (program): Array read by antidiagonals: T(n, k) = ((n+1)^k-(n-1)^k)/2.
  • A102731 (program): Numbers k such that 11*k + 23 is prime.
  • A102732 (program): Primes of the form 13n+5.
  • A102733 (program): Numbers n such that 2*n + 101 is prime.
  • A102734 (program): Primes of the form 23n+5.
  • A102736 (program): Number of permutations of n elements without cycles whose length is a multiple of 3.
  • A102741 (program): a(n) = 3^4 * binomial(n+3, 4).
  • A102743 (program): Expansion of LambertW(-x)/(x*(x-1)).
  • A102745 (program): Number of distinct prime factors of four consecutively concatenated primes.
  • A102750 (program): Numbers n such that square of largest prime dividing n does not divide n.
  • A102752 (program): Array read by antidiagonals: T(n, k) = ((n+2)^k-(n-1)^k)/3.
  • A102753 (program): Decimal expansion of (Pi^2)/2.
  • A102754 (program): Decimal expansion of (Pi^2)/2 - 4.
  • A102756 (program): Triangle T(n,k), 0<=k<=n, read by rows defined by: T(n,k) = T(n-1,k-1) + 2*T(n-1,k) + T(n-2,k-2) - T(n-2,k), T(0,0) = 1, T(n,k) = 0 if k < 0 or if n < k.
  • A102757 (program): a(n) = Sum_{i=0..n} C(n,i)^2 * i! * 3^i.
  • A102761 (program): Same as A000179, except that a(0) = 2.
  • A102762 (program): Curvatures of (largest) kissing circles along the circumference, starting with curvature = -1 and 2.
  • A102765 (program): Array read by antidiagonals: T(n, k) = ((n+4)^k-(n-1)^k)/5.
  • A102768 (program): Numbers k such that 23*k + 11 is prime.
  • A102769 (program): Decimal expansion of the volume of a dodecahedron with each edge of unit length.
  • A102770 (program): (p*q - 1)/2 where p and q are consecutive odd primes.
  • A102771 (program): Decimal expansion of area of a regular pentagon with unit edge length.
  • A102773 (program): a(n) = Sum_{i=0..n} binomial(n,i)^2*i!*4^i.
  • A102781 (program): Number of positive even numbers less than the n-th prime.
  • A102785 (program): G.f.: (x-1)/(-2*x^2 + 3*x^3 + 2*x - 1).
  • A102786 (program): Integer part of n#/((p-3)# 3#), where p=preceding prime to n.
  • A102790 (program): Integer part of n#/(p-3)#, where p=preceding prime to n.
  • A102807 (program): a(n) is the square of one plus the number consisting of n 3’s.
  • A102815 (program): “False so far” sequence.
  • A102820 (program): Number of primes between 2*prime(n) and 2*prime(n+1), where prime(n) is the n-th prime.
  • A102821 (program): Numbers n for which the square excess of n-th prime is prime.
  • A102822 (program): a(n+1) is the integer part of sqrt(2*a(n)^2).
  • A102827 (program): “True already”, base 10, start 1: a(n) is the least integer such that the sequence up to a(n-1) written in base 10 contains floor(a(n)/10) copies of the digit a(n) % 10, with a(0) = 1.
  • A102828 (program): “True already”, base 2, start 1: a(n) is the least integer such that the sequence up to a(n-1) written in base 2 contains floor(a(n)/2) copies of the digit a(n) % 2, with a(0) = 1.
  • A102831 (program): Number of n-digit 4th powers.
  • A102839 (program): a(0) = 0, a(1) = 1, and a(n) = ((2*n - 1)*a(n-1) + 3*n*a(n-2))/(n - 1) for n >= 2.
  • A102840 (program): a(0)=0, a(1)=1, a(n)=((2*n-1)*a(n-1)-5*n*a(n-2))/(n-1).
  • A102841 (program): a(n) = ((9*n^2 + 33*n + 26)*2^n + (-1)^n)/27.
  • A102845 (program): Number of prime factors of the sum of the first n odd primes.
  • A102846 (program): a(0)=1, a(1)=1, a(n) = a(n-1)*a(n-2) + 2.
  • A102851 (program): Primes of the form 19n + 5.
  • A102852 (program): Primes whose squares are congruent to 5 (modulo 19).
  • A102853 (program): Number of prime factors (with multiplicity) of number of points on surface of square pyramid.
  • A102860 (program): Number of ways to change three non-identical letters in the word aabbccdd…, where there are n types of letters.
  • A102861 (program): Numbers which in base 5 have digit-sum 4.
  • A102862 (program): Numbers of prime factors of the sum of the first n primes.
  • A102863 (program): a(n)=1 if at least one of the first n primes is a divisor of the sum of the first n primes; otherwise a(n)=0.
  • A102865 (program): Base-4 digits are, in order, the first n terms of the sequence (1, 3, 21, 203, 2021, 20203, 202021, 2020203, 20202021, 202020203, … ).
  • A102866 (program): Number of finite languages over a binary alphabet (set of binary words of total length n).
  • A102871 (program): a(n) = a(n-3) - 5*a(n-2) + 5*a(n-1), a(0) = 1, a(1) = 3, a(2) = 10.
  • A102875 (program): Let f(n) = n+2 if n == 1 mod 3, = n if n == 2 mod 3, = n-2 if n == 0 mod 3; then a(n) = Fibonacci(f(n)).
  • A102877 (program): a(0) = 1, a(1) = 1; for n>0, a(2*n) = 3*a(2n-1), a(2*n+1) = 3*a(2*n) - 2*a(n-1).
  • A102879 (program): A Chebyshev transform of the first kind of the central binomial numbers.
  • A102880 (program): A Chebyshev transform of the first kind of the Catalan numbers.
  • A102881 (program): Expansion of (1+x)/sqrt(1-4x^2-8x^3-4x^4).
  • A102882 (program): Expansion of (1+2x)/sqrt((1-3x^2)(1+4x+5x^2)).
  • A102885 (program): Index of n in the primes A000040 or nonprimes A141468.
  • A102890 (program): A102889(n) is at least a(n).
  • A102893 (program): Number of noncrossing trees with n edges and having degree of the root at least 2.
  • A102898 (program): A Catalan-related transform of 3^n.
  • A102899 (program): a(n) = ceiling(n/3)^2 - floor(n/3)^2.
  • A102900 (program): a(n) = 3*a(n-1) + 4*a(n-2), a(0)=a(1)=1.
  • A102901 (program): a(n) = a(n-1) + 6a(n-2), a(0)=1, a(1)=0.
  • A102902 (program): a(n) = 9a(n-1) - 16a(n-2).
  • A102905 (program): A modulo three sequential permutation the Fibonacci sequence (outer): permutation after the Fibonacci.
  • A102909 (program): a(n) = Sum_{j=0..8} n^j.
  • A102915 (program): Numbers n such that n3 is prime and n is a multiple of 10.
  • A102928 (program): Reduced numerators of the harmonic means of the first n positive integers.
  • A103115 (program): a(n) = 6*n*(n-1)-1.
  • A103116 (program): a(n) = Sum_{i=1..n} (n-i+1)*phi(i).
  • A103118 (program): Numbers k such that 100*k + 57 is prime.
  • A103119 (program): Numbers n such that n0999 is prime.
  • A103122 (program): Define a 1-1 correspondence between the integers Z and the nonnegative integers N by f(n) = A102370(n) if n >= 0, f(n) = A102371(-n) if n < 0; sequence gives a(n) = f^(-1)(n) for n >= 0.
  • A103127 (program): Numbers congruent to {-1, 1, 3, 5} mod 16.
  • A103128 (program): a(n) = floor(sqrt(2n-1)).
  • A103131 (program): The product of the residues in [1,n] relatively prime to n, taken modulo n.
  • A103134 (program): a(n) = Fibonacci(6n+4).
  • A103136 (program): Inverse of the Delannoy triangle.
  • A103137 (program): First column of inverse of Delannoy triangle.
  • A103138 (program): Second column of inverse of Delannoy triangle.
  • A103142 (program): a(n) = 2*a(n-1) + a(n-2) + a(n-3) + a(n-4), with a(0)=1, a(1)=2, a(3)=5, a(4)=13.
  • A103143 (program): a(n) = a(n-1) + a(n-2) + 3*a(n-3), with a(0) = 1, a(1) = 0, a(2) = 1.
  • A103144 (program): Decimal primes whose decimal representation in hex is also prime.
  • A103145 (program): a(n) = (1/6)*(n^3 + 21*n^2 + 74*n + 18).
  • A103151 (program): Number of decompositions of 2n+1 into 2p+q, where p and q are both odd primes (A065091).
  • A103154 (program): Each letter appears an even number of times in the English names for 1 through n taken together (names without “and”).
  • A103157 (program): Number of ways to choose 4 distinct points from an (n+1) X (n+1) X (n+1) lattice cube.
  • A103159 (program): a(n) = GCD(reverse(n), reversed(n+1)).
  • A103160 (program): a(n) = GCD(reverse(n!), reverse((n+1)!)).
  • A103161 (program): GCD of reverse(2^n) and reverse(2^(n+1)), where reverse(k) = A004086(k), the decimal representation of k read backwards.
  • A103162 (program): GCD of reverse(3^n) and reverse(3^(n+1)).
  • A103164 (program): Integers but with the primes squared.
  • A103166 (program): a(n) = reverse(2^n) mod 2^n.
  • A103167 (program): a(n) = 2^n mod reverse(2^n).
  • A103168 (program): a(n) is the remainder when (n written backwards) is divided by n.
  • A103175 (program): A001787 written in base 2.
  • A103177 (program): (7*3^n + 2n + 5)/4.
  • A103181 (program): In decimal representation of n: replace all even digits with 0 and all odd digits with 1.
  • A103185 (program): a(n) = Sum_{ k >= 0 such that n + k == 0 mod 2^k } 2^(k-1).
  • A103187 (program): a(n) = second term in continued fraction of n-th harmonic number.
  • A103188 (program): Numbers k such that k711 is prime.
  • A103190 (program): Numbers k such that k29 is prime.
  • A103192 (program): Trajectory of 1 under repeated application of the function n -> A102370(n).
  • A103194 (program): LAH transform of squares.
  • A103196 (program): a(n) = (1/9)(2^(n+3)-(-1)^n(3n-1)).
  • A103197 (program): Number of compositions of n into Fibonacci number of parts.
  • A103198 (program): Number of compositions of n into a square number of parts.
  • A103200 (program): a(1)=1, a(2)=2, a(3)=11, a(4)=19; a(n) = a(n-4) + sqrt(60*a(n-2)^2 + 60*a(n-2) + 1) for n >= 5.
  • A103201 (program): a(1) = 11, a(2) = 19, a(3) = 89, a(4) = 151; for n >= 5, a(n) = sqrt(a(n-4)^2 + 60*a(n-2)^2 + 4*a(n-2)*sqrt(210 + 15*a(n-4)^2)).
  • A103202 (program): A102370 sorted.
  • A103204 (program): a(1) = 2, a(2) = 4; a(n) = 2*a(n-1) - 1.
  • A103205 (program): Write numbers in decimal under each other, then read diagonals in upward direction.
  • A103208 (program): Numbers n such that 3 divides prime(1) + … + prime(n).
  • A103210 (program): a(n) = (1/n) * Sum_{i=0..n-1} C(n,i)*C(n,i+1)*2^i*3^(n-i), a(0)=1.
  • A103211 (program): a(n) = (1/n) * Sum_{i=0..n-1} C(n,i)*C(n,i+1)*3^i*4^(n-i), a(0)=1.
  • A103212 (program): a(n) = (1/n) * Sum_{i=0..n-1} C(n,i)*C(n,i+1)*(n-1)^i*n^(n-i) for n>=1, a(0)=1.
  • A103213 (program): a(n) = n! * Sum_{k=1..n} binomial(n,k)/k.
  • A103214 (program): a(n) = 24*n + 1.
  • A103215 (program): Numbers congruent to {1, 2, 5, 10, 13, 17} mod 24.
  • A103217 (program): Hexagonal numbers triangle read by rows: T(n,k)=(n+1-k)*(2*(n+1-k)-1).
  • A103218 (program): Triangle read by rows: T(n, k) = (2*k+1)*(n+1-k)^2.
  • A103219 (program): Triangle read by rows: T(n,k) = (n+1-k)*(4*(n+1-k)^2 - 1)/3+2*k*(n+1-k)^2.
  • A103220 (program): a(n) = n*(n+1)*(3*n^2+n-1)/6.
  • A103221 (program): Number of partitions of n into parts 2 and 3.
  • A103247 (program): Triangle read by rows: T(n,k) is the coefficient of x^k (0<=k<=n) in the monic characteristic polynomial of the n X n matrix with 3’s on the diagonal and 1’s elsewhere (n>=1). Row 0 consists of the single term 1.
  • A103252 (program): Array A000292(n)*A000217(k), read by antidiagonals.
  • A103260 (program): Number of partitions of 2n prime to 3 with all odd parts occurring with multiplicity 2. The even parts occur with multiplicity 1.
  • A103262 (program): McKay-Thompson series of class 36g for the Monster group.
  • A103271 (program): a(n) = (prime(n)+prime(n+1)) mod 4.
  • A103273 (program): Number of ways of writing prime(n)-1 in the form prime(i)+prime(j).
  • A103279 (program): Array read by antidiagonals, generated by the matrix M = [1,1,1;1,N,1;1,1,1];.
  • A103280 (program): Array read by antidiagonals, generated by the matrix M = [1,1,1;1,N,1;1,1,1];.
  • A103283 (program): Triangle read by rows: T(n,k) is the coefficient of x^k in the monic characteristic polynomial of the n X n matrix with 2’s on the diagonal and 1’s elsewhere (n >= 1 and 0 <= k <= n). Row 0 consists of the single term 1.
  • A103288 (program): Numbers k such that sigma(k) >= 2k-1 (union of perfect, abundant and least deficient numbers).
  • A103290 (program): n*(n-1)*(n^2-n+4)/6.
  • A103303 (program): Complete list of digits used in the counting numbers (in base 10). Also known as the “Arabic numerals”.
  • A103311 (program): A transform of the Fibonacci numbers.
  • A103312 (program): A transform of the Jacobsthal numbers.
  • A103316 (program): Riordan array (1/(1+2x), x/(1+x)).
  • A103318 (program): Number of solutions i in range [0,n-1] to i == 0 mod 2^(n-i).
  • A103321 (program): Expansion of 1 / ((1-x-x^2-x^3)*(1-x-x^3)).
  • A103322 (program): Expansion of 1 / ((1-x-x^2-x^3)*(1-x^2-x^3)).
  • A103323 (program): Square array T(n,k) read by antidiagonals: powers of Fibonacci numbers.
  • A103324 (program): Square array T(n,k) read by antidiagonals: powers of Lucas numbers.
  • A103325 (program): Fifth powers of Lucas numbers.
  • A103326 (program): a(n) = Fibonacci(5n)/Fibonacci(n).
  • A103327 (program): Triangle read by rows: T(n,k) = binomial(2n+1, 2k+1).
  • A103328 (program): Triangle T(n, k) read by rows: binomial(2n, 2k+1).
  • A103333 (program): Number of closed walks on the graph of the (7,4) Hamming code.
  • A103334 (program): Number of closed walks of length 2n at any of the nodes of degree 1 on the graph of the (7,4) Hamming code.
  • A103340 (program): Denominator of the unitary harmonic mean (i.e., the harmonic mean of the unitary divisors) of the positive integer n.
  • A103345 (program): Numerator of Sum_{k=1..n} 1/k^6 = Zeta(6,n).
  • A103346 (program): Denominators of Sum_{k=1..n} 1/k^6 = Zeta(6,n).
  • A103347 (program): Numerators of Sum_{k=1..n} 1/k^7 = Zeta(7,n).
  • A103348 (program): Denominators of sum_{k=1..n} 1/k^7 = Zeta(7,n).
  • A103349 (program): Numerators of sum_{k=1..n} 1/k^8 = Zeta(8,n).
  • A103350 (program): Denominators of sum_{k=1..n} 1/k^8 = Zeta(8,n).
  • A103351 (program): Numerators of sum_{k=1..n} 1/k^9 = Zeta(9,n).
  • A103352 (program): Denominators of sum_{k=1..n} 1/k^9 = Zeta(9,n).
  • A103354 (program): a(n) = floor(x), where x is the solution to x = 2^(n-x).
  • A103355 (program): a(n) = n - floor( sqrt(prime(n) ).
  • A103359 (program): T(n,k) = Max{p: prime p divides m where n-k<=m<=n+k}, triangle read by rows: 0<=k<n.
  • A103368 (program): Period 6: repeat [1, 1, -1, -1, 0, 0].
  • A103370 (program): Row sums of triangle A095801 (matrix square of the Narayana triangle A001263).
  • A103371 (program): Number triangle T(n,k) = C(n,n-k)*C(n+1,n-k).
  • A103372 (program): a(1) = a(2) = a(3) = a(4) = a(5) = 1 and for n>5: a(n) = a(n-4) + a(n-5).
  • A103373 (program): a(1) = a(2) = a(3) = a(4) = a(5) = a(6) = 1 and for n>6: a(n) = a(n-5) + a(n-6).
  • A103374 (program): a(1) = a(2) = a(3) = a(4) = a(5) = a(6) = a(7) = 1 and for n>7: a(n) = a(n-6) + a(n-7).
  • A103375 (program): a(1) = a(2) = a(3) = a(4) = a(5) = a(6) = a(7) = a(8) = 1 and for n>8: a(n) = a(n-7) + a(n-8).
  • A103376 (program): a(1) = a(2) = a(3) = a(4) = a(5) = a(6) = a(7) = a(8) = a(9) = 1 and for n>9: a(n) = a(n-8) + a(n-9).
  • A103377 (program): a(1)=a(2)=…=a(10)=1, a(n)=a(n-9)+a(n-10).
  • A103379 (program): k=11 case of family of sequences beyond Fibonacci and Padovan.
  • A103380 (program): k=12 case of family of sequences beyond Fibonacci and Padovan: a(n) = a(n-12) + a(n-13).
  • A103390 (program): Natural numbers but with nonprimes squared.
  • A103391 (program): ‘Even’ fractal sequence for the natural numbers: Deleting every even-index term results in the same sequence.
  • A103401 (program): Numbers k such that k211 is prime.
  • A103406 (program): Triangle read by rows: n-th row = unsigned coefficients of the characteristic polynomials of an n X n matrix with 2’s on the diagonal and 1’s elsewhere.
  • A103407 (program): Triangle of absolute values of the coefficients (in descending powers) of the characteristic polynomials of n X n matrices with 3’s on the main diagonal and 1’s elsewhere.
  • A103408 (program): Numbers n such that n2101 is prime.
  • A103409 (program): Numbers n such that n2357 is prime.
  • A103410 (program): Number of products of distinct elements in generation n, starting with two elements.
  • A103416 (program): a(n) = n - ceiling(sqrt(prime(n))).
  • A103419 (program): Number of compositions of n in which the least part is odd.
  • A103420 (program): Number of compositions of n in which the least part is even.
  • A103424 (program): Expansion of e.g.f.: 1 + sinh(2*x).
  • A103425 (program): a(n) = 3*a(n-1) + a(n-2) - 3*a(n-3).
  • A103433 (program): a(n) = Sum_{i=1..n} Fibonacci(2i-1)^2.
  • A103434 (program): a(n) = Sum_{i=1..n} Fibonacci(2i)^2.
  • A103435 (program): a(n) = 2^n * Fibonacci(n).
  • A103438 (program): Square array T(m,n) read by antidiagonals: Sum_{k=1..n} k^m.
  • A103439 (program): a(n) = Sum_{i=0..n-1} Sum_{j=0..i} (i-j+1)^j.
  • A103440 (program): a(n) = Sum[d|n, d==1 (mod 3), d^2] - Sum[d|n, d==2 (mod 3), d^2].
  • A103444 (program): Triangle read by rows: T(n,k) is number of unitary divisors of C(n,k), 0<=k<=n.
  • A103445 (program): Sum of the numbers of unitary divisors of the binomial coefficients C[n,k], k=0..n.
  • A103446 (program): Unlabeled analog of A025168.
  • A103447 (program): Triangle read by rows: T(n,k) = Moebius(binomial(n,k)) (0 <= k <= n).
  • A103448 (program): a(n) = Sum_{k=0..n} Moebius(binomial(n,k)).
  • A103450 (program): A figurate number triangle read by rows.
  • A103451 (program): Triangular array T read by rows: T(n, 0) = T(n, n) = 1, T(n, k) = 0 for 0 <= k <= n.
  • A103452 (program): Inverse of number triangle A103451.
  • A103453 (program): a(n) = 0^n + 3^n - 1.
  • A103454 (program): a(n) = 0^n + 4^n - 1.
  • A103455 (program): a(n) = 0^n + 5^n - 1.
  • A103456 (program): a(n) = 0^n + 10^n - 1.
  • A103457 (program): a(n) = 3^n + 1 - 0^n.
  • A103458 (program): a(n) = 7^n + 1 - 0^n.
  • A103459 (program): a(n) = 8^n + 1 - 0^n.
  • A103460 (program): a(n) = 9^n + 1 - 0^n.
  • A103461 (program): a(n) = (-10)^n + 1 - 0^n.
  • A103462 (program): A triangle with palindromic cubes, read by rows.
  • A103469 (program): Number of polyominoes consisting of 3 regular unit n-gons.
  • A103480 (program): Row sums of A103462.
  • A103481 (program): Diagonal sums of A103462.
  • A103485 (program): Expansion of (7 +4*x -5*x^2 -7*x^3) / ((1-x)*(1-x^2-x^3)).
  • A103486 (program): a(0)=7, a(1)=11, a(2)=13, a(3)=17; then a(n) = a(n-1)+a(n-3)-a(n-4).
  • A103488 (program): a(n) = 2^(n^2-1).
  • A103489 (program): Multiplicative suborder of 3 (mod n) = sord(3, n).
  • A103491 (program): Multiplicative suborder of 5 (mod n) = sord(5, n).
  • A103492 (program): Multiplicative suborder of 6 (mod 2n+1) = sord(6, 2n+1).
  • A103493 (program): Multiplicative suborder of 7 (mod n) = sord(7, n).
  • A103495 (program): Multiplicative suborder of 9 (mod n) = sord(9, n).
  • A103496 (program): Multiplicative suborder of 10 (mod 2n+1) = sord(10, 2n+1).
  • A103497 (program): Multiplicative suborder of 11 (mod n) = sord(11, n).
  • A103498 (program): Multiplicative suborder of 12 (mod 2n+1) = sord(12, 2n+1).
  • A103505 (program): Denominator in expansion of (1-x)*log(1-x).
  • A103516 (program): Triangle read by rows: count in a vee.
  • A103517 (program): Expansion of (1+2*x-x^2)/(1-x)^2.
  • A103519 (program): a(1) = 1, a(n) = sum of n successive numbers starting with a(n-1) + 1.
  • A103528 (program): Sum_{k = 1..n-1 such that n == k (mod 2^k)} 2^(k-1).
  • A103529 (program): Values of A102370 which are >= a new power of 2.
  • A103530 (program): a(n) = 2^n - A103529(n).
  • A103532 (program): Number of divisors of 240^n.
  • A103534 (program): Concatenations of pairs of primes that differ by 1000.
  • A103536 (program): Number of nets in a regular pyramid.
  • A103542 (program): Binary equivalents of A102370.
  • A103543 (program): Consider those values of k for which A102370(k) = k: 0, 4, 8, 16, 20, 24, 32, 36, 40, 48, 52, 56, 64, … and divide by 4: 0, 1, 2, 4, 5, 6, 8, 9, 10, 12, 13, 14, 16, 17, 18, 20, 21, 22, 24, …; sequence gives missing numbers.
  • A103566 (program): Sum of the primes > 5 modulo 3.
  • A103567 (program): Sum of the (primes > 5 modulo 5).
  • A103568 (program): Sum of the (primes > 5 modulo 7).
  • A103569 (program): Sum of the (primes > 5 modulo 11).
  • A103570 (program): Sum of the (primes > 5 modulo 13).
  • A103571 (program): Sum of the (primes > 5 modulo 17).
  • A103572 (program): Sum of the (primes > 5 modulo 19).
  • A103577 (program): Number of partitions of n into Fibonacci parts if each part is of two kinds.
  • A103578 (program): Number of divisors of m^2, where m is the smallest number with at least n divisors.
  • A103579 (program): Sophie Germain primes that are not Lucasian primes: primes p not 3 (mod 4) such that 2p + 1 is prime.
  • A103581 (program): A102371 written in base 2.
  • A103582 (program): Binary array below read by downward antidiagonals.
  • A103583 (program): Same as A103582, but read antidiagonals in upward direction.
  • A103585 (program): Consider numbers k such that (A102370(k)-k)/2 = 1; read them mod 4 to get the sequence.
  • A103586 (program): a(0)=1, for n > 0: n-th run consists of 2^n-1 copies of n+1.
  • A103588 (program): 1’s complement of A103582.
  • A103589 (program): 1’s complement of A103583.
  • A103601 (program): Numbers k such that the string 10k is the decimal expansion of a prime number.
  • A103604 (program): a(n) = C(n+6,6) * C(n+10,6).
  • A103609 (program): Fibonacci numbers repeated (cf. A000045).
  • A103610 (program): 4 X infinity array read by rows: let M = {{0, 1, 0, 0}, {0, 0, 1, 0}, {0, 0, 0, 1}, {1, 0, 1, 0}}, w[0] = {0, 0, 1, 1}’, w[n]’ = M*w[n -1]’; the n-th row of the array is w[n]’ (the prime denotes transpose).
  • A103612 (program): Number of solutions to 5+B^2=p^2+q^2 with B=2n, p,q>0 and 2p^2<5+B^2.
  • A103615 (program): Number of zeros in A103542(n) (binary equivalent of A102370(n)).
  • A103616 (program): Decimal expansion of the largest real root of the quintic equation x^5 + 2*x^4 - 2*x^3 - x^2 + 2*x -1 = 0.
  • A103621 (program): Trajectory of 7 under repeated application of the map n –> A102370(n).
  • A103623 (program): n^9 + n^8 + n^7 + n^6 + n^5 + n^4 + n^3 + n^2 + n + 1.
  • A103625 (program): Define a(1)=0, a(2)=0, a(3)=2, a(4)=4, a(5)=34, a(6)=62, a(7)=480, a(8)=870 such that from i=1 to 8: 48*a(i)^2 + 48*a(i) + 1 = j(i)^2 with j(1)=1, j(2)=1, j(3)=17, j(4)=31, j(5)=239, j(6)=433, j(7)=3329, j(8)=6031. Then a(n) = a(n-8) + 28*sqrt(48*(a(n-4)^2) + 48*a(n-4) + 1).
  • A103627 (program): Let S(n) = {n,1,n}; sequence gives concatenation S(0), S(1), S(2), …
  • A103631 (program): Triangle read by rows: T(n,k) = abs(qStirling2(n,k,q)) for q = -1, with 0 <= k <= n.
  • A103632 (program): Expansion of (1 - x + x^2)/(1 - x - x^4).
  • A103633 (program): Triangle read by rows: triangle of repeated stepped binomial coefficients.
  • A103636 (program): Sum[d|n, d==0 mod 3, d^2].
  • A103637 (program): Sum[d|n, d==1 mod 3, d^2].
  • A103638 (program): Sum[d|n, d==2 mod 3, d^2].
  • A103639 (program): a(n) = Product_{i=1..2*n} (2*i+1).
  • A103640 (program): Expansion of theta_4(q)^4 - theta_2(q)^4, where theta_2 and theta_4 are the Jacobi theta series.
  • A103644 (program): Expansion of g.f. (3x+1)/(1+2x-6x^2-27x^3).
  • A103645 (program): G.f.: (108x^2+27x+1)/(1+2x-6x^2-27x^3).
  • A103646 (program): G.f.: 9*(3x+1)/(1+2x-6x^2-27x^3).
  • A103650 (program): G.f.: x^2/((1-x^2)^2*Product_{i>0}(1-x^i)).
  • A103659 (program): (1/6) * most frequently occurring volume assumed by triangular pyramids with their 4 vertices chosen from distinct points of an (n+1)X(n+1)X(n+1) lattice cube.
  • A103668 (program): Number of semiprimes between prime(n) and prime(n+1).
  • A103675 (program): a(n) = 1 if the binary representation of n! contains 7! (bit string “1001110110000”), otherwise a(n) = 0.
  • A103681 (program): Numbers m such that in binary representation m! doesn’t contain 7!.
  • A103685 (program): Consider the morphism 1->{1,2}, 2->{1,3}, 3->{1}; a(n) is the total number of ‘3’ after n substitutions.
  • A103689 (program): a(n) is the least k such that either k*n - 1 or k*n + 1 (or both) is prime.
  • A103701 (program): Add 2 to each of the preceding digits, beginning with 1.
  • A103704 (program): Add 5 to each of the preceding digits, beginning with 1.
  • A103716 (program): Numerators of sum_{k=1..n} 1/k^10 =: Zeta(10,n).
  • A103717 (program): Denominators of sum_{k=1..n} 1/k^10 = Zeta(10,n).
  • A103719 (program): Column m=2 sequence of triangle A103718(n,m), n >= 0 (without leading zeros).
  • A103720 (program): Column m=3 sequence (unsigned) of triangle A103718(n,m), n>=0, without leading zeros.
  • A103721 (program): Column m=4 sequence of triangle A103718(n,m), n>=0, without leading zeros.
  • A103722 (program): Column m=5 sequence of triangle A103718(n,m), n>=0, without leading zeros.
  • A103729 (program): Column k=2 sequence of array A103728.
  • A103730 (program): Negative of column k=3 sequence of array A103728.
  • A103731 (program): Column k=4 sequence of array A103728.
  • A103736 (program): Fibonacci numbers with nonprime indices.
  • A103737 (program): Define a(1)=0, a(2)=0, a(3)=3, a(4)=7 such that from i=1 to 4: 30*a(i)^2 + 30*a(i) + 1 = j(i)^2, j(1)=1, j(2)=1, j(3)=19, j(4)=41 Then a(n) = a(n-4) + 4*sqrt(30*(a(n-2)^2) + 30*a(n-2) + 1).
  • A103745 (program): a(n) = (A102371(n) + n)/2.
  • A103747 (program): Trajectory of 2 under repeated application of the map n -> A102370(n).
  • A103749 (program): Expansion of x*(1+2*x)/(1+x+x^2-2*x^3).
  • A103750 (program): Expansion of (1+2*x^3)/(1-x+x^3-2*x^4).
  • A103754 (program): Number of contiguous digits i in the counting numbers, for i=0.
  • A103762 (program): a(n) = least k with Sum_{j = n..k} 1/j >= 1.
  • A103768 (program): (29*3^n - 18(n + 3)*2^n + 6n^2 + 24n + 27)/12.
  • A103770 (program): A weighted tribonacci sequence, (1,3,9).
  • A103771 (program): Expansion of 1/(1-4x-4x^2-4x^3).
  • A103772 (program): Larger of two sides in a (k,k,k-1)-integer-sided triangle with integer area.
  • A103775 (program): Number of ways to write n! as product of distinct squarefree numbers.
  • A103778 (program): Inverse of trinomial triangle A071675.
  • A103779 (program): Expansion of real root of y + y^2 + y^3 = x.
  • A103781 (program): Sum of any four successive terms is prime, a(1)=a(2)=0,a(3)=1.
  • A103796 (program): Indices of n such that A019565(n)+1 is prime.
  • A103797 (program): Indices of n such that A019565(n)-1 is prime.
  • A103799 (program): Indices n such that A019565(n)+2 is prime.
  • A103813 (program): Partial sums of A102370.
  • A103814 (program): Pentanacci constant: decimal expansion of limit of A001591(n+1)/A001591(n).
  • A103815 (program): a(n) = -1 + Product_{k=1..n} Fibonacci(k).
  • A103816 (program): Numerator of Sum_{k=1..n} (-1)^(k+1)/k!.
  • A103819 (program): Whitney transform of Jacobsthal numbers.
  • A103820 (program): Whitney transform of 3^n.
  • A103821 (program): A Whitney transform of the central binomial coefficients A000984.
  • A103826 (program): Unitary arithmetic numbers (those for which the arithmetic mean of the unitary divisors is an integer).
  • A103831 (program): For even n, a(n) = n*(n+1), for odd n, a(n) = 2*n + 1.
  • A103832 (program): For even n, a(n)=2n+1, for odd n, a(n)=n(n+1)
  • A103838 (program): Complement of A001671.
  • A103842 (program): Triangle read by rows: row n is binary expansion of 2^n-n, n >= 1.
  • A103845 (program): Product of first n Lucas numbers, plus one.
  • A103847 (program): McCarthy’s 91 Function: a(n) = n-10 if n>100, otherwise a(n) = a(a(n+11)).
  • A103848 (program): Numbers n such that sum of even digits of n is larger than sum of odd digits.
  • A103855 (program): a(n) = Prime(n)! - prime(n)# + 1.
  • A103863 (program): Hamming distance between n and A102370(n) (in binary).
  • A103868 (program): Digital expansion of Pi: numbers from each pair of successive digits, reversed.
  • A103871 (program): Numbers n such that 100n + 69 is prime.
  • A103872 (program): a(n) = 3*trinomial(n+1,0) - trinomial(n+2,0).
  • A103876 (program): A test for divisibility by the n-th prime p(n).
  • A103881 (program): Square array T(n,k) (n >= 1, k >= 0) read by antidiagonals: coordination sequence for root lattice A_n.
  • A103882 (program): a(n) = Sum_{i=0..n} C(n+1,i)*C(n-1,i-1)*C(2n-i,n).
  • A103884 (program): Square array T(n,k) read by antidiagonals: coordination sequence for lattice C_n.
  • A103885 (program): a(n) = [x^(2*n)] ((1 + x)/(1 - x))^n.
  • A103889 (program): Odd and even positive integers swapped.
  • A103890 (program): Prime(n)! / prime(n)# + 1.
  • A103897 (program): a(n) = 3*2^(n-1)*(2^n-1).
  • A103904 (program): a(n) = n*(n-1)/2 * 2^(n*(n-1)/2).
  • A103916 (program): Column k=2 sequence (without zero entries) of table A060524.
  • A103930 (program): Numerators of squares of harmonic numbers A001008/A002805.
  • A103931 (program): Denominators of squares of harmonic numbers A001008/A002805.
  • A103932 (program): Numerators of first difference of squares of harmonic numbers.
  • A103933 (program): Denominators of first difference of squares of harmonic numbers A001008/A002805.
  • A103938 (program): Number of rooted non-separable n-edge maps in the plane (planar with a distinguished outside face).
  • A103943 (program): Number of unrooted two-vertex n-edge maps in the plane (planar with a distinguished outside face).
  • A103944 (program): Number of rooted unicursal n-edge maps in the plane (planar with a distinguished outside face).
  • A103947 (program): a(n) is the number of distinct n-th powers of functions {1, 2} -> {1, 2}.
  • A103951 (program): Procedure “Remove every 10th term!” executed 10 times.
  • A103961 (program): Least k such that 2*n*k - 1 is a prime.
  • A103969 (program): Positions n such that A005941(n) = A005940(n).
  • A103970 (program): Expansion of (1 - sqrt(1 - 4*x - 12*x^2))/(2*x).
  • A103971 (program): Expansion of (1 - sqrt(1 - 4x - 16x^2))/(2x).
  • A103972 (program): Expansion of (1-sqrt(1-4x-20x^2))/(2x).
  • A103973 (program): Expansion of (sqrt(1-8*x^2)+8*x^2+2*x-1)/(2*x*sqrt(1-8*x^2)).
  • A103974 (program): Smaller sides (a) in (a,a,a+1)-integer triangle with integer area.
  • A103975 (program): Smaller side in (a,a+1,a+1)-integer triangle with integer area.
  • A103976 (program): Partial sums of A040976 (= primes-2).
  • A103977 (program): Let d_1 … d_k be the divisors of n. Then a(n) = min_{ e_1 = +-1, … e_k = +-1 } | Sum_i e_i d_i |.
  • A103978 (program): Expansion of (sqrt(1-12*x^2)+12*x^2+2*x-1)/(2*x*sqrt(1-12*x^2)).
  • A103981 (program): Number of prime factors (with multiplicity) of octahedral numbers (A005900).
  • A103982 (program): Indices of octahedral numbers (A005900) which are semiprimes.
  • A103990 (program): Reduced numerators of the hypercube line-picking integrand sqrt(Pi)*I(n,0).
  • A103991 (program): Reduced denominators of the hypercube line-picking integrand sqrt(Pi)*I(n,0).
  • A103994 (program): A129360 * A115361.
  • A103996 (program): Recurrence: a(n) = -Sum[i=0..n-1, a(i)*C(n+1,i) ], a(0)=1.
  • A104000 (program): Square array T(r,m) read by antidiagonals: number of cyclically reduced words of length m in F_r.
  • A104001 (program): Triangle T(n,k) read by rows: number of permutations in S_n avoiding all k-length patterns starting with fixed m, 2<k<=n, 1<=m<=k.
  • A104002 (program): Triangle T(n,k) read by rows: number of permutations in S_n avoiding all k-length patterns that start with 1 except one fixed pattern and containing it exactly once.
  • A104004 (program): Expansion of (1-x)(1+x)/((2x-1)(x^2+x-1)).
  • A104005 (program): a(n+3) = a(n+2) + 3a(n+1) - 2a(n); a(0) = 1, a(1) = -1, a(2)= 3.
  • A104006 (program): Primes of the form 2pq + 1, where p and q are (not necessarily distinct) odd primes.
  • A104008 (program): Area of (m,m+1,m+1)-integer triangle for m in A103975.
  • A104009 (program): Area of (a,a,a+1)-integer triangle. Corresponding a’s are in A103974.
  • A104010 (program): Sum of two successive sexy primes.
  • A104011 (program): Number of prime factors (with multiplicity) of centered dodecahedral numbers (A005904).
  • A104012 (program): Indices of centered dodecahedral numbers (A005904) which are semiprimes (A001358).
  • A104029 (program): Triangle, read by rows, of pairwise sums of trinomial coefficients (A027907).
  • A104033 (program): Triangle, read by rows, equal to the matrix inverse of triangle A103327, where A103327(n,k) = binomial(2*n+1,2*k+1).
  • A104039 (program): Number of primitive roots modulo prime(n)^2, where prime(n) is n-th prime.
  • A104040 (program): Triangular matrix T, read by rows, such that row n equals the absolute values of column (n+1) in the matrix inverse T^-1 (with extrapolated zeros): T(n,k) = -Sum_{j=1..[n+1/2]} (-1)^j*T(n-j+1,n-2*j+1)*T(n-j,k)) with T(n,n)=1 (n>=0) and T(n,n-1)=n (n>=1).
  • A104041 (program): Triangular matrix T, read by rows, such that column k is equal (in absolute value) to row (k-1) in the matrix inverse T^-1 (with extrapolated zeros) for k>0, with T(n,n)=1 (n>=0) and T(n,n-1)=-n (n>=1).
  • A104044 (program): Numbers k such that 10*k + 7 is prime and k is a multiple of ten.
  • A104045 (program): Numbers n such that n9 is prime and n is a multiple of ten.
  • A104048 (program): Numbers n such that n11 is prime and n is a multiple of ten.
  • A104055 (program): Number of numbers 0 <= i <= n such that i is a square or a cube (or both).
  • A104078 (program): Numbers which are the sum of three nonzero squares and are also divisible by 31.
  • A104085 (program): Coefficient list length of Poincaré-like polynomials made from A047845, indices of odd nonprimes (group dimension equivalent plus one).
  • A104088 (program): Largest prime <= 3^n.
  • A104097 (program): Denominators of coefficients in expansion of x^-2*(1-exp(-2*x))^2.
  • A104098 (program): Sum_{k=1..n} C(n-1,k-1)*A008292(n,k) for n>=1.
  • A104099 (program): n * (10n^2 - 6n + 1), or n*A087348(n).
  • A104103 (program): a(n) = ceiling(sqrt(prime(n))).
  • A104104 (program): a(1) = 1, if A(k) = sequence of first 2^(k-1) terms and if B(k) is A(k) with 0’s and 1’s exchanged, then A(k+1) = A(k)A(k) if a(k) = 0, A(k+1) = A(k)B(k) if a(k) = 1.
  • A104105 (program): a(1) = 1, if A(k) = sequence of first 2^k -1 terms and if B(k) is A(k) with 0’s and 1’s exchanged, then A(k+1) = A(k),1,B(k) if a(k) = 0, A(k+1) = A(k),0,B(k) if a(k) = 1.
  • A104106 (program): a(1) = 1; thereafter, if A(k) = sequence of first 2^k -1 terms, then A(k+1) = A(k),1,A(k) if a(k) = 0, and A(k+1) = A(k),0,A(k) if a(k) = 1.
  • A104110 (program): Nonnegative numbers k such that k^2 + 42 is prime.
  • A104117 (program): For n=2^k, a(n) = k+1, else 0.
  • A104120 (program): (Prime(n + 1) - Prime(n))/2 (mod 2).
  • A104121 (program): a(n)=1 if there is a partition of n^3 into n primes such that n-1 are consecutive primes and the remaining prime is larger than the sum of the n-1 consecutive primes, otherwise a(0)=0 if no such partition exists.
  • A104127 (program): (1+prime(n))^prime(n).
  • A104128 (program): a(n) = p + p^(p+1), where p = prime(n).
  • A104129 (program): Integers of the form p^(p-1)+p where p is prime.
  • A104130 (program): Numbers n such that n33 is prime and n is a multiple of ten.
  • A104135 (program): a(n) = floor(sqrt(2*Pi*n)).
  • A104136 (program): a(n) = ceiling(sqrt(2*Pi*n)).
  • A104137 (program): Number of distinct necklaces with p beads of two possible colors, allowing turning over, p being a prime greater than 2.
  • A104141 (program): Decimal expansion of 3/Pi^2.
  • A104144 (program): a(n) = Sum_{k=1..9} a(n-k); a(8) = 1, a(n) = 0 for n < 8.
  • A104145 (program): a(1) = 1; let A(k) = sequence of first 2^(k-1) terms; then A(k+1) is concatenation of A(k) and (A(k)-1) if a(k) is odd, or concatenation of A(k) and (A(k)+1) if a(k) is even.
  • A104147 (program): Number of cubes <= n-th prime.
  • A104150 (program): Shifted factorial numbers: a(0)=0, a(n) = (n-1)!.
  • A104152 (program): Numbers n such that n77 is prime and n is a multiple of ten.
  • A104153 (program): Numbers n such that n99 is prime and n is a multiple of ten.
  • A104155 (program): The 64 codons of the genetic code, giving the value 1 to thymine (T), 3 to adenine (A), 2 to cytosine (C) and 4 to guanine (G).
  • A104156 (program): a(1)=a(2)=0, a(n) = abs(2*a(n-1) - a(n-2)) - 1.
  • A104161 (program): G.f.: x*(1 - x + x^2)/((1-x)^2 * (1 - x - x^2)).
  • A104162 (program): Indicator sequence for the Fibonacci numbers.
  • A104163 (program): Primes p such that (2p+1)/3 is prime.
  • A104164 (program): Sophie Germain type primes where 5*Prime[n]=2*Prime[m]+1.
  • A104165 (program): Sophie Germain type primes where 7*Prime[n]=2*Prime[m]+1.
  • A104174 (program): Numerator of the fractional part of a harmonic number.
  • A104175 (program): From the words to the song “867-5309/Jenny” by Tommy Tutone.
  • A104177 (program): A variation on Flavius’s sieve (A000960): Start with the natural numbers; at the k-th sieving step, remove every f-th term of the sequence remaining after the (k-1)-st sieving step, where f is the (k+2)-nd Fibonacci number, f=F(k+2); iterate.
  • A104180 (program): Let f[n]=Prime[n+1]-Prime[n]; a(n) = Binomial[Prime[12],f[n]].
  • A104181 (program): Let f(n)=mod(prime(n),12); then a(n) = binomial(prime(12),f(n)).
  • A104184 (program): a(n) is the number of paths from (0,0) to (n,0) using steps of the form (1,2),(1,1),(1,0),(1,-1) or (1,-2) and staying above the x-axis. Also, a(n) is the number of possible combinations of balls on the lawn after n turns, using a Motzkin variation of the (4,2)-case of the tennis ball problem considered by D. Merlini, R. Sprugnoli and M. C. Verri.
  • A104187 (program): G.f. -(1+x^2+x^4)/((x^3+x^2+x-1)*(x-1)^2).
  • A104188 (program): a(n) = 4n*(4n - 1).
  • A104189 (program): Prime numbers arising from Schorn’s proof that there are infinitely many primes.
  • A104192 (program): a(n) = prime(n) - phi(n).
  • A104199 (program): Lower bound on a straddle prime pair.
  • A104200 (program): Upper bound on a straddle prime pair.
  • A104201 (program): Sums of straddle primes.
  • A104202 (program): Differences of straddle primes.
  • A104210 (program): Positive integers divisible by at least 2 consecutive primes.
  • A104211 (program): Integers n such that the sum of the digits of n is not prime.
  • A104212 (program): Sum of the digits of n when the sum is prime.
  • A104213 (program): Primes with nonprime sums of digits.
  • A104218 (program): Sum of opposite numbers on a clock, starting at 12.
  • A104219 (program): Triangle read by rows: T(n,k) is number of Schroeder paths of length 2n and having k peaks at height 1, for 0 <= k <= n.
  • A104220 (program): a(n) = 1 + Fibonacci(n) - (Fibonacci(n) mod 2).
  • A104221 (program): a(n) = Fibonacci(n) - (Fibonacci(n) mod 2).
  • A104230 (program): Minimal number of primes needed to sum to n^2.
  • A104234 (program): Number of k >= 1 such that k+n == 0 mod 2^k.
  • A104235 (program): Numbers n such that A102370(n) = n.
  • A104236 (program): n*Golomb’s sequence.
  • A104248 (program): Lengths of successive runs of 1’s in the Thue-Morse sequence A010060.
  • A104249 (program): a(n) = (3*n^2 + n + 2)/2.
  • A104250 (program): Sum of prime digits of n-th prime.
  • A104251 (program): Sum of nonprime digits of n-th prime.
  • A104254 (program): n^n - (-1)^n(n+1)!.
  • A104255 (program): a(n) = floor( (2n-1)!!/(2n) ).
  • A104256 (program): [ (2n-1)!!/(4n) ].
  • A104258 (program): Replace 2^i with n^i in binary representation of n.
  • A104259 (program): Triangle T read by rows: matrix product of Pascal and Catalan triangle.
  • A104260 (program): Sum of odd digits (1,3,5,7,9) of n-th prime.
  • A104261 (program): Sum of even digits (0,2,4,6,8) of n-th prime.
  • A104268 (program): a(n) = 2*4^(n-1) - (3n-1)/(2n+2)*C(2n,n).
  • A104270 (program): a(n) = 2^(n-2)*(C(n,2)+2).
  • A104273 (program): Table of Sprague-Grundy functions for a certain family of hypergraphs, read by antidiagonals.
  • A104275 (program): Numbers k such that 2k-1 is not prime.
  • A104276 (program): Number of partitions of n in which both even and odd squares occur with multiplicity 1. There is no restriction on the parts which are twice even squares.
  • A104278 (program): Numbers n such that 2n+1 and 2n-1 are not primes.
  • A104279 (program): Numbers n such that 2n+1 is prime and 2n-1 is not prime.
  • A104280 (program): Numbers n such that 2n+1 is not prime and 2n-1 is prime.
  • A104293 (program): a(n) = prime((prime(n)-1)/2).
  • A104294 (program): a(n) = prime((prime(n)+1)/2).
  • A104295 (program): a(n) = A104294(n) - A104293(n).
  • A104301 (program): Primes which are the reverse concatenation of two consecutive square numbers.
  • A104320 (program): Number of zeros in ternary representation of 2^n.
  • A104324 (program): The Fibonacci word over the nonnegative integers; or, the number of runs of identical bits in the binary Zeckendorf representation of n.
  • A104325 (program): Number of runs of equal bits in the dual Zeckendorf representation of n (A104326).
  • A104326 (program): Dual Zeckendorf representation of n or the maximal (binary) Fibonacci representation. Also list of binary vectors not containing 00.
  • A104332 (program): Primes which are the reverse concatenation of two consecutive odd numbers.
  • A104344 (program): a(n) = Sum_{k=1..n} k!^2.
  • A104350 (program): Partial products of largest prime factors of numbers <= n.
  • A104351 (program): Number of digits in decimal representation of A104350(n).
  • A104352 (program): Number of divisors of A104350(n).
  • A104354 (program): Euler’s totient of A104350(n).
  • A104355 (program): Number of trailing zeros in decimal representation of A104350(n).
  • A104356 (program): Smallest m such that A104350(m) has exactly n trailing zeros in decimal representation.
  • A104357 (program): a(n) = A104350(n) - 1.
  • A104365 (program): a(n) = A104350(n) + 1.
  • A104376 (program): a(n) = Sum_{j=0..13} n^j.
  • A104378 (program): First differences of A102370.
  • A104381 (program): Numbers k such that 10^(k-1) == 1 (mod k).
  • A104384 (program): Number of partitions of triangular numbers n*(n+1)/2 into (n-2) distinct parts for n>=3.
  • A104385 (program): Number of distinct partitions of triangular numbers n*(n+1)/2 into 3 parts for n>=1.
  • A104401 (program): a(n) = A104235(n)/4.
  • A104402 (program): Matrix inverse of triangle A091491, read by rows.
  • A104403 (program): a(0)=0; for n>0, a(n) = A102371(4n)/4.
  • A104406 (program): Number of numbers <= n having no 2 in ternary representation.
  • A104407 (program): Number of Hamiltonian groups of order <= n.
  • A104435 (program): Number of ways to split 1, 2, 3, …, 2n into 2 arithmetic progressions each with n terms.
  • A104436 (program): Number of ways to split 1, 2, 3, …, 3n into 3 arithmetic progressions each with n terms.
  • A104437 (program): Number of ways to split 1, 2, 3, …, 4n into 4 arithmetic progressions each with n terms.
  • A104449 (program): Fibonacci sequence with initial values a(0) = 3 and a(1) = 1.
  • A104454 (program): Expansion of 1/(sqrt(1-5x)*sqrt(1-9x)).
  • A104455 (program): Expansion of e.g.f. exp(5*x)*(BesselI(0,2*x) - BesselI(1,2*x)).
  • A104457 (program): Decimal expansion of 1 + phi = phi^2 = (3 + sqrt(5))/2.
  • A104458 (program): Define the first two terms to be 2 and 3. All the other terms are obtained by concatenating the two previous terms.
  • A104459 (program): Possible differences between adjacent palindromes.
  • A104461 (program): Number of instances of nonprimes m in Pythagorean triples x,y,z such that x^2 + y^2 = z^2. Except for 1, the number of instances of composite numbers m in Pythagorean triples.
  • A104462 (program): Convert the binary strings in A101305 to decimal.
  • A104463 (program): Complement of {A072756(n): n>=2}.
  • A104470 (program): Tribonacci equivalent of mousetrap sequence (A002467).
  • A104471 (program): Triangle of degree numbers for certain polynomials.
  • A104472 (program): Triangle of degree numbers for certain polynomials.
  • A104473 (program): a(n) = binomial(n+2,2)*binomial(n+6,2).
  • A104474 (program): a(n) = binomial(n+3,3)*binomial(n+7,3).
  • A104475 (program): a(n) = binomial(n+4,4) * binomial(n+8,4).
  • A104476 (program): a(n) = binomial(n+7,7)*binomial(n+11,7).
  • A104477 (program): Number of successive squarefree intervals between primes.
  • A104478 (program): a(n) = binomial(n+8,8)*binomial(n+12,8).
  • A104481 (program): Bisection of A104477.
  • A104487 (program): a(n+3) = 6a(n+2) - 10a(n+1) + 3a(n); a(0) = 1, a(1) = 4, a(2) = 14.
  • A104489 (program): Read central column in Table 3 in reference from right to left, convert to base 10.
  • A104490 (program): Read central column in Table 3 in reference from right to left.
  • A104492 (program): Cube excess of the n-th prime.
  • A104493 (program): Numbers n for which the cube excess of the n-th prime is prime.
  • A104496 (program): Expansion of 2*(2*x+1)/((x+1)*(sqrt(4*x+1)+1)).
  • A104497 (program): Expansion of sqrt(1-8x)/sqrt(1-4x).
  • A104498 (program): Expansion of (1/2)*(1-sqrt(1-8*x)/sqrt(1-4*x)).
  • A104502 (program): Number of partitions where no part is a multiple of 9.
  • A104505 (program): Triangle, read by rows, equal to the right-hand side of the triangle A084610, with row n listing the coefficients of (1+x-x^2)^n: T(n,k) = [x^(n+k)] (1+x-x^2)^n, for n>=k>=0.
  • A104506 (program): Column 1 of triangle A104505, which is equal to the right-hand side of the triangle A084610 of coefficients in (1 + x - x^2)^n.
  • A104507 (program): Row sums of triangle A104505, which is equal to the right-hand side of the triangle A084610 of coefficients in (1+x-x^2)^n.
  • A104512 (program): a(n) is the minimum number that is the first of k > 1 consecutive integers whose sum equals n, or 0 if impossible.
  • A104513 (program): The number of consecutive integers > 1 beginning with A104512(n), the sum of which equals n, or 0 if impossible.
  • A104514 (program): a(n) = least number k > 1 of consecutive integers which sum to 2*n; or a(n) = 0 if n is a power of 2.
  • A104521 (program): Fixed point of the morphism 0->{1}, 1->{1,0,1}.
  • A104522 (program): Expansion of (-1+x+3*x^2-x^3)/((x+1)(3*x-1)(x-1)^2).
  • A104523 (program): Numbers that are neither Fibonacci nor Lucas numbers.
  • A104530 (program): Expansion of (1+sqrt(1-4x))/(4sqrt(1-4x)-2).
  • A104531 (program): Expansion of (1+sqrt(1-4*x))/(5*sqrt(1-4*x)-3).
  • A104532 (program): Expansion of (1+sqrt(1-4*x))/(6*sqrt(1-4*x)-4).
  • A104533 (program): E.g.f.: exp(2x/(1-2x)).
  • A104537 (program): Expansion of g.f.: (1+x)/(1+2*x+4x^2).
  • A104538 (program): Expansion of (1 + 2*x) / (1 + 2*x + 4*x^2).
  • A104545 (program): Number of Motzkin paths of length n having no consecutive (1,0) steps.
  • A104547 (program): Number of Schroeder paths of length 2n having no UHD, UHHD, UHHHD, …, where U=(1,1),D=(1,-1), H=(2,0).
  • A104548 (program): Triangle read by rows giving coefficients of Bessel polynomial p_n(x).
  • A104550 (program): Number of horizontal segments in all Schroeder paths of length 2n (a horizontal segment is a maximal string of horizontal steps).
  • A104551 (program): Expansion of x/((1-x)*sqrt(1+4*x^2)).
  • A104553 (program): Sum of trapezoid weights of all Schroeder paths of length 2n.
  • A104554 (program): Expansion of x(1-x)/(1-x+2x^3-x^4).
  • A104555 (program): Expansion of x(1 - x)/(1 - x + x^2)^3.
  • A104556 (program): Matrix inverse of triangle A001497 of Bessel polynomials, read by rows; essentially the same as triangle A096713 of modified Hermite polynomials.
  • A104557 (program): Triangle T, read by rows, such that the unsigned columns of the matrix inverse when read downwards equals the rows of T read backwards, with T(n,n)=1 and T(n,n-1) = floor((n+1)/2)*floor((n+2)/2).
  • A104559 (program): Triangle, read by rows, of the number of left factors of peakless Motzkin paths of length n having k number of U’s and D’s (i.e., number of paths from (0,0) to the line x=n, consisting of steps U=(1,1), H=(1,0), D=(1,1), that never go below the x-axis and a U step is never followed by a D step).
  • A104562 (program): Inverse of the Motzkin triangle A064189.
  • A104563 (program): A floretion-generated sequence relating to centered square numbers.
  • A104565 (program): Reversion of Pell numbers A000129(n+1).
  • A104566 (program): Triangle read by rows: T(i,j) is the (i,j)-entry (1 <= j <= i) of the product H*R of the infinite lower triangular matrices H = [1; 1,2; 1,2,1; 1 2,1,2; …] and R = [1; 1,1; 1,1,1; 1,1,1,1; …].
  • A104567 (program): Triangle read by rows: T(i,j) = i-j+1 if j is odd; T(i,j) = 2(i-j+1) if j is even (1 <= j <= i).
  • A104568 (program): Triangle of numbers that are 0 or 1 mod 3.
  • A104569 (program): Triangle read by rows: T(i,j) is the (i,j)-entry (1 <= j <= i) of the product Q*R of the infinite lower triangular matrices Q = [1; 1,3; 1,3,1; 1 3,1,3; …] and R = [1; 1,1; 1,1,1; 1,1,1,1; …].
  • A104570 (program): Triangle read by rows: T(i,j) is the (i,j)-entry (1 <= j <= i) of the product R*Q of the infinite lower triangular matrices R = [1; 1,1; 1,1,1; 1,1,1,1; …] and Q = [1; 1,3; 1,3,1; 1,3,1,3; …].
  • A104571 (program): Triangle T(n,k) = A042948(n-k+1) read by rows, 0<=k<=n.
  • A104572 (program): Triangle read by rows: T(i,j) is the (i,j)-entry (1 <= j <= i) of the product A*B of the infinite lower triangular matrices A = [1; 3, 1; 5, 3, 1; 7, 5, 3, 1; …] and B=[1; 2,1; 1,2,1; 2,1,2,1; …].
  • A104574 (program): Sum of trapezoid weights of all Motzkin paths of length n.
  • A104578 (program): A Padovan convolution triangle.
  • A104581 (program): Expansion of 1/(1 + x + x^3 + x^4).
  • A104582 (program): Triangle read by rows: T(i,j) is the (i,j)-entry (1 <= j <= i) of the product of the lower triangular matrix (Fibonacci(i-j+1)) and of the lower triangular matrix all of whose entries are equal to 1 (for j <= i).
  • A104583 (program): Triangle read by rows: T(i,j) is the (i,j)-entry (1 <= j <= i) of the product A*B of the matrices A = [1; 3,1; 5,3,1; 7,5,3,1; …]; B = [1; 1,2; 1,2,1; 1,2,1,2; …] (both infinite lower triangular matrices).
  • A104584 (program): a(n) = (1/2) * ( 3*n^2 + n*(-1)^n ).
  • A104585 (program): a(n) = (1/2) * ( 3*n^2 - n*(-1)^n ).
  • A104586 (program): Pentagonal wave sequence triangle.
  • A104587 (program): Triangle read by rows, given by the matrix product A * B where A (A094727) = [1; 2, 3; 3, 4, 5; 4, 5, 6, 7; …] and B = [1; 1, 1; 1, 1, 1; …] (both are infinite lower triangular matrices with the other terms zero).
  • A104588 (program): Product of primes less than or equal to sqrt(n).
  • A104589 (program): a(1)=1. a(n) = a(n-1) + (sum of terms, from among terms a(1) through a(n-1), which are prime or 1).
  • A104594 (program): A129760/2.
  • A104597 (program): Triangle T read by rows: inverse of Motzkin triangle A097609.
  • A104598 (program): Expansion of (1-z-sqrt(1-4z))/(1-4z)^2.
  • A104621 (program): Heptanacci-Lucas numbers.
  • A104624 (program): Expansion of exp( arcsinh( -2*x ) ) in powers of x.
  • A104625 (program): Expansion of 1/(sqrt(1-4*x) - x^2).
  • A104626 (program): Numbers having three 1’s in their base-phi representation.
  • A104629 (program): Expansion of (1-2*x-sqrt(1-4*x))/(x^2 * (1+2*x+sqrt(1-4*x))).
  • A104630 (program): Expansion of x/(1-5*x+7*x^2-5*x^3+x^4).
  • A104631 (program): Coefficient of x^(2n+1) in the expansion of (1+x+x^2+x^3+x^4)^n.
  • A104632 (program): 1/n times A104631(n), the coefficient of x^(2n+1) in the expansion of (1+x+x^2+x^3+x^4)^n.
  • A104633 (program): Triangle T(n,k) = k*(k-n-1)*(k-n-2)/2 read by rows, 1<=k<=n.
  • A104634 (program): Triangle T(n,k) = (k-1-n)*(k-2-n)*(k+2*n)/6, 1<=k<=n.
  • A104635 (program): Odd n such that 2*n+1 is prime.
  • A104636 (program): Even n such that 2n+1 is prime.
  • A104637 (program): Number of even digits in n-th prime.
  • A104638 (program): Number of odd digits in n-th prime.
  • A104639 (program): Number of even digits in n^3.
  • A104640 (program): Number of odd digits in n^3.
  • A104643 (program): Number of arrangements that can be formed by taking n distinct things out of 25.
  • A104647 (program): a(n) = a(n-1) mod n + a(n-2) mod n; a(0) = 0, a(1) = 1.
  • A104653 (program): Number of topologically distinct trees with n vertices, including Steiner trees.
  • A104670 (program): a(n) = binomial(n+2, 2)*binomial(n+7, n).
  • A104671 (program): a(n) = C(n+3,3)*C(n+8,n+0).
  • A104672 (program): a(n) = C(n+4,4)*C(n+9,n+0).
  • A104673 (program): a(n) = C(n+5,5)*C(n+10,n+0).
  • A104674 (program): a(n) = binomial(n+6, 6) * binomial(n+11, n).
  • A104675 (program): a(n) = C(n+1,n) * C(n+6,1).
  • A104676 (program): a(n) = binomial(n+2,2) * binomial(n+7,2).
  • A104677 (program): a(n) = binomial(n+3,3)*binomial(n+8,3).
  • A104678 (program): a(n) = binomial(n+4,4) * binomial(n+9,4).
  • A104679 (program): a(n) = C(n+5,5)*C(n+10,5).
  • A104680 (program): a(n) = binomial(n+7,7)*binomial(n+12,7).
  • A104682 (program): a(n) = Sum_{j=0..14} n^j.
  • A104683 (program): Interlaces “2*n^2 - 1 is a square” with NSW numbers.
  • A104684 (program): Triangle read by rows: T(n,k) is the number of lattice paths from (0,0) to (n,n) using steps E=(1,0), N=(0,1) and D=(1,1) (i.e., bilateral Schroeder paths), having k D=(1,1) steps.
  • A104686 (program): a(n) = n*(n+1)/2 (mod 6).
  • A104688 (program): Binomial transform of Moebius sequence.
  • A104696 (program): Rearrangement of positive integers: change odd digits d to 10-d.
  • A104697 (program): Rearrangement of positive integers: change even digits d to 10-d.
  • A104698 (program): Triangle read by rows: T(n,k) = Sum_{j=0..n-k} binomial(k, j)*binomial(n-j+1, k+1).
  • A104706 (program): First terms in the rearrangements of integer numbers (see comments).
  • A104708 (program): Product of number of involutions on n letters and number of partitions of n
  • A104709 (program): Triangle read by rows: T(n,k) = Sum_{j=0..n} 2^(n-j)*binomial(j,k) for n >= 0 and 0 <= k <= n; also, Riordan array (1/((1-x)*(1-2*x)), x/(1-x)).
  • A104712 (program): Pascal’s triangle, with the first two columns removed.
  • A104713 (program): Triangle T(n,k) = binomial(n,k), read by rows, 3 <= k <=n .
  • A104714 (program): Greatest common divisor of a Fibonacci number and its index.
  • A104715 (program): Triangle T(n,k) = (2*k-1)*A000217(n-k+1) read by rows, 1<=k<=n.
  • A104716 (program): Triangle T(n,k) = (2k-3+4n)*(k-1-n)*(k-2-n)/6, 1<=k<=n.
  • A104717 (program): First terms in the rearrangements of integer numbers (see comments).
  • A104720 (program): Expansion of 1/((1-x)(1-x^2)(1-10x)).
  • A104721 (program): Expansion of (1+x)^2/(1-4*x^2).
  • A104722 (program): Self-convolution of repeated Catalan numbers.
  • A104726 (program): Triangle generated as the matrix product of A026729 and A000012 (triangular views), read by rows.
  • A104727 (program): Triangle T(n,k) = (k-1-n)*(k-2-n)*(k^2+k+2*k*n+3*n^2+5*n)/24 read by rows, 1<=k<=n.
  • A104728 (program): Triangle T(n,k) = (k-1-n)*(k-2-n)*(k-2+2*n)/2 read by rows, 1<=k<=n.
  • A104730 (program): Triangle read by rows: T(n,k)=C(n+1,k)-C(k,n-k+1).
  • A104731 (program): Triangle T(n,k) = sum_{j=k..n} (j+1)*binomial(k,j-k), read by rows, 0<=k<=n.
  • A104732 (program): Square array T[i,j]=T[i-1,j]+T[i-1,j-1], T[1,j]=j, T[i,1]=1, read by antidiagonals.
  • A104734 (program): Triangle T(n,k) = sum_{j=k..n} (2n-2j+1)*binomial(k,j-k), read by rows, 0<=k<=n.
  • A104738 (program): Positions of records in A104706.
  • A104739 (program): Positions of records in A104717.
  • A104740 (program): a(1) = 1; for n > 1: if n is even, a(n) = least k > 0 such that sum(i=1,n/2,a(2*i-1))/sum(j=1,n,a(j))>=1/4, or 1 if there is no such k; if n is odd, a(n) = largest k > 0 such that sum(i=1,(n+1)/2,a(2*i-1))/sum(j=1,n,a(j))<=1/3, or 1 if there is no such k.
  • A104743 (program): Numbers m = n + 3^n such that the equation x = 3^(m-x) has solution x = 3^n.
  • A104745 (program): a(n) = 5^n + n.
  • A104746 (program): Array T(n,k) read by antidiagonals: T(1,k) = 2^k-1 and recursively T(n,k) = T(n-1,k) + A000337(k-1), n,k >= 1.
  • A104747 (program): a(n) = (n-3)*2^n + n*(n+3)/2 + 3.
  • A104762 (program): Triangle read by rows: row n contains first n nonzero Fibonacci numbers in decreasing order.
  • A104763 (program): Triangle read by rows: Fibonacci(1), Fibonacci(2), …, Fibonacci(n) in row n.
  • A104764 (program): Triangle T(n,k) = Lucas(n-k+1) read by rows, 1<=k<=n.
  • A104765 (program): Triangle T(n,k) read by rows: row n contains the first n Lucas numbers A000204.
  • A104766 (program): Triangle T(n,k) = A001629(n-k+2) read by rows, 1<=k<=n.
  • A104767 (program): a(n)=n for n <= 3, a(n) = 2a(n-1) - 2a(n-2) + 2a(n-3) for n >= 4.
  • A104768 (program): Number of matrices G with entries in Z satisfying G^2=G+1 and having the form 2G=[1+p q-2n | q+2n 1-p].
  • A104769 (program): G.f. -x/(1+x-x^3).
  • A104770 (program): G.f. (1+x^2)/(1+x-x^3).
  • A104771 (program): G.f. (1-x+x^2)/(1+x-x^3).
  • A104777 (program): Integer squares congruent to 1 mod 6.
  • A104792 (program): Triangle T(n,k) = A000330(n-k), n>=1, 0<=k<n, read by rows.
  • A104793 (program): Triangle T(n,k) = A023537(n-k), n >= 1, 0 <= k < n, read by rows.
  • A104794 (program): Expansion of theta_4(q)^2 in powers of q.
  • A104795 (program): Triangle T(n,k) = C(n,k)+1 for k<n; T(n,k) = 1 for k=n, read by rows.
  • A104796 (program): Triangle read by rows: T(n,k) = (n+1-k)*Fibonacci(n+2-k), for n>=1, 1<=k<=n.
  • A104797 (program): Triangle T(n,k) = Fib(n-k+4)-n-k-3, n>=1, 0<=k<n, read by rows.
  • A104798 (program): Triangle T(n,k) = k*[Fib(n-k+3) - 1], read by rows.
  • A104806 (program): “Round of hypotenuse”, see comments.
  • A104854 (program): Number of n-digit numbers using digits 0 to n-1 each exactly once and containing no 3-digit sequence in increasing or decreasing order.
  • A104855 (program): Triangle read by rows: T(n,k) (0 <= k <= n) is the number of three-dimensional lattice walks consisting of n unit steps, each in one of the six coordinate directions, starting at the origin, never going below the horizontal plane and having k vertical steps.
  • A104857 (program): Positive integers that cannot be represented as the sum of distinct Lucas 3-step numbers (A001644).
  • A104858 (program): Partial sums of the little Schroeder numbers (A001003).
  • A104859 (program): Partial sums of A001764.
  • A104860 (program): Prime next to (n + n-th prime).
  • A104861 (program): Number of compositions (ordered partitions) of the n-th prime into n positive integers.
  • A104862 (program): First differences of A014292.
  • A104872 (program): Diagonal sums of A004248.
  • A104878 (program): A sum-of-powers number triangle.
  • A104879 (program): Row sums of a sum-of-powers triangle.
  • A104880 (program): Diagonal sums of a sum-of-powers triangle.
  • A104881 (program): Triangle T(n,k) = Sum_{j=0..k} (n-k)^(k-j), read by rows.
  • A104882 (program): Diagonal sums of number triangle A104881.
  • A104887 (program): Triangle T(n,k) = (n-k+1)-th prime, read by rows.
  • A104891 (program): a(0) = 0; a(n) = 5*a(n-1) + 5.
  • A104895 (program): a(0)=0; thereafter a(2n) = -2*a(n), a(2n+1) = 2*a(n) - 1.
  • A104896 (program): a(0) = 0; a(n) = 7*a(n-1) + 7.
  • A104897 (program): Difference between (n+prime(n)) and next prime.
  • A104934 (program): Expansion of (1-x)/(1 - 3*x - 2*x^2).
  • A104954 (program): Decimal expansion of the area of the regular triangle with circumradius 1.
  • A104955 (program): Decimal expansion of the area of the regular 5-gon (pentagon) of circumradius = 1.
  • A104956 (program): Decimal expansion of the area of the regular hexagon with circumradius 1.
  • A104967 (program): Matrix inverse of triangle A104219, read by rows, where A104219(n,k) equals the number of Schroeder paths of length 2n having k peaks at height 1.
  • A104969 (program): Sum of squares of terms in rows of triangle A104967.
  • A104970 (program): Sum of squares of terms in even-indexed rows of triangle A104967.
  • A104974 (program): A Fredholm-Rueppel triangle.
  • A104976 (program): Row sums of A104975.
  • A104977 (program): Defining sequence for an inverse Fredholm-Rueppel triangle.
  • A104978 (program): Triangle where g.f. satisfies: A(x,y) = 1 + x*A(x,y)^2 + x*y*A(x,y)^3, read by rows.
  • A104979 (program): Semidiagonal sums of triangle A104978: a(n) = Sum_{k=0..[n/2]} A104978(n-k,n-2*k).
  • A104981 (program): Column 1 of triangle A104980; also equals column 0 of triangle A104986, which equals the matrix logarithm of A104980.
  • A104982 (program): Column 3 of triangle A104980, omitting leading zeros.
  • A105020 (program): Array read by antidiagonals: row n (n >= 0) contains the numbers m^2-n^2, m >= n+1.
  • A105022 (program): Entries in the n-th row of Pascal’s triangle that have the 2’s bit set in their binary expansion.
  • A105023 (program): a(n) = A102370(n) - n. Or, 2*A103185(n).
  • A105024 (program): a(n) = A102371(n) + n. Or, 2*A103745.
  • A105031 (program): Binary equivalents of A103185.
  • A105032 (program): Binary equivalents of A103745.
  • A105033 (program): Read binary numbers downwards to the right.
  • A105034 (program): Binary equivalents of A105033.
  • A105036 (program): a(0) = 0, a(1) = 4, a(2) = 8, a(3) = 116, for n>3 a(n) = 26*a(n-2) - a(n-4) + 12.
  • A105037 (program): a(0) = 0, a(1) = 4, a(2) = 6, a(3) = 98, for n>3 a(n) = 22*a(n-2) - a(n-4) + 10.
  • A105038 (program): Nonnegative n such that 6*n^2 + 6*n + 1 is a square.
  • A105040 (program): Nonnegative n such that 7*n^2 + 7*n + 1 is a square.
  • A105042 (program): Numbers n such that 10n - 1 is prime.
  • A105043 (program): Numbers n such that 100*n - 1 is prime.
  • A105044 (program): Numbers n such that 1000*n - 1 is prime.
  • A105045 (program): a(0)=0, a(1)=1, a(2)=2, a(3)=3, a(4)=12; for n > 4, a(n) = 8*a(n-2) - a(n-4) - 3.
  • A105051 (program): Define a(1)=0, a(2)=0, a(3)=15, a(4)=111 then a(n)=254*a(n-2)+126-a(n-4) also sequence such that 7*(a(n)^2) + 7*a(n) + 1 = a square.
  • A105057 (program): Numbers n such that 10000 * n - 1 is prime.
  • A105058 (program): Expansion of g.f. (1+8*x-x^2)/((1+x)*(1-6*x+x^2)).
  • A105059 (program): Numbers n such that 100000n - 1 is prime.
  • A105060 (program): Triangle read by rows in which the n-th row consists of the first n nonzero terms of A033312.
  • A105062 (program): Triangle read by rows, based on the morphism f: 1->2, 2->3, 3->4, 4->5, 5->6, 6->{6,6,10,7}, 7->8, 8->9, 9->10, 10->11, 11->12, 12->{12,12,5,1}. First row is 1. If current row is a,b,c,…, then the next row is a,b,c,…,f(a),f(b),f(c),…
  • A105063 (program): Define a(1)=0, a(2)=0, a(3)=8, a(4)=24 and then a(n)=66*a(n-2)+32-a(n-4).
  • A105064 (program): Triangle read by rows: a(n,m) =a(n-1,m)+(m-1)!*n: n<=m.
  • A105065 (program): First entry of the vector v(n), where v(0) is the 2 by 2 column vector [0,1], v(n)=(M(n-1)^(n-1))v(n-1) and M(k) is the 2 x 2 matrix [[0,1],[1,k]].
  • A105067 (program): a(n) = Sum_{j=0..11} n^j.
  • A105070 (program): T(n,k) = 2^k*binomial(n,2k+1), where 0 <= k <= floor((n-1)/2, n >= 1.
  • A105072 (program): Number of permutations on [n] whose local maxima are in ascending order.
  • A105073 (program): Define a(1)=0, a(2)=2 then a(n) = 3*a(n-1) - a(n-2), a(n+1) = 3*a(n)-a(n-1) and a(n+2) = 3*a(n+1) - a(n) + 2.
  • A105076 (program): Numbers k such that 60*k^2 + 60*k + 1 is a square.
  • A105077 (program): G.f. -(x^3+5x+5)/((x^2-x+1)*(x+1)^2).
  • A105081 (program): a(n) = 1 + A003188(n - 1), n >= 1.
  • A105082 (program): Expansion of (5+4x)/(1-2x-x^2).
  • A105083 (program): Trajectory of 1 under the morphism 1 -> 12, 2 -> 3, 3 -> 1.
  • A105084 (program): Triangle read by rows: a[n, m] = a[n - 1, m] + binomial[n, m]; n <=m
  • A105085 (program): Write the terms of A102370 in base 2, read by upward-sloping diagonals and convert to base 10.
  • A105086 (program): Sum of the divisors of n minus the least nontrivial proper divisor of n.
  • A105087 (program): Absolute difference between the sums of the left and right diagonals of ordered 2 X 2 prime squares.
  • A105088 (program): Sum of the sides of ordered 2 X 2 prime squares.
  • A105089 (program): Sum of the primes in ordered 3 X 3 prime squares.
  • A105090 (program): Sum of the left diagonal in ordered 3 X 3 prime squares.
  • A105091 (program): Sum of the right diagonal in ordered 3 X 3 prime squares.
  • A105092 (program): Sum of the sides of ordered 2 prime sided prime triangles.
  • A105094 (program): Expansion of 8 * (eta(q^2) / eta(q)^2)^8 in powers of q.
  • A105095 (program): Expansion of 8*eta(2*tau)^8/eta(tau)^16 + eta(tau/2)^8/eta(tau)^16.
  • A105100 (program): Sum of ordered 3 prime sided prime triangles.
  • A105104 (program): Write A102370 in binary (A103542), read backwards, omit leading zeros, convert to base 10.
  • A105106 (program): Numbers k such that the string k101 is prime.
  • A105107 (program): Numbers n such that 10000n + 1001 is prime.
  • A105110 (program): Direct matrix (non-recursive) content of -n to n+1 symmetry matrices.
  • A105115 (program): Numbers k such that the decimal representation of 1/k is neither terminating nor purely repeating.
  • A105125 (program): Triangle read by rows: T(n,k) = n^3 + k^3, n >= 0, 0 <= k <= n.
  • A105126 (program): Primes of the form 16n+9.
  • A105127 (program): Primes of the form 32n+17.
  • A105128 (program): Primes of the form 64n+33.
  • A105129 (program): Primes of the form 128n+65.
  • A105130 (program): Primes of the form 256n+129.
  • A105131 (program): Primes of the form 512n+257.
  • A105132 (program): Primes of the form 1024n + 513.
  • A105133 (program): Numbers n such that 8n + 5 is prime.
  • A105134 (program): Numbers n such that 16n+9 is prime.
  • A105135 (program): Numbers n such that 32n+17 is prime.
  • A105136 (program): Numbers n such that 64n+33 is prime.
  • A105137 (program): Numbers n such that 128n+65 is prime.
  • A105138 (program): Numbers n such that 256n+129 is prime.
  • A105139 (program): Numbers n such that 512n+257 is prime.
  • A105140 (program): Numbers n such that 1024n+513 is prime.
  • A105145 (program): Numbers n such that the string n10001 is prime.
  • A105146 (program): Numbers k such that the string k100001 is prime.
  • A105149 (program): Number of even semiprimes k such that n^2 < k <= (n+1)^2.
  • A105150 (program): Approximation to leading digit of n-th Fibonacci number.
  • A105151 (program): Greatest numerator among the n! ratios equal to the continued fractions which have the permutations of (1,2,3,…,n) for terms.
  • A105161 (program): Difference between n and the second-smallest prime larger than n.
  • A105163 (program): a(n) = (n^3 - 7*n + 12)/6.
  • A105174 (program): Numbers k such that k*(k+1)/4 - 1 and k*(k+1)/4 + 1 are twin primes.
  • A105178 (program): Digits in order in which they appear in decimal expansion of e
  • A105186 (program): Replace odd-positioned digits with 0 in ternary representation of n.
  • A105187 (program): a(n) = determinant of the n X n matrix m(i,j)=(i+j+2)!/i!/j!.
  • A105188 (program): a(n) = determinant of the n X n matrix m(i,j)=(i+j+3)!/i!/j!.
  • A105198 (program): a(n) = n(n+1)/2 mod 4.
  • A105199 (program): Decimal expansion of arctan(2).
  • A105202 (program): Irregular triangle read by rows: row n gives the word f(f(f(…(1)))) [with n applications of f], where f is the morphism 1->{1,2,1}, 2->{2,3,2}, 3->{3,1,3}.
  • A105203 (program): Trajectory of 1 under the morphism f: 1->{1,2,1}, 2->{2,3,2}, 3->{3,1,3}.
  • A105206 (program): Number of edges in a pancyclic graph on n+2 vertices with the fewest possible edges.
  • A105209 (program): Nearest integer to the cube root of n.
  • A105216 (program): Maximum denominator among the n! ratios equal to the continued fractions which have the permutations of (1,2,3,…,n) for terms.
  • A105217 (program): Let b(n) denote the Lucas numbers, A000032: a(n) = Sum{k=0..n}C(n,k)^2*(n-k)!*b(k).
  • A105218 (program): a(n) = Sum_{k=0..n} C(n,k)^2*(n-k)!*k^3.
  • A105219 (program): a(n) = Sum_{k=0..n} C(n,k)^2*(n-k)!*k^2.
  • A105220 (program): Trajectory of 1 under the morphism 1->{1,2,1}, 2->{2,2,2}.
  • A105221 (program): a(n) is the sum of n’s distinct prime factors below n.
  • A105222 (program): Smallest integer m > 1 such that m^(n-1) == 1 (mod n).
  • A105223 (program): Number of squares between prime(n) and 2*prime(n) inclusive.
  • A105224 (program): Number of squares between n and 2*n inclusive.
  • A105225 (program): a(n+3) = 2a(n+2) - 3a(n+1) + 2a(n); a(0) = 1, a(1) = -1, a(2) = -2.
  • A105228 (program): a(n) = A102370(n) + 1.
  • A105234 (program): Central column of a Moebius-binomial triangle.
  • A105235 (program): Partial sums of the central column of a Moebius-binomial triangle.
  • A105236 (program): a(n+5) = (a(n+4)*a(n+1) + 2*a(n+3)*a(n+2))/a(n).
  • A105244 (program): Functional substitution on {1,2,3}.
  • A105249 (program): a(n) = binomial(n+2,n)*binomial(n+6,n).
  • A105250 (program): a(n) = binomial(n+3,n)*binomial(n+7,n).
  • A105251 (program): a(n) = binomial(n+4,n)*binomial(n+8,n).
  • A105252 (program): a(n) = binomial(n+5,n)*binomial(n+9,n).
  • A105253 (program): a(n) = binomial(n+6,n)*binomial(n+10,n).
  • A105254 (program): a(n) = binomial(n+7,n)*binomial(n+11,n).
  • A105260 (program): Triangle read by rows: T(n,k)=C(2n-2k,k), n>=0, 0<=k<=floor(2n/3).
  • A105262 (program): a(n)=number of tilings of a 4 X n rectangle using tiles that are either 1 X 1 squares or trominoes (here by a tromino we mean a 2 X 2 square with the upper right 1 X 1 square removed; no rotations allowed).
  • A105266 (program): a(1)=1 and, for n>1, a(n) is the smallest integer greater than a(n-1) such that no three terms x,y,z of the sequence, with x<y<z, satisfy z-y=y-x+1.
  • A105277 (program): Let F(n) denote the Fibonacci numbers, A000045: a(n) = Sum_{k=0..n} C(n,k)^2*(n-k)!*F(k).
  • A105278 (program): Triangle read by rows: T(n,k) = binomial(n,k)*(n-1)!/(k-1)!.
  • A105279 (program): a(0)=0; a(n) = 10*a(n-1) + 10.
  • A105280 (program): a(0)=0; a(n) = 11*a(n-1) + 11.
  • A105281 (program): a(0)=0; a(n)=6*a(n-1)+6.
  • A105283 (program): (2n)-th prime mod n.
  • A105284 (program): a(n)/4^n is the measure of the subset of [0,1] remaining when all intervals of the form [b/2^m - 1/2^(2m+1), b/2^m + 1/2^(2m+1)] have been removed, with b and m positive integers, b<2^m and m<=n.
  • A105291 (program): Triangle read by rows: T(m,n) = binomial(m!,n), m>=0, 0 <= n <= m!.
  • A105292 (program): Triangle read by rows: T(n,k) is the number of directed column-convex polyominoes of area n, having leftmost column of height k.
  • A105306 (program): Triangle read by rows: T(n,k) is the number of directed column-convex polyominoes of area n, having the top of the rightmost column at height k.
  • A105309 (program): a(n) = |b(n)|^2 = x^2 + 3*y*2 where (x,y,y,y) is the quaternion b(n) of the sequence b of quaternions defined by b(0)=1,b(1)=1, b(n) = b(n-1) + b(n-2)*(0,c,c,c) where c = 1/sqrt(3).
  • A105312 (program): a(n) = Sum_{j=0..15} n^j.
  • A105314 (program): Write the natural numbers as an infinite sequence of digits, starting at the left; a(n) is the subset (i.e., the position in this sequence of the “counting digits”) of the first digit of the n-th square.
  • A105320 (program): Digital expansion of Pi: numbers from each pair of successive digits.
  • A105321 (program): Convolution of binomial(1,n) and Gould’s sequence A001316.
  • A105332 (program): a(n) = n*(n+1)/2 mod 8.
  • A105333 (program): a(n) = n*(n+1)/2 mod 16.
  • A105334 (program): a(n) = n*(n+1)/2 mod 32.
  • A105335 (program): a(n) = n*(n+1)/2 mod 64.
  • A105336 (program): a(n) = n*(n+1)/2 mod 128.
  • A105337 (program): a(n) = n*(n+1)/2 mod 256.
  • A105338 (program): a(n) = n*(n+1)/2 mod 512.
  • A105339 (program): a(n) = n*(n+1)/2 mod 1024.
  • A105340 (program): a(n) = n*(n+1)/2 mod 2048.
  • A105343 (program): Elements of even index in the sequence gives A005893, points on surface of tetrahedron: 2n^2 + 2 for n > 1.
  • A105346 (program): 3-almost primes whose indices are 3-almost primes.
  • A105348 (program): An indicator sequence for the Jacobsthal numbers.
  • A105349 (program): Characteristic sequence for the Pell numbers.
  • A105350 (program): Largest squared factorial dividing n!.
  • A105352 (program): Numbers of points on successive rings of the simple square lattice.
  • A105356 (program): Records in A105354.
  • A105367 (program): Expansion of (1-x^3)/(1-x^5).
  • A105368 (program): Expansion of (1-x-x^3+x^4)/(1-x^5).
  • A105369 (program): Expansion of ((1+x)^3 - x^3)/((1+x)^5 - x^5).
  • A105370 (program): Expansion of ((1+x)^4-(1+x)x^3)/((1+x)^5-x^5).
  • A105371 (program): Expansion of (1-x)(1-x+x^2)/(1-3x+4x^2-2x^3+x^4).
  • A105372 (program): Decimal expansion of Hypergeometric2F1[ -(1/4),3/4,1,1] = sqrt(Pi)/(Gamma[1/4]*Gamma[5/4]).
  • A105374 (program): a(n) = 4*n^3 + 4*n.
  • A105384 (program): Expansion of x/(1 + x + x^2 + x^3 + x^4).
  • A105385 (program): Expansion of (1-x^2)/(1-x^5).
  • A105392 (program): Frobenius number of the subsemigroup of the natural numbers generated by successive pairs of Lucas numbers.
  • A105395 (program): A simple “Fractal Jump Sequence” (FJS).
  • A105396 (program): A simple “Fractal Jump Sequence” (FJS).
  • A105397 (program): Periodic with period 2: repeat [4,2].
  • A105398 (program): A simple “Fractal Jump Sequence” (FJS).
  • A105399 (program): Largest prime <= numbers of the form 6k+3 (duplicates removed).
  • A105420 (program): Number of partitions of n into 3-smooth parts.
  • A105422 (program): Triangle read by rows: T(n,k) is the number of compositions of n having exactly k parts equal to 1.
  • A105423 (program): Number of compositions of n+2 having exactly two parts equal to 1.
  • A105426 (program): a(0)=1, a(1)=5, a(n)=8*a(n-1)-a(n-2).
  • A105427 (program): Numbers n such that the near-repdigit number consisting of a 1 followed by n 3’s (i.e., of form 1333…33) is composite.
  • A105432 (program): Numbers n such that the near-repdigit number consisting of n-1 1’s followed by a terminal 3 (i.e., of the form 111…1113) is composite.
  • A105438 (program): Triangle, row sums = (Fibonacci numbers - 2).
  • A105441 (program): Numbers with at least two odd prime factors (not necessarily distinct).
  • A105450 (program): a(n) = binomial(n+5,6) + binomial(n+3,3) + binomial(n+2,3) + binomial(n-1,1).
  • A105452 (program): Numerator of (7 n -1)/3.
  • A105454 (program): Numbers n such that n*prime(n)+(n+1)*prime(n+1) is prime.
  • A105469 (program): Number of numbers of the form 6k+3 with prime(n) <= 6k+3 < prime(n+1).
  • A105470 (program): a(n)=1 if there is number of the form 6k+3 with prime(n) <= 6k+3 <= prime(n+1), otherwise 0.
  • A105471 (program): a(n) = Fibonacci(n) mod 100.
  • A105472 (program): Next-to-last digit of n-th Fibonacci number in decimal representation, a(n) = 0 for n <= 6.
  • A105475 (program): Triangle read by rows: T(n,k) is number of compositions of n into k parts when each even part can be of two kinds.
  • A105476 (program): Number of compositions of n when each even part can be of two kinds.
  • A105477 (program): Triangle read by rows: T(n,k) is the number of compositions of n into k parts when there are two kinds of part 2.
  • A105479 (program): a(n) = C(n,2)*Bell(n-2) (cf. A000217, A000110).
  • A105480 (program): Number of partitions of {1…n} containing 3 pairs of consecutive integers, where each pair is counted within a block and a string of more than 2 consecutive integers are counted two at a time.
  • A105481 (program): Number of partitions of {1…n} containing 4 pairs of consecutive integers, where each pair is counted within a block and a string of more than 2 consecutive integers are counted two at a time.
  • A105482 (program): Number of partitions of {1…n} containing 5 pairs of consecutive integers, where each pair is counted within a block and a string of more than 2 consecutive integers are counted two at a time.
  • A105488 (program): Number of partitions of {1…n} containing 2 detached pairs of consecutive integers, i.e., partitions in which only 1- or 2-strings of consecutive integers can appear in a block and there are exactly two 2-strings.
  • A105489 (program): Number of partitions of {1…n} containing 3 detached pairs of consecutive integers, i.e., partitions in which only 1- or 2-strings of consecutive integers can appear in a block and there are exactly three 2-strings.
  • A105490 (program): Number of partitions of {1…n} containing 4 detached pairs of consecutive integers, i.e., partitions in which only 1- or 2-strings of consecutive integers can appear in a block and there are exactly four 2-strings.
  • A105491 (program): Number of partitions of {1…n} containing 5 detached pairs of consecutive integers, i.e., partitions in which only 1- or 2-strings of consecutive integers can appear in a block and there are exactly five 2-strings.
  • A105492 (program): Number of partitions of {1,…,n} containing 2 strings of 3 consecutive integers such that only v-strings of consecutive integers can appear in a block, where v = 1,2,3.
  • A105493 (program): Number of partitions of {1,…,n} containing 3 strings of 3 consecutive integers such that only v-strings of consecutive integers can appear in a block, where v = 1,2,3.
  • A105494 (program): Number of partitions of {1,…,n} containing 4 strings of 3 consecutive integers such that only v-strings of consecutive integers can appear in a block, where v = 1,2,3.
  • A105495 (program): Triangle read by rows: T(n,k) is the number of compositions of n into k parts when parts equal to q are of q^2 kinds.
  • A105498 (program): Trajectory of 1 under the morphism 1->{1,2}, 2->{1,4}, 3->{3,4}, 4->{3,4}.
  • A105499 (program): Trajectory of 1 under the morphism 1->{2,1,2}, 2->{1,3,1}, 3->{3,2,3}.
  • A105500 (program): Trajectory of 1 under the morphism 1->{1,2}, 2->{3,2}, 3->{3,4}, 4->{1,4}.
  • A105501 (program): Numbers n such that 1 is the leading digit of the n-th Fibonacci number in decimal representation.
  • A105502 (program): Numbers m such that 2 is the leading digit of the n-th Fibonacci number in decimal representation.
  • A105503 (program): Numbers n such that 3 is the leading digit of the n-th Fibonacci number in decimal representation.
  • A105504 (program): Numbers m such that 4 is the leading digit of the n-th Fibonacci number in decimal representation.
  • A105505 (program): Numbers n such that 5 is the leading digit of the n-th Fibonacci number in decimal representation.
  • A105506 (program): Numbers m such that 6 is the leading digit of the n-th Fibonacci number in decimal representation.
  • A105507 (program): Numbers m such that 7 is the leading digit of the n-th Fibonacci number in decimal representation.
  • A105508 (program): Numbers m such that 8 is the leading digit of the m-th Fibonacci number in decimal representation.
  • A105509 (program): Numbers m such that 9 is the leading digit of the m-th Fibonacci number in decimal representation.
  • A105511 (program): Number of times 1 is the leading digit of the first n+1 Fibonacci numbers in decimal representation.
  • A105512 (program): Number of times 2 is the leading digit of the first n+1 Fibonacci numbers in decimal representation.
  • A105513 (program): Number of times 3 is the leading digit of the first n+1 Fibonacci numbers in decimal representation.
  • A105515 (program): Number of times 5 is the leading digit of the first n+1 Fibonacci numbers in decimal representation.
  • A105518 (program): Number of times 8 is the leading digit of the first n+1 Fibonacci numbers in decimal representation.
  • A105522 (program): Inverse of number triangle A105438.
  • A105523 (program): Expansion of 1-x*c(-x^2) where c(x) is the g.f. of A000108.
  • A105530 (program): Ternary modular Gray code for n.
  • A105531 (program): Decimal expansion of arctan 1/3.
  • A105532 (program): Decimal expansion of arctan(1/5).
  • A105533 (program): Decimal expansion of arctan(1/7).
  • A105553 (program): a(n) is the number of 1’s in A103528(n) written in base 2.
  • A105555 (program): Let d = number of divisors of n; a(n) = d-th prime.
  • A105559 (program): McKay-Thompson series of class 6E for the Monster group with a(0) = 3.
  • A105560 (program): a(1) = 1, and for n >= 2, a(n) = prime(bigomega(n)), where prime(n) = A000040(n) and bigomega(n) = A001222(n).
  • A105561 (program): a(n) is the m-th prime, where m is the number of distinct prime factors of n (A001221), a(1) = 1.
  • A105562 (program): a(n) is the prime whose index is the greatest prime factor of n, for n >1; a(1)=2.
  • A105563 (program): a(n) = if (exactly 4 Fibonacci numbers exist with exactly n digits) then 1, otherwise 0.
  • A105564 (program): Number of blocks of exactly 4 Fibonacci numbers having equal length <= n.
  • A105565 (program): a(n) = if (exactly 5 Fibonacci numbers exist with exactly n digits) then 1, otherwise 0.
  • A105566 (program): Number of blocks of exactly 5 Fibonacci numbers having equal length <= n.
  • A105570 (program): Nonsquarefree numbers in place: a(n) = n if n is not squarefree, 0 otherwise.
  • A105571 (program): Numbers m such that m - 2 and m + 2 are semiprimes.
  • A105574 (program): a(1) = 2; for n > 1, a(n) is the prime whose index is the least prime factor of n.
  • A105575 (program): Largest primes < numbers of the form 6k (duplicates removed).
  • A105576 (program): a(n+3) = 2a(n+2) - 3a(n+1) + 2a(n); a(0) = 3, a(1) = 4, a(2) = 0.
  • A105577 (program): a(n+3) = 2*a(n+2) - 3*a(n+1) + 2*a(n); a(0) = 1, a(1) = 5, a(2) = 6.
  • A105578 (program): a(n+3) = 2a(n+2) - 3a(n+1) + 2a(n); a(0) = 1, a(1) = 1, a(2) = 0.
  • A105579 (program): a(n+3) = 2a(n+2) - 3a(n+1) + 2a(n); a(0) = 1, a(1) = 3, a(2) = 4.
  • A105580 (program): a(n+3) = a(n) - a(n+1) - a(n+2); a(0) = -5, a(1) = 6, a(2) = 0.
  • A105581 (program): Primes whose indices are palindromic.
  • A105583 (program): Numbers k such that 101*k + 997 is prime.
  • A105584 (program): Fixed point of the morphism 1 -> 34, 2 -> 32, 3 -> 12, 4 -> 14, starting from a(0) = 1.
  • A105602 (program): Divide each Fibonacci number by its primitive part.
  • A105603 (program): Sylvester-Jacobsthal cyclotomic numbers.
  • A105604 (program): Sylvester dividends for Jacobsthal numbers.
  • A105606 (program): Sylvester dividends for Pell numbers.
  • A105610 (program): Numbers n such that both p1=2n+3 and p2=4n+5 are primes.
  • A105611 (program): a(n) is the LCM of the Jacobsthal sequence {J(1),…,J(n)}.
  • A105616 (program): Column 1 of triangle A105615.
  • A105617 (program): Column 2 of triangle A105615.
  • A105624 (program): Column 2 of triangle A105623.
  • A105627 (program): Column 1 of triangle A105626.
  • A105633 (program): Row sums of triangle A105632.
  • A105635 (program): a(n) = (2*Pell(n+1) - (1+(-1)^n))/4.
  • A105636 (program): Transform of n^3 by the Riordan array (1/(1-x^2), x).
  • A105637 (program): a(n) = a(n-2)+a(n-3)-a(n-5).
  • A105638 (program): Maximum number of intersections in self-intersecting n-gon.
  • A105639 (program): Multiples of coefficients in an asymptotic series of Ramanujan.
  • A105642 (program): Composite nonsquares and noncubes.
  • A105644 (program): a(n) = floor((Pi+e)*n).
  • A105660 (program): G.f. (1-x)(x^2-5x+3)/(x^4-6x^3+13x^2-6x+1).
  • A105661 (program): a(n)=1 if n is a prime, 2 if n is an even semiprime, otherwise 0.
  • A105670 (program): a(1)=1 then bracketing n by powers of 2 as f(t)=2^t for f(t) < n <= f(t+1), a(n) = f(t+1) - a(n-f(t)).
  • A105671 (program): a(2n) = Lucas(2n+3)^2, a(2n+1) = Lucas(2n+1)^2.
  • A105672 (program): a(1)=1, then bracketing n with powers of 3 as f(t)=3^t for f(t) < n <= f(t+1), a(n) = f(t+1) - a(n-f(t)).
  • A105673 (program): One-half of theta series of square lattice (or half the number of ways of writing n > 0 as a sum of 2 squares), without the constant term, which is 1/2.
  • A105674 (program): Highest minimal distance of any Type I (strictly) singly-even binary self-dual code of length 2n.
  • A105676 (program): Highest minimal Hamming distance of any Type 3 ternary self-dual code of length 4n.
  • A105678 (program): Highest minimal Hamming distance of any Type 4^H Hermitian linear self-dual code over GF(4) of length 2n.
  • A105679 (program): Numbers k such that 997*k + 101 is prime.
  • A105686 (program): Number of inequivalent codes attaining highest minimal Hamming distance of any Type 4^H Hermitian linear self-dual code over GF(4) of length 2n.
  • A105693 (program): a(n) = Fibonacci(2n+2)-2^n.
  • A105694 (program): 10^n-10^(n-2).
  • A105695 (program): Expansion of (1-x)*c(x/(1+x)), where c(x) is the g.f. of the Catalan numbers (A000108).
  • A105696 (program): Expansion of (1-x)/sqrt((1-3*x)/(1+x)).
  • A105700 (program): a(n)=1 if n is a prime, 2 if n is a semiprime, otherwise 0.
  • A105720 (program): Triangular matchstick numbers in the class of prime numbers: sum of n-th and next n primes.
  • A105723 (program): a(n) = 3^n - (-1)^n.
  • A105725 (program): Triangle read by rows: T(n,k)=(n+k)!/k! (0<=k<=n-1; n>=1).
  • A105728 (program): Triangle read by rows: T(n,1) = 1, T(n,n) = n and for 1 < k < n: T(n,k) = T(n-1,k-1) + 2*T(n-1,k).
  • A105734 (program): For n>2, a(n) > 0 is such that a(n-1)^2+4*a(n-2)*a(n) is a minimal square, with a(1)=1, a(2)=1.
  • A105736 (program): For n>2, a(n) > 0 is such that a(n-1)^2+4*a(n-2)*a(n) is a minimal square, a(1)=1,a(2)=3.
  • A105746 (program): a(n) = minimal c>0 such that (n+1)^2+4*n*c = d^2 is a square.
  • A105747 (program): Number of ways to use the elements of {1,..,k}, 0<=k<=2n, once each to form a collection of n (possibly empty) lists, each of length at most 2.
  • A105748 (program): Number of ways to use the elements of {1,..,k}, 0<=k<=2n, once each to form a collection of n (possibly empty) sets, each with at most 2 elements.
  • A105749 (program): Number of ways to use the elements of {1,…,k}, 0 <= k <= 2n, once each to form a sequence of n sets, each having 1 or 2 elements.
  • A105750 (program): RE(Product{k=0..n, 1+kI}), I=sqrt(-1).
  • A105751 (program): Imaginary part of Product_{k=0..n} 1+k*I, I=sqrt(-1).
  • A105752 (program): Expansion of e.g.f. cos(i*log(1 + x)), i = sqrt(-1).
  • A105754 (program): Lucas 8-step numbers.
  • A105755 (program): Lucas 9-step numbers.
  • A105760 (program): Nonnegative numbers k such that 2k+7 is prime.
  • A105770 (program): Expansion of (x^2-x+1)(4x^2+x+1) / ((1+x+x^2)(1-x)^3).
  • A105772 (program): Numbers k such that 7*k + 2 is prime.
  • A105773 (program): Numbers n such that 11*n + 97 is prime.
  • A105775 (program): Numbers n such that 97*n + 11 is prime.
  • A105783 (program): Number of terms among the first n primes that are divisors of the sum of the first n primes.
  • A105785 (program): Number of different forests of rooted trees, without isolated vertices, on n labeled nodes.
  • A105787 (program): a(1) = 1; a(m) = maximum numerator possible with a continued fraction [b(1);b(2),b(3),…b(m-1)], where (b(1),b(2),b(3),…b(m-1)) is a permutation of (a(1),a(2),a(3),…a(m-1)).
  • A105792 (program): Largest prime <= numbers congruent (2,4) mod 6 (duplicates removed).
  • A105795 (program): Shallow diagonal sums of the triangle k!*Stirling2(n,k): a(n) = Sum_{k=0..floor(n/2)} T(n-k,k) where T is A019538.
  • A105796 (program): “Stirling-Bernoulli transform” of Jacobsthal numbers.
  • A105800 (program): Greatest Fibonacci number that is a proper divisor of the n-th Fibonacci number; a(1) = a(2) = 1.
  • A105801 (program): Fibonacci-Collatz sequence: a(1)=1, a(2)=2; for n > 2, let fib = a(n-1) + a(n-2); if fib is odd then a(n) = 3*fib + 1 else a(n) = fib/2.
  • A105804 (program): a(n)=F(n-1)a(n-1)+F(n)a(n-2), where F = A000045 (Fibonacci numbers), a(0)=0, a(1)=1.
  • A105809 (program): Riordan array (1/(1-x-x^2), x/(1-x)).
  • A105810 (program): Inverse of a Fibonacci-Pascal matrix A105809.
  • A105811 (program): Expansion of (1+x-x^2)/(1+x)^2.
  • A105812 (program): Expansion of (1+x-x^2)/(1+x).
  • A105814 (program): a(n) = n^2 + (n concatenated with n).
  • A105824 (program): a(n) = sigma(n) mod 4.
  • A105825 (program): a(n) = sigma(n) (mod 5).
  • A105826 (program): a(n) = sigma(n) (mod 7).
  • A105827 (program): a(n) = sigma(n) (mod 8).
  • A105837 (program): Numbers n such that n^2 = 11*m^2 + 11*m + 1.
  • A105838 (program): Nonnegative integers n such that 11*n^2 + 11*n + 1 is a square.
  • A105840 (program): Primes of the form r(r(n)+1)+1, where A141468(n)=r(n)=n-th nonprime.
  • A105844 (program): Numbers n such that 37*n^2 + 37*n + 1 is a square.
  • A105849 (program): Row sums of number triangle A105848.
  • A105851 (program): Binomial transform triangle, read by rows.
  • A105852 (program): sigma(n) mod 9.
  • A105853 (program): a(n) = sigma(n) (mod 10), i.e., unit’s digit of sigma(n).
  • A105854 (program): Primes of the form 20*k + 3.
  • A105855 (program): A104647(n+1) - A104647(n).
  • A105856 (program): a(n) = a(n-1) + A104647(n), a(0) = 0.
  • A105861 (program): a(n) = (n/2) * Sum_{k=0..n} binomial(n,k)/gcd(n,k).
  • A105862 (program): a(n) = n * Sum_{d|n} binomial(n,d)/gcd(n,d).
  • A105863 (program): a(n) = n * Sum_{d|n} (binomial(n,d) / gcd(n,d)).
  • A105864 (program): Expansion of (1/(1-x^2))*c(x/(1-x^2)), where c(x) is the g.f. of A000108.
  • A105865 (program): Expansion of (1/(1-2*x^2))*c(x/(1-2*x^2)), where c(x) is the g.f. of A000108.
  • A105866 (program): A generalized Chebyshev transform of the Fibonacci numbers.
  • A105867 (program): A generalized Chebyshev transform of the Jacobsthal numbers.
  • A105868 (program): Triangle read by rows, T(n,k) = C(n,k)*C(k,n-k).
  • A105870 (program): Fibonacci sequence (mod 7).
  • A105871 (program): a(n) = sum{k=0..floor(n/2), C(2*n-3*k, n)*C(n-k, k)}
  • A105872 (program): a(n) = Sum_{k=0..floor(n/2)} C(2n-3k, n).
  • A105876 (program): Primes for which -4 is a primitive root.
  • A105899 (program): Period 6: repeat [1, 1, 2, 2, 3, 3].
  • A105926 (program): First differences of A000166.
  • A105927 (program): Let d(n) = A000166(n); then a(n) = ( (n^2+n-1)*d(n) + (-1)^(n-1)*(n-1) )/2.
  • A105928 (program): a(n) = ((n^3 - 4n + 1)*A000166(n) + (-1)^(n+1)*(n-1)^2) / 6.
  • A105930 (program): Starting position of the n-th prime in the almost-natural numbers sequence A007376.
  • A105931 (program): a(1) = 1 then a(n) = a(n-1) - (-1)^ceiling(n/2)*a(floor(n/2)).
  • A105938 (program): a(n) = binomial(n+2,2)*binomial(n+5,2).
  • A105939 (program): a(n) = binomial(n+3,3)*binomial(n+6,3).
  • A105940 (program): a(n) = binomial(n+5, n)*binomial(n+8, 5).
  • A105942 (program): a(n) = C(n+6,n)*C(n+9,6).
  • A105943 (program): a(n) = C(n+7,n) * C(n+10,7).
  • A105944 (program): a(n) = C(n+8,n)*C(n+11,8).
  • A105946 (program): a(n) = C(n+5,n)*C(n+3,3).
  • A105947 (program): a(n) = C(n+6,n)*C(n+4,4).
  • A105948 (program): a(n) = C(n+7,n)*C(n+5,5).
  • A105951 (program): a(2*n) = -(2^(2*n+1) + 1), a(2*n+1) = (2^(n+1) - (-1)^n)^2.
  • A105952 (program): (2n)-th Legendre polynomial P_{2n}(x), evaluated at x = 2n-1. Here the Legendre polynomials are normalized so that P_{n}(1) = 1.
  • A105954 (program): Array read by descending antidiagonals: A(n, k) = (n + 1)! * H(k, n + 1), where H(n, k) is a higher-order harmonic number, H(0, k) = 1/k and H(n, k) = Sum_{j=1..k} H(n-1, j)), for 0 <= k <= n.
  • A105955 (program): a(n) = Fibonacci(n) mod 11.
  • A105960 (program): Smallest integer q >= 1 such that difference between q*sqrt(2) and the nearest integer is <= 1/n.
  • A105961 (program): Primes p such that 20*p + 3 is prime.
  • A105963 (program): Expansion of (1+4*x)/(1-x-3*x^2).
  • A105964 (program): Expansion of x*(1+x^3-x^6+x^7)/(1-x^6)^2.
  • A105968 (program): a(n) = 4*a(n-1) - a(n-2) - 2*(-1)^n, a(0) = 1, a(1) = 4.
  • A105994 (program): Fibonacci sequence (mod 13).
  • A105995 (program): Fibonacci sequence (mod 14).
  • A105997 (program): Semiprime function n -> A001358(n) applied three times to n.
  • A105998 (program): Semiprime function n -> A001358(n) applied four times to n.
  • A106002 (program): a(n)=1 if there is a number of the form 6k+3 such that prime(n) < 6k+3 < prime(n+1), otherwise 0.
  • A106005 (program): Fibonacci sequence (mod 15).
  • A106006 (program): [n/2] + [n/3] + [n/5].
  • A106033 (program): a(n) is the least number k such that n*prime(n)+k is a perfect square.
  • A106034 (program): a(n) is the least number such that n*prime(n)+a(n) is a perfect cube.
  • A106035 (program): The “Octanacci” sequence: Trajectory of 1 under the morphism 1->{1,2,1}, 2->{1}.
  • A106036 (program): Trajectory of 1 under the morphism 1->{1,2}, 2->{1,2,3}, 3->{1,2,3,3}.
  • A106040 (program): First 9-free digit in the fractional part of the decimal expansion of (1/10^n)^(1/10^n).
  • A106043 (program): First digit other than 9 in the fractional part of the decimal expansion of (1/1000^n)^(1/1000^n).
  • A106044 (program): Difference between n-th prime and next larger perfect square.
  • A106057 (program): Primes p such that 1*p + 4 and 4*p + 1 are primes.
  • A106058 (program): 4th diagonal of triangle in A059317.
  • A106092 (program): Even numbers and primes.
  • A106093 (program): Primes with maximal digit = 9.
  • A106101 (program): Primes with minimal digit = 1.
  • A106103 (program): Primes with minimal digit = 3.
  • A106108 (program): Rowland’s prime-generating sequence: a(1) = 7; for n > 1, a(n) = a(n-1) + gcd(n, a(n-1)).
  • A106113 (program): 5th diagonal of triangle in A059317.
  • A106118 (program): Primes with maximal digit > 1.
  • A106119 (program): Primes with maximal digit > 2.
  • A106120 (program): Primes with maximal digit > 3.
  • A106121 (program): Primes with maximal digit > 4.
  • A106122 (program): Primes with maximal digit > 5.
  • A106123 (program): Primes with maximal digit > 6.
  • A106124 (program): Primes with maximal digit > 7.
  • A106137 (program): N-th semiprime mod n.
  • A106138 (program): Semiprimes (mod 2).
  • A106139 (program): Semiprimes (mod 3).
  • A106140 (program): Semiprimes (mod 4).
  • A106141 (program): Semiprimes (mod 5).
  • A106142 (program): Semiprimes (mod 6).
  • A106143 (program): Semiprimes (mod 7).
  • A106144 (program): Semiprimes (mod 8).
  • A106145 (program): Semiprimes (mod 9).
  • A106146 (program): Semiprimes (mod 10).
  • A106147 (program): Image of 1 under the repeated morphism 1 -> 21, 2 -> 32, 3 -> 43, 4 -> 14.
  • A106149 (program): Number of prime factors with multiplicity of the difference between consecutive primes.
  • A106151 (program): In binary representation of n: delete one zero in each contiguous block of zeros.
  • A106154 (program): Generation 5 of the substitution 1->{2, 1, 2}, 2->{3, 2, 3}, 3->{4, 3, 4}, 4->{5, 4, 5}, 5->{6, 5, 6}, 6->{1, 6, 1}, starting with 1.
  • A106157 (program): G.f. (1-x-x^3+x^4-2*x^2)/((1-2*x)*(x-1)^2*(x+1)^2).
  • A106160 (program): Highest minimal Hamming distance of Hermitian Type IV self-dual codes over GF(2) X GF(2) and length 2n.
  • A106174 (program): a(n) = 2*n*a(n-1) - a(n-2), with a(0)=0, a(1)=1.
  • A106180 (program): Matrix inverse of number triangle A046854.
  • A106181 (program): Expansion of c(-x^2)(1+2x-sqrt(1+4x^2))/2, c(x) the g.f. of A000108.
  • A106183 (program): Expansion of 1/sqrt(1-4x-4x^2+16x^3).
  • A106184 (program): Expansion of 1/sqrt(1-4*x-8*x^2+32*x^3).
  • A106185 (program): Expansion of 1/sqrt(1-4*x-12*x^2+48*x^3).
  • A106186 (program): Expansion of 1/sqrt(1-4x+4x^2-16x^3).
  • A106187 (program): Sequence array for central binomial numbers A000984.
  • A106188 (program): Expansion of 1/((1-x^2)*sqrt(1-4*x)).
  • A106189 (program): Expansion of 1/((1-2x^2)sqrt(1-4x)).
  • A106190 (program): Triangle read by rows: T(n,k) = binomial(2(n-k),n-k)/(1-2(n-k)).
  • A106191 (program): Expansion of sqrt(1-4x)/(1-x).
  • A106192 (program): Expansion of sqrt(1-4x)/(1-x^2).
  • A106193 (program): Expansion of sqrt(1-4x)/(1-2x^2).
  • A106194 (program): Triangle read by rows, generated from binomial transforms of odd numbers.
  • A106195 (program): Riordan array (1/(1-2*x), x*(1-x)/(1-2*x)).
  • A106197 (program): Analog of A094091 for S=4.
  • A106198 (program): Triangle, columns = successive binomial transforms of Fibonacci numbers.
  • A106201 (program): Expansion of Re(x/(1-x-2*i*x^2)), i=sqrt(-1).
  • A106202 (program): Expansion of Im(x/(1 - x - 2*i*x^2)), i=sqrt(-1).
  • A106206 (program): Coefficients of (1 + 144*x)^(1/24).
  • A106228 (program): G.f. satisfies: A(x) = 1 + x*A(x)/(1 - x*A(x)^2).
  • A106229 (program): Least j > 1 for n > 0 such that j^2 = (n^2 + 1)*(k^2) + (n^2 + 1)*k + 1 where k sequence = A106230.
  • A106230 (program): Least k > 0 for n > 0 such that (n^2 + 1)*(k^2) + (n^2 + 1)*k + 1 = j^2 where j sequence = A106229.
  • A106231 (program): Least j > 1 such that j^2 = (4*n^2 + 2)*(k^2) + (4*n^2 + 2)*k + 1.
  • A106232 (program): Least k > 0 such that (4*n^2 + 2)*(k^2) + (4*n^2 + 2)*k + 1 = j^2.
  • A106233 (program): An inverse Catalan transform of A003462.
  • A106244 (program): Number of partitions into distinct prime powers.
  • A106246 (program): Number triangle T(n,k)=C(n,k)C(2,n-k).
  • A106247 (program): Expansion of (1+2*x-x^2-2*x^3+x^4) / (1-x^2)^3.
  • A106248 (program): McKay-Thompson series of class 5B for the Monster group with a(0) = -6.
  • A106249 (program): Expansion of (1-x+x^2+x^3)/(1-x-x^4+x^5).
  • A106250 (program): Expansion of (1-x+x^2+x^3)/(1-x-x^5+x^6).
  • A106251 (program): Expansion of (1-x+x^2+x^3+x^5)/(1-x-x^6+x^7).
  • A106252 (program): Number of positive integer triples (x,y,z), with x<=y<=z<=n, such that each of x,y and z divides the sum of the other two.
  • A106253 (program): First difference of A106252.
  • A106255 (program): Triangle composed of triangular numbers, row sums = A006918.
  • A106256 (program): Numbers n such that 12*n^2 + 13 is a square.
  • A106257 (program): Numbers k such that k^2 = 12*n^2 + 13.
  • A106258 (program): Expansion of 1/sqrt(1-8x-8x^2).
  • A106259 (program): Expansion of 1/sqrt(1-12x-12x^2).
  • A106260 (program): Expansion of 1/sqrt(1-16x-16x^2).
  • A106261 (program): Expansion of 1/sqrt(1 - 20*x - 20*x^2).
  • A106262 (program): An invertible triangle of remainders of 2^n.
  • A106263 (program): Row sums of number triangle A106262.
  • A106264 (program): Diagonal sums of number triangle A106262.
  • A106268 (program): Number triangle T(n,k) = binomial(k-n, n-k)*(-1)^(n-k) = (0^(n-k) + binomial(2*(n-k), n-k))/2 if k <= n, 0 otherwise; Riordan array (1/(2-C(x)), x) where C(x) is g.f. for Catalan numbers A000108.
  • A106269 (program): Expansion of 1/((1 - x^2)*(2 - c(x))), where c(x) is the g.f. of A000108.
  • A106270 (program): Inverse of number triangle A106268; triangle T(n,k), 0 <= k <= n.
  • A106271 (program): Row sums of number triangle A106270.
  • A106272 (program): Antidiagonal sums of number triangle A106270.
  • A106291 (program): Period of the Lucas sequence A000032 mod n.
  • A106292 (program): Period of the Lucas sequence A000032 mod prime(n).
  • A106314 (program): Triangle T(n,k) composed of the squares min(n,k)^2.
  • A106315 (program): Harmonic residue of n.
  • A106316 (program): Remainder of the harmonic residue of n when divided by n.
  • A106317 (program): Numbers n such that the remainder of the harmonic residue of n when divided by n is n-1.
  • A106318 (program): Bhaskara twins: n such that 2*n^2 = X^3 and 2*n^3 = Y^2.
  • A106325 (program): Smallest semiprime not less than n.
  • A106326 (program): Smallest odd semiprime not less than n.
  • A106328 (program): Numbers j such that 8*(j^2) + 9 = k^2 for some positive number k.
  • A106329 (program): Numbers k such that k^2 = 8*j^2 + 9.
  • A106330 (program): Numbers k such that k^2 = 24*(j^2) + 25.
  • A106331 (program): Numbers j such that 24*(j^2) + 25 = k^2.
  • A106344 (program): Triangle read by rows: T(n,k) = binomial(k,n-k) mod 2.
  • A106345 (program): Diagonal sums of number triangle A106344.
  • A106347 (program): A generalized Fredholm-Rueppel sequence.
  • A106348 (program): Partial sums of a generalized Fredholm-Rueppel sequence.
  • A106349 (program): Primes indexed by semiprimes.
  • A106350 (program): Semiprimes indexed by primes.
  • A106352 (program): Number of compositions of n into 3 parts such that no two adjacent parts are equal.
  • A106370 (program): Smallest b>1 such that n contains no zeros in its base b representation.
  • A106387 (program): Numbers j such that 6j^2 + 6j + 1 = 11k.
  • A106388 (program): Numbers k such that 11k = 6j^2 + 6j + 1.
  • A106389 (program): Numbers j such that 6j^2 + 6j + 1 = 13k.
  • A106390 (program): Numbers k such that 13k = 6j^2 + 6j + 1.
  • A106391 (program): A “cosh transform” of binomial(2n,n-1).
  • A106392 (program): Expansion of 1/(1 - 6*x + 10*x^2).
  • A106393 (program): Expansion of 1/(1 - 8x + 17x^2).
  • A106397 (program): Binomial transform of Mertens’s function sequence A002321.
  • A106400 (program): Thue-Morse sequence: let A_k denote the first 2^k terms; then A_0 = 1 and for k >= 0, A_{k+1} = A_k B_k, where B_k is obtained from A_k by interchanging 1’s and -1’s.
  • A106401 (program): Expansion of (eta(q) * eta(q^9))^3 / eta(q^3)^2 in powers of q.
  • A106402 (program): Expansion of eta(q^3)^9 / eta(q)^3 in powers of q.
  • A106404 (program): Number of even semiprimes dividing n.
  • A106405 (program): Number of odd semiprimes dividing n.
  • A106406 (program): Expansion of (eta(q) * eta(q^15))^2 / (eta(q^3) * eta(q^5)) in powers of q.
  • A106407 (program): Expansion of x((1-x)(1-x^2)(1-x^4)(1-x^8)…)^2.
  • A106408 (program): Triangle, read by rows, where T(1,1) = 1; T(2,1) = T(2,2) = 2; for n > 2, T(n,n) = T(n-1,n-1) + T(n-2,n-2); T(n+1,n) = 2 * T(n,n); for all other entries, T(n,k) = T(n-1,k) + T(n-2,k).
  • A106409 (program): n XOR (greatest proper divisor of n).
  • A106434 (program): The (1,1)-entry of the matrix A^n, where A = [0,1;2,3].
  • A106435 (program): a(n) = 3*a(n-1) + 3*a(n-2), a(0)=0, a(1)=3.
  • A106436 (program): Difference array of Bell numbers A000110 read by antidiagonals.
  • A106438 (program): G.f.: x(2-5x-2x^2)/(1-6x+9x^2-x^4).
  • A106440 (program): a(n) = binomial(2n+4,n)*binomial(n+4,4).
  • A106448 (program): Table of (x+y)/gcd(x,y) where (x,y) runs through the pairs (1,1), (1,2), (2,1), (1,3), (2,2), (3,1), …
  • A106450 (program): a(n) = A004443(n) if n is odd, a(n) = A004443(n)/2 if n is even.
  • A106458 (program): Bernoulli number denominators, with zeros at the odd places.
  • A106459 (program): Expansion of f(-x, -x^3) in powers of x where f(,) is Ramanujan’s general theta function.
  • A106461 (program): Binomial transform of the Tower of Hanoi sequence.
  • A106462 (program): Binomial transform of A007318 (Pascal’s triangle by rows).
  • A106464 (program): Antidiagonal sums of number triangle A003989.
  • A106465 (program): A number triangle of GCDs mod 2.
  • A106466 (program): Interleave 1,2,3,.. with 1,1,2,2,3,3,…
  • A106467 (program): Inverse of number triangle A106465.
  • A106468 (program): Absolute value of inverse of number triangle A106465.
  • A106469 (program): Expansion of (1+x^2)(1+2x)/(1-x^2).
  • A106470 (program): Inverse of number triangle A106468.
  • A106471 (program): A number triangle with duplicated columns of the form 2^n-sum{j=0..2k-1, C(n,j)}.
  • A106472 (program): Expansion of (1 - x)^2*(1 + x) / (1 - 2*x)^2.
  • A106473 (program): Rows of A003989 expressed as base 10 numbers.
  • A106474 (program): A006579(4n+4)/4.
  • A106475 (program): An alternating sum of greatest common divisors.
  • A106476 (program): Sequence array of Euler phi function.
  • A106477 (program): Diagonal sums of Euler phi function sequence array.
  • A106478 (program): Inverse of sequence array for Euler phi function.
  • A106479 (program): First column in inverse of Euler phi sequence matrix.
  • A106480 (program): Row sums of inverse of sequence array for Euler phi function.
  • A106481 (program): An Euler phi transform of 1/(1-x^2).
  • A106483 (program): Primes p such that 2p^2 - 1 is also prime.
  • A106486 (program): Number of edges in combinatorial game trees.
  • A106487 (program): Number of leaves in combinatorial game trees.
  • A106489 (program): Triangle read by rows: T(n,k) is the number of short bushes with n edges and having the leftmost leaf at height k (a short bush is an ordered tree with no nodes of outdegree 1).
  • A106490 (program): Total number of bases and exponents in Quetian Superfactorization of n, excluding the unity-exponents at the tips of branches.
  • A106492 (program): Total sum of bases and exponents in Quetian Superfactorization of n, excluding the unity-exponents at the tips of branches.
  • A106496 (program): Binomial transform of a fractal structured sequence.
  • A106505 (program): Ordered and uniqued length of side common to the two angles, one being the double of the other, of a primitive integer-sided triangle.
  • A106507 (program): G.f.: Product_{k>0} (1-x^(2k-1))/(1-x^(2k)).
  • A106509 (program): Riordan array ((1+x)/(1+x+x^2), x/(1+x)), read by rows.
  • A106510 (program): Expansion of (1+x)^2/(1+x+x^2).
  • A106511 (program): Expansion of (1+x)^2/((1 + x + x^2)*(1 + x - x^2)).
  • A106512 (program): Array read by antidiagonals: a(n,k) = number of k-colorings of a circle of n nodes (n >= 1, k >= 1).
  • A106513 (program): A Pell-Pascal matrix.
  • A106514 (program): Expansion of (1-x)/((1-2*x)*(1-2*x-x^2)).
  • A106515 (program): A Fibonacci-Pell convolution.
  • A106516 (program): A Pascal-like triangle based on 3^n.
  • A106517 (program): Convolution of Fibonacci(n-1) and 3^n.
  • A106521 (program): Numbers m such that Sum_{k=0..10} (m+k)^2 is a square.
  • A106523 (program): Diagonal sums of number triangle A106522.
  • A106524 (program): Interleave A038573(n+1) and 2*A038573(n+1).
  • A106525 (program): Values of x in x^2 - 49 = 2*y^2.
  • A106534 (program): Sum array of Catalan numbers (A000108) read by upward antidiagonals.
  • A106539 (program): a(1)=1, a(2)=1, a(n) = (n-1)*a(n-1) - (n-2)*a(n-2) - … - a(1) for n>=3.
  • A106540 (program): a(n) = a(n-1) - 2*a(n-2) - 3*a(n-3) - … - (n-1)*a(1), with a(1) = a(2) = 1, a(3) = -1.
  • A106541 (program): a(n) = a(n-1) - 2*a(n-2) - 3*a(n-3) - … - (n-1)*a(1), with a(1) = a(2) = 2, a(3) = -2.
  • A106542 (program): a(n) = a(n-1) - 2*a(n-2) - 3*a(n-3) - … - (n-1)*a(1), a(1) = a(2) = 3, a(3) = -3.
  • A106543 (program): Composite numbers that are not perfect powers.
  • A106544 (program): Perfect squares n^2 which are not the sum of two primes (otherwise 0).
  • A106545 (program): a(n) = n^2 if n^2 is the sum of two primes, otherwise a(n) = 0.
  • A106546 (program): a(n) = n^2 if n^2 is the difference of two primes, otherwise a(n) = 0.
  • A106549 (program): a(n) = -1 if 2*n-1 is a prime, 1 if 2*n-1 is a prime squared, or 0 otherwise.
  • A106562 (program): Perfect squares which are not the sum of two primes.
  • A106563 (program): Numbers n such that n^2 is not the sum of two primes.
  • A106564 (program): Perfect squares which are not the difference of two primes.
  • A106565 (program): a(n) = 5*a(n-1) + 5*a(n-2) with a(0) = 0, a(1) = 5.
  • A106566 (program): Triangle T(n,k), 0 <= k <= n, read by rows, given by [0, 1, 1, 1, 1, 1, 1, 1, … ] DELTA [1, 0, 0, 0, 0, 0, 0, 0, … ] where DELTA is the operator defined in A084938.
  • A106567 (program): a(n) = 5*a(n-1) + 4*a(n-2), with a(0) = 4, a(1) = 4.
  • A106568 (program): Expansion of 4*x/(1 - 4*x - 4*x^2).
  • A106569 (program): a(n) = 5*a(n-1) + 3*a(n-2), where a(0) = 0, a(1) = 3.
  • A106570 (program): a(n) = 4*a(n-1) + 3*a(n-2), with a(0)=0, a(1)=3.
  • A106571 (program): Indices n of perfect squares n^2 which are not the difference of two primes.
  • A106573 (program): Perfect squares which are neither the sum nor the difference of two primes.
  • A106574 (program): Indices n of perfect squares n^2 which are neither the sum nor the difference of two primes.
  • A106576 (program): Period 20. Sequence gives last digit of A106157, starting from the first positive term.
  • A106578 (program): First differences of indices of squarefree central binomial numbers.
  • A106579 (program): Triangular array associated with Schroeder numbers: T(0,0) = 1, T(n,0) = 0 for n > 0; T(n,k) = 0 if k < n; T(n,k) = T(n,k-1) + T(n-1,k-1) + T(n-1,k).
  • A106586 (program): Digit next to last in squares ending in 6.
  • A106587 (program): Sum of n-th prime squared and n-th perfect square.
  • A106588 (program): Difference between n-th prime squared and n-th perfect square.
  • A106594 (program): a(n) = number of primitive solutions to 4n+1 = x^2 + y^2.
  • A106602 (program): Number of primitive positive solutions to 8n+2=x^2+y^2.
  • A106603 (program): a(n) = - 2*a(n-1) - 8*a(n-3), a(0) = 1, a(1) = 1, a(2) = -2.
  • A106607 (program): Expansion of (1+t^3)^2/((1-t)*(1-t^2)^2*(1-t^4)).
  • A106608 (program): a(n) = numerator of n/(n+7).
  • A106609 (program): Numerator of n/(n+8).
  • A106610 (program): Numerator of n/(n+9).
  • A106611 (program): a(n) = numerator of n/(n+10).
  • A106612 (program): a(n) = numerator of n/(n+11).
  • A106614 (program): a(n) = numerator of n/(n+13).
  • A106615 (program): a(n) = numerator of n/(n+14).
  • A106616 (program): Numerator of n/(n+15).
  • A106617 (program): Numerator of n/(n+16).
  • A106618 (program): a(n) = numerator of n/(n+17).
  • A106619 (program): a(n) = numerator of n/(n+18).
  • A106620 (program): a(n) = numerator of n/(n+19).
  • A106621 (program): a(n) = numerator of n/(n+20).
  • A106622 (program): Primes of the form r(r(r(n)+1)+1)+1, where A141468(n)=r(n)=n-th nonprime.
  • A106624 (program): Expansion of g.f.: (1 - x^2 + x^3)/((1-x^2)*(1-2*x^2)).
  • A106627 (program): Product L(n)*L_4(n), where L(n) are Lucas numbers and L_4(n) are Lucas 4-step numbers.
  • A106633 (program): Number of ways to express n as k+l*m, with k, l, m all in the range [0..n].
  • A106637 (program): Accumulation of permutation sequence on three symbols such that the a[n+2]-2*a[n+1]-a[n]=0 overall.
  • A106638 (program): 3-symbol substitution that gives a dragon fractal.
  • A106640 (program): Row sums of A059346.
  • A106641 (program): A four-symbol four-at-a-time substitution with an ordering change: q=0.
  • A106642 (program): A four-symbol four-at-a-time substitution with an ordering change: q=1.
  • A106647 (program): Replace even digits d of n with 1+d/2.
  • A106648 (program): a(n) = 3*n^2 + 6*n + 8.
  • A106649 (program): Replace each digit d (except the leading one) of n with 9-d.
  • A106664 (program): Expansion of g.f.: (1-3*x+x^2)/((1-x)*(1+x)*(1-2*x+2*x^2)).
  • A106665 (program): Alternate paper-folding (or alternate dragon curve) sequence.
  • A106666 (program): Expansion of g.f. (1-4*x^2+2*x^3)/((1-x)*(1-2*x-2*x^2+2*x^3)).
  • A106671 (program): a(n) = ( prime(n + 2) * prime(n) - prime(n + 1)^2 ) modulo 3.
  • A106690 (program): Numbers k such that 11*k - 97 is prime.
  • A106692 (program): Numbers k such that 97*k - 11 is prime.
  • A106693 (program): 3 symbols taken seven at a time symmetrically.
  • A106695 (program): Numbers k such that 101*k - 997 is prime.
  • A106701 (program): a(n) = next-to-most-significant binary digit of n-th composite positive integer.
  • A106706 (program): a(0) = 19; for n>0, successively subtract 5, subtract 3 and double.
  • A106707 (program): First entry of the vector (M^n)v, where M is the 2 X 2 matrix [[0,-1],[1,4]] and v is the column vector [0,1].
  • A106709 (program): Expansion of g.f. -2*x/(1 - 5*x + 2*x^2).
  • A106710 (program): Number of words with n letters from an alphabet of size 26 with at least two equal consecutive letters.
  • A106729 (program): Sum of two consecutive squares of Lucas numbers (A001254).
  • A106731 (program): Expansion of -2*x/(1 - 4*x + 2*x^2).
  • A106732 (program): Expansion of -3*x/(1 - 5*x + 3*x^2).
  • A106734 (program): a(n) = n^3 - 7*n + 7.
  • A106737 (program): a(n) = Sum_{k=0..n} ({binomial(n+k,n-k)*binomial(n,k)} mod 2).
  • A106740 (program): Triangle read by rows: greatest common divisors of pairs of Fibonacci numbers greater than 1: T(n, k) = gcd(Fibonacci(n), Fibonacci(k)).
  • A106742 (program): a(n) = a(a(a(a(a(n - a(n-1)))))) + a(n - a(n-2)) with a(1) = a(2) = 1.
  • A106743 (program): a(n) = -1 iff n is prime, a(n) = 1 iff n is not squarefree, otherwise (n is nonprime and squarefree) a(n) = 0.
  • A106744 (program): Given n shoelaces, each with two aglets; sequence gives number of aglet pairs that must be picked up to guarantee that the probability that no shoelace is left behind is > 1/2.
  • A106747 (program): Replace each odd digit d of n with (d-1)/2 and each even digit d with d/2.
  • A106749 (program): Define the morphism f: 1->113, 2->13, 3->2; sequence gives trajectory of 1 under f.
  • A106750 (program): Define the “Fibonacci” morphism f: 1->12, 2->1 and let a(0) = 2; then a(n+1) = f(a(n)).
  • A106753 (program): Discriminants, negated, of definite binary quadratic forms.
  • A106754 (program): Primes p with digital sum equal to 11.
  • A106755 (program): Primes p with digital sum equal to 13.
  • A106757 (program): Primes with digit sum = 16.
  • A106759 (program): Primes with digit sum = 19.
  • A106760 (program): Primes with digit sum = 20.
  • A106789 (program): Sum of two consecutive squares of Lucas 3-step numbers (A001644).
  • A106791 (program): Sum of two consecutive squares of Lucas 4-step numbers (A073817).
  • A106793 (program): Number of words (over an alphabet of size 26) of length n with all different letters.
  • A106799 (program): Number of prime factors of n apart from 2 or 3, counted with multiplicity.
  • A106803 (program): Expansion of x*(1-x)/(1-2*x-x^2+x^3).
  • A106804 (program): Expansion of g.f.: x*(2 - 9*x - 4*x^2)/((1 - 5*x + x^2)*(1 - 5*x - x^2)).
  • A106805 (program): Expansion of g.f.: 1/(1 - 2*x - x^2 + x^3).
  • A106825 (program): Trajectory of 1 under the morphism 1->1222, 2->2111.
  • A106826 (program): Trajectory of 1 under the morphism 1->{2,1}, 2->{2,3}, 3->{4,3}, 4->{4,1}.
  • A106829 (program): Given n shoelaces, each with two aglets; sequence gives number of aglets that must be picked up to guarantee that the probability that no shoelace is left behind is > 1/2.
  • A106830 (program): Numerator of Sum_{ primes p <= n} 1/p.
  • A106831 (program): Define a triangle in which the entries are of the form +-1/(b!c!d!e!…), where the order of the factorials is important; read the triangle by rows and record and expand the denominators.
  • A106832 (program): 4*n-2 and 6*n alternatively.
  • A106833 (program): 3n and 2n, alternating.
  • A106835 (program): 4 X 4 vector Markov sequence with characteristic polynomial x^4-10*x^3+25*x^2-4.
  • A106836 (program): First differences of A060833 and (from a(2) onward) also of A091067 and A255068.
  • A106837 (program): Numbers n such that both n and n+1 have odd part of form 4k+3.
  • A106838 (program): Numbers n such that n, n+1 and n+2 have odd part of form 4k+3.
  • A106839 (program): Numbers congruent to 11 mod 16.
  • A106840 (program): Numbers n such that both n and n+1 have odd part of form 4k+1.
  • A106841 (program): Numbers m such that m, m+1 and m+2 have odd part of form 4k+1.
  • A106842 (program): (1 + n + n^2)^n.
  • A106843 (program): Numbers of form 3^i * prime(j), i>=0, j>0.
  • A106844 (program): Exponent of 2 in A093641(n).
  • A106845 (program): n^2 * (n^3 + 2n^2 + 7n - 2) / 8.
  • A106846 (program): Sum {k + l*m <= n} (k + l*m), with 0 <= k,l,m <= n.
  • A106847 (program): a(n) = Sum {k + l*m <= n} (k + l*m), with 0 < k,l,m <= n.
  • A106849 (program): Values of n for which A106848(n) = n-1.
  • A106851 (program): Let M = {{0, 0, 0, 1}, {1, 4, 0, 0}, {0, 1, 0, 0}, {0, 0, 1, 4}}, v[1] = {0, 1, 1, 2}’, v[n]=M.v[n-1]; then a(n) = v[n][[1]]
  • A106852 (program): Expansion of 1/(1-x*(1-3*x)).
  • A106853 (program): Expansion of 1/(1 - x + 4*x^2).
  • A106854 (program): Expansion of 1/(1-x*(1-5*x)).
  • A106855 (program): Expansion of 1/(1-x^2(1-3x)).
  • A106859 (program): Primes of the form 2x^2 + xy + 2y^2.
  • A106863 (program): Primes of the form x^2+xy+5y^2.
  • A106865 (program): Primes of the form 2x^2 + 2xy + 3y^2.
  • A106927 (program): Primes of the form 2x^2+xy+8y^2, with x and y any integer.
  • A106949 (program): Primes of the form 2x^2 + 9y^2.
  • A106950 (program): Primes of the form x^2 + 18y^2.
  • A106952 (program): Primes of the form 3x^2-3xy+7y^2, with x and y nonnegative.
  • A107003 (program): Primes of the form 24n + 5.
  • A107006 (program): Primes of the form 4x^2-4xy+7y^2, with x and y nonnegative.
  • A107007 (program): Primes of the form 3*x^2+8*y^2.
  • A107008 (program): Primes of the form x^2 + 24*y^2.
  • A107015 (program): Number of even terms in Zeckendorf representation of n.
  • A107016 (program): Number of odd terms in Zeckendorf representation of n.
  • A107017 (program): Second largest term in Zeckendorf representation of n, a(n)=0 if n itself is a Fibonacci number.
  • A107025 (program): Binomial transform of the expansion of 1/(1-x^5-x^6).
  • A107026 (program): Row sums of inverse of Riordan array (1/(1+x),x/(1+x)^4).
  • A107033 (program): Expansion of f(x, x) * f(x, -x^2) in powers of x where f(,) is a Ramanujan theta function.
  • A107034 (program): Expansion of f(-x) * f(-x^4) in powers of x where f() is a Ramanujan theta function.
  • A107035 (program): Expansion of q * (psi(q^4) / phi(-q))^2 in powers of q where phi(), psi() are Ramanujan theta functions.
  • A107040 (program): Indices of squarefree Pell numbers.
  • A107041 (program): First differences of indices of squarefree Pell numbers.
  • A107042 (program): First differences of indices of squarefree Catalan numbers.
  • A107044 (program): A symmetric factorial triangle, read by rows: T(n,k) = min(n,k)!.
  • A107048 (program): Denominators of coefficients that satisfy: 2^n = Sum_{k=0..n} c(k)*x^k for n>=0, where c(k) = A107047(k)/a(k).
  • A107050 (program): Denominators of coefficients that satisfy: 3^n = Sum_{k=0..n} c(k)*x^k for n>=0, where c(k) = A107049(k)/a(k).
  • A107054 (program): Denominators of coefficients that satisfy: 5^n = Sum_{k=0..n} c(k)*x^k for n>=0, where c(k) = A107053(k)/a(k).
  • A107056 (program): Matrix inverse of A103247, so that T(n,k) = C(n,k)*A010842(n-k), read by rows.
  • A107058 (program): a(n) = smallest number m>0 such that prime(n)*prime(n+1)-m is a prime.
  • A107060 (program): a(n) = smallest number m >=0 such that n*prime(n)-m is a prime.
  • A107061 (program): a(n) = largest number m >0 such that n*prime(n)-a(n) is a prime.
  • A107063 (program): Expansion of q^(-1/24) * (eta(q^2) * eta(q^3)^4) / (eta(q) * eta(q^6)^2) in powers of q.
  • A107064 (program): Expansion of q^(-17/24) * (eta(q) * eta(q^6)^4) / (eta(q^2) * eta(q^3)^2) in powers of q.
  • A107065 (program): Riordan array (1/(1-x),x(1+x+x^2+x^3)).
  • A107066 (program): Expansion of 1/(1-2*x+x^5).
  • A107068 (program): Expansion of 1/((1+x)^3-x^4).
  • A107071 (program): Numbers n such that 1019*n + 1021 is prime.
  • A107073 (program): Numbers n such that the string 35n is prime.
  • A107075 (program): Centered square numbers that are also centered pentagonal numbers.
  • A107078 (program): Whether n has non-unitary prime divisors.
  • A107079 (program): Minimal number of squared primes in a squarefree gap of length n.
  • A107080 (program): McKay-Thompson series of class 4A for the Monster group.
  • A107103 (program): Column 1 of triangle A107102, which is the matrix inverse of A100862.
  • A107104 (program): Absolute row sums of triangle A107102, which is the matrix inverse of A100862.
  • A107105 (program): Triangle, read by rows, where T(n,k) = C(n,k)*(C(n,k) + 1)/2, n>=k>=0.
  • A107114 (program): Two-digit numbers from the decimal expansion of Pi.
  • A107115 (program): Three-digit numbers from the decimal expansion of Pi (version 3) – but see comments.
  • A107116 (program): Three-digit numbers from the decimal expansion of Pi (version 1).
  • A107117 (program): Three-digit numbers from the decimal expansion of Pi (version 2).
  • A107118 (program): Numbers that are both centered triangular numbers (A005448) and centered hexagonal numbers (A003215).
  • A107128 (program): Divide the even digits of n by 2!.
  • A107130 (program): Replace each odd digit d of n with (d-1)/2.
  • A107131 (program): A Motzkin related triangle.
  • A107134 (program): Primes of the form x^2+28y^2.
  • A107135 (program): Primes of the form 5x^2 + 6y^2.
  • A107144 (program): Primes of the form 5x^2 + 8y^2.
  • A107145 (program): Primes of the form x^2 + 40y^2.
  • A107151 (program): Primes of the form 5x^2 + 9y^2.
  • A107152 (program): Primes of the form x^2 + 45y^2.
  • A107167 (program): Primes of the form 5x^2 + 12y^2.
  • A107168 (program): Primes of the form 4x^2 + 15y^2.
  • A107169 (program): Primes of the form 3x^2 + 20y^2.
  • A107181 (program): Primes of the form 8x^2 + 9y^2.
  • A107223 (program): Floor(Pi*Floor(n*Pi)).
  • A107227 (program): Numbers having no odd terms in their Zeckendorf representation.
  • A107228 (program): Numbers having no even terms in their Zeckendorf representation.
  • A107230 (program): A number triangle of inverse Chebyshev transforms.
  • A107231 (program): a(n) = C(n+2,2)*C(n,floor(n/2)).
  • A107232 (program): Expansion of (1+x*c(x^2))^3/sqrt(1-4*x^2), c(x) the g.f. of A000108.
  • A107233 (program): An inverse Chebyshev transform of n^3.
  • A107239 (program): Sum of squares of tribonacci numbers (A000073).
  • A107240 (program): Sum of squares of first n tribonacci numbers (A000213).
  • A107241 (program): Sum of squares of first n tetranacci numbers (A000288).
  • A107242 (program): Sum of squares of tetranacci numbers (A001630).
  • A107243 (program): Sum of squares of pentanacci numbers (A001591).
  • A107244 (program): Sum of squares of hexanacci numbers (A001592, Fibonacci 6-step numbers).
  • A107245 (program): Sum of squares of heptanacci numbers (Fibonacci 7-step numbers).
  • A107246 (program): Sum of squares of octanacci numbers (Fibonacci 8-step numbers).
  • A107249 (program): A number triangle with repeated columns of binomial coefficients.
  • A107253 (program): a(n) = n^4 - 15*n + 15.
  • A107255 (program): a(n) = n^5 - 31*n + 31, with n*a(n) + n*( n - 1 )*31 = n^6.
  • A107256 (program): a(n) = n^6 - 63*n + 63, with n*a(n) + n*(n-1)*63 = n^7.
  • A107258 (program): Numbers not representable as Fibonacci(i) + triangular(j), i,j>=0.
  • A107259 (program): Number of ways to represent n as Fibonacci(i) + triangular(j), i,j>=0.
  • A107264 (program): Expansion of (1 - 3*x - sqrt((1-3*x)^2 - 4*3*x^2))/(2*3*x^2).
  • A107265 (program): Expansion of (1-5*x-sqrt((1-5*x)^2-4*5*x^2))/(2*5*x^2).
  • A107266 (program): Expansion of (1-6*x-sqrt((1-6*x)^2-4*6*x^2))/(2*6*x^2).
  • A107267 (program): A square array of Motzkin related transforms, read by antidiagonals.
  • A107268 (program): Sums of antidiagonals of A107267.
  • A107279 (program): a(n) = 1 if n is an odd prime, a(n) = 2 if n is a nonzero even number, otherwise a(n) = 0.
  • A107281 (program): a(0) = 1, a(1) = 1, a(2) = 2 and for n >= 1: a(n+1) = SORT[a(n) + a(n-1) + a(n-2)] where SORT places digits in ascending order and deletes 0’s.
  • A107283 (program): E.g.f. exp(x)*(x^2+x+2)/(1-x).
  • A107284 (program): a(n)/4^n is the measure of the subset of [0,1] remaining when all intervals of the form [b/2^m - 1/2^(2m), b/2^m + 1/2^(2m)] have been removed, with b and m positive integers, b < 2^m and m <= n.
  • A107285 (program): 5*401*(10^n + 1).
  • A107286 (program): a(0) = 0; for n>0, minimal prime factor of n, or 1 if n is 1 or a prime.
  • A107289 (program): Numbers k such that the sum of digits of k^2 is a prime.
  • A107293 (program): The (1,1)-entry of the matrix M^n, where M is the 5 X 5 matrix [[0,1,0,0,0],[0,0,1,0,0], [0,0,0,1,0], [0,0,0,0,1], [1,0,-1,1,1]].
  • A107294 (program): GCD of (n + prime(n)) and (n + 1 + prime(n+1)).
  • A107298 (program): a(n) = 3*a(n-1)-a(n-2)-2*a(n-3)+a(n-4), n>5.
  • A107299 (program): a(n) = 4*a(n-1)-2*a(n-2)-3*a(n-3)+2*a(n-4), n>5.
  • A107300 (program): a(n) = 2*a(n-1) + 2*a(n-2) - 2*a(n-3) with a(0)=3, a(1)=2, a(3)=8.
  • A107303 (program): Numbers k such that (3*k - 5) is prime.
  • A107304 (program): Numbers k such that 5k - 7 is prime.
  • A107305 (program): Numbers k such that 11*k - 13 is prime.
  • A107306 (program): Numbers k such that (17*k - 19) is prime.
  • A107307 (program): G.f. (1-x-2*x^2-x^3+x^4)/((x-1)^3*(6*x^2+2*x-1)).
  • A107308 (program): Numbers k such that (29*k - 31) is prime.
  • A107309 (program): Concatenation of twin primes in reverse order.
  • A107316 (program): Floor(exp(n)/n).
  • A107317 (program): Semiprimes of the form 2*(m^2 + m + 1) (implying that m^2 + m + 1 is a prime).
  • A107319 (program): a(n) = C(n+8,8)*C(n+6,6).
  • A107323 (program): If n-th prime is 6m-1, then a(n) = 6m+1. If n-th prime is 6m+1, then a(n) = 6m-1.
  • A107324 (program): Floor(A063655(n)/2).
  • A107325 (program): a(n) = ceiling(A063655(n)/2).
  • A107330 (program): a(n) = 4*a(n-1)-a(n-2)-3*a(n-3)+a(n-4), n>5.
  • A107332 (program): The (1,3)-entry of the matrix M^n, where M is the 5x5 matrix [[0,1,0,0,0],[0,0,1,0,0],[0,0,0,1,0],[0,0,0,0,1],[1,0,-1,1,1]].
  • A107334 (program): G.f.: (3-4*x-3*x^2)/(1-2*x-3*x^2+2*x^3).
  • A107345 (program): From the binary representation of n: binomial(number of zeros, number of blocks of contiguous zeros).
  • A107346 (program): Differences between successive permutations of 1,2,3,4,5 regarded as decimal numbers arranged in increasing order.
  • A107347 (program): Number of even semiprimes strictly between prime(n) and 2*prime(n).
  • A107351 (program): Expansion of (1+x^3)/((1-x)^3*(1-x^2)^3*(1-x^3)).
  • A107358 (program): Dying rabbits: a(n) = Fibonacci(n) for n <= 12; for n >= 13, a(n) = a(n-1) + a(n-2) - a(n-13).
  • A107359 (program): A003754(n+1) - A003754(n).
  • A107361 (program): G.f. 1/((3*x-1)*(x^2-x-1)).
  • A107366 (program): Numbers k such that 101*k + 103 is prime.
  • A107368 (program): a(n) = a(n-1) + a(n-2) - a(n-3) + a(n-5).
  • A107369 (program): Numbers n such that 103*n + 101 is prime.
  • A107371 (program): Numbers k such that 101*k - 103 is prime.
  • A107372 (program): Numbers n such that 103*n - 101 is prime.
  • A107373 (program): a(n) = (n/2)*binomial(n-1, floor((n-1)/2)) - 2^(n-2).
  • A107375 (program): a(n) = 6*a(n-1)-6*a(n-3)-a(n-4).
  • A107376 (program): a(n) = 7*a(n-1)-7*a(n-3)-a(n-4).
  • A107377 (program): Expansion of x*(1-4*x-3*x^2)/(1-5*x+5*x^3+x^4).
  • A107378 (program): Expansion of x*(1-3*x-2*x^2)/(1-4*x+4*x^3+x^4).
  • A107382 (program): a(n) = 4*a(n-1)-4*a(n-3)-a(n-4).
  • A107383 (program): a(n) = 2*a(n-2) + 2*a(n-3).
  • A107384 (program): a(n)= a(n-1) +3*a(n-2) -3*a(n-4).
  • A107385 (program): a(n) = a(n-1)+4*a(n-2)-4*a(n-4).
  • A107386 (program): a(n) = 2*a(n-1) - 2*a(n-3) + a(n-4), n>6.
  • A107387 (program): Expansion of x*(1-2*x-x^2)/( (1-x)*(1+x)*(1-3*x+x^2)).
  • A107388 (program): Expansion of x*(3*x-1)*(2*x-1) / ( (1-x)*(1+x)*(x^2-4*x+1) ).
  • A107389 (program): Expansion of x*(1-6*x+7*x^2)/( (1-x)*(1+x)*(1-5*x+x^2)).
  • A107391 (program): Expansion of sin(x)^2 * sinh(x)^2.
  • A107392 (program): Number of (inequivalent) fuzzy subgroups of the direct sum of group of integers modulo p^n and group of integers modulo 2 for a prime p with (p,2) = 1. Z_{p^n} + Z_2.
  • A107393 (program): a(n) = -1 if n is a prime, else a(n) = 1 if n is the sum of three odd primes, else a(n) = 2 if n is the sum of two primes, else a(n) = 0.
  • A107394 (program): C(n+2,2)*C(n+4,2).
  • A107395 (program): a(n) = C(n+4,4)*C(n+6,4).
  • A107396 (program): a(n) = binomial(n+5, 5) * binomial(n+7, 5).
  • A107397 (program): a(n) = binomial(n+6, 6) * binomial(n+8, 6).
  • A107398 (program): a(n) = binomial(n+7, 7) * binomial(n+9, 7).
  • A107399 (program): a(n) = C(n+8,8)*C(n+10,8).
  • A107400 (program): Numbers k such that 107*k + 109 is prime.
  • A107401 (program): a(n) = -a(n-1)+4*a(n-2)+4*a(n-3)-a(n-4)-a(n-5).
  • A107403 (program): Expansion of e.g.f. 1/(1-3*sinh(x)).
  • A107405 (program): Numbers n such that 109*n + 107 is prime.
  • A107406 (program): Numbers n such that 107*n - 109 is prime.
  • A107407 (program): Numbers n such that 109*n - 107 is prime.
  • A107409 (program): Each term is sum of three previous terms mod 10.
  • A107410 (program): Each term is sum of three previous terms mod 9.
  • A107417 (program): a(n) = C(n+2,2)*C(n+5,5).
  • A107418 (program): a(n) = C(n+3,3)*C(n+6,6).
  • A107419 (program): a(n) = C(n+4,4)*C(n+7,7).
  • A107420 (program): a(n) = C(n+5,5)*C(n+8,8).
  • A107421 (program): a(n) = C(n+6,6)*C(n+9,9).
  • A107422 (program): a(n) = binomial(n+7,7) * binomial(n+10,10).
  • A107423 (program): Numbers k equal prime(n)*prime(n+1) such that k+1 is a square and k-1 is even semiprime.
  • A107427 (program): Maximal number of simple triangular regions that can be formed by drawing n line segments in the Euclidean plane.
  • A107430 (program): Triangle read by rows: row n is row n of Pascal’s triangle (A007318) sorted into increasing order.
  • A107436 (program): a(n) = (a^5)(n-1) + a(n-a(n-1)) = a(a(a(a(a(n-1))))) + a(n-a(n-1)), a(1) = a(2) = 1.
  • A107443 (program): G.f. (3*x^2+1)/((1-x)*(2*x^2+x+1)*(2*x^2-x+1)).
  • A107444 (program): a(n) = C(n^3, n).
  • A107446 (program): a(n) = binomial(n^4, n).
  • A107450 (program): Additive persistence of the prime numbers.
  • A107453 (program): 1 followed by repetitions of the period-4 sequence 1,1,1,2.
  • A107454 (program): Number of nonisomorphic generalized Petersen graphs P(n,k) with girth 5 on 2n vertices for 1<=k<=Floor[(n-1)/2].
  • A107458 (program): Expansion of g.f.: (1-x^2-x^3)/( (1+x)*(1-x-x^3) ).
  • A107459 (program): Number of nonisomorphic bipartite generalized Petersen graphs P(2n,k) with girth 6 on 4n vertices for 1<=k<n.
  • A107461 (program): Number of gap-free compositions of n into distinct parts, cf. A107428.
  • A107463 (program): a(0)=0, a(n)=1 if n is 1 or is a prime, otherwise sum of prime factors of n with multiplicity.
  • A107464 (program): Number of fuzzy subgroups of rank 3 cyclic group of order (p^n)*q*r where p, q and r are three distinct prime.
  • A107471 (program): a(n) = 3*prime(n) - 2*prime(n+1).
  • A107473 (program): Sum of numerator and denominator of product{p|n,p=primes} (1 -1/p).
  • A107479 (program): a(n) = a(n-2) + a(n-3) + a(n-4) + a(n-5) + a(n-6) + a(n-7).
  • A107480 (program): a(n) = a(n-1) + a(n-3) + a(n-4) + a(n-5) + a(n-7).
  • A107487 (program): Ordered semiperimeters of Pythagorean triangles.
  • A107490 (program): Coefficients of a certain theta series.
  • A107491 (program): Coefficients of a certain theta series.
  • A107492 (program): Coefficients of a certain theta series.
  • A107493 (program): Coefficients of a certain theta series.
  • A107495 (program): Coefficients of a certain theta series.
  • A107496 (program): Coefficients of a certain theta series.
  • A107505 (program): Theta series of quadratic form with Gram matrix [ 2, 1, 0, 1; 1, 4, 1, 0; 0, 1, 4, -2; 1, 0, -2, 8].
  • A107576 (program): a(n)=perimeter of n-th triangle listed at A107572.
  • A107583 (program): a(n) = 3^n - 3*n.
  • A107584 (program): a(n) = 4^n - 4*n.
  • A107585 (program): a(n) = 5^n - 5*n.
  • A107587 (program): Number of Motzkin n-paths with an even number of up steps.
  • A107597 (program): Antidiagonal sums of triangle A107105: a(n) = Sum_{k=0..n} A107105(n-k,k), where A107105(n,k) = C(n,k)*(C(n,k) + 1)/2.
  • A107599 (program): a(n) = 0,1,2 (resp.) if (1/2)[prime(n-1)+prime(n+1)] is less than, equal to or greater than prime(n) (resp.).
  • A107604 (program): Order of appearance of twos in the Fibonacci substitution :triangular in form.
  • A107615 (program): Coefficient list length of Poincaré-like polynomials made from A047845, indices of 4*n+1 nonprimes as the m(i) exponents.
  • A107616 (program): Triangle read by rows, generated from arithmetic sequences.
  • A107620 (program): Primes multiplied alternately by 3 and 2.
  • A107621 (program): Primes multiplied alternately by 2 and 3.
  • A107622 (program): Primes plus alternately 2 and 3.
  • A107623 (program): Primes plus alternately 3 and 2.
  • A107635 (program): McKay-Thompson series of class 32a for the Monster group.
  • A107638 (program): Order of appearance of ones in the Fibonacci substitution :triangular in form.
  • A107643 (program): Numbers n such that the string 75n is prime.
  • A107653 (program): Expansion of q / (chi(q) * chi(q^3))^6 in powers of q where chi() is a Ramanujan theta function.
  • A107659 (program): a(n) = Sum_{k=0..n} 2^max(k, n-k).
  • A107660 (program): Sum 3^max(k,n-k),k=0..n.
  • A107661 (program): Array read by antidiagonals: T(n,m) = Sum m^max(k,n-k),k=0..n.
  • A107663 (program): a(2n) = 2*4^n-1, a(2n+1) = (2^(n+1)+1)^2; interlaces A083420 with A028400.
  • A107665 (program): Numbers with semiprime digits (digits 4, 6, 9 only).
  • A107680 (program): Repeating k-th ternary repunit (A003462) 2^k times, k >= 0.
  • A107684 (program): Union of sequences 2^k-1, 2^k and 2^k+1.
  • A107706 (program): Quadratic recurrence a(n)=2a(n-1)^2+a(n-2), a(0)=a(1)=1.
  • A107712 (program): a(n) = Product_{k=1..n} prime(k+n).
  • A107713 (program): Convolution of 2^n*n! and n!.
  • A107715 (program): Primes whose decimal representation contains only digits from the set {0,1,2,3}.
  • A107716 (program): Inverse INVERT transform of triple factorial numbers (3*n-2)!!! (A007559).
  • A107730 (program): Numbers n such that prime(n+1) has the same last digit as prime(n).
  • A107731 (program): Row 7 of the array in A107735.
  • A107732 (program): Column 1 of the array in A107735.
  • A107733 (program): Column 2 of the array in A107735.
  • A107737 (program): Numbers n such that, in prime decomposition of n, sum of all prime factors and their orders is prime.
  • A107738 (program): Primes as a sum of prime factors and their orders in prime decomposition of some n.
  • A107740 (program): Number of numbers m such that prime(n) = m + (digit sum of m).
  • A107742 (program): G.f.: Product_{j>=1} Product_{i>=1} (1 + x^(i*j)).
  • A107743 (program): Numbers m such that m+(digit sum of m) is a composite number.
  • A107744 (program): Smallest prime factor of 6*n+1.
  • A107745 (program): Smallest prime factor of 6*n-1.
  • A107746 (program): Numbers n such that the least prime factor of 6*n+1 > the least prime factor of 6*n-1, A107744(n) > A107745(n).
  • A107747 (program): Numbers n such that the least prime factor of 6*n+1 < the least prime factor of 6*n-1, A107744(n) < A107745(n).
  • A107749 (program): OrdinaryUnitarySigma(n): If n = Product p_i^r_i then OUSigma(n) = Sigma(2^r_1)*UnitarySigma(n/2^r_1).
  • A107750 (program): If n=0 then 0, else smallest number greater than its predecessor and having either more or fewer zeros in its binary representation.
  • A107751 (program): a(n) = A107750(n+1) - A107750(n).
  • A107755 (program): Numbers k such that Sum_{j=1..k} Catalan(j) == 0 (mod 3).
  • A107756 (program): Numbers k such that Sum_{j=1..k} Catalan(j) == 1 (mod 3).
  • A107757 (program): Numbers k such that Sum_{j=1..k} Catalan(j) == 2 (mod 3).
  • A107758 (program): (+2)Sigma(n): If n = Product p_i^r_i then a(n) = Product (2 + Sum p_i^s_i, s_i=1 to r_i) = Product (1 + (p_i^(r_i+1)-1)/(p_i-1)), a(1) = 1.
  • A107759 (program): a(n) = (+2)UnitarySigma(n): if n = Product p_i^r_i then a(n) = Product (2 + p_i^r_i).
  • A107760 (program): Expansion of eta(q^3) * eta(q^2)^6 / (eta(q)^3 * eta(q^6)^2) in powers of q.
  • A107767 (program): a(n) = (1 + 3^n - 2*3^(n/2))/4 if n is even, (1 + 3^n - 4*3^((n-1)/2))/4 if n odd.
  • A107769 (program): a(n) = (A001333(n+1) - 2*A005409(floor((n+3)/2)) - 1) / 4.
  • A107770 (program): Index of greater of twin primes in the primes.
  • A107771 (program): Numbers n such that 2*n + 5 and 5*n + 2 are primes.
  • A107782 (program): In binary representation of n: (number of zeros) minus (number of blocks of contiguous zeros).
  • A107785 (program): Sequence obtained using characteristic polynomial that is Laplace transform of the tribonacci characteristic polynomial: -s^4*L(t^3 -t^2 -t -1) = s^3 +s^2 +2*s -6.
  • A107786 (program): a(n) = |b(n)| where b(n) = -b(n-1) + 6*b(n-3) with b(0)=0, b(1)=1, b(2)=1.
  • A107789 (program): Trajectory of 2 under evenly many applications of the morphism 1 -> 2, 2 -> 114, 3 -> 4, 4 -> 233.
  • A107790 (program): Ones order in the tribonacci substitution of three symbols.
  • A107791 (program): Twos order in the tribonacci substitution of three symbols.
  • A107792 (program): Threes order in the tribonacci substitution of three symbols.
  • A107793 (program): Differences between successive indices of 1’s in the ternary tribonacci sequence A305390.
  • A107795 (program): First differences of indices of 2’s in A305389.
  • A107796 (program): First differences of indices of 3’s in A305389.
  • A107800 (program): a(n) = number of distinct primes dividing A006049(n) (and dividing (A006049(n)+1).
  • A107817 (program): Slowest increasing sequence where 2 consecutive integers sum up to a prime.
  • A107818 (program): Slowest increasing sequence where (product of 2 consecutive integers)-1 is prime.
  • A107819 (program): Slowest increasing sequence where a(n)+n is prime.
  • A107820 (program): a(1)=3, a(2)=5; thereafter a(n) = n+5.
  • A107836 (program): Slowest increasing sequence where a(n)+(first digit of a(n)) is prime.
  • A107839 (program): a(n) = 5*a(n-1) - 2*a(n-2); a(0)=1, a(1)=5.
  • A107840 (program): a(n)= 3*a(n-1) -3*a(n-3) +a(n-4), n>6.
  • A107841 (program): Series reversion of x(1-3x)/(1-x).
  • A107842 (program): A number triangle of lattice walks.
  • A107843 (program): Number of iterations of McCarthy 91 Function until it terminates.
  • A107844 (program): Highest value obtained in the recursion of McCarthy’s 91 function until it terminates.
  • A107849 (program): Expansion of (1 + x)^2 / ((1 - x^2 - 2*x^3)*(1 + x^4)).
  • A107852 (program): Expansion of -x*(x^2+1)*(x+1)^2/((2*x^3+x^2-1)*(x^4+1)).
  • A107853 (program): G.f. x*(x-1)*(x+1)^3/((2*x^3+x^2-1)*(x^4+1)).
  • A107854 (program): G.f. x*(x^2+1)*(x^3-x-1)/((2*x^3+x^2-1)*(x^4+1)).
  • A107857 (program): a(n) = floor[(phi + n mod 2)*a(n-1)], a(1)=1.
  • A107858 (program): a(n) = b(k), where b(k) = Fibonacci(n-1) and k = floor( n*(1+sqrt(5))/2 ).
  • A107862 (program): Triangle, read by rows, where T(n,k) = C(n*(n-1)/2 - k*(k-1)/2 + n-k, n-k).
  • A107863 (program): Column 1 of triangle A107862; a(n) = binomial(n*(n+1)/2 + n, n).
  • A107867 (program): Triangle, read by rows, where T(n,k) = C(n*(n-1)/2-k*(k-1)/2+n-k+1,n-k).
  • A107868 (program): Column 0 of triangle A107867; a(n) = C( n*(n-1)/2 + n + 1, n).
  • A107869 (program): Column 1 of triangle A107867; a(n) = binomial( n*(n+1)/2 + n+1, n).
  • A107870 (program): Triangle, read by rows, where T(n,k) = C(n*(n-1)/2-k*(k-1)/2+n-k+2, n-k).
  • A107871 (program): Column 0 of triangle A107870; a(n) = C( n*(n-1)/2 + n+2, n).
  • A107872 (program): Column 1 of triangle A107870; a(n) = C(n*(n+1)/2 + n+2, n).
  • A107873 (program): Triangle, read by rows, where T(n,k) = binomial(n*(n-1)/2 - k*(k-1)/2 + n-k+3, n-k).
  • A107874 (program): Column 0 of triangle A107873; a(n) = C( n*(n-1)/2 + n+3, n).
  • A107875 (program): Column 1 of triangle A107873; a(n) = C( n*(n+1)/2 + n+3, n).
  • A107891 (program): a(n) = (n+1)*(n+2)^2*(n+3)^2*(n+4)*(3n^2 + 15n + 20)/2880.
  • A107895 (program): Euler transform of n!.
  • A107903 (program): Generalized NSW numbers.
  • A107904 (program): Expansion of (1+6x)/(1-12x^2).
  • A107905 (program): Decimal expansion of (5+sqrt(21))/2.
  • A107906 (program): Expansion of (1+8x)/(1-16x^2).
  • A107907 (program): Numbers having consecutive zeros or consecutive ones in binary representation.
  • A107908 (program): a(n) = (n+1)*(n+2)^2*(n+3)^2*(n+4)*(3*n+5)/720.
  • A107915 (program): a(n) = binomial(n+4,4)*binomial(n+5,4)*binomial(n+6,4)/75.
  • A107916 (program): a(n) = binomial(n+3,2)*binomial(n+4,3)*binomial(n+5,5)/12.
  • A107917 (program): a(n) = (n+1)(n+2)^2*(n+3)^3*(n+4)^2*(n+5)(n^2 + 6n + 10)/86400.
  • A107920 (program): Lucas and Lehmer numbers with parameters (1 +- sqrt(-7))/2.
  • A107929 (program): Smallest list of integers from 1 to n such that sum of any two adjacent terms is a square.
  • A107941 (program): a(n) = (n+1)(n+2)^2*(n+3)^2*(n+4)^2*(n+5)(3n^2 + 13n + 15)/43200.
  • A107942 (program): a(n) = (n+1)(n+2)^3*(n+3)^3*(n+4)(2n+5)/4320.
  • A107943 (program): a(n) = (n+1)*(n+2)^2*(n+3)^2*(n+4)^2*(n+5)*(2n+3)/8640.
  • A107946 (program): Start with S(0)={1}, then S(k+1) equals the concatenation of S(k) with the partial sums of S(k); the limit gives this sequence.
  • A107947 (program): Partial sums of A107946.
  • A107953 (program): Number of chains in the power set lattice of an (n+3)-element set X_(n+3) of specification n^1 2^1 1, that is, n identical objects of one kind, 2 identical objects of another kind and one other kind. It is the same as the number of fuzzy subsets X_(n+3).
  • A107954 (program): Number of chains in the power set lattice, or the number of fuzzy subsets of an (n+4)-element set X_(n+4) with specification n elements of one kind, 3 elements of another and 1 of yet another kind.
  • A107955 (program): Number of chains in the power set lattice or the number of fuzzy subsets of an (n+5)-element set X_(n+5) with specification n elements of one kind, 4 elements of another and 1 of yet another kind.
  • A107957 (program): Partial sums of A107947.
  • A107959 (program): a(n) = (n+1)*(n+2)^2*(n+3)^2*(n+4)*(n^2 + 5*n + 5)/720.
  • A107960 (program): Numbers n such that 11*n - 1 is prime.
  • A107961 (program): Pythagorean semiprimes: products of two Pythagorean primes (A002313).
  • A107962 (program): a(n) = (n+1)(n+2)^2*(n+3)(n+4)(5n^2 + 18n + 15)/720.
  • A107963 (program): a(n) = (n+1)*(n+2)*(n+3)*(n+4)*(5*n^2 + 19*n + 15)/360.
  • A107965 (program): a(n) = (n+1)(n+2)^2*(n+3)^2*(n+4)(11n^4 + 110n^3 + 439n^2 + 820n + 600)/86400.
  • A107966 (program): a(n) = (n+1)(n+2)^3*(n+3)^2*(n+4)(5n^2 + 23n + 30)/8640.
  • A107967 (program): a(n) = (n+1)(n+2)^3*(n+3)^2*(n+4)(n^2 + 4n + 5)/1440.
  • A107968 (program): a(n) = (n+1)*(n+2)^3*(n+3)^2*(n+4)*(3n+5)/1440.
  • A107970 (program): a(n) = (n+1)*(n+2)^3*(n+3)*(2n+3)*(2n+5)/360.
  • A107971 (program): a(n) = (n+1)(n+2)(n+3)(35n^3 + 153n^2 + 232n + 120)/720.
  • A107972 (program): Triangle read by rows: T(n,k) = (k+1)(k+2)(n+2)(3n-2k+3)/12 for 0<=k<=n.
  • A107973 (program): Numbers of the form a^2 + b for a= 21 to 40 and b= 20 to 1 step -1.
  • A107978 (program): Products of two primes of the form 4n+3 (A002145).
  • A107979 (program): a(n) = 4*a(n-1) + 2*a(n-2) for n>1, with a(0)=2, a(1)=9.
  • A107980 (program): Triangle read by rows: T(n,k) = (n+2)*(k+1)*(k+2)*(2*n-k+2)*(2*n-k+3)/24.
  • A107982 (program): Gaussian-Pythagorean semiprimes. Products of a prime of the form 2 or 4n+1 (A002313) and a prime of the form 4n+3 (A002145).
  • A107983 (program): Triangle read by rows: T(n,k) = (k+1)(n+2)(n+3)(n-k+2)(n-k+1)/12 for 0<=k<=n.
  • A107984 (program): Triangle read by rows: T(n,k) = (k+1)*(n+2)*(2n-k+3)*(n-k+1)/6 for 0 <= k <= n.
  • A107985 (program): Triangle read by rows: T(n,k) = (k+1)(n+2)(n-k+1)/2 for 0 <= k <= n.
  • A107986 (program): Composite numbers of the form p+2 where p is prime.
  • A107987 (program): Odd composite numbers of the form p+2 where p is prime.
  • A107991 (program): Complexity (number of maximal spanning trees) in an unoriented simple graph with nodes {1,2,…,n} and edges {i,j} if i + j > n.
  • A107992 (program): Numbers n such that 11*n - 3 is prime.
  • A107994 (program): Numbers n such that 11*n - 2 is prime.
  • A107995 (program): Chebyshev polynomial of the second kind U[n,x] evaluated at x=n+2.
  • A108012 (program): a(n)= 8*a(n-1) -16*a(n-2) +4*a(n-4).
  • A108014 (program): Expansion of (x^2-2*x)/(x^4-x^2+2*x-1).
  • A108019 (program): a(n) = (8^n - 1)*4/7.
  • A108020 (program): a(n) is the number whose binary representation is the concatenation of n strings of the four digits “1100”.
  • A108021 (program): Numbers n whose binary representation is the first Fibonacci(n) binary digits of the pattern 1010101010101010…
  • A108027 (program): Numbers n such that 137*n + 139 is prime.
  • A108028 (program): Numbers k such that 139*k + 137 is prime.
  • A108029 (program): Numbers n such that 149*k + 151 is prime.
  • A108030 (program): Numbers k such that 151*k + 149 is prime.
  • A108031 (program): Inverse Moebius transform of Lucas numbers (A000032).
  • A108032 (program): Triangle T(n,k), 0<=k<=n, read by rows, defined by : T(0,0) = 1, T((n,k) = 0 if n<k or if k<0, T(n,k) = k*T(n-1, k-1) + (2n-2k-1)*T(n-1, k).
  • A108033 (program): n!*(3*n^2-13*n+14)/6.
  • A108035 (program): Triangle read by rows: n-th row is n-th nonzero Fibonacci number repeated n times.
  • A108036 (program): Triangle read by rows: the triangle in A108035 surrounded by a border of 0’s.
  • A108037 (program): Triangle read by rows: n-th row is n-th nonzero Fibonacci number repeated n+1 times.
  • A108038 (program): Triangle read by rows: g.f. = (x+y+x*y)/((1-x-x^2)*(1-y-y^2)).
  • A108039 (program): Replace each entry 2^i(2j+1) of the triangle in A008280 with i and replace 0’s with *’s; then the entries n in the new triangle do not occur beyond diagonal a(n), measured from the left edge and taking the left edge to be diagonal number 1.
  • A108040 (program): Reflection of triangle in A008280 in vertical axis.
  • A108044 (program): Triangle read by rows: right half of Pascal’s triangle (A007318) interspersed with 0’s.
  • A108045 (program): Triangle read by rows: lower triangular matrix obtained by inverting the lower triangular matrix in A108044.
  • A108046 (program): Inverse Moebius transform of Fibonacci numbers 0, 1, 1, 2, 3, 5, 8, …
  • A108047 (program): Concatenation of the previous pair of numbers, with the first two terms both 1.
  • A108051 (program): a(n+1) = 4*(a(n)+a(n-1)) for n>1, a(1)=1, a(2)=6.
  • A108053 (program): Maximum number of diagonals of a regular n-gon that meet at a non-center point.
  • A108058 (program): Numbers n such that 179*n + 181 is prime.
  • A108059 (program): Numbers n such that 181*n + 179 is prime.
  • A108060 (program): Numbers n such that 191*n + 193 is prime.
  • A108061 (program): Numbers n such that 193*n + 191 is prime.
  • A108073 (program): Triangle in A071943 with rows reversed.
  • A108077 (program): Largest prime p such that p-1 divides n.
  • A108078 (program): Determinant of a Hankel matrix with factorial elements.
  • A108079 (program): a(n) = Sum_{i=0..n} C(2n+i,n+i).
  • A108080 (program): Sum_{i=0..n} C(2n+i,n-i).
  • A108081 (program): a(n) = Sum_{i=0..n} binomial(2*n-i, n+i).
  • A108082 (program): Sum_{i=0..n} binomial(2n+i,2i).
  • A108086 (program): Triangle, read by rows, where T(0,0) = 1, T(n,k) = (-1)^(n+k)*T(n-1,k) + T(n-1,k-1); a signed version of Pascal’s triangle.
  • A108087 (program): Array, read by antidiagonals, where A(n,k) = exp(-1)*Sum_{i>=0} (i+k)^n/i!.
  • A108090 (program): Numbers of the form (11^i)*(13^j).
  • A108095 (program): Coefficients of series whose square is the weight enumerator of the [8,4,4] Hamming code (see A002337).
  • A108099 (program): a(n) = 8n^2 + 8n + 4.
  • A108100 (program): (2*n-1)^2+(2*n+1)^2.
  • A108103 (program): Fixed point of the square of the morphism: 1->3, 2->1, 3->121, starting with 1.
  • A108104 (program): Sequence A000930 with terms repeated.
  • A108105 (program): 2^floor(n/5).
  • A108118 (program): Integers not divisible by 3 or 4.
  • A108120 (program): Floor[n*1/Sin[1]], or Beatty sequence for 1/sin(1).
  • A108122 (program): G.f.: (1-2*x^2)/(1-x-2*x^2-x^3).
  • A108124 (program): E.g.f. x/(1+sin(x)).
  • A108125 (program): Expansion of e.g.f.: x/(1 - log(1+x)).
  • A108126 (program): Maximal number of squares of side 1 in an ellipse of semiaxes n,2n.
  • A108131 (program): Array read by antidiagonals: A(k,n) = C(n^k, n).
  • A108136 (program): a(1)=1; a(2)=1; a(3)=1; a(n) = 3*a(n-1) + 2*a(n-2) + a(n-3).
  • A108137 (program): Primes p such that p + 6^k is composite for all k >= 0.
  • A108138 (program): n to the power of the smallest prime divisor of n.
  • A108139 (program): n to the power of the largest prime divisor of n.
  • A108140 (program): a(n) = 4*a(n-1) -3*a(n-2) -2*a(n-3) +a(n-4), n>8.
  • A108141 (program): Least k such that the number (n+1)(n+2)(n+3)…(n+k) >= n^n.
  • A108143 (program): a(n)= 5*a(n-1) -a(n-2) -a(n-3).
  • A108144 (program): Numbers n such that (n-1)/P(n-1) is a power of two > 1, where P(n) is the largest prime factor of n.
  • A108146 (program): a(n)= 4*a(n-1) -a(n-2) -a(n-3).
  • A108151 (program): a(n) = n^2 + 3*n + 1 if prime or 0 if composite.
  • A108152 (program): a(n)= 3*a(n-1) +2*a(n-2) +a(n-3).
  • A108153 (program): a(n) = 3*a(n-1) + 2*a(n-2) + a(n-3).
  • A108154 (program): a(n) = n^2 - n + 1 if prime else 0.
  • A108161 (program): Partial sums of the positive integers n according to the rule: if n is square then add sqrt(n) else add n.
  • A108164 (program): Semiprimes p*q where both p and q are primes of the form 6n+1 (A002476).
  • A108165 (program): a(n)=a(n-1) +A108173(n+1) -A108173(n).
  • A108171 (program): Tribonacci version of A076662 using beta positive real Pisot root of x^3 - x^2 - x - 1.
  • A108172 (program): Semiprimes p*q where p is a prime of the form 6n+1 (A002476) and q is a prime of the form 6n-1 (A007528).
  • A108173 (program): Let beta = A058265. Sequence gives a(n) = 1 + ceiling((n-1)*beta^2).
  • A108174 (program): Partial sums of the positive integers n according to the rule: if n is square then subtract n, otherwise add n.
  • A108177 (program): Integers of the form 2^(4n-1) or 2^(4n), n>0 and their immediate neighbors, together with -1, 0 and 1.
  • A108178 (program): a(n) = (n+1)(n+2)^2*(n+3)^2*(n+4)(7n^2 + 23n + 20)/2880.
  • A108181 (program): Semiprimes of the form 4n + 1.
  • A108187 (program): Numbers n such that 11*n - 5 is prime.
  • A108188 (program): a(n) = (n-1)*(a(n-1)+a(n-2)+a(n-3)).
  • A108189 (program): a(n) = (n-1)*(a(n-2)+a(n-3))
  • A108195 (program): a(n) = n^2 + 5*n - 1.
  • A108196 (program): Expansion of (x-1)*(x+1) / (8*x^2 + 1 - 3*x + x^4 - 3*x^3).
  • A108197 (program): Number of composite numbers between two successive semiprimes.
  • A108198 (program): Triangle read by rows: T(n,k) = binomial(2k+2,k+1)*binomial(n,k)/(k+2) (0 <= k <= n).
  • A108201 (program): Numbers of the form (5^i)*(12^j), with i, j >= 0.
  • A108204 (program): a(n) = 2*(n-1)*a(n-1) -(n-1)*a(n-2) with a(0)=0, a(1)=1.
  • A108205 (program): a(n) = 2*(n-1)*a(n-1)+(n-1)*a(n-2) with a(0)=0, a(1)=1.
  • A108206 (program): a(n)= 3*(n-1)*a(n-1) +(n-1)*a(n-2), with a(0)=1, a(1)=1.
  • A108207 (program): a(n)= 5*(n-1)*a(n-1) -(n-1)*a(n-2), with a(0)=0, a(1)=1.
  • A108208 (program): a(n) = 4*(n-1)*a(n-1) -2*(n-1)*a(n-2), with a(0)=0, a(1)=2.
  • A108209 (program): a(n) = 5*(n-1)*a(n-1) -2*(n-1)*a(n-2) with a(0)=0, a(1)=2.
  • A108210 (program): Let M[n] be the 2 X 2 matrix {{0, -3}, {(n - 1), 5*(n - 1)}} and let v[1] = {0, 1}’, v[n] = M[n]*v[n - 1]’. Then a[n] is the first entry of v[n].
  • A108211 (program): a(n) = 16*n^2 + 1.
  • A108213 (program): a(0)=44; if n odd, a(n) = a(n-1)/2, otherwise a(n) = 4*a(n-1).
  • A108214 (program): Denominator of the O(x^2) term in the Maclaurin series of the square of the Jacobi polynomial P^{a,b}_n(z) about z=1-x for real positive x.
  • A108215 (program): 4-almost primes equal to the product of two successive semiprimes.
  • A108216 (program): Number of semiprimes between 10n and 10n + 9.
  • A108217 (program): a(0) = 1, a(1) = 1, a(n) = n! + (n-2)! for n >= 2.
  • A108218 (program): Numbers of the form (11^i)*(12^j), with i, j >= 0.
  • A108221 (program): Primes of the form ceiling(sqrt(prime(n))).
  • A108225 (program): a(0) = 0, a(1) = 2; for n >= 2, a(n) = (a(n-1) + a(n-2))*(a(n-1) - a(n-2) + 1)/2.
  • A108228 (program): a(n) = (A003961(n) - 1)/2, a permutation of the nonnegative integers.
  • A108229 (program): n occurs Lucas number L(n) times (A000204).
  • A108230 (program): a(1) = 0, a(n) = order of prime A088387(n).
  • A108232 (program): Numbers n such that 11*n - 7 is prime.
  • A108233 (program): Numbers n such that 11*n + 5 is prime.
  • A108245 (program): If n-th prime is 4m - 1, then a(n) = 4m + 1. If n-th prime is 4m + 1, then a(n) = 4m - 1.
  • A108246 (program): Number of labeled 2-regular graphs with no multiple edges, but loops are allowed (i.e., each vertex is endpoint of two (usual) edges or one loop).
  • A108248 (program): a(n) = ceiling(n/24) + ceiling((n+1)/24).
  • A108257 (program): Numbers n such that concatenating n and the sum of factorials of the digits of n produces a prime.
  • A108261 (program): 2nd order recursive series having the property that the product of any two adjacent terms is a triangular number, T(b) = b(b+1)/2 where b equals term a(n) of related series A108262.
  • A108262 (program): Second order recursive series having the property that the product of any two adjacent terms equals 4 times a triangular number. That is a(n)*a(n+1)= 4*T(c) = 2c(c+1), where c = the term a(n+1) of related series A108261.
  • A108263 (program): Triangle read by rows: T(n,k) is the number of short bushes with n edges and k branchnodes (i.e., nodes of outdegree at least two). A short bush is an ordered tree with no nodes of outdegree 1.
  • A108269 (program): Numbers of the form (2*m - 1)*4^k where m >= 1, k >= 1.
  • A108281 (program): Numbers that are both triangular and pentagonal of the second kind.
  • A108282 (program): a(n) = k*a(n-1) + a(n-2) where k = A003842(a); a(0) = 1.
  • A108283 (program): Triangle read by rows, generated from (…, 3, 2, 1).
  • A108285 (program): Triangle read by rows, generated from (1, 2, 3, …).
  • A108286 (program): Triangle read by rows; columns are simple recursive sequences.
  • A108288 (program): Main diagonal of table A060543; a(n) = C((n+1)^2-1, n*(n+1)).
  • A108289 (program): Antidiagonal sums of table A060543.
  • A108292 (program): Row sums of triangle A108290.
  • A108294 (program): a(n) = the least prime p such that p-6n-3 is a power of 2 and 2p-6n-3 is prime, or -1 if no such prime exists.
  • A108295 (program): Values of 2p-6n-3 associated with A108294.
  • A108296 (program): Diagonal sums of the number triangle associated to A086617.
  • A108299 (program): Triangle read by rows, 0 <= k <= n: T(n,k) = binomial(n-[(k+1)/2],[k/2])*(-1)^[(k+1)/2].
  • A108300 (program): a(n+2) = 3*a(n+1) + a(n), with a(0) = 1, a(1) = 5.
  • A108302 (program): Concatenate n and the sum of the digits of n raised to their own power (A045503).
  • A108306 (program): Expansion of (3*x+1)/(1-3*x-3*x^2).
  • A108308 (program): Expansion of 1/(1-x^2*c(2x)), c(x) the g.f. of A000108.
  • A108309 (program): Consider the triangle of odd numbers where the n-th row has the next n odd numbers. The sequence is the number of primes in the n-th row.
  • A108313 (program): Sum of primes q with prime(n) < q < 2*prime(n).
  • A108314 (program): Sum of primes p with n^2 < p < (n+1)^2.
  • A108319 (program): Numbers of the form (2^i)*(3^j)*(7^k), with i, j, k >= 0.
  • A108321 (program): a(n) = n^2 if n^2 is not the difference of two primes; otherwise a(n) = 0.
  • A108340 (program): A083952 read mod 2.
  • A108341 (program): Numbers n such that 997*n - 1009 is prime.
  • A108342 (program): Numbers n such that 1009*n - 997 is prime.
  • A108347 (program): Numbers of the form (3^i)*(5^j)*(7^k), with i, j, k >= 0.
  • A108350 (program): Number triangle T(n,k) = Sum_{j=0..n-k} binomial(k,j)*binomial(n-j,k)*((j+1) mod 2).
  • A108351 (program): Diagonal sums of symmetric triangle A108350.
  • A108354 (program): Expansion of 1/((1-x)^2(1+x^2)^2) in powers of x.
  • A108355 (program): Expansion of (1+2x^2)/((1-x)^2(1+x^2)^2).
  • A108356 (program): Count, repeating multiples of 3 four times, all other numbers twice.
  • A108357 (program): Expansion of (1+x^2+x^4)/(1-x^8).
  • A108360 (program): Expansion of (1-2x)^2/((1-x)^2(1-2x-x^2)^2).
  • A108362 (program): Pair reversal of Fibonacci numbers.
  • A108366 (program): L(n,n), where L is defined as in A108299.
  • A108367 (program): L(n,-n), where L is defined as in A108299.
  • A108368 (program): Coefficients of x/(1-3*x-3*x^2-x^3).
  • A108369 (program): Coefficients of x/(1+3*x+3*x^2-x^3).
  • A108396 (program): Triangle read by rows: T(n,k) = n*(1+n^k)/2, 0<=k<=n.
  • A108397 (program): Sums of rows of the triangle in A108396.
  • A108398 (program): a(n) = n*(1 + n^n)/2.
  • A108400 (program): a(n) = Product_{k = 0..n} (2^k * k!).
  • A108404 (program): Expansion of (1-4x)/(1-8x+11x^2).
  • A108411 (program): a(n) = 3^floor(n/2). Powers of 3 repeated.
  • A108412 (program): Expansion of (1 + x + x^2)/(1 - 4x^2 + x^4).
  • A108413 (program): Expansion of (1+x+5x^2+2x^3) / (1-4x^2+x^4).
  • A108414 (program): Number of integer k:s for which max{x^(k-x) | x integer, 0<x<k} = n^(k-n).
  • A108415 (program): a(n) = 1, 2 or 3 (resp.) if prime(n) is weak, balanced or strong (resp.).
  • A108424 (program): Number of paths from (0,0) to (3n,0) that stay in the first quadrant, consist of steps u=(2,1), U=(1,2), or d=(1,-1) and do not touch the x-axis, except at the endpoints.
  • A108426 (program): Triangle read by rows: T(n,k) is number of paths from (0,0) to (3n,0) that stay in the first quadrant (but may touch the horizontal axis), consisting of steps u=(2,1),U=(1,2), or d=(1,-1) and have k peaks of the form Ud.
  • A108427 (program): Number of peaks of the form Ud in all paths from (0,0) to (3n,0) that stay in the first quadrant (but may touch the horizontal axis), consisting of steps u=(2,1), U=(1,2), or d=(1,-1).
  • A108429 (program): Triangle read by rows: T(n,k) is number of paths from (0,0) to (3n,0) that stay in the first quadrant (but may touch the horizontal axis), consisting of steps u=(2,1), U=(1,2), or d=(1,-1) and have k down steps (d).
  • A108430 (program): Number of d steps in all paths from (0,0) to (3n,0) that stay in the first quadrant (but may touch the horizontal axis), consisting of steps u=(2,1), U=(1,2), or d=(1,-1).
  • A108432 (program): Number of paths from (0,0) to (3n,0) that stay in the first quadrant (but may touch the horizontal axis), consisting of steps u=(2,1),U=(1,2), or d=(1,-1) and have no hills (a hill is either a ud or a Udd starting at the x-axis).
  • A108434 (program): Number of paths from (0,0) to (3n,0) that stay in the first quadrant (but may touch the horizontal axis), consisting of steps u=(2,1),U=(1,2), or d=(1,-1) and have no hills of the form ud (a hill is either a ud or a Udd starting at the x-axis).
  • A108436 (program): Number of returns to the x-axis in all paths from (0,0) to (3n,0) that stay in the first quadrant (but may touch the horizontal axis), consisting of steps u=(2,1), U=(1,2), or d=(1,-1).
  • A108440 (program): Triangle read by rows: T(n,k) is number of paths from (0,0) to (3n,0) that stay in the first quadrant (but may touch the horizontal axis), consisting of steps u=(2,1), U=(1,2), or d=(1,-1) and having k u=(2,1) steps among the steps leading to the first d step.
  • A108442 (program): Number of paths from (0,0) to (3n,0) that stay in the first quadrant (but may touch the horizontal axis), consisting of steps u=(2,1), U=(1,2), or d=(1,-1) and having only u steps among the steps leading to the first d step.
  • A108447 (program): Number of paths from (0,0) to (3n,0) that stay in the first quadrant (but may touch the horizontal axis), consisting of steps u=(2,1),U=(1,2), or d=(1,-1) and have no peaks of the form ud.
  • A108448 (program): Number of peaks of the form ud in all paths from (0,0) to (3n,0) that stay in the first quadrant (but may touch the horizontal axis), consisting of steps u=(2,1), U=(1,2), or d=(1,-1).
  • A108449 (program): Number of paths from (0,0) to (3n,0) that stay in the first quadrant (but may touch the horizontal axis), consisting of steps u=(2,1),U=(1,2), or d=(1,-1) and having no pyramids (a pyramid is a sequence u^pd^p or U^pd^(2p) for some positive integer p, starting at the x-axis).
  • A108450 (program): Number of pyramids in all paths from (0,0) to (3n,0) that stay in the first quadrant (but may touch the horizontal axis), consisting of steps u=(2,1), U=(1,2), or d=(1,-1) (a pyramid is a sequence u^pd^p or U^pd^(2p) for some positive integer p, starting at the x-axis).
  • A108452 (program): Number of paths from (0,0) to (3n,0) that stay in the first quadrant (but may touch the horizontal axis), consisting of steps u=(2,1),U=(1,2), or d=(1,-1) and having no pyramids of the first kind (a pyramid of the first kind is a sequence u^pd^p for some positive integer p, starting at the x-axis).
  • A108453 (program): Number of pyramids of the first kind in all paths from (0,0) to (3n,0) that stay in the first quadrant (but may touch the horizontal axis), consisting of steps u=(2,1),U=(1,2), or d=(1,-1) (a pyramid of the first kind is a sequence u^pd^p for some positive integer p, starting at the x-axis).
  • A108474 (program): Expansion of 1/((1-2x)*(1+4x^2)).
  • A108475 (program): Expansion of (1-3*x) / (1-5*x-5*x^2+x^3).
  • A108476 (program): Expansion of (1-4x)/(1-6x-12x^2+8x^3).
  • A108477 (program): A symmetric number triangle based on 2^n.
  • A108478 (program): Diagonal sums of number triangle A108477.
  • A108479 (program): Diagonal sums of number triangle A086645.
  • A108480 (program): Expansion of (1-x-2x^2)/(1-2x-3x^2-4x^3+4x^4).
  • A108484 (program): Sum binomial(2n-2k,2k)3^k, k=0..floor(n/2).
  • A108485 (program): Sum binomial(2n-2k,2k)2^(n-k), k=0..floor(n/2).
  • A108486 (program): Sum binomial(2n-2k,2k)3^k*2^(n-k), k=0..floor(n/2).
  • A108487 (program): Sum binomial(2n-2k,2k)10^(n-k), k=0..floor(n/2).
  • A108488 (program): Expansion of 1/sqrt(1 -2*x -3*x^2 -4*x^3 +4*x^4).
  • A108489 (program): Expansion of 1/sqrt(1-2x-5x^2-6x^3+9x^4).
  • A108490 (program): Expansion of 1/sqrt(1-4x-8x^2-24x^3+36x^4).
  • A108494 (program): Expansion of f(-q) / f(q) in powers of q where f() is a Ramanujan theta function.
  • A108495 (program): a(n) = (n^7 - n)/6.
  • A108497 (program): Triangle read by rows: T(n,k) = k^(n+1)-k mod n, showing 1<=k<=n.
  • A108498 (program): Triangle read by rows: T(n,k) = sum_i{1<=i<=n} k^i mod n, showing 1<=k<=n.
  • A108499 (program): Number of values of k (1<=k<=n) where k^(n+1) = k mod n, or equivalently where sum_i{1<=i<=n} k^i = 0 mod n.
  • A108500 (program): Number of values of k (1<=k<=n) where k^(n+1) != k mod n, or equivalently where sum_i{1<=i<=n} k^i != 0 mod n.
  • A108513 (program): Numbers of the form (2^i)*(5^j)*(7^k), with i, j, k >= 0.
  • A108514 (program): If n is a power of 2, a(n)=n; otherwise a(n) = (p-1)*n/p where p = smallest odd prime divisor of n.
  • A108520 (program): Expansion of 1/(1+2*x+2*x^2).
  • A108524 (program): Number of ordered rooted trees with n generators.
  • A108546 (program): Lexicographically earliest permutation of primes such that for n>1 forms 4*k+1 and 4*k+3 alternate.
  • A108552 (program): Integer values of (1*2*…*k)/(1+2+…+k) = k!/T(k) = A000142(k)/A000217(k), k>=1.
  • A108561 (program): Triangle read by rows: T(n,0)=1, T(n,n)=(-1)^n, T(n+1,k)=T(n,k-1)+T(n,k) for 0 < k < n.
  • A108562 (program): Primes of the form prime(n) + prime(n+1) - 2n - 1.
  • A108568 (program): a(n) = prime(n) + prime(n+1) - 2n - 1.
  • A108570 (program): Squares of lesser of twin primes.
  • A108576 (program): Number of 3 X 3 magic squares (with distinct positive entries) having all entries < n.
  • A108577 (program): Number of symmetry classes of 3 X 3 magic squares (with distinct positive entries) having all entries < n.
  • A108578 (program): Number of 3 X 3 magic squares with magic sum 3n.
  • A108579 (program): Number of symmetry classes of 3 X 3 magic squares (with distinct positive entries) having magic sum 3n.
  • A108580 (program): Numbers whose sum of bits when written in binary > sum of decimal digits.
  • A108581 (program): Positive triangular numbers repeated their own number of times.
  • A108582 (program): n appears n^3 times.
  • A108584 (program): Numbers k such that 10*k - 97 is prime.
  • A108586 (program): Floor(2*n*Pi/(2*Pi-1)).
  • A108587 (program): Floor(n/(1-sin(1))).
  • A108588 (program): Numbers n such that 10*n + 97 is prime.
  • A108589 (program): Floor(n*Pi/(Pi-2)).
  • A108594 (program): Numbers n such that 10*n + 101 is prime.
  • A108595 (program): Numbers n such that 10*n + 103 is prime.
  • A108598 (program): Floor(n*((5+sqrt(5))/4)).
  • A108600 (program): Number of freely braided permutations of length n; the freely braided permutations are those that avoid 3421, 4231, 4312 and 4321.
  • A108601 (program): Numbers n such that 7*n - 911 is prime.
  • A108604 (program): Squares of the form prime(k)*prime(k+1) + 2*prime(k+1).
  • A108605 (program): Semiprimes with prime sum of factors: twice the lesser of the twin prime pairs.
  • A108611 (program): Excess of Beatty-function of 1/sin(1) over n.
  • A108612 (program): Beatty-2 (or nested Beatty) sequence for 1/sin(1).
  • A108613 (program): Excess of Beatty-2 function of 1/sin(1) over n^2.
  • A108623 (program): G.f. satisfies x = (A(x)-(A(x))^2)/(1-A(x)-(A(x))^2).
  • A108624 (program): G.f. satisfies x = (A(x)+(A(x))^2)/(1-A(x)-(A(x))^2).
  • A108625 (program): Square array, read by antidiagonals, where row n equals the crystal ball sequence for A_n lattice.
  • A108626 (program): Antidiagonal sums of square array A108625, in which row n equals the crystal ball sequence for A_n lattice.
  • A108627 (program): Logarithmic g.f.: Sum_{n>=1} a(n)/n*x^n = log(G108626(x)), where G108626(x) is g.f. for A108626.
  • A108628 (program): n-th term of the crystal ball sequence for A_{n+1} lattice for n >= 0.
  • A108632 (program): Semiprimes with prime digits (only digits 2,3,5,7 in semiprimes).
  • A108634 (program): Semiprimes with ordered digits.
  • A108636 (program): Semiprimes with even digits.
  • A108644 (program): Square table T(n,n) read by ascending antidiagonals: T(i,i)=i*i, if i>j T(i,j)=i*(i-1)+j, if j>i T(i,j)=(j-1)*(j-1)+i.
  • A108645 (program): a(n) = (n+1)(n+2)^2*(n+3)^2*(n+4)(2n^2 + 6n + 5)/720.
  • A108647 (program): a(n) = (n+1)^2*(n+2)^2*(n+3)^2*(n+4)/144.
  • A108648 (program): a(n) = (n+1)^2*(n+2)^3*(n+3)/24.
  • A108649 (program): a(n) = (n+1)(n+2)(n+3)(13n^3 + 69n^2 + 113n + 60)/360.
  • A108650 (program): a(n) = (n+1)^2*(n+2)*(n+3)*(3*n+4)/24.
  • A108651 (program): Multiples of 8 that are divisible by no prime > 5.
  • A108662 (program): Numbers whose sum of squares of digits is a prime.
  • A108666 (program): Number of (1, 1)-steps in all Delannoy paths of length n.
  • A108667 (program): Triangle read by rows: T(n,k) = 9k*n + 14(n+k) + 20 (0 <= k <= n).
  • A108669 (program): Triangle read by rows: T(n,k) = 11*k*n + 14*(n+k) + 20 (0 <= k <= n).
  • A108670 (program): a(n) = (n+1)(n+2)^3*(n+3)(n+4)(5n^2 + 16n + 15)/1440.
  • A108671 (program): a(n) = (n+1)(n+2)^3*(n+3)(13n^2 + 37n + 30)/720.
  • A108673 (program): a(n) = (n+1)(n+2)(n+3)(2n+3)(10n^2 + 27n + 20)/360.
  • A108674 (program): a(n) = (n+1)^2 * (n+2)^2 * (2*n+3) / 12.
  • A108675 (program): a(n) = (n+1)*(n+2)*(61*n^4 + 366*n^3 + 845*n^2 + 888*n + 360)/720.
  • A108676 (program): a(n) = (n+1)^2*(n+2)*(5*n^2 + 15*n + 12)/24.
  • A108677 (program): a(n) = (n+1)*(n+2)*(n+3)*(n+4)*(19*n^2 + 47*n + 30)/720.
  • A108678 (program): a(n) = (n+1)^2*(n+2)*(2n+3)/6.
  • A108679 (program): a(n) = (n+1)*(n+2)^2*(n+3)^2*(n+4)^2*(n+5)^2*(n+6)/86400.
  • A108680 (program): Kekulé numbers for certain benzenoids.
  • A108681 (program): a(n) = (n+1)*(n+2)^2*(n+3)*(n+4)*(n+5)*(2*n+3)/720.
  • A108682 (program): a(n) = (n+1)*(n+2)^2*(n+3)*(n+4)*(4*n^2+15*n+15)/720.
  • A108683 (program): a(n) = (n+1)*(n+2)*(n+3)*(n+4)*(7*n^2 + 20*n + 15)/360.
  • A108684 (program): a(n) = (n+1)*(n+2)*(n+3)*(19*n^3 + 111*n^2 + 200*n + 120)/720.
  • A108689 (program): Smallest integer q >= 1 such that difference between q*Pi and the nearest integer is <= 1/n.
  • A108696 (program): Generated by a sieve: see comments.
  • A108704 (program): Number of partitions of 112233…nn into n pairs.
  • A108711 (program): Number of partitions of n with floor(2n/3) parts.
  • A108713 (program): Number of possible canonical minimal transition-complete sequences over n objects.
  • A108715 (program): First differences of A025480.
  • A108719 (program): Primes which can be partitioned into a sum of distinct primes in more than one way.
  • A108720 (program): a(n)=a(n-1)+sum of digits(a(n-1))*sum of digits(a(n-2)).
  • A108724 (program): Numbers n such that 11*n + 17 is prime.
  • A108725 (program): Numbers n such that 11*n + 19 is prime.
  • A108726 (program): Numbers n such that 11*n + 29 is prime.
  • A108727 (program): Numbers n such that 11*n + 31 is prime.
  • A108732 (program): a(0)=22; if n odd, a(n) = a(n-1)/2, otherwise a(n) = 4*a(n-1).
  • A108733 (program): Expansion of (1+18*x)^(1/3).
  • A108734 (program): Expansion of (1 + 24*x)^(1/2).
  • A108735 (program): Expansion of sqrt(1 + 12*x).
  • A108738 (program): a(n) = n/(smallest odd prime divisor of n), if any.
  • A108741 (program): Member r=100 of the family of Chebyshev sequences S_r(n) defined in A092184.
  • A108742 (program): Row sums of a triangle related to the Jacobsthal polynomials.
  • A108744 (program): Decimal expansion of B = Sum_{ n > 0 } 1/A007559(n).
  • A108747 (program): Triangle read by rows: T(n,k) is the number of Grand Dyck paths of semilength n and having k returns to the x-axis.
  • A108751 (program): Numbers n such that 11*n - 911 is prime.
  • A108752 (program): Numbers k such that 12 divides k*(k+1).
  • A108753 (program): Difference between the n-th partial sum of the squares (A000330) and the n-th partial sum of the primes (A007504).
  • A108754 (program): Difference between partial sum of the first n primes and n^2.
  • A108756 (program): A triangle related to the Jacobsthal polynomials.
  • A108757 (program): Numbers n such that 1000n + 911 is prime.
  • A108758 (program): a(n) = 2*a(n-1) - a(n-4) + a(n-5) with a(-1)=a(0)=a(1)=1, a(2)=2, a(3)=4, a(4)=7.
  • A108762 (program): Numbers n such that 911*n + 13 is prime.
  • A108763 (program): If n-th prime is 8m+1, then a(n) = 8m+3. If n-th prime is 8m+3, then a(n) = 8m+5. If n-th prime is 8m+5, then a(n) = 8m+7. If n-th prime is 8m+7, then a(n) = 8m+1.
  • A108765 (program): G.f. (1 - x + x^2)/((1-3*x)*(x-1)^2).
  • A108766 (program): a(n) = A007290(n+2) - 1 = 2*C(n+2,3) - 1.
  • A108767 (program): Triangle read by rows: T(n,k) is number of paths from (0,0) to (3n,0) that stay in the first quadrant (but may touch the horizontal axis), consisting of steps u=(1,1), d=(1,-2) and have k peaks (i.e., ud’s).
  • A108769 (program): Numbers m such that m^2 + (m+1)^2 is a semiprime.
  • A108771 (program): Numbers of the form (12^i)*(13^j), with i, j >= 0.
  • A108773 (program): Concatenation of n and the sum of the digits of n.
  • A108775 (program): a(n) = floor(sigma(n)/n).
  • A108782 (program): Difference between n and the largest number with the same digit set as n.
  • A108784 (program): Difference between A107757 and A107755.
  • A108786 (program): Yet another version of the Catalan triangle A008315.
  • A108791 (program): a(2n) = -5*(fibonacci(6n+2))^2, a(2n+1) = (lucas(6n+5))^2.
  • A108793 (program): Semiprimes that can be partitioned into a sum of semiprimes in more than one way.
  • A108803 (program): A108802 read mod 4.
  • A108804 (program): Self-convolution of A010060 (Thue-Morse sequence).
  • A108805 (program): A108804 read mod 4.
  • A108812 (program): 11^n mod 50.
  • A108813 (program): Decimal expansion of the continued fraction 2/(5+4/(7+6/(9+8/(11+10/(13+12/…
  • A108815 (program): Indices of triangular numbers which are products of 3 primes.
  • A108838 (program): Triangle of Dyck paths counted by number of long interior inclines.
  • A108850 (program): Number of 1’s in the binary expansion of the repunits.
  • A108851 (program): a(n) = 4*a(n-1) + 3*a(n-2), a(0) = 1, a(1) = 2.
  • A108852 (program): Number of Fibonacci numbers <= n.
  • A108854 (program): Numbers n such that 10*n - 127 is prime.
  • A108855 (program): Numbers n such that 10*n + 127 is prime.
  • A108856 (program): Numbers n such that 10*n - 131 is prime.
  • A108857 (program): Numbers n such that 10*n + 131 is prime.
  • A108863 (program): Number of Dyck paths containing exactly one UUUD.
  • A108865 (program): Numbers n such that the perfect deficiency of n (A109883) is prime.
  • A108866 (program): Numerator of Sum_{k=1..n} 2^k/k.
  • A108869 (program): E.g.f. : exp(6x)/(1-x).
  • A108870 (program): Tokuda’s good set of increments for Shell sort.
  • A108872 (program): Sums of ordinal references for a triangular table read by columns, top to bottom.
  • A108873 (program): Numbers n whose base 3 representations, interpreted as base 10 integers, are semiprimes.
  • A108874 (program): Numbers n such that 41*n + 43 is prime.
  • A108882 (program): Period doubling sequence starting with ‘1 0 1’.
  • A108891 (program): Triangle read by rows: T(n,k) = number of Schroeder (or royal) n-paths (A006318) containing k returns to the diagonal y=x. (A northeast step lying on y=x contributes a return.)
  • A108895 (program): Partial sums of quadruple factorial numbers n!!!! (A007662).
  • A108896 (program): Numbers whose outer two digits are 9’s and inner digits are 4’s.
  • A108898 (program): a(n+3) = 3*a(n+2) - 2*a(n), a(0) = -1, a(1) = 1, a(2) = 3.
  • A108899 (program): Numbers n such that 11*n + 2357 is prime.
  • A108902 (program): Numbers n such that 23*n + 2357 is prime.
  • A108903 (program): Numbers such that the outer 2 digits are 9 and the inner digits are 5.
  • A108904 (program): Numbers such that the outer two digits are 9’s and the inner digits are 7’s.
  • A108906 (program): First differences of A006899.
  • A108908 (program): Largest n-digit number coprime to n.
  • A108909 (program): Sum of k-digit multiples of n where k is the number of digits in n.
  • A108911 (program): Difference between n and the sum of the factorials of its digits.
  • A108916 (program): Triangle of Schroeder paths counted by number of diagonal steps not preceded by an east step.
  • A108918 (program): Reversed binary words in reversed lexicographic order.
  • A108919 (program): Number of series-reduced labeled trees with n nodes.
  • A108920 (program): Number of positive integers k>n such that n+k divides n^2+k^2.
  • A108922 (program): Expansion of 1/((x^8+1)*(x-1)^2).
  • A108923 (program): Expansion of 1/((x^8+1)*(1-x)^3).
  • A108924 (program): J(n)^2+J(n+1)^2, with J(n) the Jacobsthal number A001045(n).
  • A108928 (program): a(n) = 8*n^2 - 3.
  • A108929 (program): Expansion of (1-x^4-2*x^3)/((x-1)*(x^2+x+1)*(x^2+4*x-1)).
  • A108931 (program): a(2n) = -A106328(n), a(2n+1) = A054488(n).
  • A108935 (program): Numbers n such that 7*n + 911 is prime.
  • A108936 (program): Numbers n such that 11*n + 911 is prime.
  • A108937 (program): Numbers n such that 911*n + 11 is prime.
  • A108938 (program): Numbers n such that 911*n + 7 is prime.
  • A108942 (program): Degrees of irreducible representations of SL(2,7).
  • A108943 (program): Square root of A108945(n).
  • A108945 (program): Squares equal to the sum of the n-th twin prime pair and minimal square k^2.
  • A108946 (program): a(2n) = A001570(n), a(2n+1) = -A007654(n+1).
  • A108951 (program): Primorial inflation of n: Fully multiplicative with a(p) = p# for prime p, where x# is the primorial A034386(x).
  • A108953 (program): Convolution of 3^n*n! and n!.
  • A108954 (program): a(n) = pi(2*n) - pi(n). Number of primes in the interval (n,2n].
  • A108955 (program): Floor(Li(2n) - Li(n)).
  • A108956 (program): Floor(R(2n) - R(n)).
  • A108958 (program): Number of unordered pairs of distinct length-n binary words having the same number of 1’s.
  • A108964 (program): Write n in balanced ternary notation, omit any zeros and form the left-to-right alternating sum mod 3.
  • A108969 (program): Numbers n such that 43*n + 41 is prime.
  • A108975 (program): Product of all primes with primitive root 2 less than or equal to some prime with primitive root 2.
  • A108976 (program): Numbers n such that 17*n + 19 is prime.
  • A108977 (program): Numbers n such that 19*n + 17 is prime.
  • A108978 (program): Numbers k such that 29*k + 31 is prime.
  • A108979 (program): Numbers n such that 31*n + 29 is prime.
  • A108980 (program): Numbers k such that the string k9111 is prime.
  • A108981 (program): a(n) = 3a(n-1) + 4a(n-2), a(0) = 1, a(1) = 5.
  • A108982 (program): Inverse binomial of A003949.
  • A108983 (program): Inverse binomial transform of A003950.
  • A108984 (program): Inverse binomial transform of A003951.
  • A108985 (program): Expansion of (x+1)*(x^3-x^2-x-1)/((1-x)*(x^2+2*x-1)*(x^2+x+1)).
  • A109001 (program): Triangle, read by rows, where g.f. of row n equals the product of (1-x)^n and the g.f. of the coordination sequence for root lattice B_n, for n >= 0.
  • A109002 (program): Maximal difference between two n-digit numbers.
  • A109004 (program): Table of gcd(n,m) read by antidiagonals, n >= 0, m >= 0.
  • A109007 (program): a(n) = gcd(n,3).
  • A109008 (program): a(n) = gcd(n,4).
  • A109009 (program): a(n) = gcd(n,5).
  • A109010 (program): a(n) = gcd(n,7).
  • A109011 (program): a(n) = gcd(n,8).
  • A109012 (program): a(n) = gcd(n,9).
  • A109013 (program): a(n) = gcd(n,10).
  • A109014 (program): a(n) = gcd(n,11).
  • A109015 (program): a(n) = gcd(n,12).
  • A109016 (program): Concatenate n and the sum of factorials of the digits of n.
  • A109017 (program): a(n) = Kronecker symbol (-6/n).
  • A109020 (program): (2*7^n - 3*3^n + 1)/6.
  • A109021 (program): (2*7^n - 6*3^n + 4)/6.
  • A109033 (program): Number of permutations in S_n avoiding the patterns 1342 and 2143.
  • A109034 (program): First differences of A109033.
  • A109039 (program): Expansion of eta(q) * eta(q^3) * (eta(q^4) * eta(q^6) / eta(q^12))^2 in powers of q.
  • A109040 (program): Expansion of 1-eta(q)eta(q^3)(eta(q^4)eta(q^6))^2/eta(q^12)^2 in powers of q.
  • A109041 (program): Expansion of eta(q)^9 / eta(q^3)^3 in powers of q.
  • A109042 (program): Table read by antidiagonals: T(n,m) = lcm(n,m) (n >= 0, m >= 0).
  • A109043 (program): a(n) = lcm(n,2).
  • A109044 (program): a(n) = lcm(n,3).
  • A109045 (program): a(n) = lcm(n,4).
  • A109046 (program): a(n) = lcm(n, 5).
  • A109047 (program): a(n) = lcm(n, 6).
  • A109048 (program): a(n) = lcm(n, 7).
  • A109049 (program): a(n) = lcm(n, 8).
  • A109050 (program): a(n) = lcm(n, 9).
  • A109051 (program): a(n) = lcm(n,10).
  • A109052 (program): a(n) = lcm(n,11).
  • A109053 (program): a(n) = lcm(n,12).
  • A109064 (program): Expansion of eta(q)^5 / eta(q^5) in powers of q.
  • A109065 (program): Numerator of the fraction due in month n of the total interest for a one-year installment loan based on the Rule of 78s (each denominator is 78).
  • A109066 (program): Number of prime digits in n-th prime.
  • A109067 (program): 3-almost primes of the form semiprime + 1.
  • A109075 (program): Number of primes which use each of 0-to-n decimal digits exactly once.
  • A109078 (program): Number of symmetric Dyck paths of semilength n and having no hills (i.e., no peaks at level 1).
  • A109081 (program): Reversion of x*(1-x)*(1-x^2)*(1-x^3)/(1-x^6).
  • A109082 (program): Depth of rooted tree having Matula-Goebel number n.
  • A109083 (program): Convolution of A002324 and A010815.
  • A109091 (program): Expansion of (1 - eta(q)^5 / eta(q^5)) / 5 in powers of q.
  • A109094 (program): Length of the longest path (repeated edges not allowed) between two arbitrary, distinct nodes in K_n, the complete graph on n vertices.
  • A109105 (program): a(n) = (8*sqrt(5)/25)((sqrt(5) + 2)((15 + 5*sqrt(5))/2)^n + (sqrt(5) - 2)((15 - 5*sqrt(5))/2)^n.
  • A109106 (program): a(n) = (1/sqrt(5))*((sqrt(5) + 1)*((15 + 5*sqrt(5))/2)^(n-1) + (sqrt(5) - 1)*((15 - 5*sqrt(5))/2)^(n-1)).
  • A109107 (program): a(n) = (1/sqrt(26))((5+sqrt(26))^(n+1)-(5-sqrt(26))^(n+1)).
  • A109108 (program): a(n) = 10a(n-1) + a(n-2), a(0)=1, a(1)=9.
  • A109109 (program): a(0)=1, a(1)=4, a(n) = 10a(n-1) + a(n-2).
  • A109110 (program): a(n) = 2a(n-1) + a(n-2) - a(n-3); a(0)=4, a(1)=9, a(2)=20.
  • A109112 (program): a(n) = 6*a(n-1) - 3*a(n-2), a(0)=2, a(1)=13.
  • A109113 (program): a(n) = 6a(n-1) + 3a(n-2), a(0)=2, a(1)=14.
  • A109114 (program): a(n) = 5*a(n-1) - 3*a(n-2), a(0)=1, a(1)=6.
  • A109115 (program): a(n) = 4*a(n-1) + 3*a(n-2), a(0)=1, a(1)=6.
  • A109116 (program): a(n) = (n+1)^3*(n+2)^2*(n+5).
  • A109117 (program): a(n) = (n+1)^3*(2n+1)(5n+1).
  • A109118 (program): a(n) = 2*(n^2 + 3*n + 1)^3.
  • A109119 (program): a(n) = 2(5n^2 + 5n + 1)^3.
  • A109120 (program): a(n) = 10*(n+1)^3*(n+2)*(5*n+7)^2.
  • A109121 (program): a(n) = 10(n+1)^3*(2n+1)(7n+5)^2.
  • A109123 (program): a(n) = 4*(n+1)^2*(n+3)^2*(5*n^2 + 20*n + 12).
  • A109124 (program): a(n) = (n+1)*(n+2)^3*(n+3)^4*(n+4)^3*(n+5)*(2n+5)*(2n+7)/7257600.
  • A109127 (program): Expansion of q^(-1/8) * (eta(q^3) - eta(q)^3) / 3 in powers of q.
  • A109128 (program): Triangle read by rows: T(n,k) = T(n-1,k-1) + T(n-1,k) + 1 for 0<k<n, T(n,0) = T(n,n) = 1.
  • A109129 (program): Width (i.e., number of non-root vertices having degree 1) of the rooted tree with Matula-Goebel number n.
  • A109130 (program): Magic constant of smallest order-n perfect magic cube.
  • A109133 (program): Numbers k such that (sum of digits)*(number of digits) + 1 is prime.
  • A109134 (program): Decimal expansion of Phi, the real root of the equation 1/x = (x-1)^2.
  • A109139 (program): Numerators associated with the continued fraction of the differences of consecutive prime numbers.
  • A109140 (program): Denominators associated with A109139.
  • A109161 (program): Triangle read by rows: T(n, k) = n*(n+9) + k + 5, with T(0, 0) = 5 and T(1, 0) = 15.
  • A109163 (program): a(n) = A019565(n-th prime).
  • A109164 (program): a(n) = 4*a(n-1) - 4*a(n-2) + a(n-3), n >= 3; a(0)=1, a(1)=6, a(2)=20.
  • A109165 (program): a(n) = 5*a(n-2) - 2*a(n-4), n >= 4; a(n) = (1/6)*(-1)^n + 4/3)*2^n - 1/2.
  • A109168 (program): Continued fraction expansion of the constant x (A109169) such that the continued fraction of 2*x yields the continued fraction of x interleaved with the positive even numbers.
  • A109170 (program): Continued fraction expansion of 2*x which equals the continued fraction of x (A109168) interleaved with positive even numbers.
  • A109173 (program): Recursive form of A109845 but with a(1)=1.
  • A109174 (program): Number of steps to reach 1 in the modified `3x+1’-type problem defined by: If a_n is even then a_(n+1) = a_n/2. If a_n is = 1 (mod 4) then a_(n+1) = 3a_n+1. If a_n is = 3 (mod 4) then a_(n+1) = 3a_n-1.
  • A109175 (program): Minimum number of moves to solve the first Panex puzzle of order n of transferring a side tower to the center column.
  • A109180 (program): The set N of numbers such that each positive integer can be written in the form F + n, where F is a Fibonacci number and n in N, in an even number of ways.
  • A109187 (program): Triangle read by rows: T(n,k) is number of Grand Motzkin paths of length n having k (1,0)-steps.
  • A109188 (program): Number of (1,0) steps in all Grand Motzkin paths of length n.
  • A109190 (program): Number of (1,0)-steps at level zero in all Grand Motzkin paths of length n.
  • A109194 (program): Number of returns to the x-axis (i.e., d or u steps hitting the x-axis) in all Grand Motzkin paths of length n. (A Grand Motzkin path of length n is a path in the half-plane x>=0, starting at (0,0), ending at (n,0) and consisting of steps u=(1,1), d=(1,-1) and h=(1,0).).
  • A109196 (program): Number of returns to the x-axis from above (i.e., d steps hitting the x-axis) in all Grand Motzkin paths of length n.
  • A109214 (program): Product of a(n-1) and digit reversal of a(n-2).
  • A109217 (program): a(n) is the binary string of length n+1 that has 0’s at indices that are squares and 1’s elsewhere, where the most significant digit has index 0.
  • A109220 (program): Expansion of (1+x-x^2)/(1-2x-2x^2+x^4).
  • A109221 (program): A number triangle related to the Fibonacci polynomials.
  • A109222 (program): Row sums of a triangle related to the Fibonacci polynomials.
  • A109223 (program): Number triangle related to the Fibonacci polynomials.
  • A109225 (program): Triangle read by rows: T(n,0) = T(n,n) = 1 and for 0 < k < n: T(n,k) = T(n-1,k-1) + 1 - T(n-1,k-1) mod 2 + T(n-1,k).
  • A109227 (program): Binary strings that have 1’s where primes occur, 0’s elsewhere and every term ends with the n-th prime index.
  • A109231 (program): a(n) = floor(n*cosh(1)).
  • A109232 (program): a(n) = floor(n*(e^2+1)/(e-1)^2).
  • A109234 (program): a(n) = floor(n*sinh(1)).
  • A109235 (program): a(n) = floor(n*(e^2-1)/(e^2-2*e-1)).
  • A109237 (program): a(n) = floor(n*coth(1)).
  • A109238 (program): a(n) = floor(n*(e^2+1)/2).
  • A109241 (program): Expansion of 1/((1-10*x)*(1-100*x)).
  • A109242 (program): Expansion of 1/((1-x)(1-10x)(1-100x)).
  • A109244 (program): A tree-node counting triangle.
  • A109246 (program): Riordan array (1-x-2x^2,x(1-x)).
  • A109247 (program): Expansion of (1 - 3*x^2 - 3*x^3 + x^4)/(1 + x^4).
  • A109248 (program): Expansion of (1-x-2*x^2)/(1-x^2+x^3).
  • A109253 (program): Number of elements of the Weyl group of type B where a reduced word contains all of the simple reflections.
  • A109255 (program): a(n) = (p^2 - 1) / 12, where p is the n-th prime of the form 4*k+1.
  • A109256 (program): a(n) = n^6 - 11n^4 + 36n^2 - 36.
  • A109259 (program): a(n) = floor(n*sqrt(2)^sqrt(2)).
  • A109260 (program): a(n) = floor(n*sqrt(2)^sqrt(2)/(sqrt(2)^sqrt(2)-1)).
  • A109262 (program): A Catalan transform of the Fibonacci numbers.
  • A109263 (program): A Catalan transform of F(n-1)-0^n.
  • A109264 (program): Riordan array (1-x-x^2,x(1-x)).
  • A109265 (program): Row sums of Riordan array (1-x-x^2,x(1-x)).
  • A109266 (program): Diagonal sums of Riordan array (1-x-x^2,x(1-x)).
  • A109267 (program): Riordan array (1/(1 - x*c(x) - x^2*c(x)^2), x*c(x)) where c(x) is the g.f. of A000108.
  • A109269 (program): Numbers n such that n^2 < (1/2)*(prevprime(n^2)+nextprime(n^2).
  • A109270 (program): Numbers n such that n^2 > (1/2)(prevprime(n^2)+nextprime(n^2)).
  • A109274 (program): Numbers n such that n+1 is prime, 2n+1 composite.
  • A109288 (program): Semiprimes equal to p*q + 1, where p and q are distinct primes.
  • A109301 (program): a(n) = rhig(n) = rote height in gammas of n, where the “rote” corresponding to a positive integer n is a graph derived from the primes factorization of n, as illustrated in the comments.
  • A109313 (program): Difference between prime factors of n-th semiprime.
  • A109325 (program): Zsigmondy numbers for a = 3, b = 2: Zs(n, 3, 2) is the greatest divisor of 3^n - 2^n (A001047) that is relatively prime to 3^m - 2^m for all positive integers m < n.
  • A109338 (program): Triangle read by rows: T(n,k) = number of inequivalent binary sequences of length n and weight k, where two sequences are said to be equivalent if they have the same set of phrases in their Ziv-Lempel encodings (the phrases can appear in a different order in the two sequences).
  • A109340 (program): Expansion of x^2*(1+x+4*x^2)/((1+x+x^2)*(1-x)^3).
  • A109341 (program): Take a deck of 52 cards face-down, split it in half and flip one deck and reinsert it into the other deck such that the cards are alternatingly face up and face down. This sequence is the number of face-up cards after repeating this process n times.
  • A109344 (program): a(n) consists of n 4’s, n-1 8’s and a single 9 (in that order).
  • A109345 (program): a(n) = 5^((n^2 - n)/2).
  • A109352 (program): a(n) = sum of the prime divisors of the n-th squarefree composite number.
  • A109353 (program): a(n) is the sum of the distinct prime divisors of A024619(n).
  • A109354 (program): a(n) = 6^((n^2 - n)/2).
  • A109358 (program): Square root of squares of form 2*p + 3, where p is prime.
  • A109359 (program): Expansion of x*(1+x^2+3*x^3+2*x^4+x^5+4*x^6) / ((x^2+1)*(x^2-x+1)*(x-1)^2*(x+1)^2).
  • A109360 (program): Expansion of x*(1+4*x+5*x^2-x^3+6*x^4+x^5-4*x^6) / ((x^2+1)*(x^2-x+1)*(x-1)^2*(x+1)^2).
  • A109362 (program): Period 6: repeat [0, 0, 1, 2, 0, 3].
  • A109363 (program): a(n) = 4*2^n - 3*n - 5.
  • A109365 (program): a(-1)=a(0)=1 and recursively a(n) = prime(n)*(a(n-1)+a(n-2)).
  • A109366 (program): a(-1)=0, a(0)=1 and recursively a(n) = prime(n)*(a(n-1)+a(n-2)).
  • A109367 (program): Squares of the form 2*p + 3, where p is a prime.
  • A109369 (program): Numbers n such that the string 33n is the decimal expansion of a prime number.
  • A109370 (program): Numbers n such that the string 22n is the decimal expansion of a prime number.
  • A109371 (program): Numbers k such that the string 11k is prime.
  • A109372 (program): Numbers k such that k * (sum of the digits of k raised to their own power) + 1 is prime.
  • A109373 (program): Semiprimes of the form semiprime + 1.
  • A109375 (program): Bisection of A093411.
  • A109377 (program): Expansion of ( 2+x+2*x^2 ) / ( 1-2*x+x^2-x^3 ).
  • A109381 (program): Maximum digit of n^2 written in factorial base.
  • A109386 (program): G.f. is the logarithm of the g.f. of A107742: Sum_{n>=1} (a(n)/n)*x^n = Log( Sum_{n>=0} A107742(n)*x^n ).
  • A109388 (program): Maximum number of pairwise incomparable subcubes of the discrete n-cube. Largest antichain in partial ordering {0,1,*)^n where 0 and 1 are less than *. Maximum number of implicants in an irredundant disjunctive normal form for n Boolean variables.
  • A109389 (program): Expansion of q^(-1/12)eta(q)eta(q^6)/(eta(q^2)eta(q^3)) in powers of q.
  • A109391 (program): a(n) = (n^(n+1))*(n + 1)/2 = A000217(n)*A000312(n).
  • A109392 (program): Partial sums of A109391.
  • A109394 (program): A000934(A000934(n)).
  • A109395 (program): Denominator of phi(n)/n = Product_{p|n} (1 - 1/p); phi(n)=A000010(n), the Euler totient function.
  • A109398 (program): a(n) = (1/n!)*Sum_{k=0..n} (n+k)!.
  • A109403 (program): Examine the sequence of all (even or odd) semiprimes, A001358, and record the averages of any pair of successive terms of the same parity.
  • A109408 (program): Cubes whose digits sum to a prime.
  • A109410 (program): Prime numbers p such that p = digit sum of cubes in A109408.
  • A109411 (program): Partition the sequence of positive integers into minimal groups so that sum of terms in each group is a semiprime; sequence gives sizes of the groups.
  • A109413 (program): a(n) equals the (n*(n+1)/2)-th partial sum of the self-convolution of A010054, which has the g.f.: Sum_{n>=0} x^(n*(n+1)/2).
  • A109414 (program): a(n) equals the (n*(n+1)/2)-th partial sum of the self-convolution cube of A010054, which has the g.f.: Sum_{k>=0} x^(k*(k+1)/2).
  • A109415 (program): a(n) equals the (n*(n+1)/2)-th partial sum of the self-convolution 4th power of A010054, which has the g.f.: Sum_{k>=0} x^(k*(k+1)/2).
  • A109421 (program): Numbers n such that tau(n)/bigomega(n) is an integer [tau(n)=number of divisors of n; bigomega(n)=number of prime divisors of n, counted with multiplicities].
  • A109422 (program): Numbers n such that tau(n)/bigomega(n) is not an integer [tau(n) =number of divisors of n; bigomega(n)=number of prime divisors of n, counted with multiplicities].
  • A109423 (program): Numbers n such that sigma(n)/bigomega(n) is an integer [sigma(n) = sum of divisors of n; bigomega(n) = number of prime divisors of n, counted with multiplicity].
  • A109430 (program): Period 24.
  • A109431 (program): Binary strings that have 1’s where ‘evil numbers’ occur, 0’s elsewhere and every term ends with the n-th evil number index (counting with 0 = first).
  • A109437 (program): a(-1) = a(0) = 0, a(1) = 1; a(n) = 5a(n-1) - 5a(n-2) + a(n-3) + 2*(-1)^(n+1), alternatively a(n) = 3a(n-1) + 3a(n-2) - a(n-3).
  • A109438 (program): a(n) = 5a(n-1) - 5a(n-2) + a(n-3) + 2*(-1)^(n+1), alternatively a(n) = 3a(n-1) + 3a(n-2) - a(n-3).
  • A109442 (program): Cumulative sum of smallest prime power >= n.
  • A109443 (program): Cumulative sum of largest prime power <= n.
  • A109444 (program): Cumulative sum of mosaic numbers (A000026).
  • A109446 (program): Binomial coefficients C(n,k) with n-k even, read by rows.
  • A109447 (program): Binomial coefficients C(n,k) with n-k odd, read by rows.
  • A109449 (program): Triangle read by rows, T(n,k) = binomial(n,k)*A000111(n-k), 0 <= k <= n.
  • A109450 (program): Triangle T(n,k), 0<=k<=n, read by rows, given by [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, …] DELTA [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, …] where DELTA is the operator defined in A084938.
  • A109451 (program): a(1)=1; a(n) = smallest positive integer not already present such that a(n-1) and a(n) have a different number of 1’s in their binary expansions.
  • A109453 (program): Cumulative sum of initial digits of n.
  • A109454 (program): Sum of non-Fibonacci numbers between successive Fibonacci numbers: a(n) = Sum_{k=F(n)+1..F(n+1)-1)} k.
  • A109466 (program): Riordan array (1, x(1-x)).
  • A109469 (program): Cumulative sum of coefficients of ménage hit polynomials (A000033).
  • A109470 (program): Sum of first n noncubes.
  • A109474 (program): a(1)=1, a(2)=3; thereafter, a(n) = least positive integer > a(n-1) and not equal to a(i)+a(j)+a(k) for 1<=i<=j<=k<=n-1.
  • A109489 (program): Value of Product[k/sd(k,2),k=1..n], where sd(k,b) is the sum of the digits of k represented in base b.
  • A109491 (program): Value of Product_{k=1..n} sigma(k)/sd(k,2), where sd(k,b) is the sum of the digits of k represented in base b.
  • A109493 (program): a(n) = 7^((n^2 - n)/2).
  • A109498 (program): Number of closed walks of length 2n on the Heawood graph from a given node.
  • A109499 (program): Number of closed walks of length n on the complete graph on 5 nodes from a given node.
  • A109500 (program): Number of closed walks of length n on the complete graph on 6 nodes from a given node.
  • A109501 (program): Number of closed walks of length n on the complete graph on 7 nodes from a given node.
  • A109502 (program): Array read by antidiagonals: T(m,n) is the number of closed walks of length n on the complete graph on m nodes, m >= 1, n >= 0.
  • A109506 (program): Expansion of (1 - phi(-q)^4)/ 8 in powers of q where phi() is a Ramanujan theta function.
  • A109511 (program): Number of subsets of the first n numbers having a common divisor greater than 1.
  • A109512 (program): Integers which are not the sum of n and A001462(n).
  • A109516 (program): a(n) is the (1,2)-entry of the n-th power of the 2 X 2 matrix [0,1;n-1,n-1].
  • A109517 (program): a(n) is the (1,2)-entry of the n-th power of the 2 X 2 matrix [0,1;n-1,2(n-1)].
  • A109518 (program): a(n)=the (1,2)-entry of the n-th power of the 2 X 2 matrix [0,1;n-1,3(n-1)].
  • A109519 (program): a(n) is the (1,2)-entry of the n-th power of the 2 X 2 matrix [0,-1;n-1,n-1].
  • A109520 (program): a(n)=the (1,2)-entry of the n-th power of the 2 X 2 matrix [0,-1;n-1,2*(n-1)].
  • A109521 (program): a(n)=the (1,2)-entry of the n-th power of the 2 X 2 matrix [0,-1;n-1,3*(n-1)].
  • A109522 (program): a(n) = the (1,2)-entry in the matrix P^n + F^n, where the 2 X 2 matrices P and F are defined by P=[0,1;1,0] and F=[0,1;1,1].
  • A109523 (program): a(n) is the sum of the (1,2)- and (1,3)-entries of the matrix P^n + T^n, where the 3 X 3 matrices P and T are defined by P = [0,1,0; 0,0,1; 1,0,0] and T = [0,1,0; 0,0,1; 1,1,1].
  • A109524 (program): a(n)=the sum of the (1,2)- and (1,3)-entries of the matrix P^n + T^n, where the 3 X 3 matrices P and T are defined by P=[0,1,0;0,0,1;1,0,0] and T=[0,1,0;0,0,1;1,1,0].
  • A109534 (program): a(0)=1, a(n)=n+a(n-1) if n mod 2=0, a(n)=3n-a(n-1) if n mod 2 = 1.
  • A109535 (program): a(0) = 1, a(n) = n+a(floor(n/2)) if n mod 2 = 0, a(n) = 2n-a(floor((n-1)/2)) if n mod 2 = 1.
  • A109536 (program): a(0) = 1, a(n) = n+a(floor(n/2)) if n mod 2 = 0, a(n) = n-a(floor((n-1)/2)) if n mod 2 = 1.
  • A109537 (program): a(0)=a(1)=a(2)=a(3)=a(4)=a(5)=1; a(n)=a(n-1)+a(n-2)-a(n-4)+a(n-6) for n>=6.
  • A109538 (program): a(n) = a(n-2) + a(n-3) + a(n-4) + a(n-5) + a(n-6) + a(n-7).
  • A109539 (program): a(n) = a(n-2)+a(n-3)+a(n-4)+a(n-5)+a(n-6)+a(n-7)+a(n-8).
  • A109540 (program): a(n) = a(n-2)+a(n-3)+a(n-4)+a(n-5)+a(n-6)+2*a(n-7)+a(n-8).
  • A109541 (program): a(n) = a(n-2)+a(n-3)+a(n-4)+a(n-5)+2*a(n-6)+a(n-7).
  • A109543 (program): a(n) = a(n-1) + a(n-3) + a(n-5), with a(1..5) = 1.
  • A109544 (program): Expansion of (1 + x - x^3 - 2*x^4)/(1 - x^2 - x^3 - x^4 - x^5).
  • A109545 (program): a(n) = 2*a(n-1) + a(n-2) + a(n-3).
  • A109546 (program): (4^(n+1)-(-1)^n 9 )/5.
  • A109554 (program): pi(n)[prime(n+1)-prime(n)], where pi(n) is the number of prime numbers less than or equal to n and prime(k) is the k-th prime.
  • A109555 (program): prime(k) for those k where floor(2*(((prime(k + 1) - prime(k))*PrimePi(k)) mod (8*k)) / k) = m with m = 0.
  • A109570 (program): E.g.f.: x/(1-sinh(x)).
  • A109572 (program): E.g.f.: x/[1-tan(x)].
  • A109573 (program): E.g.f.: 2*x/(1+exp(-2*x)).
  • A109576 (program): E.g.f.: x/(1+3x-4x^3)=x/[1-T(3,x)], where T(3,x) is a Chebyshev polynomial.
  • A109578 (program): a(n) = (pi(n+1)-pi(n)) * (prime(n+1)-prime(n)), where pi(k) is the number of prime numbers less than or equal to k (= A000720(k)) and prime(k) is the k-th prime number (= A000040(k)).
  • A109579 (program): Sum([pi(j+1)-pi(j)][prime(j+1)-prime(j)],j=1..n), where pi(k) is the number of prime numbers less than or equal to k and prime(k) is the k-th prime.
  • A109581 (program): E.g.f.: x/(1+x-x^3).
  • A109582 (program): Expansion of e.g.f.: -1/(1+x-x^3).
  • A109583 (program): Let x^3/(-1-x+x^3)=Sum[b[n]*x^n/n1,{n,0,Infinity}]; a(n) = Abs[b[n]]
  • A109584 (program): a(n) = (prime(n+1) - prime(n))^pi(n).
  • A109585 (program): a(n) = ( prime(n+1) - prime(n) )^(n+1).
  • A109588 (program): n followed by n^2 followed by n^3.
  • A109592 (program): Sequence and first differences include all even numbers exactly once and no odd numbers.
  • A109594 (program): n followed by n^3 followed by n^2.
  • A109595 (program): n^3 followed by n^2 followed by n.
  • A109599 (program): a(n) = A070864(n+8) - 4.
  • A109603 (program): Numbers n such that 43*n - 41 is prime.
  • A109604 (program): Numbers n such that 41*n - 43 is prime.
  • A109606 (program): Number of numbers k with 1 < k < n which are relatively prime to n.
  • A109607 (program): Sum of coprimes of n greater than 1.
  • A109608 (program): Numbers n such that the number of digits required to write the prime factors of n equals the number of digits of n.
  • A109609 (program): Expansion of 1/((x-1)*(x+1)*(x^2+x+1)*(x^2+x-1)*(x^2-x+1)*(x^2+1)*(x^4-x^2+1)).
  • A109610 (program): Expansion of (1+3*x^4-2*x^7+x^10-x^12)/((x+1)*(x^2+1)*(x^2+x+1)*(x^2-x+1)*(x^4-x^2+1)*(x-1)^2).
  • A109612 (program): Numbers n such that the string 44n is prime.
  • A109613 (program): Odd numbers repeated.
  • A109614 (program): n^3 followed by n followed by n^2.
  • A109620 (program): a(n) = (1/3)*n^3 - n^2 - (1/3)*n - 1.
  • A109622 (program): Number of different isotemporal classes of diasters with n peripheral edges.
  • A109624 (program): Totally multiplicative sequence with a(p) = (p-1)*(p+3) = p^2+2p-3 for prime p.
  • A109629 (program): Sequence of Mahler coefficients of the Gray code function.
  • A109630 (program): The winning position when playing the “eeny meeny miny moe” game with n players and eliminating every 8th player.
  • A109632 (program): In the game of bridge, a(n) is the penalty for going down n tricks in a vulnerable, doubled contract.
  • A109633 (program): In the game of bridge, a(n) is the penalty for going down n tricks in a non-vulnerable, doubled contract.
  • A109634 (program): Number of 1’s that appear among all ternary strings of length n that contain no consecutive 1’s.
  • A109635 (program): Sum of prime(n) and n-th digit of Pi after the decimal point.
  • A109637 (program): Numbers n such that the string 55n is prime.
  • A109639 (program): Numbers n such that the string 66n is prime.
  • A109645 (program): Primes whose decimal expansion has the form ij, where i and j are integers with j < i.
  • A109652 (program): a(n) = prime(A000201(n)).
  • A109653 (program): Sequence and first differences include all prime numbers exactly once.
  • A109664 (program): a(1) = 1; for n>1, a(n) = Sum_{i=1..n-1} a(i)*prime(i).
  • A109674 (program): a(n)^(n/a(n)) = A092975(n) and a(n) is a prime.
  • A109678 (program): Sequence and first differences include all square numbers exactly once.
  • A109680 (program): a(n) = 2^(4n-2) - A104403(n).
  • A109681 (program): “Sloping ternary numbers”: write numbers in ternary under each other (right-justified), read diagonals in upward direction, convert to decimal.
  • A109683 (program): Ternary equivalents of A109681.
  • A109697 (program): Number of partitions of n into parts each equal to 1 mod 5.
  • A109698 (program): Number of partitions of n into parts each equal to 2 mod 5.
  • A109699 (program): Number of partitions of n into parts each equal to 3 mod 5.
  • A109700 (program): Number of partitions of n into parts each equal to 4 mod 5.
  • A109701 (program): Number of partitions of n into parts each equal to 1 mod 6.
  • A109702 (program): Number of partitions of n into parts each equal to 5 mod 6.
  • A109703 (program): Number of partitions of n into parts each equal to 1 mod 7.
  • A109704 (program): Number of partitions of n into parts each equal to 2 mod 7.
  • A109705 (program): Number of partitions of n into parts each equal to 3 mod 7.
  • A109707 (program): Number of partitions of n into parts each equal to 5 mod 7.
  • A109712 (program): UnitarySigmaUnitaryPhi(n) or USUP(n).
  • A109718 (program): Periodic sequence with period {0,1,0,3}, or n^3 mod 4.
  • A109720 (program): Periodic sequence {0,1,1,1,1,1,1} or n^6 mod 7.
  • A109722 (program): Sum of first 2n primes.
  • A109723 (program): Sum of the first 2n+1 primes.
  • A109724 (program): Sum of the first n^2 primes.
  • A109725 (program): Divide primes in groups with 2n+1 elements and add together.
  • A109731 (program): a(n) = - 4*a(n-2) - a(n-4), a(0) = 1, a(1) = -4, a(2) = -6, a(3) = 15.
  • A109742 (program): a(n) = d(n-1) + d(n-2) + (n-1)[d(n-2) + 2d(n-3) + d(n-4)], where d(n), the derangement numbers, are given in A000166. (Let d(n) = 0 if n < 0.)
  • A109743 (program): a(2)=1; for n>2, a(n) = A109742(n)/3.
  • A109747 (program): E.g.f.: exp(-exp(-x)+1+x).
  • A109753 (program): n^3 mod 8; the periodic sequence {0,1,0,3,0,5,0,7}.
  • A109754 (program): Matrix defined by: a(i,0) = 0, a(i,j) = i*Fibonacci(j-1) + Fibonacci(j), for j > 0; read by ascending antidiagonals.
  • A109763 (program): Primes repeated.
  • A109764 (program): Sum of the first n^2 squares.
  • A109765 (program): Expansion of x/((4*x-1)*(2*x-1)*(x+1)).
  • A109767 (program): Triangle T(n,k), 0 <= k <= n, defined by T(n,k) = 2^k*A001497(n,k).
  • A109768 (program): a(n) = gcd(3^n-2,2^n-3).
  • A109770 (program): Prime(1^2) + prime(2^2) + … + prime(n^2).
  • A109771 (program): G.f.: sqrt(1+6*x+x^2).
  • A109774 (program): a(n) = (3^(n-1) - 1) * (3^n - 1)/2.
  • A109779 (program): a(n) = n! * Sum_{k=1..n} H(k)*(n+1-k)!, where H(k) = Sum_{j=1..k} 1/j.
  • A109780 (program): a(n) = n! * Sum_{k=1..n} H(k)*(n-k)!, where H(k) = Sum_{j=1..k} 1/j.
  • A109782 (program): Expansion of x*(1+2*x^2-2*x^3+x^4) / ((x-1)*(x^2-2*x-1)*(x^2-x+1)*(x+1)^2).
  • A109785 (program): Expansion of (1+x+x^2+x^7+x^8-2*x^10-x^12) / ((x+1)*(x^2+1)*(x^2+x+1)*(x^2-x+1)*(x^4-x^2+1)*(x-1)^2).
  • A109786 (program): Expansion of -(x+2*x^2+3*x^3-1+5*x^4)/((x+1)*(x^2-3*x+1)*(1+x^2)).
  • A109787 (program): Expansion of -(1-x-2*x^2+11*x^4-3*x^3) / ((x-1)*(x+1)*(x^2-3*x+1)*(1+x^2)).
  • A109792 (program): Expansion of e.g.f. log(1+x)/(1-x)^2.
  • A109794 (program): a(2n) = A001906(n+1), a(2n+1) = A002878(n).
  • A109795 (program): a(n)= n*(1+floor(n/10)).
  • A109801 (program): Cumulative sum of squares of primes indexed by squares.
  • A109803 (program): Expansion of (x^2+1)*(x+1)^2 / ((x-1)*(x^2+x+1)*(x^2+2*x-1)).
  • A109804 (program): Cumulative sum of initial digits of (n base 6).
  • A109805 (program): a(n) = prime(n+2)*prime(n+1) - prime(n)*prime(n+1).
  • A109808 (program): a(n) = 2*7^(n-1).
  • A109810 (program): Number of permutations of the positive divisors of n, where every element is coprime to its adjacent elements.
  • A109814 (program): a(n) is the largest k such that n can be written as sum of k consecutive positive integers.
  • A109815 (program): n^2 followed by n^3 followed by n.
  • A109816 (program): n^2 followed by n followed by n^3.
  • A109818 (program): Sum of primes between n and n^2.
  • A109819 (program): Product of primes between n and n^2.
  • A109823 (program): a(n) is the minimal b >= n such that sum of consecutive integers from n to b is a semiprime.
  • A109824 (program): a(n) is the number of consecutive integers starting with n summing up to a semiprime.
  • A109825 (program): Initial terms of groups in the partition of the sequence of natural numbers A109411.
  • A109826 (program): Final terms of groups in the partition of the sequence of natural numbers A109411.
  • A109827 (program): Numbers written in an alternating binary-then-ternary base.
  • A109834 (program): Startorial numbers: product of initial digits of integers 1 through n.
  • A109841 (program): a(n) is the minimal j >= n such that the sum of consecutive integers from n to j is a palindrome.
  • A109842 (program): Number of consecutive integers starting with n needed to sum to a palindrome.
  • A109844 (program): a(1) = 1, a(2) = 2, next terms up to a(2n-1) are obtained by multiplying previous terms a(n-1) by n+1, a(n-2) by n+2 etc. a(2) by (2n-2) and a(1) by 2n-1. On similar lines a(2n) = 2n*a(2n-2), a(2n+1) = (2n+1)*a(2n-1) and so on.
  • A109845 (program): a(1) = 2; a(2n) = least common multiple of all previous terms + 1. a(2n+1) = least common multiple of all previous terms - 1.
  • A109846 (program): Absolute difference between n and its 9’s complement.
  • A109847 (program): Least common multiple of n and its 9’s complement.
  • A109848 (program): Highest common factor of n and its 9’s complement.
  • A109851 (program): a(1) = 1, a(2) = 2; for n > 2, sum of absolute differences of all combinations of pairs of previous terms.
  • A109853 (program): a(n) = A109852(2^n).
  • A109857 (program): Next 2n-1 odd numbers in decreasing order followed by next 2n even numbers in decreasing order.
  • A109866 (program): 9’s complement of the digits of the golden ratio phi (A001622): 9.999999999999… - 1.6180339887… = 8.3819660112501051517954131656334…
  • A109868 (program): Numbers which can be differences of successive palindromes in order of their first occurrence.
  • A109873 (program): a(n) = product of terms in row n of Pascal’s triangle (A001142) divided by n^k, where n^k is the largest power of n dividing it.
  • A109882 (program): Palindromes with either no internal digits or all internal digits are 0.
  • A109883 (program): Start subtracting from n its divisors beginning from 1 until one reaches a number smaller than the last divisor subtracted or reaches the last nontrivial divisor < n. Define this to be the perfect deficiency of n. Then a(n) = perfect deficiency of n.
  • A109895 (program): Group the natural numbers so that every 2n-th group product is divisible by the single number in the next group. (1), (2,3,4,5), (6), (7,8,9,10,11), (12), (13,14,15,16,17,18,19),(20), (21,22,23,24,25,26,27),(28),… Sequence contains the single members of the odd numbered groups.
  • A109896 (program): Group the natural numbers so that every 2n-th group product is divisible by the single number in the next group. (1), (2,3,4,5), (6), (7,8,9,10,11), (12), (13,14,15,16,17,18,19),(20), (21,22,23,24,25,26,27),(28),… Sequence contains the number of terms in the 2n-th group.
  • A109900 (program): The (n,r)-th term of the following triangle is T(n)-T(r) for r = 0 to n. The n-th row contains n+1 terms. T(n) = the n-th triangular number = n(n+1)/2. Sequence contains the sum of terms at a 45-degree angle.
  • A109901 (program): a(n) = binomial(n^2, n*(n+1)/2).
  • A109906 (program): A triangle of coefficients based on A000045 and Pascal’s triangle: t(n,m)=Fibonacci[(n - m + 1)]*Fibonacci[(m + 1)]*Binomial[n, m].
  • A109909 (program): a(n) = number of primes of the form k*(n-k)-1.
  • A109915 (program): Product of all composite numbers k such that n<k<prime(r) where prime(r-1)<=n, or 1 if this set of k is empty.
  • A109916 (program): a(n) = n-th digit after decimal point in e^n.
  • A109921 (program): a(2n) = prime(n). a(2n+1) = sum of composite numbers between prime(n) and prime(n+1). We define a(1) = 1.
  • A109922 (program): a(n) = floor(lcm(1,2,…n)/(1+2+…+n)).
  • A109923 (program): a(n) = lcm(1,2,3,…,prime(n))/(1 + 2 + … + prime(n)).
  • A109925 (program): Number of primes of the form n - 2^k.
  • A109932 (program): a(n) = f^n(n) = f applied n times to n, where f(n) = A007425(n).
  • A109934 (program): Composite numbers which are not the sum of two distinct primes.
  • A109940 (program): Largest k-digit multiple of n where k is the number of digits in n.
  • A109952 (program): Degrees Centigrade for which Fahrenheit is a prime.
  • A109954 (program): Riordan array (1/(1+x)^3,x/(1+x)^2).
  • A109955 (program): Number triangle binomial(n+2k,3k).
  • A109956 (program): Inverse of Riordan array (1/(1-x), x/(1-x)^3), A109955.
  • A109960 (program): Number triangle binomial(n+3k,4k).
  • A109961 (program): Expansion of (1-x)^3/(1-4x+5x^2-4x^3+x^4).
  • A109962 (program): Inverse of Riordan array (1/(1-x), x/(1-x)^4), A109960.
  • A109964 (program): a(n) = floor(sqrt(Sum_{i<n} a(i))), with a(0)=1.
  • A109965 (program): Sum_i {i<n} floor(sqrt(a(i))) with a(0) = 1.
  • A109966 (program): a(n) = 8^((n^2-n)/2).
  • A109970 (program): Riordan array (1,x(1-x)^2).
  • A109971 (program): Inverse of Riordan array (1,x(1-x)^2), A109970.
  • A109975 (program): Second differences of A045623, prefixed by an initial 1.
  • A109980 (program): Number of Delannoy paths of length n with no (1,1)-steps on the line y=x.
  • A109983 (program): Triangle read by rows: T(n, k) (0<=k<=2n) is the number of Delannoy paths of length n, having k steps.
  • A109984 (program): a(n) = number of steps in all Delannoy paths of length n.
  • A109990 (program): Numbers n such that the string 77n is prime.
  • A109991 (program): Numbers k such that the string 88k is prime.
  • A109992 (program): Numbers n such that the string 99n is prime.
  • A109995 (program): Number of unlabeled ordered minimal T_0-covers of an n-set, cf. A094545.
  • A109999 (program): Integer part of Lorentz gamma factor = 1/sqrt(1 - (beta)^2) for beta = 0.9999…(with 9 appearing n times) = 1 - 10^(-n).
  • A110001 (program): n followed by n^2 followed by n^3 followed by n^4.
  • A110003 (program): n followed by n^3 followed by n^2 followed by n^4.
  • A110004 (program): n followed by n^3 followed by n^4 followed by n^2.
  • A110005 (program): n followed by n^2 followed by n^4 followed by n^3.
  • A110006 (program): a(n)=n-floor(phi*floor(phi^-1*floor(phi*floor(phi^-1*n)))) where phi=(1+sqrt(5))/2.
  • A110007 (program): a(n)=n-floor(phi*floor(phi^-1*floor(phi*floor(phi^-1*floor(phi*floor(phi^-1*n)))))) where phi=(1+sqrt(5))/2.
  • A110008 (program): n followed by n^4 followed by n^3 followed by n^2.
  • A110009 (program): n followed by n^4 followed by n^2 followed by n^3.
  • A110010 (program): a(n)=n-F(F(F(F(n)))) where F(x)=floor(phi*floor(x/phi)) and phi=(1+sqrt(5))/2.
  • A110011 (program): a(n)=n-F(F(F(F(F(n)))))=n-F^5(n) where F(x)=floor(phi*floor(x/phi)) and phi=(1+sqrt(5))/2.
  • A110012 (program): a(n) = n - F(F(n)) where F(x)=floor(sqrt(2)*floor(x/sqrt(2)).
  • A110013 (program): Squares of the form 4p + 5, where p is a prime.
  • A110014 (program): Primes p such that 6p + 7 is a square.
  • A110015 (program): Squares of the form 6p + 7, where p is a prime.
  • A110016 (program): Numbers n such that (n^2-7)/6 is prime.
  • A110026 (program): Minimal number of times a rectangular grid of n X n+1 elements can be slid along a 45-degree line before a rotated version of the initial grid appears.
  • A110034 (program): Row sums of a characteristic triangle for the Fibonacci numbers.
  • A110035 (program): Row sums of an unsigned characteristic triangle for the Fibonacci numbers.
  • A110036 (program): Constant terms of the partial quotients of the continued fraction expansion of 1 + Sum_{n>=0} 1/x^(2^n), where each partial quotient has the form {x + a(n)} after the initial constant term of 1.
  • A110037 (program): Signed version of A090678 and congruent to A088567 mod 2.
  • A110043 (program): a(0) = 1, a(1) = 2; for n>1, a(n) = n*a(n-1) + (-1)^n.
  • A110044 (program): a(0) = 11, a(1) = 23; for n > 1, a(n) = |a(n-1) - a(n-2)|.
  • A110046 (program): Expansion of (1+4*x-12*x^2-16*x^3)/((2*x+1)*(2*x-1)*(4*x^2+4*x-1)).
  • A110047 (program): Expansion of (1+2*x-4*x^2)/((2*x+1)*(2*x-1)*(4*x^2+4*x-1)).
  • A110048 (program): Expansion of 1/((1+2*x)*(1-4*x-4*x^2)).
  • A110050 (program): Expansion of (2+9*x-24*x^3+16*x^4-30*x^2) / ((1-x)*(2*x+1)*(2*x-1)*(4*x^2+4*x-1)).
  • A110051 (program): Expansion of (1-x+2*x^3+x^2)/((1-x)*(2*x+1)*(2*x-1)*(4*x^2+4*x-1)).
  • A110052 (program): Expansion of x*(-1+4*x)/((x-1)*(2*x-1)*(4*x^2+4*x-1)).
  • A110061 (program): Expansion of x^2*(-3+4*x)/(1-x^3+x^4).
  • A110062 (program): Expansion of (1 - x + 2*x^2) / (1 - x^3 + x^4).
  • A110063 (program): Expansion of -(3 - x + 2*x^2) / (1 - x^3 + x^4).
  • A110064 (program): a(n+4) = a(n+1) - a(n), a(0) = 1, a(1) = -4, a(2) = 0, a(3) = 1.
  • A110083 (program): a(n+1) = Sum_{k=0..n} (n!/k!)*binomial(n,k)*a(k).
  • A110088 (program): tau(n)^omega(n), where tau=A000005 and omega=A001221.
  • A110090 (program): Numerators of sequence of rationals defined by r(n) = n for n<=1 and for n>1: r(n) = (sum of denominators of r(n-1) and r(n-2))/(sum of numerators of r(n-1) and r(n-2)).
  • A110091 (program): Denominators of sequence of rationals defined by r(n) = n for n<=1 and for n>1: r(n) = (sum of denominators of r(n-1) and r(n-2))/(sum of numerators of r(n-1) and r(n-2)).
  • A110098 (program): Triangle read by rows: T(n,k) (0 <= k <= n) is the number of Delannoy paths of length n, having k return steps to the line y = x from the line y = x+1 (i.e., E steps from the line y=x+1 to the line y = x).
  • A110099 (program): Number of return steps to the line y = x from the line y = x+1 (i.e., E steps from the line y = x+1 to the line y = x) in all Delannoy paths of length n.
  • A110110 (program): Number of symmetric Schroeder paths of length 2n (A Schroeder path of length 2n is a lattice path from (0,0) to (2n,0) consisting of U=(1,1), D=(1,-1) and H=(2,0) steps and never going below the x-axis).
  • A110111 (program): Sequence associated to the recurrence b(n) = b(n-1) + 3*b(n-2).
  • A110113 (program): Diagonal sums of A083856.
  • A110117 (program): a(n) = floor(n * (sqrt(2) + sqrt(3))).
  • A110118 (program): a(n) = floor(n*(sqrt(6) + sqrt(2) + 2)/4).
  • A110122 (program): Number of Delannoy paths of length n with no EE’s crossing the line y = x (i.e., no two consecutive E steps from the line y = x+1 to the line y = x-1).
  • A110127 (program): Number of EE’s crossing the line y = x (i.e., two consecutive E steps from the line y = x+1 to the line y = x-1) in all Delannoy paths of length n.
  • A110129 (program): Central coefficients of a scaled Legendre triangle.
  • A110131 (program): Determinant of n X n matrix M_{i,j} = 2^i*P_i(j), where P_i(j) is the Legendre polynomial of order i at j and i and j are 0-based.
  • A110132 (program): a(n) = floor(n/2)^ceiling(n/2).
  • A110133 (program): Numbers which are the sides that belong to only one primitive Pythagorean triangle.
  • A110138 (program): a(n) = ceiling(n/2)^floor(n/2).
  • A110139 (program): Floor(n/2)^floor(n/2).
  • A110140 (program): Binomial transform of n^n (with interpolated zeros).
  • A110144 (program): Terms of A110142 at positions p(n)+1, where p(n) = A000041(n) is the number of partitions of n; a(n) = A110142(p(n)+1) for n>=1, with a(0) = 1.
  • A110145 (program): a(n) = Sum_{k=0..n} C(n,k)^2*mod(k,2).
  • A110146 (program): n^(n+1) mod n+2.
  • A110147 (program): 10^((n^2-n)/2).
  • A110149 (program): a(0) = 1, a(1) = 3; for n>1, a(n) = n*a(n-1) + (-1)^n.
  • A110152 (program): G.f.: A(x) = Product_{n>=1} 1/(1 - 2^n*x^n)^(2/2^n).
  • A110153 (program): G.f.: A(x) = Product_{n>=1} 1/(1 - 3^n*x^n)^(3/3^n).
  • A110157 (program): a(n) = a(rad(n) - 1) + 1, where rad(n) is the squarefree kernel of n, rad=A007947.
  • A110158 (program): Expansion of x^4 / ((x+1)*(2*x^3-2*x^2-2*x+1)*(x-1)^2).
  • A110159 (program): a(n) = (n+1)(n+2)(n+3)(9n^2 + 26n + 20)/120.
  • A110161 (program): Expansion of x(1-x^2)/(1-x^2+x^4).
  • A110162 (program): Riordan array ((1-x)/(1+x), x/(1+x)^2).
  • A110164 (program): Expansion of (1-x^2)/(1+2x).
  • A110165 (program): Riordan array (1/sqrt(1-6x+5x^2),(1-3x-sqrt(1-6x+5x^2))/(2x).
  • A110166 (program): Row sums of Riordan array A110165.
  • A110167 (program): Diagonal sums of Riordan array A110165.
  • A110168 (program): Riordan array ((1-x^2)/(1+3x+x^2),x/(1+3x+x^2)).
  • A110169 (program): Triangle read by rows: T(n,k) (0<=k<=n) is the number of Delannoy paths of length n that start with exactly k (1,1) steps.
  • A110170 (program): First differences of the central Delannoy numbers (A001850).
  • A110171 (program): Triangle read by rows: T(n,k) (0 <= k <= n) is the number of Delannoy paths of length n that start with exactly k (0,1) steps (or, equivalently, with exactly k (1,0) steps).
  • A110180 (program): Triangle of generalized central trinomial coefficients.
  • A110181 (program): Row sums of number triangle A110180.
  • A110184 (program): Number of (1,1)-steps on the lines y=x, y=x+1 and y=x-1 in all Delannoy paths of length n.
  • A110185 (program): Coefficients of x in the partial quotients of the continued fraction expansion exp(1/x) = [1, x - 1/2, 12*x, 5*x, 28*x, 9*x, 44*x, 13*x, …]. The partial quotients all have the form a(n)*x except the constant term of 1 and the initial partial quotient which equals (x - 1/2).
  • A110190 (program): Number of (1,0)-steps on the lines y=0 and y=1 in all Schroeder paths of length 2n (a Schroeder path of length 2n is a path from (0,0) to (2n,0), consisting of steps U=(1,1), D=(1,-1) and H=(2,0) and never going below the x-axis).
  • A110191 (program): Decimal expansion of 1/6 - 1/(2*Pi).
  • A110195 (program): a(n) = 11^((n^2-n)/2).
  • A110197 (program): Number triangle of sums of squared binomial coefficients.
  • A110198 (program): Diagonal sums of number triangle A110197.
  • A110199 (program): a(n) = Sum_{k=0..floor(n/2)} Catalan(k).
  • A110202 (program): a(n) = sum of squares of numbers < 2^n having exactly 2 ones in their binary representation.
  • A110206 (program): Row sums of triangle A110205, where A110205(n,k) equals the sum of cubes of numbers < 2^n having exactly k ones in their binary expansion.
  • A110208 (program): 1 + sum of first n semiprimes.
  • A110209 (program): 1 + sum of first n 3-almost primes.
  • A110210 (program): a(n+3) = 6*a(n) - 5*a(n+2), a(0) = -1, a(1) = 1, a(2) = -5.
  • A110211 (program): a(n+3) = 6*a(n) - 5*a(n+2), a(0) = -1, a(1) = 3, a(2) = -15.
  • A110212 (program): a(n+3) = 6*a(n) - 5*a(n+2), a(0) = -1, a(1) = 5, a(2) = -25.
  • A110213 (program): a(n+3) = 6*a(n) - 5*a(n+2), a(0) = 1, a(1) = -7, a(2) = 35.
  • A110224 (program): a(n) = Fibonacci(n)^3 + Fibonacci(n+1)^3.
  • A110226 (program): 1 + sum of first n 4-almost primes.
  • A110236 (program): Number of (1,0) steps in all peakless Motzkin paths of length n (can be easily translated into RNA secondary structure terminology).
  • A110239 (program): Number of (1,1) steps in all peakless Motzkin paths of length n.
  • A110240 (program): Decimal form of binary integer produced by the ON cells at n-th generation following Wolfram’s Rule 30 cellular automaton starting from a single ON-cell represented as 1.
  • A110241 (program): J(n)^3+J(n+1)^3, where J(n) = the Jacobsthal number A001045(n).
  • A110254 (program): Square-indexed values of A110243.
  • A110256 (program): Denominators in the fractional coefficients that form the partial quotients of the continued fraction representation of the inverse tangent of 1/x.
  • A110257 (program): Numerators in the coefficients that form the odd-indexed partial quotients of the continued fraction representation of the inverse tangent of 1/x.
  • A110258 (program): Denominators in the coefficients that form the odd-indexed partial quotients of the continued fraction representation of the inverse tangent of 1/x.
  • A110260 (program): Denominators in the coefficients that form the even-indexed partial quotients of the continued fraction representation of the inverse tangent of 1/x.
  • A110266 (program): Number of blocks of ON cells in n-th row of triangle generated by Wolfram’s “Rule 30”.
  • A110267 (program): Total number of black cells at the first n generations of a single black cell following Wolfram’s Rule 30 cellular automaton.
  • A110269 (program): n mod 2 + n mod 3.
  • A110270 (program): a(n) = (n mod 2)*(n mod 3).
  • A110271 (program): Inverse of Riordan array (1/(1-x)^2,x(1-x)/(1+x)), A104698.
  • A110272 (program): a(n) = Pell(n)^3.
  • A110273 (program): a(n) = Pell(n)^3 + Pell(n+1)^3.
  • A110277 (program): Values of n such that the perfect deficiency (A109883) of n is a square.
  • A110284 (program): Squares of the form 4p - 3, where p is a prime.
  • A110286 (program): a(n) = 15*2^n.
  • A110287 (program): 17*2^n.
  • A110288 (program): 19*2^n.
  • A110291 (program): Riordan array (1/(1-x),x(1+2x)).
  • A110293 (program): a(2*n) = A001570(n), a(2*n+1) = A011943(n+1).
  • A110294 (program): a(2*n) = A028230(n), a(2*n+1) = -A067900(n+1).
  • A110295 (program): a(n) = prime(n)*2^(n-1).
  • A110299 (program): a(n) = Sum_{i=0..n-1} 2^i*prime(n-i).
  • A110301 (program): Integers written in base “triangle”.
  • A110303 (program): Alternators.
  • A110307 (program): Expansion of (1+2*x)/((x^2+x+1)*(x^2+5*x+1)).
  • A110308 (program): Expansion of -x*(2+x)/((x^2+x+1)*(x^2+5*x+1)).
  • A110309 (program): Expansion of (1+3*x+x^2)/((x^2+5*x+1)*(x^2+x+1)).
  • A110310 (program): Expansion of (1-x+x^2)/((x^2+x+1)*(x^2+5*x+1)).
  • A110311 (program): Expansion of 1 / ((x^2+5*x+1)*(x^2+x+1)).
  • A110313 (program): Expansion of e.g.f. exp(x)/(1-x-x^2).
  • A110314 (program): Inverse of number triangle related to Fibonacci numbers.
  • A110315 (program): Diagonal sums of the Fibonacci related number triangle A110314.
  • A110316 (program): a(n) is the number of different shapes of balanced binary trees with n nodes. The tree is balanced if the total number of nodes in the left and right branch of every node differ by at most one.
  • A110318 (program): Number of arcs covered by other arcs in all RNA secondary structures of size n+5 (i.e., with n+5 nodes).
  • A110319 (program): Triangle read by rows: T(n,k) (1 <= k <= n) is number of RNA secondary structures of size n (i.e., with n nodes) having k blocks (an RNA secondary structure can be viewed as a restricted noncrossing partition).
  • A110320 (program): Number of blocks in all RNA secondary structures with n nodes (an RNA secondary structure can be viewed as a restricted noncrossing partition).
  • A110321 (program): A Jacobsthal number related number triangle.
  • A110322 (program): Row sums of a number triangle related to the Jacobsthal numbers.
  • A110324 (program): Inverse of a number triangle related to the Jacobsthal numbers.
  • A110325 (program): Row sums of number triangle related to the Jacobsthal numbers.
  • A110326 (program): Diagonal sums of triangle A110324.
  • A110327 (program): Triangle read by rows: T(n,k) = n!*Pell(n-k+1)/k!, where Pell(n)=A000129(n).
  • A110328 (program): Row sums of a number triangle related to the Pell numbers.
  • A110330 (program): Inverse of a number triangle related to the Pell numbers.
  • A110331 (program): Row sums of a number triangle related to the Pell numbers.
  • A110332 (program): Diagonal sums of number a triangle related to the Pell numbers.
  • A110344 (program): a(n) = Sum_{k=0..n-1} (n+k) = n(3n-1)/2 if n is even; a(n) = Sum_{k=0..n-1} (n-k) = n(n+1)/2 if n is odd.
  • A110345 (program): a(n) = n + (n+1) + (n+2) + … n terms if n is odd, else a(n) = n + (n-1) + (n-2) + … n terms = n(n+1)/2 = n-th triangular number if n is even.
  • A110346 (program): Largest multiple of n in n + (n-1) +(n-2) + … (n-k).
  • A110347 (program): a(n) = meantorial(n) = the product of the set of n closest numbers with an arithmetic mean of n.
  • A110348 (program): a(2) = 1 by definition; otherwise a(n) = A109347(n)/n.
  • A110349 (program): a(n) = n + (n+1) + (n-1) + (n+2) + (n-2) … n terms.
  • A110350 (program): Least sum (n+1) + (n+2) + …+(n+k) >= (n(n+1)/2), the n-th triangular number.
  • A110356 (program): Array read by antidiagonals: T(n,k) (n>=3, k>=3) = minimal number of polygonal pieces in a dissection of a regular n-gon to a regular k-gon (conjectured).
  • A110357 (program): Least integer of the form n*(n+k)/(n-k).
  • A110359 (program): a(n) = n+1 if n+1 is a prime else a(n) = 2n+1 if 2n+1 is a prime else a(n) = 2*(2n+1) +1 =g(n) if this number is prime else the next candidate is 2* (g(n) +1 etc.
  • A110365 (program): a(1)=2, a(n+1) = a(n)*A010888(a(n)).
  • A110369 (program): (Digit 1 repeated n times) + n.
  • A110370 (program): Floor[ (digits n times n) divided by digits (n times 1)].
  • A110371 (program): a(n)=[(n+1)(n+2)(n+3)…(2n)]/(1+2+3+…+n).
  • A110372 (program): a(n) = F(n+1)!/F(n)! where F(n) = n-th Fibonacci number.
  • A110373 (program): a(n) = Sum_{prime p <= n} n!/p.
  • A110376 (program): a(n) = Sum_{r < n, gcd(r,n)=1} n!/r.
  • A110377 (program): a(n) = Sum_{r < n, gcd(r,n)=1} n!/r!.
  • A110378 (program): a(n) = Sum_{prime p <= n} n!/p!.
  • A110379 (program): a(n) = Sum_{composite c <= n} n!/c!.
  • A110380 (program): a(n) = min{p + q + r + …} where p,q,r,… are distinct unary numbers - containing only ones, i.e., of the form (10^k - 1)/9 - formed by using a total of n ones.
  • A110382 (program): Numbers which are sum of distinct unary numbers (containing only ones), i.e., numbers which are sum of distinct numbers of the form (10^k - 1)/9.
  • A110388 (program): a(n) = F(n)*F(n+1) mod 9, where F(n) = n-th Fibonacci number.
  • A110389 (program): Integers with mutual residues -1.
  • A110391 (program): a(n) = L(3*n)/L(n), where L(n) = Lucas number.
  • A110396 (program): 10’s complement factorial of n: a(n) = (10’s complement of n)*(10’s complement of n-1)*…*(10’s complement of 2)*(10’s complement of 1).
  • A110397 (program): a(n) = (10^k - n)(10^k + n), where k is the number of digits in n.
  • A110399 (program): Expansion of (theta_3(q)*theta_3(q^7) - 1)/2 in powers of q.
  • A110412 (program): Sum_{d<n is a divisor of n} tau(n-d).
  • A110414 (program): n! concatenated with n divided by n.
  • A110415 (program): a(n) = n concatenated with n! divided by n.
  • A110422 (program): a(n) = sum( (-1)^(r+1)*(n-r)*r, r = 1..floor(n/2) ).
  • A110425 (program): The r-th term of the n-th row of the following array contains the sum of r successively decreasing integers beginning from n. 0<r<=n. e.g. the row corresponding to 4 contains 4, (3+2),{(1) +(0)+(-1)}, {(-2)+(-3)+(-4)+(-5)} —-> 4,5,0,-14 1 2 1 3 3 -3 4 5 0 -14 5 7 3 -10 -35 6 9 6 -6 -30 -69 … Sequence contains the array by rows.
  • A110426 (program): The r-th term of the n-th row of the following array contains the sum of r successively decreasing integers beginning from n. 0<r<=n. e.g. the row corresponding to 4 contains 4, (3+2),{(1) +(0)+(-1)}, {(-2)+(-3)+(-4)+(-5)} —-> 4,5,0,-14 1 2 1 3 3 -3 4 5 0 -14 5 7 3 -10 -35 6 9 6 -6 -30 -69 … Sequence contains the row sums.
  • A110427 (program): The r-th term of the n-th row of the following array contains the sum of r successively decreasing integers beginning from n. 0 < r <= n. Sequence contains the leading diagonal.
  • A110428 (program): a(1) = 1 and a(2) = 2. Subsequent terms are generated like this: if a(m) is the last term available – say a(2) – then a(m+1) = a(m) * a(m-1), a(m+2) = a(m) * a(m-1) * a(m-2), …, a(2*m-1) = a(m) * a(m-1) * a(m-2) * … * a(2) * a(1), a(2*m) = a(2*m-1) * a(2*m-2), and so on.
  • A110430 (program): Arithmetic mean of all n-digit positive even numbers.
  • A110431 (program): Average of positive multiples of 3 with n decimal digits, rounded down.
  • A110436 (program): A weighted sum of Jacobi function values.
  • A110437 (program): A weighted sum of Jacobi function values.
  • A110440 (program): Triangular array formed by the little Schröder numbers s(n,k).
  • A110441 (program): Triangular array formed by the Mersenne numbers.
  • A110444 (program): Binary expansion of A074988.
  • A110446 (program): Triangle of Delannoy paths counted by number of diagonal steps not preceded by an east step.
  • A110448 (program): G.f.: A(x) = exp( Sum_{n>=1} A056045(n)/n*x^n ), where A056045(n) = Sum_{d|n} binomial(n,d).
  • A110449 (program): Triangle read by rows: T(n,k) = n*((2*k+1)*n+1)/2, 0<=k<=n.
  • A110450 (program): a(n) = n*(n+1)*(n^2+n+1)/2.
  • A110451 (program): a(n) = n*(4*n^2 + 2*n + 1).
  • A110467 (program): Convolution of 4^n*n! and n!.
  • A110468 (program): a(n) = (2*n + 1)!/(n + 1).
  • A110469 (program): Convolution of J(n)*n! and n! where J(n)=A001045(n), n-th Jacobsthal number.
  • A110471 (program): Prime analog of Baum-Sweet sequence: a(n) = 1 if binary representation of n contains no block of consecutive zeros of exactly prime length; otherwise a(n) = 0.
  • A110473 (program): Integers not in “array with primes”.
  • A110475 (program): Number of symbols ‘*’ and ‘^’ to write the canonical prime factorization of n.
  • A110477 (program): a(n) = Sum_{k=1..n} k*(prime(k) - k).
  • A110480 (program): Numbers n such that (n^2+6)/5 is prime.
  • A110481 (program): Squares of the form 5p - 6, where p is prime.
  • A110482 (program): Primes p such that 5*p - 6 is square.
  • A110484 (program): Squares of the form p*q + p + q + 2, where p and q are primes.
  • A110485 (program): n^2 followed by n followed by n^4 followed by n^3.
  • A110491 (program): Expansion of e.g.f.: sqrt(1+2x)/sqrt(1-2x).
  • A110494 (program): Least k such that prime(n)^2 divides binomial(2k,k).
  • A110496 (program): Least k such that prime(n)^3 divides binomial(2k,k).
  • A110497 (program): a(1) = 1; a(m) = maximum denominator possible with a continued fraction [b(1);b(2),b(3),…,b(m-1)], where (b(1),b(2),b(3),…,b(m-1)) is a permutation of (a(1),a(2),a(3),…,a(m-1)).
  • A110501 (program): Unsigned Genocchi numbers (of first kind) of even index.
  • A110503 (program): Triangle, read by rows, which shifts one column left under matrix inverse.
  • A110505 (program): Numerators of unsigned columns of triangle A110504: a(n) = n!*A110504(n,0) = (-1)^k*n!*A110504(n+k,k) for all k >= 0.
  • A110506 (program): Riordan array (1/(1-xc(2x)),xc(2x)/(1-xc(2x))), c(x) the g.f. of A000108.
  • A110507 (program): Number of nodes in the smallest cubic graph with crossing number n.
  • A110509 (program): Riordan array (1, x(1-2x)).
  • A110510 (program): Riordan array (1, x*c(2x)), c(x) the g.f. of A000108.
  • A110511 (program): Riordan array (1/(1+x), x(1-x)/(1+x)^2).
  • A110512 (program): Expansion of (1 + x)/(1 + x + 2x^2).
  • A110513 (program): Expansion of (1 + x)/(1 + 2x + x^3).
  • A110514 (program): Expansion of (1 - x + x^2 + x^3)/(1 - x^2 - x^4 + x^6).
  • A110515 (program): Sequence array for (1 - x + x^2 + x^3)/(1 - x^4).
  • A110516 (program): Expansion of (1-x+x^2+x^3)/(1+x-x^4-x^5).
  • A110517 (program): Riordan array (1,x(1-3x)).
  • A110518 (program): Riordan array (1, x*c(3x)), c(x) the g.f. of A000108.
  • A110519 (program): Riordan array (1/(1-xc(3x)), xc(3x)/(1-xc(3x))), c(x) the g.f. of A000108.
  • A110520 (program): Expansion of 1/(1-2*x*c(3*x)), c(x) the g.f. of A000108.
  • A110522 (program): Riordan array (1/(1+x), x(1-2x)/(1+x)^2).
  • A110523 (program): Expansion of (1 + x)/(1 + x + 3*x^2).
  • A110524 (program): Expansion of (1 + x)/(1 + 2*x + 2*x^3).
  • A110525 (program): Expansion of 1/(1-x^2*c(3x)), c(x) the g.f. A000108.
  • A110526 (program): a(n+3) = 3*a(n+2) + 5*a(n+1) + a(n), a(0) = 0, a(1) = 1, a(2) = 3.
  • A110527 (program): a(n+3) = 3*a(n+2) + 5*a(n+1) + a(n), a(0) = 0, a(1) = 1, a(2) = 8.
  • A110528 (program): a(n+3) = 3*a(n+2) + 5*a(n+1) + a(n), a(0) = 1, a(1) = 10, a(2) = 37.
  • A110532 (program): a(n) = floor(n/2) + floor(n/5).
  • A110533 (program): a(n) = floor(n/2) * floor(n/5).
  • A110547 (program): Number of sides of regular polygons whose interior angles (in degrees) are not integers.
  • A110548 (program): One of the three ordered sets of positive integers that solves the minimal magic die puzzle.
  • A110549 (program): Period 8: repeat [1, 2, 4, 3, 3, 4, 2, 1].
  • A110550 (program): Periodic {1,3,2,4,4,2,3,1}.
  • A110551 (program): Period 6: repeat [1, 3, 5, 5, 3, 1].
  • A110552 (program): A triangular array related to A077028 and distributing the values of A007582.
  • A110555 (program): Triangle of partial sums of alternating binomial coefficients: T(n,k) = Sum_{j=0..k} binomial(n,j)*(-1)^j; n >= 0, 0 <= k <= n.
  • A110556 (program): a(n) = binomial(2*n-1,n)*(-1)^n for n>0; a(0) = 1.
  • A110558 (program): Numbers n such that (n^2-8)/8 is prime.
  • A110559 (program): Least j such that j*n^2 -1 and j*n^2 +1 are twin primes.
  • A110560 (program): Numerators of T(n+1)/n! reduced to lowest terms, where T(n) are the triangular numbers A000217.
  • A110561 (program): Denominators of T(n+1)/n! reduced to lowest terms, where T(n) are the triangular numbers A000217.
  • A110562 (program): Numbers n such that n in binary representation has a block of exactly a nontrivial pentagonal number of zeros.
  • A110565 (program): Results from a change in the rules leading to sequence A097357.
  • A110566 (program): a(n) = lcm{1,2,…,n}/denominator of harmonic number H(n).
  • A110567 (program): a(n) = n^(n+1) + 1.
  • A110568 (program): Period 6: repeat [1, 0, 2, 2, 0, 1].
  • A110569 (program): Period 6: repeat [2, 1, 3, 3, 1, 2].
  • A110571 (program): Sums of rows of the triangle in A110570.
  • A110573 (program): Numbers n such that the string 666n is prime.
  • A110574 (program): Binary strings that have 1’s where ‘odious numbers’ occur, 0’s elsewhere and every term ends with the n-th odious number index.
  • A110586 (program): Squares of the form 6p+7 for p prime (A110015) that are squares of a prime.
  • A110587 (program): Primes p such that 6q+7=p^2, q prime.
  • A110588 (program): Squares of the form 2*p+3 that are squares of primes.
  • A110589 (program): Primes p such that 2*q+3 = p^2, where q is prime.
  • A110591 (program): Number of digits in base-4 representation of n.
  • A110592 (program): Number of digits in base-5 representation of n. String length of A007091.
  • A110593 (program): a(1) = 3, a(n+1) = 2*(3^n).
  • A110594 (program): a(1) = 4, a(2) = 12, for n>1: a(n) = 3*4^(n-1).
  • A110595 (program): a(1)=5. For n > 1, a(n) = 4*5^(n-1) = A005054(n).
  • A110601 (program): a(n) = phi(n)*tau(n)^2, where phi is Euler’s totient function and tau(n) is the number of divisors of n.
  • A110603 (program): Numbers n whose base 5 representations, interpreted as base 10 integers, are semiprimes.
  • A110604 (program): Numbers n whose base 6 representations, interpreted as base 10 integers, are semiprimes.
  • A110605 (program): Numbers n whose base 7 representations, interpreted as base 10 integers, are semiprimes.
  • A110606 (program): Numbers n whose base 8 representations, interpreted as base 10 integers, are semiprimes.
  • A110607 (program): Numbers n whose base 9 representations, interpreted as base 10 integers, are semiprimes.
  • A110608 (program): Number triangle T(n,k) = binomial(n,k)*binomial(2n,n-k).
  • A110609 (program): a(n) = n * C(2*n,n-1).
  • A110610 (program): Maximal value of sum(p(i)p(i+1),i=1..n), where p(n+1)=p(1), as p ranges over all permutations of {1,2,…,n}.
  • A110611 (program): Minimal value of sum(p(i)p(i+1),i=1..n), where p(n+1)=p(1), as p ranges over all permutations of {1,2,…,n}.
  • A110613 (program): a(n+3) = 5*a(n+2) - 2*a(n+1) - 8*a(n), a(0) = 1, a(1) = 0, a(2) = 3.
  • A110614 (program): a(n+3) = 5*a(n+2) - 2*a(n+1) - 8*a(n), a(0) = 1, a(1) = 5, a(2) = 15.
  • A110616 (program): A convolution triangle of numbers based on A001764.
  • A110617 (program): The decimal expansion of 1/64532 (related to an optimal mixed strategy for Hofstadter’s million dollar game).
  • A110622 (program): n^2 followed by n followed by n^3 followed by n^4.
  • A110650 (program): n^2 followed by n^4 followed by n followed by n^3.
  • A110651 (program): n^2 followed by n^4 followed by n^3 followed by n.
  • A110652 (program): n^2 followed by n^3 followed by n^4 followed by n.
  • A110653 (program): n^2 followed by n^3 followed by n followed by n^4.
  • A110654 (program): a(n) = ceiling(n/2), or: a(2*k) = k, a(2*k+1) = k+1.
  • A110655 (program): a(n) = A110654(A110654(n)).
  • A110656 (program): a(n) = A110654(A110654(A110654(n))).
  • A110657 (program): a(n) = A028242(A028242(n)).
  • A110658 (program): a(n) = A028242(A028242(A028242(n))).
  • A110659 (program): a(n) = A028242(A110654(n)).
  • A110660 (program): Oblong (promic) numbers repeated.
  • A110661 (program): Triangle read by rows: T(n,k) = total number of divisors of k, k+1, …, n (1 <= k <= n).
  • A110662 (program): Triangle read by rows: T(n,k) is the sum of the sums of divisors of k, k+1, …, n (1 <= k <= n).
  • A110663 (program): Triangle read by rows: T(n,k) = Sum_{j=k..n} phi(j) (1<=k<=n), where phi is Euler’s totient function.
  • A110664 (program): Triangle read by rows: T(n,k)=sum(bigomega(j),j=k..n) (1<=k<=n), where bigomega(j) is the number of prime divisors of j, counted with multiplicities.
  • A110665 (program): Sequence is {a(0,n)}, where a(m,0)=0, a(m,n) = a(m-1,n)+a(m,n-1) and a(0,n) is such that a(n,n) = n for all n.
  • A110666 (program): Sequence is {a(1,n)}, where a(m,n) is defined at sequence A110665.
  • A110667 (program): Sequence is {a(2,n)}, where a(m,n) is defined at sequence A110665.
  • A110668 (program): Sequence is {a(3,n)}, where a(m,n) is defined at sequence A110665.
  • A110669 (program): Sequence is {a(4,n)}, where a(m,n) is defined at sequence A110665.
  • A110670 (program): Sequence is {a(5,n)}, where a(m,n) is defined at sequence A110665.
  • A110671 (program): Sequence is {a(6,n)}, where a(m,n) is defined at sequence A110665.
  • A110672 (program): Sequence is {a(7,n)}, where a(m,n) is defined in sequence A110665.
  • A110673 (program): Numbers that are neither the sum nor the difference of two primes.
  • A110678 (program): a(n) = -n^2 - n + 72.
  • A110679 (program): a(n+3) = 3*a(n+2) + 5*a(n+1) + a(n), a(0) = 1, a(1) = 2, a(2) = 11.
  • A110681 (program): A convolution triangle of numbers based on A071356.
  • A110691 (program): Kekulé numbers for certain benzenoids.
  • A110695 (program): Kekulé numbers for certain benzenoids of trigonal symmetry.
  • A110696 (program): Kekulé numbers for certain benzenoids of trigonal symmetry.
  • A110697 (program): Kekulé numbers for certain benzenoids of trigonal symmetry.
  • A110707 (program): Number of linear arrangements of n blue, n red and n green items such that there are no adjacent items of the same color (first and last elements considered as adjacent).
  • A110728 (program): Digital factorial: a(0) = 1, a(n) = n * (the sum of the digits of a(n-1)).
  • A110729 (program): Factorial terms of Digital factorial (A110728).
  • A110730 (program): Irregular triangle read by rows in which row n lists n 1’s followed by (n-1) 2’s followed by (n-3) 3’s … followed by 1 n.
  • A110737 (program): Row sums in A112668.
  • A110738 (program): a(n) = common ratio for row n in A112668.
  • A110739 (program): Arithmetic mean of row n in A112668.
  • A110748 (program): Form triangle shown below, in which the n-th row contains n terms of an arithmetic progression with first term 1 and common difference n. Then a(n) = terms of the n-th row (mod 10), concatenated.
  • A110749 (program): Triangle read by rows with the n-th row containing the first n multiples of n with digits reversed.
  • A110751 (program): Numbers n such that n and its digital reversal have the same prime divisors.
  • A110765 (program): Let n in binary be a k-digit number say abbaaa… where a = 1 and b = 0. a(n) = 2^a*3^b*5^b*7*a… primes in increasing order raised to the powers starting from the MSB.
  • A110766 (program): Fractalization of Pi.
  • A110769 (program): The r-th term of the n-th row of the following triangle contains sum of r successive numbers in decreasing order beginning from T(n)-T(r-1) where T(n) is the n-th triangular number. 1 3 3 6 9 6 10 17 18 10 15 27 33 30 15 … Sequence contains the triangle by rows.
  • A110770 (program): Triangle read by rows: T(n,k) = binomial(t(n) - t(k-1),k), where t(j) = j*(j+1)/2; 1<=k<=n.
  • A110771 (program): The r-th term of the n-th row of the following triangle is C[{T(n)-T(r-1)},r] where T(n) is the n-th triangular number. 1 3 1 6 10 1 10 36 35 1 … Sequence contains the row sums.
  • A110779 (program): Fractalization of e.
  • A110800 (program): n-th digit after decimal point in decimal expansion of n/(n+1).
  • A110801 (program): Numbers n such that 12n + 1 is prime.
  • A110803 (program): n times the number of digits in the decimal expansion of n.
  • A110804 (program): a(1) = 10, a(n) = a(n-1) times the number of digits in a(n-1).
  • A110805 (program): Sum of digits of n times number of digits of n.
  • A110807 (program): n times largest n-digit number.
  • A110808 (program): Least factorial obtained as n(n-1)…(n-k).
  • A110809 (program): a(1) = 3, a(2n) = a(2n-1)*(a(2n-1)+1)/2, a(2n+1) = a(2n)*(a(2n)-1)/2.
  • A110810 (program): Binomial transform of A000796.
  • A110812 (program): Fractalization of sqrt 2.
  • A110813 (program): A triangle of pyramidal numbers.
  • A110814 (program): Inverse of a triangle of pyramidal numbers.
  • A110822 (program): G.f.: square root of weight enumerator of [16,5,8] Reed-Muller code RM(1,4).
  • A110824 (program): G.f.: square root of weight enumerator of [32,6,16] Reed-Muller code RM(1,5).
  • A110826 (program): G.f.: square root of weight enumerator of [64,7,32] Reed-Muller code RM(1,6).
  • A110828 (program): G.f.: square root of weight enumerator of [128,8,64] Reed-Muller code RM(1,7).
  • A110831 (program): a(n) = 3*n^2 + 27*n + 1.
  • A110833 (program): a(n) = (prime(n)+1)^2.
  • A110837 (program): Number of ways to fold a strip of n stamps taking account of order and direction of folds.
  • A110847 (program): Weight enumerator of [32,31,2] Reed-Muller code RM(4,5).
  • A110851 (program): Weight enumerator of [64,63,2] Reed-Muller code RM(5,6).
  • A110854 (program): A155750(n)-A155067(n) = prime(2n+2)-prime(2n+1)-prime(2n)+prime(2n-1).
  • A110858 (program): Triangle read by rows: number of order-preserving partial transformations (of an n-element chain) of width and waist both equal to r (width(alpha) = |Dom(alpha)| and waist(alpha) = max(Im(alpha)).
  • A110862 (program): Highest minimal distance of odd formally self-dual binary codes of length 2n.
  • A110867 (program): Highest minimal distance of Type I but not Type II additive Hermitian self-dual codes of length n over GF(4).
  • A110870 (program): Highest minimal distance of Type II additive Hermitian self-dual codes of length n over GF(4).
  • A110872 (program): Numbers n such that (n^2+7)/8 is prime.
  • A110873 (program): Squares of the form 8p - 7, where p is prime.
  • A110882 (program): a(n) is the least integer x such that x^n < 2 * (x-1)^n.
  • A110883 (program): Sum of consecutive digits in the decimal expansion of Pi.
  • A110892 (program): Sum of the squares of digits of n^2.
  • A110893 (program): Numbers with a semiprime number of prime divisors (counted with multiplicity).
  • A110895 (program): Number of integers between a(n) and a(n+1) equals the n-th prime.
  • A110901 (program): Product_{k=1..n} (A013929(k)), the product of the first n positive integers that are each divisible by at least one square >= 4.
  • A110903 (program): Difference between the factorial of n and the double factorial of n.
  • A110906 (program): Expansion of (1 +34*x +121*x^2)/((1-x)*(x^2 -14*x +1)).
  • A110907 (program): Number of points in the standard root system version of the D_3 (or f.c.c.) lattice having L_infinity norm n.
  • A110914 (program): “Self-convolution mod 3” of central Delannoy numbers (see comment).
  • A110916 (program): Number of squares between 10n and 10n+9 (inclusive).
  • A110923 (program): Final two digits of prime(n), with leading zero omitted.
  • A110934 (program): Difference between 3-almostprime(n) and 3-almostprime(n+2).
  • A110935 (program): a(n) = if n mod 2 = 0 then 8*F(n)-n otherwise 8*F(n)-4, where F() = Fibonacci numbers A000045.
  • A110936 (program): a(n) = denominator(Bernoulli(prime(n) - 1))/prime(n).
  • A110947 (program): a(n) = permanent of an n X n matrix M of zeros and ones defined as follows: if we concatenate the rows of M to form a vector v of length n^2, v_i = 1 only if i = 1 or a multiple of 2.
  • A110952 (program): Triangle read by rows: T(n,k) = number of permutations of [n] where the first increasing run has length k and the last increasing run has length n-k-1, 0<k<n-1.
  • A110953 (program): Starting a priori with the fraction 1/1, the denominators of fractions built according to the rule: add top and bottom to get the new bottom, add top and 9 times the bottom to get the new top.
  • A110954 (program): a(1) = 1; a(n) = nextprime(2.5*a(n-1)) for n > 1.
  • A110959 (program): Numbers n such that 23*n^2 + 1 is prime.
  • A110960 (program): Numbers n such that 23*n^2 + 4 is prime.
  • A110961 (program): Numbers n such that 23*n^2 + 9 is prime.
  • A110962 (program): Fractalization of A025480, zero-based version of Kimberling’s paraphrases sequence.
  • A110963 (program): Fractalization of Kimberling’s paraphrases sequence beginning with 1.
  • A110964 (program): Numbers k such that 23*k^2 + 16 is prime.
  • A110965 (program): Numbers k such that 23*k^2 + 25 is prime.
  • A110966 (program): Numbers k such that 23*k^2 + 36 is prime.
  • A110967 (program): Numbers k such that 23*k^2 + 49 is prime.
  • A110974 (program): Numbers n such that 23*n^2 - 1 is prime.
  • A110976 (program): Sequence of numerators associated with the continued fraction based on the sequence d(n)= distance of n from closest prime ( A051699).
  • A110977 (program): Sequence of denominators associated with the continued fraction based on the sequence d(n)= distance of n from closest prime ( A051699).
  • A110994 (program): Numbers n such that 23*n^2 - 4 is prime.
  • A110998 (program): Numbers n such that 23*n^2 - 9 is prime.
  • A110999 (program): Numbers n such that 23*n^2 - 16 is prime.
  • A111002 (program): a(n) = gcd(f(n), f(n+1)) where f(n) = n^4 + n^2 + 1.
  • A111003 (program): Decimal expansion of Pi^2/8.
  • A111006 (program): Another version of Fibonacci-Pascal triangle A037027.
  • A111007 (program): Triangle T(n,m) which contains in row n the rounded ordinate value at abscissa m along the upper rim of the circle with diameter n centered at (n/2, 1).
  • A111008 (program): a(n) = A000367(n)/A141590(n).
  • A111017 (program): a(n) = (A102877(n+1) - A102877(n))/2.
  • A111018 (program): Indices of Catalan numbers that are divisible by 3.
  • A111019 (program): Indices of Catalan numbers that are == 1 mod 3 (cf. A000108).
  • A111020 (program): Indices of Catalan numbers (A000108) that are == 2 mod 3.
  • A111025 (program): Number of cubes between 10n and 10n+9 (inclusive).
  • A111029 (program): Magic products of 3 X 3 multiplicative magic squares.
  • A111033 (program): Sum of squares of first n digits of Pi.
  • A111034 (program): Sum of squares of digits of e.
  • A111040 (program): Numbers n such that 2*n^2 + 9 is prime.
  • A111041 (program): Numbers n such that 2*n^2 + 25 is prime.
  • A111043 (program): Partial sums of squares of digits of golden ratio phi (A001622).
  • A111046 (program): Difference between squares of twin prime pairs.
  • A111048 (program): a(n) = least i such that prime(n)/prime(n+1) < 1 - 1/i.
  • A111049 (program): Triangle T(n,k), 0 <= k <= n, read by rows, given by [1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, …] DELTA [1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, …] where DELTA is the operator defined in A084938.
  • A111051 (program): Numbers n such that 3*n^2 + 1 is prime.
  • A111052 (program): Numbers n such that 3*n^2 + 4 is prime.
  • A111053 (program): Number of permutations which avoid the patterns 1324 and (2143 with Bruhat restriction {2<->3}). Also the number of permutations whose graphs are acyclic.
  • A111054 (program): Sum of squares of digits of decimal expansion of square root of 2.
  • A111059 (program): Product{k=1 to n} (A005117(k)), the product of the first n squarefree positive integers.
  • A111060 (program): a(n) = sum of primes dividing the n-th squarefree positive integer.
  • A111061 (program): Begin with 1,2 In binary 1, 10. To get the sequence, left pad binary number with its precedent: 1,10, 110, 10110, 11010110, 1011011010110, etc. Note the number of bits of the n-th term is the (n-1)st Fibonacci number. Now convert back to decimal 1,2,6,22,214,5846, …
  • A111062 (program): Triangle T(n, k) = binomial(n, k) * A000085(n-k), 0 <= k <= n.
  • A111063 (program): a(0) = 1; a(n) = (n-1)*a(n-1) + n.
  • A111066 (program): Numbers with digits 1 and 2 and at least one of each.
  • A111068 (program): Numbers k such that 3*k^2 + 16 is prime.
  • A111069 (program): Numbers k such that 3*k^2 + 25 is prime.
  • A111071 (program): Difference between the product of two consecutive primes and the next prime.
  • A111072 (program): Write the digit string 0123456789, repeated infinitely many times. Then, starting from the first “0” digit at the left end, move to the right by one digit (to the “1”), then two digits (to the “3”), then three digits (to the “6”), four digits (“0”), five digits (“5”), and so on. Partial sums of the digits thus reached are 0, 1, 4, 10, 10, 15, …
  • A111074 (program): Let t(n) denote the triangular numbers (A000217). Sequence mixes t(n+2) and t(n).
  • A111077 (program): Smallest squarefree integer > the n-th term of the Fibonacci sequence.
  • A111080 (program): Sum of numbers under a triangle on a spiral staircase of width 10.
  • A111082 (program): Numbers n such that 3*n^2 + 49 is prime.
  • A111083 (program): Numbers k such that 3*k^2 + 64 is prime.
  • A111087 (program): Neither primes nor semiprimes.
  • A111089 (program): Largest prime factor of 2n.
  • A111092 (program): Primes congruent to {1,69} mod 70.
  • A111093 (program): Like sequence A111072 but moving right by the squares of the sequence of positive integers.
  • A111094 (program): Numbers k such that 18*k + 1 is prime.
  • A111096 (program): Partial sums of A137701.
  • A111097 (program): Maximum likelihood estimate of the number of distinguishable marbles in an urn if repeated random sampling of one marble with replacement yields n different marbles before the first repeated marble.
  • A111099 (program): Sum of even Fermat coefficients rounded to nearest integer.
  • A111102 (program): Cumulative sum of squares of Kolakoski sequence (A000002).
  • A111108 (program): a(n) = A001333(n) - (-2)^(n-1), n > 0.
  • A111110 (program): Expansion of x*(x^4 - x^3 + 4x^2 - 3x + 1)/(1 - 5x + 9x^2 - 8x^3 + 2x^4 - x^5).
  • A111113 (program): a(2^m) = 1, a(2^m+1) = -1 (m>0), otherwise a(n) = 0.
  • A111114 (program): Integer part of prime(n)/pi(n).
  • A111121 (program): a(n) = a(n-3)^3 + a(n-2)^2 + a(n-1); a(1) = -1, a(2) = 0, a(3) = 1.
  • A111125 (program): Triangle read by rows: T(k,s) = ((2*k+1)/(2*s+1))*binomial(k+s,2*s), 0 <= s <= k.
  • A111132 (program): a(n+1) = a(n) + (a(n) - a(n-1) + a(n) mod 10) mod 10 with a(0)=0 and a(1)=1.
  • A111133 (program): Number of partitions of n into at least two distinct parts.
  • A111135 (program): Product_{k=1..n} F(p(k)), where p(k) is the k-th prime and F(k) is the k-th Fibonacci number.
  • A111136 (program): a(n) = Sum_{k=1..n} Fibonacci(prime(k)).
  • A111138 (program): Let b(n) denote the number of nontriangular numbers less than or equal to n. Then a(n) = b(n-1) + a(b(n-1)), with a(1) = a(2) = 0, a(3) = 1.
  • A111139 (program): a(n) = n!*Sum_{k=0..n} Fibonacci(k)/k!.
  • A111140 (program): a(n) = (n!/(n+1))*Sum_{k=0..n} binomial(n+k-1,k)/k!.
  • A111144 (program): a(n) = n*(n+13)*(n+14)/6.
  • A111145 (program): Length of the Cunningham chain initiated by the n-th Sophie Germain prime.
  • A111147 (program): Numbers n such that 5*n^2 + 1 is prime.
  • A111148 (program): Numbers n such that 5*n^2 + 4 is prime.
  • A111149 (program): Numbers n such that 5*n^2 + 9 is prime.
  • A111150 (program): a(n) is the number of integers of the form (n+k)/|(n-k)| for k>0.
  • A111153 (program): Sophie Germain semiprimes: semiprimes n such that 2n+1 is also a semiprime.
  • A111160 (program): G.f.: C - Z; where C is the g.f. for the Catalan numbers (A000108) and Z is the g.f. for A055113 with offset 0.
  • A111165 (program): Let qf(a,q) = Product(1-a*q^j,j=0..infinity); g.f. is qf(q,q^3)/qf(q^2,q^3).
  • A111166 (program): Let p < q be consecutive primes; p is in the sequence if p/(q-p) is a record.
  • A111168 (program): Semiprimes n such that 2*n - 1 is also a semiprime.
  • A111170 (program): Semiprimes S such that 3*S + 1 is also a semiprime.
  • A111171 (program): Semiprimes S such that 3*S - 1 is also a semiprime.
  • A111174 (program): Numbers k such that 24*k + 1 is prime.
  • A111175 (program): Numbers n such that 30*n + 1 is prime.
  • A111177 (program): Number of base n numbers in which each digit appears at most once (all unnecessary 0’s deleted).
  • A111179 (program): a(n) = Sum_{k=1..n} prime(k)!, where prime(k) is k-th prime.
  • A111181 (program): Prime(n) - Pi(n).
  • A111186 (program): Difference between the closest squares surrounding squarefree composite numbers.
  • A111192 (program): Product of the n-th sexy prime pair.
  • A111196 (program): a(n) = 2^(-n)*Sum_{k=0..n} binomial(2*n+1, 2*k+1)*A000364(n-k).
  • A111199 (program): Numbers n such that 4k + 9 is prime.
  • A111204 (program): Difference between the closest squares surrounding a squarefree composite number and n have a common divisor greater than 1.
  • A111208 (program): Number of primes <= n-th triangular number.
  • A111209 (program): Difference between the powers of two and the primes.
  • A111213 (program): Difference between the closest squares surrounding prime p is prime.
  • A111214 (program): Score for an n-letter word in the game of Boggle.
  • A111215 (program): Numbers k such that 4k + 5 is prime.
  • A111216 (program): a(n) = 31*a(n-1)-a(n-2).
  • A111217 (program): d_7(n), tau_7(n), number of ordered factorizations of n as n = rstuvwx (7-factorizations).
  • A111218 (program): d_8(n), tau_8(n), number of ordered factorizations of n as n = rstuvwxy (8-factorizations).
  • A111219 (program): d_9(n), tau_9(n), number of ordered factorizations of n as n = rstuvwxyz (9-factorizations).
  • A111220 (program): d_10(n), tau_10(n), number of ordered factorizations of n as n = rstuvwxyza (10-factorizations).
  • A111221 (program): d_11(n), tau_11(n), number of ordered factorizations of n as n = rstuvwxyzab (11-factorizations).
  • A111222 (program): Integers that can be expressed as the sum of 4 factorials.
  • A111223 (program): Numbers n such that 5*n + 2 is prime.
  • A111224 (program): Numbers n such that 5*n + 7 is prime.
  • A111225 (program): Numbers n such that 5*n + 8 is prime.
  • A111226 (program): Numbers n such that 5*n + 12 is prime.
  • A111230 (program): Numbers n such that 5*n + 14 is prime.
  • A111234 (program): a(1)=2; thereafter a(n) = (largest proper divisor of n) + (smallest prime divisor of n).
  • A111235 (program): a(1)=a(2)=a(3)=a(4)=1. For n >= 5, a(n)= a(n-1)*a(n-2) + a(n-3)*a(n-4).
  • A111236 (program): a(1)=a(2)=a(3)=a(4)=1. For n >= 5, a(n)= (a(n-1)+a(n-2)) * (a(n-3)+a(n-4)).
  • A111249 (program): Numbers n such that 7*n + 8 is prime.
  • A111250 (program): Numbers n such that 7*n + 10 is prime.
  • A111251 (program): Numbers k such that 3*k^2 + 3*k + 1 is prime.
  • A111254 (program): a(n) = Prime[n+2]+Prime[n]+1.
  • A111255 (program): Primes in A111254.
  • A111262 (program): a(n) = (1/n)*Sum_{k=1..n} F(4*k)*B(2*n-2*k)*binomial(2*n,2*k)), where F are Fibonacci numbers and B are Bernoulli numbers.
  • A111277 (program): Number of permutations avoiding the patterns {2413,4213,2431,4231,4321}; also number of permutations avoiding the patterns {3142,3412,3421,4312,4321}; number of weak sorting class based on 2413 or 3142.
  • A111279 (program): Number of permutations avoiding the patterns {3241,3421,4321}; number of weak sorting class based on 3241.
  • A111281 (program): Number of permutations avoiding the patterns {2413,2431,4213,3412,3421,4231,4321,4312}; number of strong sorting class based on 2413.
  • A111282 (program): Number of permutations avoiding the patterns {1432,2431,3412,3421,4132,4231,4312,4321}; number of strong sorting class based on 1432.
  • A111283 (program): Number of permutations avoiding the patterns {4321, 45132, 45231, 35412, 53412, 45213, 43512, 45312, 456123, 451623, 356124}; number of strong sorting class based on 4321.
  • A111284 (program): Number of permutations of [n] avoiding the patterns {2143, 2341, 2413, 2431, 3142, 3241, 3412, 3421, 4123, 4213, 4231, 4321, 4132, 4312}; number of strong sorting classes based on 2143.
  • A111285 (program): Number of permutations avoiding the patterns {2431, 3421, 4231, 4321, 24513, 42513, 34512, 43512}; number of strong sorting class based on 2431.
  • A111286 (program): Number of permutations avoiding the patterns {1342, 1432, 2341, 2431, 3142, 3241, 3412, 3421, 4132, 4231, 4312, 4321}; number of strong sorting class based on 1342.
  • A111288 (program): a(1) = a(2) = a(3) = a(4) = 1. For n>= 5, a(n) = a(n-1)*a(n-3) + a(n-2)*a(n-4).
  • A111289 (program): a(1) = a(2) = a(3) = a(4) = 1. For n>= 5, a(n) = a(n-1)*a(n-4) + a(n-2)*a(n-3).
  • A111290 (program): a(1)=1, a(n) = n + (sum of distinct primes dividing a(n-1)).
  • A111292 (program): Numbers n such that 6*n^2 + 6*n + 1 is prime.
  • A111294 (program): Numbers n such that 23*n + 2 is prime.
  • A111295 (program): Number of partitions of 3n+1.
  • A111297 (program): First differences of A109975.
  • A111305 (program): Composite numbers k such that a^(k-1) == 1 (mod k) only when a == 1 (mod k).
  • A111306 (program): d_12(n), tau_12(n), number of ordered factorizations of n as n = rstuvwxyzabc (12-factorizations).
  • A111312 (program): Numbers n such that 11*n + 2 is prime.
  • A111314 (program): a(n) = a(n-1) + a(n-2) + 2 where a(0) = a(1) = 1.
  • A111317 (program): Let f(a,q) = Product_{j>=0} (1 - a*q^j); g.f. is f(q^2,q^3) / f(q,q^3).
  • A111318 (program): Numbers n such that 4 divides prime(1)+…+prime(n).
  • A111329 (program): Number of partitions of T where T = (3n + 1) if n is even and T=(3n + 1)/2 if n is odd.
  • A111330 (program): Let qf(a,q) = Product_{j >= 0} (1-a*q^j); g.f. is qf(q,q^4)/qf(q^3,q^4).
  • A111333 (program): Number of odd numbers <= n-th prime.
  • A111335 (program): Let qf(a,q) = Product(1-a*q^j,j=0..infinity); g.f. is qf(q^3,q^4)/qf(q,q^4).
  • A111343 (program): G.f. A(x/(1-x)), where A = g.f. for A090351.
  • A111350 (program): Squares n such that 2*n + 1 is a semiprime.
  • A111351 (program): Semiprimes of the form 2*n + 1, where n is a square.
  • A111352 (program): a(n+3) = a(n+2) + 3*a(n+1) + a(n).
  • A111362 (program): Sequence defined by an recurrence.
  • A111365 (program): a(n) = 5*a(n-1) + 3*a(n-2) where a(0) = a(1) = 1.
  • A111367 (program): Numbers k such that 7*k + 5 is prime.
  • A111368 (program): The number of maximal determinant {-1,1} matrices of order n.
  • A111369 (program): Numbers k such that 13*k + 11 is prime.
  • A111370 (program): Number of partitions of (6*n + 1).
  • A111374 (program): Series expansion of the reciprocal of the Goellnitz-Gordon continued fraction.
  • A111384 (program): a(n) = binomial(n,3) - binomial(floor(n/2),3) - binomial(ceiling(n/2),3).
  • A111385 (program): a(n) = binomial(n,4) - binomial(floor(n/2),4) - binomial(ceiling(n/2),4).
  • A111386 (program): a(1) = 1, a(2) = 3; for n >= 3, take a(n) to be the smallest odd number not occurring earlier such that a(n-1) divides the concatenation a(n-2)a(n).
  • A111393 (program): Number of digits in n^3.
  • A111394 (program): a(n) = product of first n integers not divisible by 3.
  • A111395 (program): First digit of powers of 5 (n>=1).
  • A111396 (program): a(n) = n*(n+7)*(n+8)/6.
  • A111397 (program): Composite numbers (modulo 3).
  • A111398 (program): Numbers which are the cube roots of the product of their proper divisors.
  • A111405 (program): a(n) = f(f(n+1)) - f(f(n)), where f(0) = 0 and f(m) = bigomega(m) = A001222(m) for m > 0.
  • A111406 (program): a(n) = f(f(n+1)) - f(f(n)), where f(m) = pi(m) = A000720(m), with f(0) = 0.
  • A111407 (program): a(n) = f(f(n+1)) - f(f(n)), where f(0) = 0 and f(m) = tau(m) = A000005(m) for m > 0.
  • A111408 (program): f(f(n+1))-f(f(n)), where f(0)=0, and for m>0, f(m) = sigma(m) = A000203(m).
  • A111409 (program): a(n) = f(f(n+1)) - f(f(n)), where f(0)=0, and for m>0, f(m) = phi(m) = A000010(m).
  • A111412 (program): f(f(n+1))-f(f(n)), where f(m) = wt(m) = A000120(m).
  • A111417 (program): a(n) = A034869(n) - A008311(n).
  • A111418 (program): Right-hand side of odd-numbered rows of Pascal’s triangle.
  • A111424 (program): Sum_{i=1..n} (2i)!/i!.
  • A111425 (program): a(n) = tribonacci(Fibonacci(n)).
  • A111426 (program): Difference between largest and smallest prime factor of the n-th composite number.
  • A111427 (program): Tribonacci(tetranacci(n)).
  • A111428 (program): Tribonacci(pentanacci(n)).
  • A111429 (program): Tribonacci(hexanacci(n)).
  • A111430 (program): Tribonacci(heptanacci(n)).
  • A111431 (program): a(n) = Fibonacci(tribonacci(n)).
  • A111432 (program): Fibonacci(tetranacci(n)).
  • A111433 (program): Fibonacci(pentanacci(n)).
  • A111435 (program): a(n) = Fibonacci(hexanacci(n)).
  • A111438 (program): Fibonacci(heptanacci(n)), restricted to nonzero heptanacci numbers.
  • A111451 (program): Number of partitions of P where P=(5*n + 1) if n is even and P=((5*n + 1)/2) if n is odd.
  • A111454 (program): a(n) = (n-4)^(n-3) - (n-3)^(n-4) + 1.
  • A111455 (program): Numbers n such that 101*n + 97 is prime.
  • A111457 (program): Number of semiprimes smaller than the n-th prime.
  • A111458 (program): Numbers that cannot be represented as the sum of at most three Fibonacci numbers (with repetitions allowed).
  • A111459 (program): Generalized Somos-4 sequence with a(n-2)^2 replaced by a(n-2)^5.
  • A111466 (program): a(1) = 1, a(n+1) = a(n) - F(n+1), if F(n+1) <= a(n), else a(n+1) = a(n) + F(n+1). F(n) is the n-th Fibonacci number (A000045).
  • A111484 (program): Triangular numbers all of whose digits are nonprimes.
  • A111490 (program): Antidiagonal sums of the numerical array defined by M(n,k) = 1 + (k-1) mod n.
  • A111491 (program): a(0) = 1; for n>0, a(n) = (2^n-1)*a(n-1)-(-1)^n.
  • A111492 (program): Triangle read by rows: a(n,k) = (k-1)! * C(n,k).
  • A111495 (program): Floor of 10^n/Li(10^n) - 1.
  • A111500 (program): Number of squares in an n X n grid of squares with diagonals.
  • A111501 (program): Numbers n such that n^3 - n^2 + 1 is prime.
  • A111505 (program): Right half of Pascal’s triangle (A007318) with zeros.
  • A111515 (program): Number of partitions of T where T=(7*n + 1) if n is even and T=((7*n + 1)/2) if n is odd.
  • A111517 (program): Numbers n such that (7*n + 1)/2 is prime.
  • A111526 (program): Number triangle T(n,k)=C((n+k)/2,k)(n+1)(1+(-1)^(n-k))/(2(k+1)); T(n,k)=(-1)^((n-k)/2)*A053120(n+1,k+1)/2^k; Riordan array ((1+x^2)/(1-x^2)^2,x/(1-x^2)).
  • A111527 (program): Inverse of A111526. Row sums have general term C(n,floor(n/2))*(cos(Pi*n/2) + sin(Pi*n/2)).
  • A111529 (program): Row 2 of table A111528.
  • A111530 (program): Row 3 of table A111528.
  • A111531 (program): Row 4 of table A111528.
  • A111532 (program): Row 5 of table A111528.
  • A111533 (program): Row 6 of table A111528.
  • A111537 (program): Column 1 of triangle A111536.
  • A111538 (program): Column 2 of triangle A111536; also equals column 0 of triangle A111541, which is the matrix log of triangle A111536.
  • A111545 (program): Column 1 of triangle A111544.
  • A111546 (program): Column 2 of triangle A111544.
  • A111547 (program): Column 3 of triangle A111544; also found in column 0 of triangle A111549, which equals the matrix logarithm of A111544.
  • A111554 (program): Column 1 of triangle A111553.
  • A111555 (program): Column 2 of triangle A111553.
  • A111556 (program): Column 3 of triangle A111553.
  • A111566 (program): a(n) = ((1+sqrt(8))*(2+sqrt(2))^n + (1-sqrt(8))*(2-sqrt(2))^n)/2.
  • A111567 (program): Binomial transform of A048654: generalized Pellian with second term equal to 4.
  • A111568 (program): Triangle read by rows: row n contains n terms of the arithmetic progression having first term 1 and common difference 2[n^(n-1)-1]/(n-1).
  • A111569 (program): a(n) = a(n-1) + a(n-3) + a(n-4) for n>3, a(0) = -1, a(1) = 1, a(2) = 2, a(3) = 1.
  • A111570 (program): a(n) = a(n-1) + a(n-3) + a(n-4), n >= 4.
  • A111571 (program): a(n) = a(n-1) + a(n-3) + a(n-4), n >= 4.
  • A111572 (program): a(n) = a(n-1) + a(n-3) + a(n-4), n >= 4.
  • A111573 (program): a(n) = a(n-1) + a(n-3) + a(n-4), n >= 4.
  • A111574 (program): a(n) = a(n-1) + a(n-3) + a(n-4), n >= 4.
  • A111575 (program): Powers of 3 repeated four times.
  • A111587 (program): a(n) = 2*a(n-1) + 2*a(n-3) + a(n-4), a(0) = 1, a(1) = 4, a(2) = 9, a(3) = 20.
  • A111589 (program): Triangle read by rows: number of idempotent order-preserving partial transformations (of an n-element totally ordered set) of width k (width(alpha) = |Dom(alpha)|
  • A111595 (program): Triangle of coefficients of square of Hermite polynomials divided by 2^n with argument sqrt(x/2).
  • A111596 (program): The matrix inverse of the unsigned Lah numbers A271703.
  • A111597 (program): Lah numbers: a(n) = n!*binomial(n-1,6)/7!.
  • A111598 (program): Lah numbers: a(n) = n!*binomial(n-1,7)/8!.
  • A111599 (program): Lah numbers: a(n) = n!*binomial(n-1,8)/9!.
  • A111600 (program): Lah numbers: a(n) = n!*binomial(n-1,9)/10!.
  • A111601 (program): Exponential (binomial) convolution of A001818 (with interspersed zeros) and A000142 (factorials).
  • A111602 (program): Third column (m=2) of unsigned triangle A111595.
  • A111607 (program): Fourth column of A109626.
  • A111636 (program): Triangle read by rows: T(n,k) (0<=k<=n) is the number of labeled graphs having k blue nodes and n-k green ones and only nodes of different colors can be joined by an edge.
  • A111637 (program): Number of labeled graphs having n blue nodes and n green ones, where edges join only nodes of different colors.
  • A111639 (program): Expansion of (3+8*x-3*x^2-2*x^3)/((x^2+4*x+1)*(x^2-2*x-1)).
  • A111640 (program): Expansion of (-1+3*x+x^2-x^3)/((x^2+4*x+1)*(x^2-2*x-1)).
  • A111641 (program): Expansion of -(1+x+3*x^2+x^3)/((x^2+4*x+1)*(x^2-2*x-1)).
  • A111642 (program): Expansion of 2*(x-1)*(x+1)/((x^2+4*x+1)*(x^2-2*x-1)).
  • A111643 (program): Expansion of 2*(x+1)^2/((x^2+4*x+1)*(x^2-2*x-1)).
  • A111644 (program): Expansion of -(1+x^2)/((x^2+4*x+1)*(x^2-2*x-1)).
  • A111645 (program): Expansion of (x+1)*(1-3*x)/((x^2+4*x+1)*(x^2-2*x-1)).
  • A111647 (program): a(n) = A001541(n)*A001653(n)*A002315(n).
  • A111648 (program): a(n) = A001541(n)^2 + A001653(n)^2 + A002315(n)^2.
  • A111650 (program): 2n appears n times (n>0).
  • A111651 (program): n appears 3n times.
  • A111652 (program): 3n appears n times.
  • A111653 (program): n-th composite number appears n times.
  • A111654 (program): n appears n-th composite number times.
  • A111655 (program): n-th composite number appears n-th composite number times.
  • A111657 (program): n-th composite number appears n-th prime times.
  • A111661 (program): Expansion of eta(q)^4 * eta(q^2) * eta(q^6)^5 / eta(q^3)^4 in powers of q.
  • A111663 (program): Expansion of (-1+x^3+x^6+x^9)/((1-x)*(2*x-1)*(x^2+1)*(x^2+x+1)*(x^4-x^2+1)).
  • A111665 (program): Expansion of (-1+x+2*x^2+5*x^4+3*x^3) / ((x-1)*(x+1)*(x^2-3*x+1)*(1+x^2)).
  • A111666 (program): Expansion of (-2+3*x+3*x^2+4*x^3+3*x^4-5*x^5)/((x-1)*(x+1)*(1+x^2)*(x^2-3*x+1)).
  • A111683 (program): n^k - n! where n^k > n! >= n^(k-1).
  • A111684 (program): Least k such that the product of n consecutive integers beginning with k exceeds n^n.
  • A111685 (program): n + n(n+1) + n(n+1)(n+2) + …, with n terms.
  • A111686 (program): (n+1) + (n+1)(n+2) + …, with n terms.
  • A111687 (program): Comprimorial(n): the product of the first n primes and the first n composite numbers.
  • A111688 (program): Primes and composite numbers alternately in increasing order.
  • A111690 (program): Least integer multiple of 1/n, truncated to n digits after decimal.
  • A111693 (program): The number system may be represented by linearly stringing together all the square domains. The number of the domain is given by r. It is noted that this has the same value as the circuit number in the Ellerstein square spiral. One below each odd square is a zero-centered octagonal number, which is divisible by 8. The value of this is eight times a triangular number. It may be seen that there are r octads in each square domain. The sequence is the first prime number in the first octad of each square domain.
  • A111694 (program): a(1) = 1+2-3 = 0, a(2) = 4+5+6-7 = 8, a(3) = 8+9+10+11-12 = 26, a(4) = 13+14+15+16+17-18 = 57, …
  • A111695 (program): a(n) = C(n,a)*C(n,b)*C(n,c)… where n = abc… are the decimal digits of n.
  • A111700 (program): Number of integers between p(n) and p(n+1) which are coprime to (p(n+1)-p(n)), where p(n) is the n-th prime.
  • A111701 (program): Least integer obtained when n is divided by prime(1), then by prime(2), then by prime(3), …, stopping as soon as one of the primes does not divide it. In particular, a(2n-1) = 2n-1.
  • A111706 (program): a(n) = concatenation of k times the k-th digit of n.
  • A111707 (program): a(n) = Sum_{k = 1..ceiling(w/2)} d(k) * d(w+1-k), where (d(1), …, d(w)) is the decimal expansion of n.
  • A111708 (program): a(n) = n concatenated with 9’s complement of n.
  • A111710 (program): Consider the triangle shown below in which the n-th row contains the n smallest numbers greater than those in the previous row such that the arithmetic mean is an integer. Sequence contains the leading diagonal.
  • A111711 (program): Leading column of triangle mentioned in A111710.
  • A111712 (program): Arithmetic mean of the n-th row of triangle mentioned in A111710.
  • A111713 (program): Number of reduced tree pairs of n-carets.
  • A111715 (program): Sum of the squares of the first n squarefree numbers.
  • A111721 (program): a(n) = a(n-1) + a(n-2) + 5 where a(0) = a(1) = 1.
  • A111723 (program): Number of partitions of an n-set with an odd number of blocks of size 1.
  • A111724 (program): Number of partitions of an n-set with an even number of blocks of size 1.
  • A111728 (program): Decimal expansion of (11/4)^(1/3).
  • A111732 (program): Sum of the squares of the first n nonsquarefree numbers (A013929).
  • A111733 (program): a(n) = a(n-1) + a(n-2) + 7 where a(0) = a(1) = 1.
  • A111734 (program): Expansion of (1-x)*(2*x^2+2*x+1) / ((x^2-x-1)*(x^2+x+1)).
  • A111735 (program): Distance between k*(n-th prime) and next prime, k=3 case.
  • A111736 (program): Distance between k*(n-th prime) and next prime, k=4 case.
  • A111737 (program): Distance between k*(n-th prime) and next prime, k=5 case.
  • A111738 (program): Distance between k*(n-th prime) and next prime, k=6 case.
  • A111739 (program): Distance between k*(n-th prime) and next prime, k=7 case.
  • A111740 (program): Distance between k*(n-th prime) and next prime, k=8 case.
  • A111741 (program): Distance between k*(n-th prime) and next prime, k=9 case.
  • A111742 (program): Distance between k*(n-th prime) and next prime, k=10 case.
  • A111744 (program): a(2k-1) = k-th prime of form 1 mod 4, a(2k) = k-th prime of form 3 mod 4.
  • A111745 (program): a(2k-1) = k-th prime congruent to 3 mod 4, a(2k) = k-th prime congruent to 1 mod 4.
  • A111746 (program): Number of squares in the interior of the square with vertices (n,0), (0,n), (-n,0) and (0,-n) in a square (x,y)-grid.
  • A111748 (program): a(n) = 1 if n-th composite number is squarefree, otherwise a(n) = 0.
  • A111752 (program): Number of partitions of {1,..,n} into lists with an even number of lists of size 1, where a list means an ordered subset (cf. A000262).
  • A111753 (program): Number of partitions of {1,..,n} into lists with an odd number of lists of size 1, where a list means an ordered subset, cf. A000262.
  • A111755 (program): Excess of n over a greedy sum of distinct squares.
  • A111766 (program): Numbers occurring in three Pythagorean triples of the form: odd: a, (a^2-1)/2, (a^2+1)/2 or even: a, a^2/4-1, a^2/4+1.
  • A111774 (program): Numbers that can be written as a sum of at least three consecutive positive integers.
  • A111775 (program): Number of ways n can be written as a sum of at least three consecutive integers.
  • A111776 (program): Triangle read by rows: number of idempotent order-preserving partial transformations (of an n-element chain) of waist k (waist(alpha) = max(Im(alpha)).
  • A111777 (program): Fourth column (m=3) of unsigned triangle A111595.
  • A111778 (program): Fifth column (m=4) of unsigned triangle A111595.
  • A111779 (program): Sixth column (m=5) of unsigned triangle A111595.
  • A111780 (program): Seventh column (m=6) of unsigned triangle A111595.
  • A111781 (program): Eighth column (m=7) of unsigned triangle A111595.
  • A111782 (program): Ninth column (m=8) of unsigned triangle A111595.
  • A111783 (program): Tenth column (m=9) of unsigned triangle A111595.
  • A111784 (program): Eleventh column (m=10) of unsigned triangle A111595.
  • A111802 (program): n^2-n-1 for n>3; a(1)=1; a(2)=2; a(3)=3.
  • A111805 (program): Number triangle T(n,k)=binomial(2(n+k),4k).
  • A111806 (program): Riordan array (1/(1+3x+2x^2),x/(1+3x+2x^2)).
  • A111808 (program): Left half of trinomial triangle (A027907), triangle read by rows.
  • A111850 (program): Number of numbers m <= n such that 0 equals the first digit after decimal point of square root of n in decimal representation.
  • A111851 (program): Number of numbers m <= n such that 1 equals the first digit after decimal point of square root of n in decimal representation.
  • A111852 (program): Number of numbers m <= n such that 2 equals the first digit after decimal point of square root of n in decimal representation.
  • A111853 (program): Number of numbers m <= n such that 3 equals the first digit after decimal point of square root of n in decimal representation.
  • A111854 (program): Number of numbers m <= n such that 4 equals the first digit after decimal point of square root of n in decimal representation.
  • A111856 (program): Number of numbers m <= n such that 6 equals the first digit after decimal point of square root of n in decimal representation.
  • A111857 (program): Number of numbers m <= n such that 7 equals the first digit after decimal point of square root of n in decimal representation.
  • A111858 (program): Number of numbers m <= n such that 8 equals the first digit after decimal point of square root of n in decimal representation.
  • A111859 (program): Number of numbers m <= n such that 9 equals the first digit after decimal point of square root of n in decimal representation.
  • A111862 (program): Second digit after decimal point of square root of n in decimal representation.
  • A111863 (program): Smallest prime factor of 6*n-1 that is congruent to 5 modulo 6.
  • A111868 (program): The work performed by a function f:{1,…,n} -> {1,…,n} is defined to be work(f) = Sum_{i=1..n} |i - f(i)|; a(n) is equal to sum(work(f)) where the sum is over all functions f:{1,…,n}->{1,…,n}.
  • A111873 (program): The work performed by a partial function f:{1,…,n}->{1,…,n} is defined to be work(f)=sum(|i-f(i)|,i in dom(f)); a(n) is equal to sum(work(f)) where the sum is over all partial functions f:{1,…,n}->{1,…,n}.
  • A111874 (program): The work performed by a partial function f:{1,…,n}->{1,…,n} is defined to be work(f)=sum(|i-f(i)|,i in dom(f)); a(n) is equal to sum(work(f)) where the sum is over all injective partial functions f:{1,…,n}->{1,…,n}.
  • A111876 (program): Denominator of Sum_{k = 0..n} 1/((k+1)*(2*k+1)).
  • A111877 (program): Sequence related to f(n) = 1/1 + 1/3 + … + 1/(2n+1).
  • A111878 (program): a(n) = denominator(digamma(n+7/2)/2 + log(2) + euler_gamma/2)/15; a(n)=denominator(f(n+2)/15) = A111877(n+1)/5.
  • A111882 (program): Row sums of triangle A111595 (normalized rescaled squared Hermite polynomials).
  • A111883 (program): Unsigned row sums of triangle A111595 (normalized rescaled squared Hermite polynomials).
  • A111884 (program): E.g.f.: exp(x/(1+x)).
  • A111889 (program): A repeated permutation of {0,…,8}.
  • A111890 (program): Number of numbers m <= n such that 0 equals the second digit after decimal point of square root of n in decimal representation.
  • A111893 (program): Number of numbers m <= n such that 3 equals the second digit after decimal point of square root of n in decimal representation.
  • A111894 (program): Number of numbers m <= n such that 4 equals the second digit after decimal point of square root of n in decimal representation.
  • A111903 (program): The work performed by a partial function f:{1,…,n}->{1,…,n} is defined to be work(f)=sum(|i-f(i)|,i in dom(f)); a(n) is equal to sum(work(f)) where the sum is over all order-preserving partial functions f:{1,…,n}->{1,…,n}.
  • A111911 (program): a(n) = (4*n+1)!/( (2*n+1)! * ((n+1)!)^2 ).
  • A111915 (program): Expansion of -x^2*(x-1)*(x^2-x+1)*(x+x^2+1)/(1-x^4+x^8).
  • A111917 (program): The i-th term of the generalized Fibonacci sequence [0,k,k,2k,3k,…] is given by the formula F(i) = round( k/sqrt(5) * phi^i ) provided i >= s(k); a(n) = smallest value of k such that s(k) = n.
  • A111918 (program): Numerator of x(n) = Sum_{k=1..n} ((odd part of k)/(k^3)).
  • A111919 (program): Denominator of x(n) = Sum_{k=1..n} ((odd part of k)/(k^3)).
  • A111920 (program): Numerator of x(n) = Sum_{k=1..n} ((odd part of k)/(k^4)).
  • A111921 (program): Denominator of x(n) = Sum_{k=1..n} ((odd part of k)/(k^4)).
  • A111922 (program): Numerator of x(n) = Sum_{k=1..n} ((odd part of k)/(k^5)).
  • A111923 (program): Denominator of x(n) = Sum_{k=1..n} ((odd part of k)/(k^5)).
  • A111924 (program): Triangle of Bessel numbers read by rows. Row n gives T(n,n), T(n,n-1), T(n,n-2), …, T(n,1) for n >= 1.
  • A111926 (program): Expansion of x^4/((1-2*x)*(x^2-x+1)*(x-1)^2).
  • A111927 (program): Expansion of x^3 / ((x-1)*(2*x-1)*(x^2-x+1)).
  • A111928 (program): Numerator of f(n) := Product_{i=1..n} sigma(i)/i.
  • A111929 (program): Numerator of x(n) = Sum_{k=1..n} ((odd part of k)/(k^2)).
  • A111930 (program): Denominator of x(n) = Sum_{k=1..n} ((odd part of k)/(k^2)).
  • A111932 (program): Expansion of q * (psi(q) * psi(q^3))^2 in powers of q where psi() is a Ramanujan theta function.
  • A111934 (program): Denominator of f(n) := Product_{i=1..n} sigma(i)/i.
  • A111935 (program): Numerator of n-th term of the harmonic series after removal of all terms 1/m from Sum_{m=1..n} 1/m for which m contains a 9 in its decimal representation.
  • A111936 (program): Denominator of n-th term of the harmonic series after removal of all terms 1/m from Sum_{m=1..n} 1/m for which m contains a 9 in its decimal representation.
  • A111938 (program): a(n) = n times number of divisors of n of form 4m+1 - n times number of divisors of form 4m+3.
  • A111939 (program): Number of primes < semiprime(n).
  • A111940 (program): Triangle P, read by rows, that satisfies P^-1 = P(n+1,k+1) for n >= k >= 0, with P(k,k)=1 and P(k+1,1)=P(k+1,0) for k >= 0, where [P^-1] denotes the matrix inverse of P.
  • A111942 (program): Column 0 of the matrix logarithm (A111941) of triangle A111940, which shifts columns left and up under matrix inverse; these terms are the result of multiplying the element in row n by n!.
  • A111946 (program): Triangle read by rows: T(n,k) = gcd(Fibonacci(n), Fibonacci(k)), 1 <= k <= n.
  • A111951 (program): Period 8: repeat [0,3,1,2,2,1,3,0].
  • A111952 (program): a(n) = 3*n mod 7.
  • A111954 (program): a(n) = A000129(n) + (-1)^n.
  • A111955 (program): a(n) = A078343(n) + (-1)^n.
  • A111956 (program): Triangle read by rows: T(n,k) = gcd(Lucas(n), Lucas(k)), 1 <= k <= n.
  • A111957 (program): Triangle read by rows: T(n,k) = gcd(Fibonacci(n), Lucas(k)), 1 <= k <= n.
  • A111958 (program): Lucas numbers (A000032) mod 8.
  • A111959 (program): Renewal array for aerated central binomial coefficients.
  • A111960 (program): Renewal array for central trinomial numbers A002426.
  • A111961 (program): Expansion of 1/(sqrt(1-2x-3x^2)-x).
  • A111962 (program): Expansion of 1/(sqrt(1-2x-3x^2)-x^2).
  • A111963 (program): Inverse of renewal array for central trinomial numbers.
  • A111965 (program): Riordan array (1/sqrt(1-6x+5x^2),x/(1-6x+5x^2)).
  • A111966 (program): Expansion of 1/(sqrt(1-6x+5x^2)-x).
  • A111968 (program): a(n) = Sum_{k=0..n} C(n,k)^2*C(n+k,k)^3, where C := binomial.
  • A111972 (program): a(n) = Max(omega(k): 1<=k<=n), where omega(n) = A001221(n), the number of distinct prime factors of n.
  • A111973 (program): Expansion of ((eta(q^2)eta(q^4))^6/(eta(q)eta(q^8))^4-1)/4 in powers of q.
  • A111980 (program): Union of pairs of consecutive primes p, q with q-p = 4.
  • A111981 (program): Numbers n such that 2n-1 and 2n+3 are consecutive primes.
  • A111982 (program): Row sums of abs(A111967).
  • A111983 (program): G.f.: A(x) = Sum_{n>=0} (2*n+1) * 8^n * x^(n*(n+1)/2).
  • A111989 (program): G.f.: 1/(1-6*x+8*x^3).
  • A111990 (program): Convolution of A111989 with itself.
  • A111993 (program): Fifth convolution of Schroeder’s (second problem) numbers A001003(n), n>=0.
  • A111994 (program): Sixth convolution of Schroeder’s (second problem) numbers A001003(n), n>=0.
  • A111995 (program): Seventh convolution of Schroeder’s (second problem) numbers A001003(n), n >= 0.
  • A111996 (program): Eighth convolution of Schroeder’s (second problem) numbers A001003(n), n>=0.
  • A111997 (program): Ninth convolution of Schroeder’s (second problem) numbers A001003(n), n>=0.
  • A111998 (program): Tenth convolution of Schroeder’s (second problem) numbers A001003(n), n>=0.
  • A112000 (program): One half of third column (k=2) of triangle A111999.
  • A112019 (program): a(n) = Sum_{k=0..n} binomial(n,k)*binomial(n+k,k)^2.
  • A112028 (program): a(n) = Sum_{k=0..n} binomial(n+k,k)^3.
  • A112029 (program): a(n) = Sum_{k=0..n} binomial(n+k, k)^2.
  • A112030 (program): a(n) = (2 + (-1)^n) * (-1)^floor(n/2).
  • A112031 (program): Numerator of 3/4 + 1/4 - 3/8 - 1/8 + 3/16 + 1/16 - 3/32 - 1/32 + 3/64 + ….
  • A112032 (program): Denominator of 3/4 + 1/4 - 3/8 - 1/8 + 3/16 + 1/16 - 3/32 - 1/32 + 3/64 …
  • A112033 (program): a(n) = 3 * 2^(floor(n/2) + 1 + (-1)^n).
  • A112035 (program): a(n) = Sum_{k=0..n} k*C(n,k)^2*C(n+k,k)^3, where C := binomial.
  • A112036 (program): a(n) = Sum_{k=0..n} k*C(n,k)^3*C(n+k,k), where C := binomial.
  • A112039 (program): Let b(0)=1/2, b(n) = b(n-1) + Prime[n]/2; a(n)=b(2*n).
  • A112040 (program): Terms in A112039 that are divisible by 3, divided by 3.
  • A112044 (program): Let b(0)=1/2, b(n) = (b(n-1)+Prime[n])/2; sequence gives 2^(n+1)*b(n).
  • A112045 (program): Positions of primes (A000040) among nonsquares A000037.
  • A112051 (program): a(1)=1, a(n) = first index i (> a(n-1)), where A112046(i) gets a value distinct from any values A112046(1)..A112046(a(n-1)).
  • A112052 (program): a(n) = 2*A112051(n)+1.
  • A112062 (program): Positive integers i for which A112049(i) == 2.
  • A112063 (program): Positive integers i for which A112049(i) == 3.
  • A112072 (program): Odd numbers n for which 3 is the smallest i (>= 1) with Jacobi symbol J(i,n) getting either a value 0 or -1.
  • A112073 (program): Odd numbers n for which 5 is the smallest i (>= 1) with Jacobi symbol J(i,n) getting either a value 0 or -1.
  • A112087 (program): a(n) = 4*(n^2 - n + 1).
  • A112088 (program): Number of leaf nodes in a binary tree.
  • A112091 (program): Number of idempotent order-preserving partial transformations (of an n-element chain).
  • A112094 (program): Denominator of 3*Sum_{i=1..n} 1/(i^2*C(2*i,i)).
  • A112097 (program): Numerator of Sum_{i=1..n} 1/C(2*i,i).
  • A112098 (program): Denominator of Sum_{i=1..n} 1/C(2*i,i).
  • A112099 (program): Numerator of Sum_{i=1..n} 1/(i*C(2*i,i)).
  • A112100 (program): Denominator of Sum_{i=1..n} 1/(i*C(2*i,i)).
  • A112101 (program): Number of interval orders of magnitude n having no duplicate holdings (NODH).
  • A112102 (program): Numerator of Sum_{i=1..n} 1/(i^3*C(2*i,i)).
  • A112103 (program): Denominator of Sum_{i=1..n} 1/(i^3*C(2*i,i)).
  • A112128 (program): Expansion of phi(q^4) / phi(q) in powers of q where phi() is a Ramanujan theta function.
  • A112132 (program): Period 4: repeat [1, 3, 1, 7].
  • A112133 (program): First differences of A112063.
  • A112141 (program): Product of the first n semiprimes.
  • A112142 (program): McKay-Thompson series of class 8B for the Monster group.
  • A112143 (program): McKay-Thompson series of class 8D for the Monster group.
  • A112144 (program): McKay-Thompson series of class 8a for the Monster group.
  • A112148 (program): McKay-Thompson series of class 12B for the Monster group.
  • A112150 (program): McKay-Thompson series of class 16a for the Monster group.
  • A112151 (program): McKay-Thompson series of class 16b for the Monster group.
  • A112152 (program): McKay-Thompson series of class 16c for the Monster group.
  • A112157 (program): McKay-Thompson series of class 18i for the Monster group.
  • A112160 (program): McKay-Thompson series of class 24E for the Monster group.
  • A112161 (program): McKay-Thompson series of class 24G for the Monster group.
  • A112171 (program): McKay-Thompson series of class 32c for the Monster group.
  • A112172 (program): McKay-Thompson series of class 32d for the Monster group.
  • A112176 (program): McKay-Thompson series of class 36f for the Monster group.
  • A112192 (program): Coefficients of replicable function number “48h”.
  • A112205 (program): McKay-Thompson series of class 72a for the Monster group.
  • A112227 (program): A scaled Hermite triangle.
  • A112228 (program): Product of the first n (semiprimes - 1).
  • A112231 (program): Repeat each prime in the sequence of natural numbers.
  • A112232 (program): Repeat each composite number in the sequence of natural numbers.
  • A112240 (program): Expansion of exp(x/(1-x-2x^2)).
  • A112242 (program): E.g.f. exp( x*(1+x)/(1-x) ).
  • A112243 (program): Expansion of exp(x*(1+x)/(1-2*x)).
  • A112248 (program): a(n) = n mod floor(log_2(n)).
  • A112249 (program): Numbers m such that m mod floor(log_2(m)) = 0.
  • A112250 (program): Numbers m such that m mod floor(log_2(m)) > 0.
  • A112251 (program): Numbers m such that m mod log_2(m) = 1.
  • A112259 (program): Expansion of x*(1+8*x)/((1-8*x)*(1+11*x+64*x^2)).
  • A112260 (program): Expansion of -x*(8*x^2-4*x+1) / ((2*x-1)*(4*x^2-x+1)).
  • A112261 (program): a(n) = A112260(n+1) - A112260(n).
  • A112270 (program): One third of the sum of the first n primes, when an integer.
  • A112275 (program): Smallest number greater than n having at least as many divisors as n.
  • A112278 (program): a(0) = 1; a(n) = prime(mod(a(n-1),100))+1.
  • A112279 (program): a(1)=1; a(n)=prime(mod(a(n-1),100)).
  • A112280 (program): Coefficients, read modulo 9, of the cube of q-series (q;q)_oo.
  • A112282 (program): a(n) = (-1)^n*(2*n+1) (mod 9).
  • A112292 (program): An invertible triangle of ratios of double factorials.
  • A112293 (program): Row sums of number triangle A112292.
  • A112294 (program): Diagonal sums of number triangle A112292.
  • A112295 (program): Inverse of a double factorial related triangle.
  • A112296 (program): Smret suoiverp eht fo mus fo esrever.
  • A112298 (program): Expansion of (a(q) - 3*a(q^2) + 2*a(q^4)) / 6 in powers of q where a() is a cubic AGM theta function.
  • A112299 (program): Expansion of x * (1 - x) * (1 - x^2) * (1 - x^3) / (1 - x^8) in powers of x.
  • A112300 (program): Expansion of x * (1 - x)^2 * (1 - x^2) / (1 - x^6) in powers of x.
  • A112301 (program): Expansion of (eta(q) * eta(q^16))^2 / (eta(q^2) * eta(q^8)) in powers of q.
  • A112305 (program): Let T(n) = A000073(n+1), n >= 1; a(n) = smallest k such that n divides T(k).
  • A112306 (program): a(n) = number of terms in s(n), where s(n) is defined in A096055.
  • A112307 (program): Triangle read by rows: T(n,k) is number of Dyck paths of semilength n with height of second peak equal to k (n>=1; 0<=k<=n-1).
  • A112308 (program): Sum of the heights of the second peaks in all Dyck paths of semilength n+2.
  • A112310 (program): Number of terms in lazy Fibonacci representation of n.
  • A112312 (program): Least index k such that the n-th prime divides the k-th tribonacci number.
  • A112325 (program): Number of even semiprimes <= semiprime(n).
  • A112326 (program): Triangle read by rows: T(n,k)=2^k*binomial(2n-k,n-k), 1<=k<=n.
  • A112327 (program): Triangle read by rows: T(n,k)=k^3*2^k*binomial(2n-k,n-k)/(2n-k) (1<=k<=n).
  • A112328 (program): a(n) = (n+1)*binomial(2n+2,n+1)-3*4^n+binomial(2n,n).
  • A112329 (program): Number of divisors of n if n odd, number of divisors of n/4 if n divisible by 4, otherwise 0.
  • A112332 (program): a(n) = Product_{k=0..n-1} k!*binomial(2k,k).
  • A112333 (program): An invertible triangle of ratios of triple factorials.
  • A112334 (program): Inverse of number triangle A112333.
  • A112335 (program): Row sums of number triangle A112334.
  • A112336 (program): A number triangle related to the central binomial coefficients.
  • A112337 (program): a(1)=1, a(2) = 2. a(n) = a(n-2) + (largest prime dividing a(n-1)).
  • A112341 (program): Number of primes between (prime(n)-1)^2 and prime(n)^2.
  • A112342 (program): Number of primes between (n-th composite - 1)^2 and (n-th composite)^2.
  • A112347 (program): Kronecker symbol (-1, n) except a(0) = 0.
  • A112351 (program): Triangle read by rows, generated from (…, 5, 3, 1).
  • A112352 (program): Triangular numbers that are the sum of two distinct positive triangular numbers.
  • A112353 (program): Triangular numbers that are the sum of three distinct positive triangular numbers.
  • A112355 (program): Triangular numbers that are the sum of three positive triangular numbers.
  • A112358 (program): The following triangle is based on Pascal’s triangle. The r-th term of the n-th row is sum of C(n,r) successive integers so that the sum of all the terms of the row is (2^n)*(2^n+1)/2, the 2^n -th triangular number. Sequence contains the triangle read by rows.
  • A112359 (program): Product of n-th row of A112358.
  • A112367 (program): a(n) = A000217(n-k), where k is the largest triangular number less than n.
  • A112368 (program): a(n) = Sum_{i=0..n} 2^i*i!.
  • A112369 (program): -1 + Sum_{i=0..n} 2^i*i!.
  • A112370 (program): Sum_{i=0..n} 3^i*i!.
  • A112376 (program): Sum of base and exponent of prime powers.
  • A112377 (program): A self-descriptive fractal sequence: if 1 is subtracted from every term and any zero terms are omitted, the original sequence is recovered (this process may be called “lower trimming”).
  • A112378 (program): Adding 1 to every term produces the same sequence as omitting the 0’s.
  • A112381 (program): Zero-free semiprimes.
  • A112385 (program): a(n) = 6*binomial(4*n-1,n-1)/(4*n-1).
  • A112387 (program): a(1)=1, a(2)=2, a(n)= 2^(n/2) if even and a(n-1)-a(n-2) if odd.
  • A112391 (program): Primes p such that 23*p + 2 is also prime.
  • A112392 (program): Squares of the form 3*k - 2 where k is a semiprime.
  • A112393 (program): Semiprimes n such that 3*n - 2 is a square.
  • A112399 (program): a(n) = Sum_{k=1..n, gcd(k,n)=1} mu(k), where mu(k) = A008683(k) (the Moebius function).
  • A112403 (program): G.f.: (1-16*x+28*x^2+56*x^3-140*x^4+56*x^5+28*x^6-16*x^7+x^8)/(x^2-x+1)^8.
  • A112413 (program): Triangle read by rows: T(n,k) is the number of Dyck paths of semilength n and starting with exactly k UD’s, where U=(1,1), D=(1,-1) (0 <= k <= n).
  • A112414 (program): 3n+7.
  • A112415 (program): a(n) = C(1+n,1) * C(2+n,1) * C(4+n,2).
  • A112416 (program): Next-to-most-significant binary digit of the n-th prime.
  • A112421 (program): Number of 6 element subsets of {1,2,3,…,n} for which the sum-set has 12 elements.
  • A112423 (program): Number of 6-element subsets of {1,2,3,…,n} which have a sum-set with 14 elements.
  • A112440 (program): Next term is the sum of the last 10 digits in the sequence, beginning with a(10) = 9.
  • A112447 (program): a(2*n) = A001045(n+2); a(2*n+1) = A001045(n+1).
  • A112448 (program): a(n) = 1 if 2*n+1 is prime, otherwise a(n) = minimal residue of (-1)^binomial(n+2,2) mod (2n+1).
  • A112455 (program): a(n) = -a(n-2) - a(n-3).
  • A112456 (program): Least triangular number divisible by n-th prime.
  • A112458 (program): Let b(n) = A112455(n). Then b(n)/n is an integer iff n is prime (at least for the first few values, as for the Perrin sequence). This sequence is the values of b(p)/p, where p is the n th prime.
  • A112459 (program): Absolute value of coefficient of term [x^(n-3)] in characteristic polynomial of maximum matrix A of size n X n, where n >= 3. Maximum matrix A(i,j) is MAX(i,j), where indices i and j run from 1 to n.
  • A112460 (program): Absolute value of coefficient of term [x^(n-4)] in characteristic polynomial of maximum matrix A of size n X n, where n >= 4. Maximum matrix A(i,j) is MAX(i,j), where indices i and j run from 1 to n.
  • A112461 (program): Absolute value of coefficient of term [x^(n-5)] in characteristic polynomial of maximum matrix A of size n X n, where n >= 5. Maximum matrix A(i,j) is MAX(i,j), where indices i and j run from 1 to n.
  • A112462 (program): Absolute value of coefficient of term [x^(n-6)] in characteristic polynomial of maximum matrix A of size n X n, where n >= 6. Maximum matrix A(i,j) is MAX(i,j), where indices i and j run from 1 to n.
  • A112463 (program): Absolute value of coefficient of term [x^(n-7)] in characteristic polynomial of maximum matrix A of size n X n, where n >= 7. Maximum matrix A(i,j) is MAX(i,j), where indices i and j run from 1 to n.
  • A112464 (program): Absolute value of coefficient of term [x^(n-8)] in characteristic polynomial of maximum matrix A of size n X n, where n >= 8. Maximum matrix A(i,j) is MAX(i,j), where indices i and j run from 1 to n.
  • A112465 (program): Riordan array (1/(1+x),x/(1-x)).
  • A112466 (program): Riordan array ((1+2x)/(1+x), x/(1+x)).
  • A112467 (program): Riordan array ((1-2x)/(1-x), x/(1-x)).
  • A112468 (program): Riordan array (1/(1-x), x/(1+x)).
  • A112469 (program): Partial sums of (-1)^n*F(n-1).
  • A112475 (program): Riordan array (1/(1+x),x(1+x)/(1-x)).
  • A112476 (program): Diagonal sums of Riordan array (1/(1+x),x(1+x)/(1-x)).
  • A112477 (program): Riordan array ((1-x+sqrt(1+6x+x^2))/2, (sqrt(1+6x+x^2)-x-1)/2).
  • A112478 (program): Expansion of (1 + x + sqrt(1 + 6*x + x^2))/2.
  • A112484 (program): Array where n-th row contains the primes < n and coprime to n.
  • A112488 (program): Third column of triangle A112486 used for e.g.f.s of |Stirling1| = |A008275| diagonals.
  • A112489 (program): Fourth column of triangle A112486 used for e.g.f.s of |Stirling1|=|A008275| diagonals.
  • A112494 (program): Sixth diagonal of the Stirling2 triangle A048993 and sixth column of triangle A008278.
  • A112495 (program): Third column of triangle A112493 used for e.g.f.s of Stirling2 diagonals.
  • A112498 (program): Third column of second-order Eulerian triangle A008517 divided by 2.
  • A112502 (program): Third column of triangle A112500.
  • A112503 (program): Fourth column of triangle A112500.
  • A112504 (program): Fifth column of triangle A112500.
  • A112508 (program): Counts the objects described in A047969 and A089246 when grouped by minimum part. (Row sums give A047970).
  • A112509 (program): Maximum number of numbers represented by substrings of an n-bit number’s binary representation.
  • A112517 (program): Riordan array (1,x(1+x)(1-x(1+x)).
  • A112518 (program): Expansion of 1/(1-x+2x^3+x^4).
  • A112520 (program): Expansion of 2/(3-sqrt(3-2*sqrt(1-4x))).
  • A112521 (program): Sequence related to NOR bracketings.
  • A112523 (program): Expansion of x*(1+3*x-4*x^2-5*x^3-4*x^6+4*x^5+3*x^4) / ((1+4*x^2)*(1+x^2)*(1-x^2+x^4)).
  • A112524 (program): a(n) = a(n-1) + 2*n^2 with a(1) = 1.
  • A112525 (program): Expansion of 1/(1 - 100*x^2 - 100*x^3).
  • A112526 (program): Characteristic function for powerful numbers.
  • A112532 (program): First differences of [0, A047970].
  • A112539 (program): Half-baked Thue-Morse: at successive steps the sequence or its bit-inverted form is appended to itself.
  • A112541 (program): a(n) = Sum_{k=0..n} (n-k)! * n^k.
  • A112543 (program): Numerators of fractions n/k in array by antidiagonals.
  • A112544 (program): Denominators of fractions n/k in array by antidiagonals.
  • A112552 (program): A modified Chebyshev transform of the second kind.
  • A112553 (program): Expansion of 1/( (1+x^2)*(1-x+x^2) ).
  • A112554 (program): Riordan array (c(x^2)^2, x*c(x^2)), c(x) the g.f. of A000108.
  • A112555 (program): Triangle T, read by rows, such that the m-th matrix power satisfies T^m = I + m*(T - I) and consequently the matrix logarithm satisfies log(T) = T - I, where I is the identity matrix.
  • A112556 (program): Sums of squared terms in rows of triangle A112555.
  • A112557 (program): Smallest number of stones in Tchoukaillon (or Mancala, or Kalahari) solitaire which make use of (2*n-1)-th hole for n>=1; a bisection of A002491.
  • A112558 (program): Generalized Mancala solitaire (A002491); to get n-th term, start with n and successively round up to next 4 multiples of n-1, n-2, …, 1, for n>=1.
  • A112559 (program): Numbers k such that both k and 4k + 1 are in A005098.
  • A112560 (program): Sieve performed by successive iterations of steps where step m is: keep m terms, remove the next 2 and repeat; as m = 1,2,3,.. the remaining terms form this sequence.
  • A112561 (program): Sieve performed by successive iterations of steps where step m is: keep m terms, remove the next 3 and repeat; as m = 1,2,3,.. the remaining terms form this sequence.
  • A112562 (program): Sieve performed by successive iterations of steps where step m is: keep m terms, remove the next 4 and repeat; as m = 1,2,3,.. the remaining terms form this sequence.
  • A112563 (program): Sieve performed by successive iterations of steps where step m is: keep m terms, remove the next 5 and repeat; as m = 1,2,3,.. the remaining terms form this sequence.
  • A112565 (program): Main diagonal of square table A112564 of generalized Flavius Josephus sieves.
  • A112566 (program): a(n) = (A112565(n) - 1)/n for n>=1.
  • A112568 (program): Secondary diagonal of square table A112564 of generalized Flavius Josephus sieves.
  • A112575 (program): Chebyshev transform of the second kind of the Pell numbers.
  • A112576 (program): A Chebyshev-related transform of the Fibonacci numbers.
  • A112577 (program): A Chebyshev-related transform of the Jacobsthal numbers.
  • A112581 (program): Number of partitions of n into 5-smooth parts.
  • A112591 (program): a(n) = prime(n) XOR prime(n + 1).
  • A112594 (program): Natural function used for generating x^2 and sqrt(x) only using iteration and Q(x) (the characteristic function of sqrt).
  • A112595 (program): Sequence of numerators of the continued fraction derived from the sequence of the number of distinct factors of a number (A001221, also called omega (n)).
  • A112596 (program): Sequence of denominators of the continued fraction derived from the sequence of the numbers of distinct factors of a number (A001221, also called omega(n)).
  • A112598 (program): a(1)=a(2)=1. For n >= 3, a(n) is smallest integer > a(n-1) such that gcd(a(n), a(n-1) + a(n-2)) > 1.
  • A112603 (program): Number of representations of n as the sum of a square and a triangular number.
  • A112604 (program): Number of representations of n as a sum of three times a square and two times a triangular number.
  • A112605 (program): Number of representations of n as a sum of a square and six times a triangular number.
  • A112606 (program): Number of representations of n as a sum of six times a square and a triangular number.
  • A112607 (program): Number of representations of n as a sum of a triangular number and twelve times a triangular number.
  • A112608 (program): Number of representations of n as a sum of a twice a square and three times a triangular number.
  • A112609 (program): Number of representations of n as a sum of three times a triangular number and four times a triangular number.
  • A112610 (program): Number of representations of n as a sum of two squares and two triangular numbers.
  • A112618 (program): Let T(n) = A000073(n+1), n >= 1; a(n) = smallest k such that prime(n) divides T(k).
  • A112620 (program): If b(n,1) = n; b(n,m) is number of terms among {b(n,1), b(n,2), …, b(n,m-1)} which are coprime to m, then a(n) = b(n,n).
  • A112621 (program): If p^b(p,n) is the highest power of the prime p dividing n, then a(n) = sum_{p|n} b(p,n)^b(p,n).
  • A112622 (program): If p^b(p,n) is the highest power of the prime p dividing n, then a(n) = product_{p|n} b(p,n)^b(p,n).
  • A112623 (program): If p^b(p,n) is the highest power of the prime p dividing n, then a(n) = sum_{p|n} b(p,n)!.
  • A112624 (program): If p^b(p,n) is the highest power of the prime p dividing n, then a(n) = Product_{p|n} b(p,n)!.
  • A112626 (program): Triangle read by rows: T(n,k) = Sum_{j=0..n} binomial(n, k+j)*2^(n-k-j).
  • A112627 (program): Decimal equivalent of number defined by last k bits of the infinite binary string …0011001100110011 (numbers with leading zeros omitted).
  • A112632 (program): Excess of 3k - 1 primes over 3k + 1 primes, beginning with 2.
  • A112638 (program): Power each digit individually according to its position and add the numbers.
  • A112639 (program): a(n) = floor(r^n) where r is the smallest Pisot number (real root r=1.3247179… of x^3-x-1).
  • A112651 (program): Numbers k such that k^2 == k (mod 11).
  • A112652 (program): a(n) squared is congruent to a(n) (mod 12).
  • A112653 (program): a(n) squared is congruent to a(n) (mod 13).
  • A112654 (program): Numbers k such that k^3 == k (mod 11).
  • A112655 (program): a(n) cubed is congruent to a(n) (mod 13).
  • A112657 (program): A Motzkin transform of Jacobsthal numbers.
  • A112658 (program): Dean’s Word: Omega 2,1: the trajectory of 0 -> 01, 1 -> 21, 2 -> 03, 3 -> 23.
  • A112661 (program): Sum of digits of sum of previous 3 terms.
  • A112667 (program): a(n+1) is the sum of the units digit of a(n) and the square of the tens digit of a(n).
  • A112668 (program): Triangle read by rows: row n gives an n-term geometric progression with first term 1 such that the sum of the n terms is a multiple of n.
  • A112677 (program): Sum of digits of the sum of the previous 4 terms.
  • A112681 (program): Primes such that the sum of the predecessor and successor primes is divisible by 3.
  • A112685 (program): a(n)=5a(n-2)+2a(n-3).
  • A112689 (program): A modified Chebyshev transform of the Jacobsthal numbers.
  • A112690 (program): Expansion of 1/(1+x^2-x^3-x^5).
  • A112691 (program): a(n) = J(n+1) mod J(n), J(n)=A001045(n).
  • A112693 (program): Row sums of array A112692.
  • A112695 (program): Number of steps needed to reach 4,2,1 in Collatz’ 3*n+1 conjecture.
  • A112696 (program): Partial sum of Catalan numbers A000108 multiplied by powers of 2.
  • A112697 (program): Partial sum of Catalan numbers (A000108) multiplied by powers of 3.
  • A112698 (program): Partial sum of Catalan numbers A000108 multiplied by powers of 4.
  • A112699 (program): Partial sum of Catalan numbers A000108 multiplied by powers of 5.
  • A112700 (program): Partial sum of Catalan numbers A000108 multiplied by powers of 6.
  • A112701 (program): Partial sum of Catalan numbers A000108 multiplied by powers of 7.
  • A112702 (program): Partial sum of Catalan numbers A000108 multiplied by powers of 8.
  • A112703 (program): Partial sum of Catalan numbers A000108 multiplied by powers of 9.
  • A112704 (program): Partial sum of Catalan numbers A000108 multiplied by powers of 10.
  • A112705 (program): Triangle built from partial sums of Catalan numbers A000108 multiplied by powers.
  • A112706 (program): Row sums of triangle A112705.
  • A112707 (program): Triangle built from partial sums of Catalan numbers multiplied by powers of nonpositive numbers.
  • A112708 (program): Row sums of triangle A112707 (partial sums of Catalan numbers multiplied by powers of negative numbers).
  • A112709 (program): Unsigned row sums of triangle A112707 (partial sums of Catalan numbers multiplied by powers of negative numbers).
  • A112710 (program): Partial sums of Catalan numbers A000108 multiplied by powers of -3.
  • A112711 (program): Partial sums of Catalan numbers A000108 multiplied by powers of -4.
  • A112712 (program): Expansion of x/(1 - x + 2*x^2 - 2*x^3 + 2*x^4 - x^5 + x^6).
  • A112713 (program): Expansion of x/(1 - x + x^5 - x^6).
  • A112714 (program): Numbers of the form k*2^m-1 with k<2^m and k odd.
  • A112715 (program): Primes in A112714.
  • A112739 (program): Array counting nodes in rooted trees of height n in which the root and internal nodes have valency k (and the leaf nodes have valency one).
  • A112740 (program): Row sums of number triangle A112739.
  • A112742 (program): a(n) = n^2*(n^2 - 1)/3.
  • A112744 (program): Least k such that 6*k*prime(n)^2 -1 is prime, where prime(i)=i-th prime.
  • A112745 (program): Least k such that 6*k*prime(n)^2 +1 is prime, where prime(i)=i-th prime.
  • A112746 (program): Least k such that 6*k*prime(n)^2 - 1 and 6*k*prime(n)^2 + 1 are twin primes.
  • A112751 (program): Number of numbers less than or equal to n of the form 3^i*5^j.
  • A112757 (program): Greatest common divisors of consecutive 5-smooth numbers.
  • A112758 (program): Number of distinct prime factors of n-th 5-smooth number.
  • A112759 (program): Total number of prime factors of n-th 5-smooth number.
  • A112760 (program): Exponent of 2 (value of i) in n-th number of the form 2^i*3^j*5^k.
  • A112761 (program): Exponent of 3 (value of j) in n-th number of the form 2^i*3^j*5^k.
  • A112762 (program): Exponent of 5 (value of k) in n-th number of the form 2^i*3^j*5^k.
  • A112763 (program): Smallest prime factor of the n-th 5-smooth number.
  • A112764 (program): Greatest prime factor of the n-th 5-smooth number.
  • A112765 (program): Exponent of highest power of 5 dividing n. Or, 5-adic valuation of n.
  • A112770 (program): Products of pairs of terms from A003627.
  • A112771 (program): Semiprimes of the form 6n + 1.
  • A112772 (program): Semiprimes of the form 6n+2.
  • A112773 (program): 3 together with primes multiplied by 3.
  • A112774 (program): Semiprimes of the form 6n+4.
  • A112775 (program): Numbers n such that 6n+1 is semiprime.
  • A112776 (program): Numbers n such that 6n+5 is semiprime.
  • A112777 (program): Numbers n such that 2*n^2 + 1 is a semiprime.
  • A112787 (program): Next term is the sum of previous term and the square of the sum of its decimal digits, with a(0) = 10.
  • A112805 (program): Expansion of solution of functional equation.
  • A112806 (program): Expansion of solution of functional equation.
  • A112807 (program): Expansion of solution of functional equation.
  • A112808 (program): Expansion of solution of functional equation.
  • A112821 (program): Numbers n such that lcm(1,2,3,…,n)/19 equals the denominator of the n-th harmonic number H(n).
  • A112823 (program): Greatest p less than or equal to n with p and q both prime, p+q = 2n.
  • A112830 (program): Table of number of domino tilings of generalized Aztec pillows of type (1, …, 1, 3, 1, …, 1)_n.
  • A112831 (program): Number of non-intersecting cycle systems in a particular directed graph.
  • A112832 (program): Number of non-intersecting cycle systems in a particular directed graph.
  • A112835 (program): Small-number statistic from the enumeration of domino tilings of a 3-pillow of order n.
  • A112848 (program): Expansion of eta(q)*eta(q^2)*eta(q^18)^2/(eta(q^6)*eta(q^9)) in powers of q.
  • A112849 (program): Number of congruence classes (epimorphisms/vertex partitionings induced by graph endomorphisms) of undirected cycles of even length: |C(C_{2*n})|.
  • A112850 (program): Number of graph endomorphisms of undirected cycles of even length: |End(C_2n)|.
  • A112851 (program): a(n) = (n-1)*n*(n+1)*(n+2)*(2*n+1)/40.
  • A112857 (program): Triangle T(n,k) read by rows: number of Green’s R-classes in the semigroup of order-preserving partial transformations (of an n-element chain) consisting of elements of height k (height(alpha) = |Im(alpha)|).
  • A112865 (program): a(n) = (-1)^(n + floor(n/4) + floor(n/4^2) + …).
  • A112867 (program): Greater of two ternary (base 3) numbers (each using only 0’s and 1’s, the latter’s positions never coinciding) such that the decimal representation of their difference is n.
  • A112873 (program): Partial sums of A032378.
  • A112883 (program): A skew Jacobsthal-Pascal matrix.
  • A112884 (program): Number of bits required to represent binomial(2^n, 2^(n-1)).
  • A112885 (program): Primes of the form k + prime(k-1).
  • A112886 (program): Positive integers that have no triangular divisors > 1.
  • A112887 (program): Semiprime(n) - composite(n).
  • A112899 (program): A skew Pell-Pascal triangle.
  • A112925 (program): Largest squarefree integer < the n-th prime.
  • A112926 (program): Smallest squarefree integer > the n-th prime.
  • A112929 (program): Number of squarefree integers less than the n-th prime.
  • A112930 (program): a(n) = order of n-th term of A112926 among squarefree integers.
  • A112934 (program): a(0) = 1; a(n+1) = Sum_{k=0..n} a(k)*A001147(n-k), where A001147 = double factorial numbers.
  • A112935 (program): Logarithmic derivative of A112934 such that a(n)=(1/2)*A112934(n+1) for n>0, where A112934 equals the INVERT transform of double factorials A001147.
  • A112936 (program): INVERT transform (with offset) of triple factorials (A008544), where g.f. satisfies: A(x) = 1 + x*[d/dx x*A(x)^3]/A(x)^3.
  • A112937 (program): Logarithmic derivative of A112936 such that a(n)=(1/3)*A112936(n+1) for n>0, where A112936 equals the INVERT transform (with offset) of triple factorials A008544.
  • A112938 (program): INVERT transform (with offset) of quadruple factorials (A008545), where g.f. satisfies: A(x) = 1 + x*[d/dx x*A(x)^4]/A(x)^4.
  • A112939 (program): Logarithmic derivative of A112938 such that a(n)=(1/4)*A112938(n+1) for n>0, where A112938 equals the INVERT transform (with offset) of quadruple factorials A008545.
  • A112940 (program): INVERT transform (with offset) of quintuple factorials (A008546), where g.f. satisfies: A(x) = 1 + x*[d/dx x*A(x)^5]/A(x)^5.
  • A112941 (program): Logarithmic derivative of A112940 such that a(n)=(1/5)*A112940(n+1) for n>0, where A112940 equals the INVERT transform (with offset) of quintuple factorials A008546.
  • A112942 (program): INVERT transform (with offset) of sextuple factorials (A008543), where g.f. satisfies: A(x) = 1 + x*[d/dx x*A(x)^6]/A(x)^6.
  • A112943 (program): Logarithmic derivative of A112942 such that a(n)=(1/6)*A112942(n+1) for n>0, where A112942 equals the INVERT transform (with offset) of sextuple factorials A008543.
  • A112952 (program): Smaller of two ternary (base 3) numbers (each using only 0’s and 1’s, the latter’s positions never coinciding) such that the decimal representation of their difference is n.
  • A112953 (program): a(1) = 0; a(n) = pi(n)^pi(n) for n>1, where pi is the prime counting function (A000720).
  • A112957 (program): a(1) = a(2) = a(3) = 1; for n > 1, a(n+3) = a(n)^2 + a(n+1)^2 + a(n+2)^2.
  • A112958 (program): a(1) = a(2) = a(3) = a(4) = 1; for n>1: a(n+4) = a(n)^2 + a(n+1)^2 + a(n+2)^2 + a(n+3)^2.
  • A112963 (program): Sum(mu(i)*tau(j): i+j=n), with mu=A008683 and tau=A000005.
  • A112964 (program): Sum(mu(i)*sigma(j): i+j=n), with mu=A008683 and sigma=A000203.
  • A112967 (program): Sum(Omega(i)*Omega(j): i+j=n), with Omega=A001222.
  • A112970 (program): A generalized Stern sequence.
  • A112971 (program): Row sums of the matrix ((1,xc(x))^2 mod 2), where c(x) is the g.f. of A000108.
  • A112973 (program): Riordan array (1/(1-x-x^2), x(1+x)/(1-x-x^2)^2).
  • A112976 (program): Position of n-th prime in A112975.
  • A112983 (program): 2^(n+1) mod n.
  • A112984 (program): Numbers k such that 2^k mod k-1 is odd.
  • A112985 (program): 2^(2^n mod n-1).
  • A112986 (program): Crossing number of K_{4,n} on the real projective plane.
  • A112987 (program): a(n) = 2^(2^n mod n) for n > 0; a(0) = 2.
  • A112988 (program): Position of n-th prime in A089088.
  • A112991 (program): a(n)=ceiling(2^(mod(2^n,n)+1)/3)-ceiling(2^mod(2^n,n)/3).
  • A112997 (program): Sum of first n primes minus sum of their indices.
  • A113009 (program): {Sum of the digits of n} raised to the power {number of digits of n}.
  • A113010 (program): {Number of digits of n} raised to the power of {the sum of the digits of n}.
  • A113011 (program): Decimal expansion of 1/(e^(1/2)-1).
  • A113012 (program): Numerators of convergents to 1 + 2/(3 + 4/(5 + 6/(7 + …))).
  • A113013 (program): Denominators of convergents to 1 + 2/(3 + 4/(5 + 6/(7 + …))).
  • A113014 (program): Decimal expansion of value of the continued fraction 1/(2+3/(4+5/(6+7/….
  • A113016 (program): Primes that remain primes when their decimal representation is interpreted duodecimally.
  • A113020 (program): Number triangle whose row sums are the Fibonacci numbers.
  • A113021 (program): Expansion of x^2/(1 - 2*x + 2*x^2 - x^3 - x^4).
  • A113022 (program): a(n) = size of union of 2^k (mod 10^n), 0 < k <= 5^n.
  • A113023 (program): Number of terms in A095810 which have n digits.
  • A113025 (program): Triangle of integer coefficients of polynomials P(n,x) of degree n, and falling powers of x, arising in diagonal Padé approximation of exp(x).
  • A113029 (program): a(1) = 2, a(2) = 3; for n > 2, a(n) = least prime equal to the sum of two or more previous terms.
  • A113032 (program): a(n) = Sum_{k=0..floor(n/8)} binomial(n-5*k, 3*k).
  • A113045 (program): Number triangle binomial(n,floor((n-k)/2)) mod 3.
  • A113046 (program): Diagonal sums of number triangle binomial(n, floor((n-k)/2)) mod 3.
  • A113047 (program): a(n) = C(3n,n)/(2n+1) mod 3.
  • A113048 (program): Binomial(4n,n)/(3n+1) mod 4.
  • A113049 (program): Triangle of sums of Jacobsthal numbers related to binomial(4n,n)/(3n+1) mod 4.
  • A113050 (program): a(1) = a(2) = 1; for n>2, a(n+1) = a(n) + a(n-1) iff n is prime, otherwise a(n+1) = a(n) + 1.
  • A113051 (program): a(1) = a(2) = 1; for n>2, a(n+1) = a(n) + a(n-1) iff a(n) is prime, otherwise a(n+1) = a(n) + 1.
  • A113052 (program): Binomial(5n,n)/(4n+1) mod 5.
  • A113059 (program): a(n) = n!*Sum_{k=0..n} A000296(k)/k!, n=0,1,… .
  • A113060 (program): a(n) = n!*Sum_{k=0..n} bell(k+1)/k!, n=0,1…, where bell(n) are the Bell numbers, cf. A000110.
  • A113061 (program): Sum of cube divisors of n.
  • A113062 (program): Expansion of theta series of hexagonal net with respect to a node.
  • A113063 (program): Associated with theta series of hexagonal net with respect to a node.
  • A113066 (program): Expansion of (1 + x)^2/((1 + x + x^2)*(1 + 3*x + x^2)).
  • A113067 (program): Expansion of -x/((x^2+x+1)*(x^2+3*x+1)); Invert transform gives signed version of Tetrahedral numbers A000292.
  • A113070 (program): Expansion of ((1+x)/(1-2x))^2.
  • A113071 (program): Expansion of ((1+x)/(1-3*x))^2.
  • A113072 (program): Tridiagonal matrix associated with coordination sequences.
  • A113115 (program): Primes p such that 17*p + 2 is also prime.
  • A113117 (program): a(1) = 2; for n>1, a(n) is the smallest integer > a(n-1) such that all primes <= a(n-1) divide at least one integer k for a(n-1) < k <= a(n).
  • A113119 (program): Total number of digits in all n-digit nonnegative integers.
  • A113125 (program): A simple tridiagonal matrix.
  • A113126 (program): A simple 4-diagonal matrix.
  • A113127 (program): Expansion of (1 + x + x^2 + x^3)/(1-x)^2.
  • A113128 (program): A simple 4-diagonal matrix based on (1+x)^3.
  • A113139 (program): Number triangle, equal to half of Delannoy square array A008288.
  • A113141 (program): Inverse of a Delannoy related triangle.
  • A113142 (program): Expansion of x(1-3x+x^2+x^3)/(1+x)^2.
  • A113144 (program): Row 3 of table A113143; equal to INVERT of triple (or 3-fold) factorials shifted one place right.
  • A113145 (program): Row 4 of table A113143; equal to INVERT of quartic (or 4-fold) factorials shifted one place right.
  • A113146 (program): Row 5 of table A113143; equal to INVERT of quintic (or 5-fold) factorials shifted one place right.
  • A113147 (program): Row 6 of table A113143; equal to INVERT of 6-fold factorials shifted one place right.
  • A113148 (program): Row 7 of table A113143; equal to INVERT of 7-fold factorials shifted one place right.
  • A113149 (program): Row 8 of table A113143; equal to INVERT of 8-fold factorials shifted one place right.
  • A113151 (program): Primes p such that 19*p + 2 is also prime.
  • A113161 (program): a(1) = 1, a(n+1) = largest prime <= a(n)+n.
  • A113166 (program): Total number of white pearls remaining in the chest - see Comments.
  • A113167 (program): Triangle read by rows; n-th row begins with n and contains n primes greater than n and not already used.
  • A113168 (program): Sum of digits of first n palindromes.
  • A113169 (program): Primes p such that 13*p + 2 is also prime.
  • A113170 (program): Ascending descending base exponent transform of odd numbers A005408.
  • A113175 (program): Replace each prime p in prime-factorization of n with p-th Fibonacci number.
  • A113176 (program): Product_{p|n} F(p), where F(p) is the p-th Fibonacci number and where the product is over the distinct prime divisors of n.
  • A113177 (program): If, for p prime, p^(m_{n,p}) is the highest power of p dividing n with m>=0, then a(n) = Sum_{p prime} F(p)*(m_{n,p}), where F(p) = p-th Fibonacci number.
  • A113178 (program): Sum_{p|n} F(p), where F(p) is the p-th Fibonacci number and where the sum is over the distinct prime divisors of n.
  • A113179 (program): Expansion of 1/sqrt((1-2x)^2-8x^3).
  • A113180 (program): Expansion of 1/sqrt((1-2*x)^2-8*x^4).
  • A113183 (program): Number of unrooted two-face maps in the plane (considered up to orientation-preserving homeomorphism) with the faces of equal degree n: planar maps with a distinguished outside face.
  • A113184 (program): Absolute difference between sum of odd divisors of n and sum of even divisors of n.
  • A113186 (program): Expansion of (25phi(q)phi^3(q^5)-phi^5(q)/phi(q^5)-24)/40 in powers of q where phi(q) is a Ramanujan theta function.
  • A113187 (program): Inverse of twin-prime related triangle A111125.
  • A113214 (program): Riordan array (1+2x,x(1+x)).
  • A113215 (program): Repeat A006218(n) 2n+1 times.
  • A113216 (program): Triangle of polynomials P(n,x) of degree n related to Pi (see comment) and derived from Padé approximation to exp(x).
  • A113217 (program): Parity of decimal digital root of n.
  • A113224 (program): a(2n) = A002315(n), a(2n+1) = A082639(n+1).
  • A113225 (program): a(2n) = A011900(n), a(2n+1) = A001109(n+1).
  • A113231 (program): Ascending descending base exponent transform of triangular numbers (A000217).
  • A113235 (program): Number of partitions of {1,..,n} into any number of lists of size not equal to 2, where a list means an ordered subset, cf. A000262.
  • A113236 (program): Number of partitions of {1,..,n} into any number of lists of size not equal to 3, where a list means an ordered subset, cf. A000262.
  • A113237 (program): E.g.f.: exp(x*(1 - x^3 + x^4)/(1-x)).
  • A113240 (program): Expansion of (1/(1-x))*sum(k>=2,x^k/(1-2x^k)).
  • A113241 (program): Sum{k=1..n, tau(2k)-1}.
  • A113242 (program): Numbers of the form 3^i +/- 3^j.
  • A113245 (program): a(n) = floor(binomial(2n,2k)/binomial(n,k)).
  • A113246 (program): a(2^n+a) = a(2^(n-1)+a) [if 0 <= a < 2^(n-1)], 3^n-a(2^n-a) [if 2^(n-1) <= a < 2^n].
  • A113247 (program): Number of permutations pi in S_n such that maj pi and maj pi^(-1) have the same parity where maj is the major index. Equivalently, the number of pi such that maj pi and inv pi have the same parity where inv is the inversion number.
  • A113248 (program): Number of permutations pi in S_n such that maj pi and maj pi^(-1) have opposite parity where maj is the major index. Equivalently, the number of pi such that maj pi and inv pi have opposite parity where inv is the inversion number.
  • A113259 (program): Expansion of psi(x)^5 / psi(x^5) - 25*x^2 * psi(x) * psi(x^5)^3 in powers of x where psi() is a Ramanujan theta function.
  • A113260 (program): Expansion of (-1 + psi(q)^5/psi(q^5) - 25q^2 psi(q)*psi(q^5)^3)/5 in powers of q where psi(q) is a Ramanujan theta function.
  • A113261 (program): Expansion of (9*phi(q)*phi(q^3)^5 - phi(q)^5*phi(q^3))/8 in powers of q where phi(q) is a Ramanujan theta function.
  • A113262 (program): One quarter of the number of solutions to a^2 + b^2 + 3*c^2 + 3*d^2 = n.
  • A113264 (program): Partial sums of Catalan numbers A000108 multiplied by powers of -5.
  • A113265 (program): Partial sums of Catalan numbers A000108 multiplied by powers of -6.
  • A113266 (program): Partial sums of Catalan numbers A000108 multiplied by powers of -7.
  • A113267 (program): Partial sums of Catalan numbers A000108 multiplied by powers of -8.
  • A113268 (program): Partial sums of Catalan numbers A000108 multiplied by powers of -9.
  • A113269 (program): Partial sums of Catalan numbers A000108 multiplied by powers of -10.
  • A113271 (program): Ascending descending base exponent transform of 2^n.
  • A113276 (program): Decimal expansion of de Bruijn’s constant.
  • A113277 (program): Expansion of q^(-1/3) * eta(q^2)^5 / eta(q)^2 in powers of q.
  • A113278 (program): Triangle T, read by rows, such that the matrix square, T^2, forms a simple 2-diagonal triangle where T^2 = 1 and T^2 = 2*(n+1) for n>=0.
  • A113280 (program): A symmetrical triangle of coefficients: t(n,m)=(n - m)*(n - m + 2)*m*(m + 2) + 1.
  • A113281 (program): Self-convolution equals A113224.
  • A113282 (program): Logarithmic derivative of the g.f. of A113281.
  • A113283 (program): Even bisection of A113281: a(n) = A113281(2*n).
  • A113284 (program): Odd bisection of A113281: a(n) = A113281(2*n+1).
  • A113291 (program): a(n) = A113290(n,1)/(n+1) for n>=0, where A113290 is the matrix log of triangle A113287.
  • A113292 (program): Column 0 of triangle A113290, which is the matrix log of A113287.
  • A113296 (program): Cumulative product of double factorial A006882.
  • A113300 (program): Sum of even-indexed terms of tribonacci numbers.
  • A113301 (program): Sum of odd-indexed terms of tribonacci numbers.
  • A113306 (program): Expansion of q * f(-q, -q^11) / f(-q^5, -q^7) in powers of q where f(, ) is Ramanujan’s general theta function.
  • A113310 (program): Riordan array ((1+x)/(1-x),x/(1+x)).
  • A113311 (program): Expansion of (1+x)^2/(1-x).
  • A113312 (program): Expansion of (1+x)^2/(1-2x^2+x^3).
  • A113313 (program): Riordan array (1-2x,x/(1-x)).
  • A113321 (program): Lexicographically earliest permutation of the natural numbers such that all positive differences between succeeding terms occur exactly once.
  • A113322 (program): First differences of A113321.
  • A113323 (program): A113321(A113321(n)).
  • A113324 (program): Inverse integer permutation of A113321.
  • A113325 (program): A113324(A113324(n)).
  • A113327 (program): a(n) = Sum_{k=0..n} 2^k*A111146(n,k).
  • A113328 (program): a(n) = Sum_{k=0..n} 3^k*A111146(n,k).
  • A113329 (program): a(n) = Sum_{k=0..n} 4^k*A111146(n,k).
  • A113335 (program): a(n) = 3^5 * binomial(n+4, 5).
  • A113337 (program): Number of noncrossing partitions of [n] with all blocks of odd size and 1 and n in the same block.
  • A113338 (program): Positive integers of the form (18*m^2+1)/11.
  • A113396 (program): Prime(n+1)^2-prime(n)^2 (mod prime(n+1)).
  • A113397 (program): What are the values of k in the term Prime(n+1)^2-Prime(n)^2 = a+k*(Prime(n+1)) if “a” is element of {0,1,…,Prime(n+1)-1}.
  • A113402 (program): Algebraic degree of cos(Pi/n) for constructible n-gons (A003401).
  • A113405 (program): Expansion of x^3/(1 - 2*x + x^3 - 2*x^4) = x^3/( (1-2*x)*(1+x)*(1-x+x^2) ).
  • A113406 (program): Half the number of integer solutions to x^2 + 4 * y^2 = n.
  • A113407 (program): Expansion of psi(x) * phi(x^2) in powers of x where psi(), phi() are Ramanujan theta functions.
  • A113409 (program): A transform of the central binomial coefficients A001405.
  • A113411 (program): Excess of number of divisors of 2n+1 of form 8k+1, 8k+3 over those of form 8k+5, 8k+7.
  • A113413 (program): A Riordan array of coordination sequences.
  • A113414 (program): Expansion of Sum_{k>0} x^k/(1-(-x^2)^k).
  • A113415 (program): Expansion of Sum_{k>0} x^k/(1-x^(2k))^2.
  • A113416 (program): Expansion of eta(q^2)^7*eta(q^4)/(eta(q)*eta(q^8)^2) in powers of q.
  • A113417 (program): Expansion of phi(x) * phi(-x)^2 * psi(x^4) in powers of x where phi(), psi() are Ramanujan theta functions.
  • A113418 (program): Expansion of (eta(q^2)^7*eta(q^4)/(eta(q)*eta(q^8))^2-1)/2 in powers of q.
  • A113419 (program): Expansion of phi(x)^2 * phi(-x) * psi(x^4) in powers of x where phi(), psi() are Ramanujan theta functions.
  • A113422 (program): a(n) = floor((5*n^2+1)/3).
  • A113424 (program): a(n) = (6n)!/((3n)!(2n)!n!).
  • A113428 (program): Expansion of f(-x^2, -x^3) in powers of x where f(, ) is Ramanujan’s general theta function.
  • A113429 (program): Expansion of f(-x, -x^4) in powers of x where f(, ) is Ramanujan’s general theta function.
  • A113435 (program): a(n) = a(n-1) + Sum_{k=0..n/3} a(n-3k) with a(0)=1.
  • A113436 (program): First row of A113435.
  • A113437 (program): Second row of A113435.
  • A113438 (program): Third row of A113435.
  • A113439 (program): a(n) = a(n-1) + Sum_{k=1..floor(n/4)} a(n-4k), with a(0)=1.
  • A113440 (program): First row of A113439.
  • A113441 (program): Second row of A113439.
  • A113442 (program): Third row of A113439.
  • A113443 (program): Fourth row of A113439.
  • A113444 (program): a(n) = a(n-1) + Sum_{0<k<=n/5} a(n-5k) with a(0)=1.
  • A113446 (program): Expansion of (phi(q)^2 - phi(q^3)^2) / 4 in powers of q where phi() is a Ramanujan theta function.
  • A113447 (program): Expansion of i * theta_2(i * q^3)^3 / (4 * theta_2(i * q)) in powers of q^2.
  • A113448 (program): Expansion of (eta(q^2)^2 * eta(q^9) * eta(q^18)) / (eta(q) * eta(q^6)) in powers of q.
  • A113449 (program): Sum of the square root of n-th square triangular number and n-th Pell (or lambda) number (A000129).
  • A113450 (program): Difference between the square root of n-th square triangular number and n-th lambda number given by the recurrence f(n) = 2f(n-1) + f(n-2), f(1) = 1, f(2)= 2.
  • A113452 (program): a(n) is the n-th smallest permanental minor of any H_m (m >= n), where H_m is the square matrix of order m with 1’s on or below the super diagonal and 0’s elsewhere.
  • A113453 (program): Triangle giving maximal permanent P(n,k) of an n X n lower Hessenberg (0,1)-matrix with exactly k 1’s for 2 <= n <= k <= 2n, read by rows.
  • A113459 (program): Least number that begins an arithmetic progression of n numbers with the same prime signature.
  • A113473 (program): n repeated 2^(n-1) times.
  • A113474 (program): a(n) = a(floor(n/2)) + floor(n/2) with a(1) = 1.
  • A113476 (program): Decimal expansion of (log(2) + Pi/sqrt(3))/3.
  • A113479 (program): Starting with the fraction 4/1 as the first term, a(n) is the numerator of the reduced fraction of the n-th term according to the rule: if n is even, multiply the previous term by n/(n+1); otherwise multiply the previous term by (n+1)/n.
  • A113486 (program): a(n) = A113166(n) - Fibonacci(n-1), where Fibonacci(n) = A000045(n).
  • A113487 (program): Numbers k such that 17*k + 2 is prime.
  • A113488 (program): Numbers k such that 19*k + 2 is prime.
  • A113497 (program): Ascending descending base exponent transform of sequence A000034(n) = 1 + n mod 2.
  • A113502 (program): A number n is included if at least one of its divisors > 1 is a triangular number (i.e., is of the form m(m+1)/2, m >= 2).
  • A113510 (program): Numbers k such that 29*k + 2 is prime.
  • A113519 (program): Semiprimes in A056105.
  • A113523 (program): a(n) = largest composite nonnegative integer <= n.
  • A113524 (program): Semiprimes in A056106.
  • A113525 (program): Semiprimes in A056107.
  • A113526 (program): Define the first two terms to be 1 and 3. All the other terms are obtained by concatenating the two previous terms.
  • A113527 (program): Semiprimes in A056108.
  • A113528 (program): Semiprimes in A056109.
  • A113530 (program): Semiprimes in A003215.
  • A113531 (program): a(n) = 1 + 2*n + 3*n^2 + 4*n^3 + 5*n^4 + 6*n^5.
  • A113532 (program): a(n) = 1 + 2*n + 3*n^2 + 4*n^3 + 5*n^4 + 6*n^5 + 7*n^6.
  • A113536 (program): Numbers k such that k^2 + 13 is prime.
  • A113541 (program): Numbers n such that 18n^2+1 is multiple of 19.
  • A113549 (program): a(n) = product of n successive numbers up to n, if n is even a(n) = n*(n-1)*.. = n!,if n is odd a(n) = n(n+1)(n+2)… ‘n’ terms.
  • A113550 (program): a(n) = product of n successive numbers up to n, if n is odd a(n) = n*(n-1)*.. = n!,if n is even a(n) = n(n+1)(n+2)… ‘n’ terms.
  • A113551 (program): a(n) = product of next n even numbers beginning with n if n is even, otherwise product of next n odd numbers beginning with n.
  • A113553 (program): Numbers k such that A113552(k) is odd.
  • A113555 (program): n-th digit after decimal of the successive approximation of the golden ratio. n-th digit after decimal of F(n+1)/F(n).
  • A113574 (program): a(n) is the least n-digit number whose k-th digit is prime if k is prime, composite if k is composite, and 1 if k=1.
  • A113580 (program): Define prime(0) = 1; then a(n) = sum prime(d), where d ranges over the decimal digits of n.
  • A113581 (program): Define prime(0) = 1; then a(n) = product prime(d), where d ranges over all the decimal digits of n.
  • A113582 (program): Triangle T(n,m) read by rows: T(n,m) = (n - m)*(n - m + 1)*m*(m + 1)/4 + 1.
  • A113596 (program): P(P(n))-P(P(n-1)), where P(n) = n(n+1)(n+2)/6 (cf. A000292).
  • A113597 (program): a(n) = F(F(n+1)) - F(F(n)), where F() = Fibonacci numbers.
  • A113601 (program): Intersection of A002144 and A005098.
  • A113605 (program): a(1) = a(2) = a(3) = 1; a(n) = a(n-3) + gcd(a(n-1), a(n-2)).
  • A113618 (program): a(n) = 1 + 2*n + 3*n^2 + 4*n^3 + 5*n^4 + 6*n^5 + 7*n^6 + 8*n^7.
  • A113630 (program): 1 + 2*n + 3*n^2 + 4*n^3 + 5*n^4 + 6*n^5 + 7*n^6 + 8*n^7 + 9*n^8.
  • A113632 (program): 1 + 2*n + 3*n^2 + 4*n^3 + 5*n^4 + 6*n^5 + 7*n^6 + 8*n^7 + 9*n^8 + 10*n^9.
  • A113636 (program): In the sequence of positive integers add 1 to each nonprime number.
  • A113637 (program): In the sequence of positive integers subtract 1 from each nonprime number.
  • A113638 (program): In the sequence of nonnegative integers subtract 1 from each prime number.
  • A113646 (program): a(n) is the smallest composite integer which is >= n.
  • A113648 (program): A variant of Josephus Problem in which 2 persons are to be eliminated at the same time.
  • A113651 (program): 2*JacobiSymbol(p,5) mod p^2 for p=prime(n).
  • A113652 (program): Expansion of (1 - theta_4(q)^2) / 4 in powers of q.
  • A113655 (program): Invert blocks of three in the sequence of natural numbers.
  • A113657 (program): Decimal expansion of 1/1089.
  • A113660 (program): Expansion of phi(x)^3 / phi(x^3) where phi() is a Ramanujan theta function.
  • A113661 (program): Expansion of (phi(x)^3/phi(x^3) - 1)/6 where phi() is a Ramanujan theta function.
  • A113675 (program): Decimal expansion of 1/8991.
  • A113677 (program): a(n) = (2*n+1)!*(2*n-2)!/(2*((n-1)!)*(n!)^2), n=1,2,… .
  • A113678 (program): Sequence array for A078008.
  • A113679 (program): Expansion of (1-x-2x^2)/(1-x).
  • A113680 (program): Riordan array ((1-x-2x^2)/(1-x),x).
  • A113681 (program): Expansion of f(-x^2, -x^3)^2 / f(-x, -x^2) in powers of x where f() is Ramanujan’s two-variable theta function.
  • A113682 (program): Expansion of 2/(sqrt(1-2*x-3*x^2)*(1+x+sqrt(1-2*x-3*x^2))).
  • A113684 (program): Expansion of x(1-x^2-x^3)/((1-x)(1-x-x^2))^2.
  • A113687 (program): Expansion of q^(-7/12)eta(q)eta(q^6)^3/(eta(q^2)eta(q^3)) in powers of q.
  • A113690 (program): Semiprimes in A054552.
  • A113691 (program): Semiprimes in A033951.
  • A113692 (program): Semiprimes in A054567.
  • A113693 (program): Semiprimes in A054556.
  • A113694 (program): Decimal expansion of 10/44955.
  • A113697 (program): Floor[n concatenated with n+2 divided by n+1].
  • A113704 (program): Triangular indicator function for divisibility, read by rows.
  • A113705 (program): Inverse Moebius transform of powers of 10.
  • A113709 (program): a(n) is the composite between p(n) and p(n+1), where p(n) is the n-th prime, which is divisible by (p(n+1)-p(n)).
  • A113710 (program): a(n) = A113709(n)/(prime(n+1) - prime(n)).
  • A113724 (program): A variant of Golomb’s sequence using even numbers: a(n) is the number of times 2*n+2 occurs, starting with a(1) = 2.
  • A113726 (program): A Jacobsthal convolution.
  • A113727 (program): A Pell convolution.
  • A113728 (program): a(n) is the integer between p(n) and p(n+2) which is divisible by (p(n+2)-p(n)), where p(n) is the n-th prime.
  • A113742 (program): Generalized Mancala solitaire (A002491); to get n-th term, start with n and successively round up to next 5 multiples of n-1, n-2, …, 1, for n>=1.
  • A113743 (program): Generalized Mancala solitaire (A002491); to get n-th term, start with n and successively round up to next 6 multiples of n-1, n-2, …, 1.
  • A113744 (program): Generalized Mancala solitaire (A002491); to get n-th term, start with n and successively round up to next 7 multiples of n-1, n-2, …, 1, for n>=1.
  • A113745 (program): Generalized Mancala solitaire (A002491); to get n-th term, start with n and successively round up to next 8 multiples of n-1, n-2, …, 1, for n>=1.
  • A113746 (program): Generalized Mancala solitaire (A002491); to get n-th term, start with n and successively round up to next 9 multiples of n-1, n-2, …, 1, for n>=1.
  • A113747 (program): Generalized Mancala solitaire (A002491); to get n-th term, start with n and successively round up to next 10 multiples of n-1, n-2, …, 1, for n>=1.
  • A113748 (program): Generalized Mancala solitaire (A002491); to get n-th term, start with n and successively round up to next 11 multiples of n-1, n-2, …, 1, for n>=1.
  • A113753 (program): a(n) = Fibonacci(n-1) + prime(n).
  • A113754 (program): Number of possible squares on an n^2 X n^2 grid.
  • A113755 (program): Sequence implicit in Jaroma’s corollary to Nagura’s theorem on primes.
  • A113763 (program): Non-multiples of 13, or numbers not divisible by 13.
  • A113765 (program): Define the first two terms to be 1 and 7. All the other terms are obtained by concatenating the two previous terms.
  • A113766 (program): a(n) is the product of those primes which divide some iterate of the Euler totient function but do not divide n itself.
  • A113768 (program): a(1) = 1, a(n+1) = a(n) + floor(a(n)^(1/3)).
  • A113770 (program): Partial sums of A113311(n)^2.
  • A113772 (program): Determinant of the 2 X 2 matrices where the first column is consecutive triangular numbers and the second column is the corresponding consecutive Fibonacci numbers.
  • A113773 (program): Number of distinct prime factors of A008352.
  • A113774 (program): Number of partitions of {1,…,n} into block sizes not a multiple of 3.
  • A113775 (program): Number of sets of lists (cf. A000262) whose list sizes are not a multiple of 3.
  • A113778 (program): Invert blocks of four in the sequence of natural numbers.
  • A113779 (program): Each term is the sum of the next two digits.
  • A113780 (program): Number of solutions to 24*n+1 = x^2+24*y^2, x a positive integer, y an integer.
  • A113784 (program): Difference between semiprime(n) and semiprime(n+2).
  • A113790 (program): In each block of 5 consecutive natural numbers, swap first and 2nd and swap 4th and 5th.
  • A113793 (program): Triangle T(n,m) read by rows: T(n,m) = phi(n - m + 1) * phi(m + 1).
  • A113801 (program): Numbers that are congruent to {1, 13} mod 14.
  • A113802 (program): Numbers that are congruent to {2, 12} mod 14.
  • A113803 (program): Numbers that are congruent to {3, 11} mod 14.
  • A113804 (program): Numbers that are congruent to 4 or 10 mod 14.
  • A113805 (program): Numbers that are congruent to {5, 9} mod 14.
  • A113806 (program): Numbers that are congruent to {6, 8} mod 14.
  • A113818 (program): Decimal expansion of the integer (101101101101101101101101101)/9.
  • A113823 (program): Tribonacci analog of A055502.
  • A113825 (program): Number of distinct prime factors of A008351(n).
  • A113828 (program): a(n) = Sum[2^(A047260(i)-1), {i,1,n}].
  • A113829 (program): a(n) = a(n-1) + 2^(k(n)), where k(n) is the n-th term of the sequence of numbers that are congruent to {0,3,4,5,7,8} mod 12.
  • A113835 (program): a(n) = a(n-1) + 2^(A007494(n-1)).
  • A113836 (program): a(n) = Sum[2^(A001651(i-1)-1), {i,1,n}].
  • A113837 (program): A number k is included if d(sigma(k)) > sigma(d(k)), where d(k) is number of positive divisors of k and sigma(k) is sum of positive divisors of k.
  • A113841 (program): a(n) = a(n-1) + 2^A047240(n) for n>1, a(1)=1.
  • A113848 (program): a(1) = a(2) = 1, a(n+2) = 2*a(n) + a(n+1)^2.
  • A113849 (program): Numbers whose prime factors are raised to the fourth power.
  • A113850 (program): Numbers whose prime factors are raised to the fifth power.
  • A113851 (program): Numbers whose prime factors are raised to the sixth power.
  • A113852 (program): Numbers whose prime factors are raised to the seventh power.
  • A113854 (program): a(n) = sum(2^(A047240(i)-1), i=1..n).
  • A113857 (program): a(n) = binomial(4+2*n, n) * binomial(9+2*n, 4+n).
  • A113859 (program): Expansion of (7-14*x+6*x^2)/((1-x)*(2*x^2-4*x+1)); related to the binomial transform of Pell numbers A000129 (see formula and comment for A007070).
  • A113861 (program): a(n) = (1/9)*((6*n - 7)*2^(n-1) - (-1)^n).
  • A113863 (program): Expansion of Molien series for representation Sym^2(R^n) of the automorphism group of the lattice E_8.
  • A113865 (program): Number of digits of Bell number A000110(n).
  • A113866 (program): Primes in the sequence A064491.
  • A113867 (program): a(n) = a(n-1) + 2^(A047258(n)) for n>1, a(1)=1.
  • A113870 (program): a(n) = a(n-1) + 2^(k(n)), where k(n) is the n-th term of the sequence formed by k(1)=0 together with the numbers A042963.
  • A113871 (program): G.f.: 1/(Sum_{k>=0} (k!)^2 x^k).
  • A113873 (program): a(3n) = a(3n-1) + a(3n-2), a(3n+1) = 2n*a(3n) + a(3n-1), a(3n+2) = a(3n+1) + a(3n).
  • A113874 (program): a(3n) = a(3n-1) + a(3n-2), a(3n+1) = 2n*a(3n) + a(3n-1), a(3n+2) = a(3n+1) + a(3n).
  • A113876 (program): a(n) = a(n-1) + 2^(k(n)), where k(n) is the n-th term of the sequence formed by k(1)=0 together with the numbers A042964.
  • A113888 (program): C(2*n+1,n)*C(2*n+6,n+1).
  • A113894 (program): a(n) = binomial(2*n, n) * binomial(5+2*n, n).
  • A113895 (program): a(n) = C(2+2*n, n) * C(7+2*n, 2+n).
  • A113901 (program): Product of omega(n) and bigomega(n) = A001221(n)*A001222(n), where omega(x): number of distinct prime divisors of x. bigomega(x): number of prime divisors of x, counted with multiplicity.
  • A113902 (program): Product of omega(n!) and bigomega(n!).
  • A113903 (program): Sum of omega(n!) and bigomega(n!).
  • A113904 (program): Starting with 1, each number is the previous number plus the product of the index number and the sum of the digits of the previous number.
  • A113909 (program): Square table of odd numbers which are neither squares nor one less than squares, read by antidiagonals.
  • A113911 (program): Prime numbers not appearing in the nextprime(x^2) sequence A007491.
  • A113920 (program): G.f.: (x^3 - x + 1)^3/(x^3*(1 - x)^3).
  • A113923 (program): A Farey like level n=2 rational function as a coefficient expansion.
  • A113924 (program): a(n) = gcd(A113605(n+1), A113605(n)). Also, for n >= 2, a(n) = A113605(n+2) - A113605(n-1).
  • A113925 (program): a(1)=0. a(1)=1. a(n+2) = gcd(a(n+1) + a(n), n).
  • A113935 (program): a(n) = prime(n) + 3.
  • A113946 (program): Series expansion of Farey rational polynomial based on A112627.
  • A113953 (program): A Jacobsthal triangle.
  • A113954 (program): Expansion of (1-2x^2)/((1-2x)(1+x)^2).
  • A113955 (program): Riordan array (1/((1-4x)c(x)),xc(x)/sqrt(1-4x)), c(x) the g.f. of A000108.
  • A113956 (program): Expansion of (1/((1-4x)c(x)))/(1-x^2c(x)/sqrt(1-4x)), c(x) the g.f. of A000108.
  • A113957 (program): Sum of the divisors of n which are not divisible by 7.
  • A113968 (program): a(0) = 0 and a(n) = (5*(-4)^n + 16*(-1)^n + 9*4^n)/240 for n >= 1.
  • A113973 (program): Expansion of phi(x^3)^3/phi(x) where phi() is a Ramanujan theta function.
  • A113974 (program): Expansion of (1-phi(x^3)^3/phi(x))/2 where phi() is a Ramanujan theta function.
  • A113975 (program): Devil’s Farey: coefficient expansion of a quadratic over quadratic that has 123 roots and a Farey p[1/2]=1 ( correction).
  • A113976 (program): a(n) = 4*a(n-1) - 3*a(n-2), for n>3, with a(0) = 14, a(1) = 133, a(2) = 616, and a(3) = 2128.
  • A113978 (program): a(n)=Sum(d|n)(10^(n-d)).
  • A113979 (program): Number of compositions of n with an even number of 1’s.
  • A113980 (program): Number of compositions of n with an odd number of 1’s.
  • A113998 (program): Reverse of triangle A051731.
  • A113999 (program): a(n) = Sum_{ k, k|n } 10^(k-1).
  • A114000 (program): Triangle read by rows: column k has g.f. = Sum_{k>0} x^k/(1-x^(2*k+1)).
  • A114001 (program): Rows of A114000 expressed as decimals (a sequence related to the number of divisors of 2n-1).
  • A114002 (program): Expansion of x^k(1+x^(k+1))/(1-x^(k+1)).
  • A114003 (program): Rows sums of triangle A114002.
  • A114004 (program): Inverse of triangle A114002.
  • A114005 (program): First column of number triangle A114004.
  • A114006 (program): Row sums of number triangle A114004.
  • A114010 (program): a(1) = a(2) = 2, Let k(n) = (prime(n) + prime(n+1))/2. Then a(k(n)) = k(n). a(k(n)-i) = prime(n), a(k(n)+i) = prime(n+1) until the next prime occurs.
  • A114011 (program): Least multiple of prime(n) ending in digit 1.
  • A114013 (program): Least multiple of prime(n) ending in digit 9.
  • A114014 (program): Expansion of g.f. (1 + 2*x)^4/((1 + x)*(1 - 16*x^2)).
  • A114039 (program): G.f.: 1/Sum_{k>=0} k!*(k!+1)*x^k/2.
  • A114040 (program): a(0) = 1, a(1) = 9, a(n) = 6*a(n-1) - a(n-2) - 4.
  • A114046 (program): Numbers x such that x^2 - 92*y^2 = 1 for some y.
  • A114047 (program): x such that x^2 - 13*y^2 = 1.
  • A114048 (program): x-values in the solution to x^2 - 19*y^2 = 1.
  • A114049 (program): x such that x^2 - 21*y^2 = 1.
  • A114050 (program): x-values in the solution to x^2 - 22*y^2 = 1.
  • A114051 (program): x such that x^2 - 23*y^2 = 1.
  • A114052 (program): x such that x^2 - 27*y^2 = 1.
  • A114054 (program): Decimal expansion of 998998998998998998998998998/9.
  • A114059 (program): a(n) = binomial(3+2*n, n) * binomial(8+2*n, 3+n).
  • A114090 (program): Sums of 2 distinct nonnegative cubes.
  • A114091 (program): Number of partitions of n into parts that are distinct mod 3.
  • A114099 (program): Number of partitions of n into parts with digital root = 9.
  • A114103 (program): n multiples of n such that a(n) is a multiple of n. The n-th group contains n multiples of n. Arranged sequentially the n-th term is a multiple of n.
  • A114104 (program): a(n) = A114103(n)/n.
  • A114105 (program): The sum of the next n terms of A114103.
  • A114112 (program): a(1)=1, a(2)=2; thereafter a(n) = n+1 if n odd, n-1 if n even.
  • A114113 (program): a(n) = sum{k=1 to n} (A114112(k)). (For n>=2, a(n) = sum{k=1 to n} (A014681(k)) =sum{k=1 to n} (A103889(k)).).
  • A114114 (program): An invertible partition matrix.
  • A114116 (program): 1’s-counting matrix: row sums give number of 1’s in binary expansion of n+1.
  • A114117 (program): Inverse of 1’s counting matrix A114116.
  • A114118 (program): Number triangle T(n,k)=sum{j=0..n, C(floor((n+k+j)/3),k)C(k,floor((n+k+j)/3))}.
  • A114119 (program): Row sums of triangle A114118.
  • A114121 (program): Expansion of (sqrt(1 - 4*x) + (1 - 2*x))/(2*(1 - 4*x)).
  • A114122 (program): Expansion of (1+x)^2/(1+2x-4x^3-4x^4).
  • A114123 (program): Riordan array (1/(1-x), x*(1+x)^2/(1-x)^2).
  • A114143 (program): Possible sums of the final scores of completed American football games where both teams score.
  • A114144 (program): A variant of the Josephus Problem in which three persons are to be eliminated at the same time.
  • A114160 (program): E.g.f. is A(x) = (1-log(B(x)))/B(x), where B(x) = sqrt(1-2*x).
  • A114161 (program): E.g.f.: (3-log(1-2*x))/(1-2*x)^(1/2).
  • A114162 (program): C(n,k)*Floor((n-k)/2)!.
  • A114164 (program): Riordan array (1/(1-2x), x(1-x)/(1-2x)^2).
  • A114180 (program): Numbers n with mu(n) = mu(n+1) = mu(n+2).
  • A114182 (program): F(4n) - 2n - 1 where F(n) = Fibonacci numbers. Also, the floor of the log base phi of sequence A090162 (phi = (1+Sqrt(5))/2).
  • A114185 (program): a(n) = Fibonacci(2*n) - n - 1.
  • A114186 (program): Running sums of consecutive integers with all primes set to 2.
  • A114188 (program): Riordan array (1/(1-x),x(1+x)/(1-x)^2).
  • A114189 (program): Riordan array (1/(1+xc(-2x)), xc(-2x)/(1+xc(-2x)), c(x) the g.f. of A000108.
  • A114191 (program): Expansion of 1/(1+x*c(-2*x)), c(x) the g.f. of A000108.
  • A114192 (program): Riordan array (1/(1-2x),x/(1-2x)^2).
  • A114193 (program): Riordan array (1/(1+2xc(-2x)),xc(-2x)/(1+2xc(-2x)), c(x) the g.f. of A000108.
  • A114195 (program): Riordan array (1/(1-3x),x(1-x)/(1-3x)^2).
  • A114196 (program): Expansion of (1-3x)/(1-6x+8x^2+x^3).
  • A114198 (program): a(n) = Sum_{k=0..n} binomial(n,k)^2*F(k+1).
  • A114199 (program): Row sums of a Pascal-Fibonacci triangle.
  • A114201 (program): C(1+2*n,1+n)*C(6+2*n,0+n)
  • A114203 (program): Row sums of a Pascal-Jacobsthal triangle.
  • A114204 (program): Sum {binomial(n,k)^2*J(k+1),k,0,n} with J(n)=A001045(n).
  • A114209 (program): Number of permutations of [n] having exactly two fixed points and avoiding the patterns 123 and 231.
  • A114210 (program): Number of derangements of [n] avoiding the patterns 123 and 231.
  • A114211 (program): a(n) = (5*n^3+12*n^2+n+6)/6.
  • A114212 (program): Generalized Gould sequence.
  • A114214 (program): Diagonal sums of number triangle A114213.
  • A114215 (program): Number of derangements of [n] avoiding the patterns 123, 132 and 213.
  • A114216 (program): a(0)=0; thereafter a(n) = largest odd divisor of a(n-1) + prime(n).
  • A114219 (program): Number triangle (k-(k-1)*0^(n-k))*[k<=n].
  • A114220 (program): a(n) = Sum_{k=0..floor(n/2)} k-(k-1)*0^(n-2k).
  • A114226 (program): Row sums of a Pascal-Thue-Morse triangle.
  • A114238 (program): a(n) = binomial(2+2*n, 2+n) * binomial(7+2*n, n).
  • A114239 (program): a(n) = (n+1)(n+2)^3*(n+3)(n^2 + 4n + 5)/120.
  • A114240 (program): a(n) = (n+1)(n+2)^2*(n+3)(7n^2 + 23n + 20)/240.
  • A114241 (program): a(n) = (n+1)*(n+2)*(n+3)*(11*n^2 + 29*n + 20)/120.
  • A114242 (program): a(n) = (n+1)(n+2)^2*(n+3)^2*(n+4)(2n+5)/720.
  • A114243 (program): a(n) = (n+1)*(n+2)^2*(n+3)*(n+4)*(3*n+5)/240.
  • A114244 (program): a(n) = (n+1)*(n+2)^2*(n+3)*(7n^2 + 28n + 30)/360.
  • A114251 (program): C(3+2*n,3+n)*C(8+2*n,0+n)
  • A114252 (program): C(4+2*n,4+n)*C(9+2*n,0+n)
  • A114253 (program): a(n) = C(5+2*n,5+n)*C(10+2*n,0+n).
  • A114254 (program): Sum of all terms on the two principal diagonals of a 2n+1 X 2n+1 square spiral.
  • A114269 (program): Numbers k such that k^2 + 6 is prime.
  • A114270 (program): Numbers k such that k^2 + 7 is prime.
  • A114271 (program): Numbers k such that k^2 + 8 is prime.
  • A114272 (program): Numbers k such that k^2 + 9 is prime.
  • A114273 (program): Numbers k such that k^2 + 10 is prime.
  • A114274 (program): Numbers k such that k^2 + 11 is prime.
  • A114275 (program): Numbers k such that k^2 + 12 is prime.
  • A114277 (program): Sum of the lengths of the second ascents in all Dyck paths of semilength n+2.
  • A114278 (program): A triangle generated by a family of Sierpinski-triangle related polynomials.
  • A114279 (program): Row sums of number triangle A114278.
  • A114283 (program): Sequence array for binomial transform of Jacobsthal numbers A001045(n+1).
  • A114284 (program): Riordan array ((1-3*x)/(1-x), x).
  • A114285 (program): Expansion of (1-3*x)/((1-x)*(1-x^2)).
  • A114300 (program): Number of non-intersecting cycle systems in a particular directed graph.
  • A114307 (program): Length of the cycle for Lucas numbers mod 10^n.
  • A114310 (program): (n-1)!*(n!-n*(n-1)/2).
  • A114311 (program): a(n) = n! - n(n-1)/2.
  • A114322 (program): Largest number whose 4th power has n digits.
  • A114327 (program): Table T(n,m) = n - m read by upwards antidiagonals.
  • A114329 (program): Triangle T(n,k) is the number of partitions of an n-set into lists (cf. A000262) with k lists of size 1.
  • A114334 (program): Divisors of 6^6.
  • A114335 (program): Numbers k such that k^2 + 1 and k^2 - 3 are both prime.
  • A114338 (program): Number of divisors of n!! (double factorial = A006882(n)).
  • A114347 (program): Cumulative sum of triple factorial numbers a(n) = n!!! (A007661).
  • A114350 (program): Primes of the form 2x^3 + x + 1.
  • A114351 (program): Primes of the form 3x^3+x+1.
  • A114352 (program): Primes of the form 5x^3+x+1.
  • A114353 (program): Primes of the form 7x^3+x+1.
  • A114354 (program): Primes of the form 9x^3+x+1.
  • A114364 (program): a(n) = n*(n+1)^2.
  • A114372 (program): Number of partitions of n into parts with an odd number of prime factors that are all distinct.
  • A114374 (program): Number of partitions of n into parts that are not squarefree.
  • A114375 (program): a(n) = (a(n-1) XOR a(n-2)) + 1, a(0) = a(1) = 0.
  • A114378 (program): Area of annuli of consecutive integer thickness.
  • A114379 (program): Sums of p-th to the q-th prime where p and q are twin primes.
  • A114389 (program): Bisection of A065621.
  • A114390 (program): a(n) = A065621(n^2).
  • A114398 (program): Positions where A000695 is a square.
  • A114399 (program): Squares in A000695.
  • A114400 (program): Square roots of A114399.
  • A114403 (program): Triprime gaps. First differences of A014612.
  • A114404 (program): 4-almost prime gaps. First differences of A014613.
  • A114405 (program): 5-almost prime gaps. First differences of A014614.
  • A114406 (program): 6-almost prime gaps. First differences of A046306.
  • A114407 (program): 7-almost prime gaps. First differences of A046308.
  • A114408 (program): 8-almost prime gaps. First differences of A046310.
  • A114410 (program): Cumulative sum of double primorials (A079078).
  • A114411 (program): Triple primorial n### = n#3.
  • A114420 (program): Quadruple primorial n#### = n#4.
  • A114421 (program): Quintuple primorial n##### = n#5.
  • A114422 (program): Riordan array (1/sqrt(1-2*x-3*x^2), M(x)-1) where M(x) is the g.f. of the Motzkin numbers A001006.
  • A114423 (program): Multifactorial array read by ascending antidiagonals.
  • A114425 (program): Product of the first n 3-almost primes (A014612).
  • A114426 (program): Product of the first n 4-almost primes (A014613).
  • A114427 (program): Decimal expansion of the real solution of x^3-x^2-x-4=0.
  • A114431 (program): Decimal expansion of the real solution of x^3 - x^2 - 2x - 4 = 0.
  • A114433 (program): Last digit (the checksum) of 10-digit ISBN numbers, 10 is represented as “X”.
  • A114434 (program): To obtain a(n), write the n-th composite number as a product of primes, add 1 to each prime and multiply.
  • A114435 (program): Indices of 4-almost prime triangular numbers.
  • A114436 (program): Indices of 5-almost prime triangular numbers.
  • A114437 (program): Indices of 6-almost prime triangular numbers.
  • A114439 (program): Indices of semiprime pentagonal numbers.
  • A114441 (program): Indices of 3-almost prime pentagonal numbers.
  • A114443 (program): Indices of 4-almost prime pentagonal numbers.
  • A114444 (program): a(n) = 16*n*(n+2).
  • A114445 (program): Indices of 5-almost prime pentagonal numbers.
  • A114446 (program): Indices of 7-almost prime pentagonal numbers.
  • A114447 (program): Indices of 6-almost prime pentagonal numbers.
  • A114448 (program): Array a(n,k) = n^k (mod k) read by antidiagonals (k>=1, n>=1).
  • A114450 (program): a(n)=(2n)!*(sum{k=1…2n}1/k)/(2n+1).
  • A114454 (program): Numbers n such that the n-th hexagonal number is a 3-almost prime.
  • A114455 (program): Numbers n such that the n-th hexagonal number is a 4-almost prime.
  • A114456 (program): Numbers n such that the n-th hexagonal number is a 5-almost prime.
  • A114458 (program): Integer part of sqrt(n)+sqrt(n+1)+sqrt(n+2).
  • A114459 (program): Integer part of sqrt(n)+sqrt(n+1)+sqrt(n+2)+sqrt(n+3).
  • A114460 (program): Integer part of sqrt(n)+sqrt(n+1)+sqrt(n+2)+sqrt(n+3)+sqrt(n+4).
  • A114464 (program): Number of Dyck paths of semilength n having no ascents of length 2 that start at an even level.
  • A114465 (program): Number of Dyck paths of semilength n having no ascents of length 2 that start at an odd level.
  • A114476 (program): Triangle read by rows: inverse of triangle in A061554 with signs in each column +,+,-,-,+,+,-,-,…
  • A114479 (program): Kekulé numbers for certain benzenoids.
  • A114480 (program): Kekulé numbers for certain benzenoids.
  • A114481 (program): Kekulé numbers for certain benzenoids.
  • A114482 (program): Let S(1)=1, S(2)=10; S(2n)=concatenation of S(2n-1), S(2n-2) and 0; and S(2n+1)=concatenation of S(2n), S(2n) and 0. Sequence gives S(infinity).
  • A114487 (program): Number of Dyck paths of semilength n having no UUDD’s starting at level 0.
  • A114494 (program): Triangle read by rows: T(n,k) is number of hill-free Dyck paths of semilength n and having k returns to the x-axis. (A Dyck path is said to be hill-free if it has no peaks at level 1.)
  • A114495 (program): Number of returns to the x-axis in all hill-free Dyck paths of semilength n (a Dyck path is said to be hill-free if it has no peaks at level 1).
  • A114496 (program): a(n) = Sum of binomial(n,k)*binomial(2n+k,k) over all k.
  • A114504 (program): Numbers n such that the n-th hexagonal number is a 6-almost prime.
  • A114505 (program): Numbers n such that the n-th hexagonal number is a 7-almost prime.
  • A114507 (program): Number of Dyck paths of semilength n having no ascents of length 3.
  • A114509 (program): Number of Dyck paths of semilength n having no ascents of length 4.
  • A114514 (program): The digits on a numerical pad from upper left to lower right.
  • A114515 (program): Number of peaks in all hill-free Dyck paths of semilength n (a Dyck path is hill-free if it has no peaks at level 1).
  • A114517 (program): Numbers n such that n-th heptagonal number is semiprime.
  • A114518 (program): Numbers n such that A008475(n) is prime.
  • A114519 (program): a(n) = A008475(A114518(n)).
  • A114520 (program): Composites in sequence A114518.
  • A114521 (program): a(n) = A008475(A114520(n)).
  • A114522 (program): Numbers n such that sum of distinct prime divisors of n is prime.
  • A114525 (program): Triangle of coefficients of the Lucas (w-)polynomials.
  • A114540 (program): Number of correct decimal digits given by the n-th convergent to the golden ratio.
  • A114543 (program): Expansion of x*(1+x)/((1+2x)(1-2x-768x^2)).
  • A114548 (program): Numbers n such that n-th heptagonal number is 3-almost prime.
  • A114551 (program): Continued fraction expansion of the constant (A114550) equal to Sum_{n>=0} 1/A112373(n) such that the partial quotients satisfy a(2n) = A112373(n) for n > 0 and a(2n+1) = A112373(n+1)/A112373(n) for n >= 0.
  • A114553 (program): a(n) = 25*a(n-2) + 48*a(n-3) with a(0) = 0, a(1) = a(2) = 1.
  • A114554 (program): Numbers n such that n-th heptagonal number is 4-almost prime.
  • A114555 (program): Smallest nonsquarefree integer > the n-th term of the Fibonacci sequence.
  • A114556 (program): Numbers n such that n-th heptagonal number is 5-almost prime.
  • A114558 (program): Numbers n such that n-th heptagonal number is 6-almost prime.
  • A114559 (program): Numbers n such that n-th heptagonal number is 7-almost prime.
  • A114562 (program): The first occurrence of n in A111701.
  • A114564 (program): Numbers of the form n=12s+7, where q=4s+3 is a prime for which the order of 2 is either q-1 or (q-1)/2.
  • A114567 (program): Numbers k such that the binary expansion of n mod 2^k is the postorder traversal of a binary tree, where 1 indicates a node and 0 indicates there are no children on that side.
  • A114569 (program): a(n) = 9*4^n - 1.
  • A114570 (program): Let the decimal expansion of n be d_1 d_2 … d_k; then a(n) = Sum_{i=1..k} d_i^(k+1-i).
  • A114574 (program): a(n) = p*p! where p = prime(n).
  • A114587 (program): Number of peaks at odd levels in all hill-free Dyck paths of semilength n+3 (a hill in a Dyck path is a peak at level 1).
  • A114589 (program): Number of hill-free Dyck paths of semilength n+3 and having no peaks at even levels (a hill in a Dyck path is a peak at level 1).
  • A114590 (program): Number of peaks at even levels in all hill-free Dyck paths of semilength n+2 (a hill in a Dyck path is a peak at level 1).
  • A114604 (program): Numerator of partial sums of A005329/A006125.
  • A114606 (program): Numbers n such that n-th octagonal number is 3-almost prime.
  • A114607 (program): Start with 1 0 1 0 then add a one every time (e.g. 1 1 0 1 1 1 0 1 1 1 1 0 …).
  • A114618 (program): Numbers n such that n-th octagonal number is 4-almost prime.
  • A114619 (program): a(n) = 2*A079291(n) (twice squares of Pell numbers).
  • A114620 (program): 2*A084158 (twice Pell triangles).
  • A114621 (program): Numbers n such that n-th octagonal number is 5-almost prime.
  • A114633 (program): a(n) = (n+1)*(n+2)/2 * Sum_{k=0..floor(n/2)} n!/(n-2*k)!.
  • A114634 (program): Numbers n such that n-th octagonal number is 6-almost prime.
  • A114635 (program): Numbers n such that n-th octagonal number is 7-almost prime.
  • A114636 (program): Numbers n such that n-th octagonal number is 8-almost prime.
  • A114637 (program): Nonnegative numbers excluding 1 and 2.
  • A114643 (program): Number of real primitive Dirichlet characters modulo n.
  • A114646 (program): Let M(n) be the n X n matrix m(i,j)=min(i,j) for 1<=i,j<=n then a(n) is the trace of M(n)^(-4).
  • A114647 (program): Expansion of (3 -4*x -3*x^2)/((1-x^2)*(1-2*x-x^2)); a Pellian-related sequence.
  • A114652 (program): a(1)=1. For n>1, a(n) = a(n-1) + (number of terms among {a(1),a(2),…,a(n-1)} which are coprime to n).
  • A114653 (program): A114652(n+1) - A114652(n).
  • A114654 (program): Discriminant of the polynomial x^n + x + 1.
  • A114655 (program): Triangle read by rows: T(n,k) is the number of Schroeder paths of length 2n and having k weak ascents (1<=k<=n). A Schroeder path of length 2n is a lattice path from (0,0) to (2n,0) consisting of U=(1,1), D=(1,-1) and H=(2,0) steps and never going below the x-axis. A weak ascent in a Schroeder path is a maximal sequence of consecutive U and H steps.
  • A114656 (program): Triangle read by rows: T(n,k) is the number of double rise-bicolored Dyck paths (double rises come in two colors; also called marked Dyck paths) of semilength n and having k peaks (1 <= k <= n).
  • A114687 (program): Triangle read by rows: T(n,k) is the number of double rise-bicolored Dyck paths (double rises come in two colors; also called marked Dyck paths) of semilength n and having k double rises (0 <= k <= n-1).
  • A114688 (program): Expansion of (1 +3*x -x^2)/((1-x^2)*(1-2*x-x^2)); a Pellian-related sequence.
  • A114689 (program): Expansion of (1 +4*x -x^2)/((1-x^2)*(1-2*x-x^2)); a Pellian-related sequence.
  • A114693 (program): Number of returns to the x-axis in all hill-free Schroeder paths of length 2n+4. A Schroeder path of length 2n is a lattice path from (0,0) to (2n,0) consisting of U=(1,1), D=(1,-1) and H=(2,0) steps and never going below the x-axis. A hill is a peak at height 1.
  • A114696 (program): Expansion of (1+4*x+x^2)/((1-x^2)*(1-2*x-x^2)); a Pellian-related sequence.
  • A114697 (program): Expansion of (1+x+x^2)/((1-x^2)*(1-2*x-x^2)); a Pellian-related sequence.
  • A114698 (program): Let M(n) be the n X n matrix m(i,j)=min(i,j) for 1<=i,j<=n then a(n) is the trace of M(n)^(-3).
  • A114710 (program): Number of hill-free Schroeder paths of length 2n that have no horizontal steps on the x-axis.
  • A114713 (program): Number of ascents in all peakless Motzkin paths of length n+3.
  • A114723 (program): G.f.: x*(1 - 2*x^2)/(1 - x - 3*x^2 - 3*x^3 - x^4).
  • A114743 (program): a(1) =4, a(2) = 6, a(n+1) = least composite number of the form k*(a(n-1)) - a(n), not included earlier.
  • A114745 (program): a(1) = 1, a(2) = 3, a(n+1) = least number of the form k*(a(n-1)) - a(n), not included earlier.
  • A114751 (program): The following triangle contains n consecutive numbers beginning from n in ascending order if n is odd else in descending order. Sequence contains the triangle by rows.
  • A114752 (program): a(2n)=2n, a(2n+1)=4n+1.
  • A114753 (program): First column of A114751.
  • A114760 (program): n-th digit after decimal point of the successive approximations to phi = .618…; equally, n-th digit after decimal point of F(n)/F(n+1).
  • A114761 (program): a(n) = (floor(sqrt(2)*10^n))^2.
  • A114762 (program): a(n) = floor(3^(1/2)*10^n)^2.
  • A114763 (program): a(n) = floor(sqrt(5)*10^n)^2.
  • A114764 (program): a(n) = floor(sqrt(6)*10^n)^2.
  • A114765 (program): a(n) = floor(sqrt(7) * 10^n)^2.
  • A114766 (program): a(n) = floor(sqrt(8)*10^n)^2.
  • A114767 (program): Floor[2^(1/3)*10^n]^3.
  • A114768 (program): a(n) = floor(3^(1/3)*10^n)^3.
  • A114769 (program): a(n) = floor(4^(1/3)*10^n)^3.
  • A114770 (program): Floor[5^(1/3)*10^n]^3.
  • A114771 (program): Floor[6^(1/3)*10^n]^3.
  • A114772 (program): Floor[7^(1/3)*10^n]^3.
  • A114773 (program): Floor[9^(1/3)*10^n]^3.
  • A114775 (program): Expansion of x^2*(1+x^2)*(1 - x^4 + x^7)/((1 - x^4 + x^6)*(1 - x^4 - x^6)).
  • A114778 (program): Cumulative product of triple factorial A007661.
  • A114779 (program): Cumulative product of quadruple factorial A007662.
  • A114790 (program): Cumulative product of quintuple factorial A085157.
  • A114793 (program): a(1) = a(2) = 1; for n>2, a(n) = a(n-2)^3 + a(n-1)^2.
  • A114795 (program): {concatenation n, n-1, n-2, …3,2,1} mod n.
  • A114796 (program): Cumulative product of sextuple factorial A085158.
  • A114797 (program): a(n) = n multiplied by the least nontrivial nondivisor of n.
  • A114798 (program): Cubic polynomial coefficients such that an elliptical term is zero.
  • A114799 (program): Septuple factorial, 7-factorial, n!7, n!!!!!!!, a(n) = n*a(n-7) if n > 1, else 1.
  • A114800 (program): Octuple factorial, 8-factorial, n!8, n!!!!!!!!.
  • A114803 (program): Integers when g2^3-27*g3^2=0 in cubic polynomials of the form: w^2=4*x^3-g2*x-g3.
  • A114805 (program): Cumulative sum of quintuple factorial numbers n!!!!! (A085157).
  • A114806 (program): Nonuple factorial, 9-factorial, n!9, n!!!!!!!!!.
  • A114810 (program): Number of complex, weakly primitive Dirichlet characters modulo n.
  • A114811 (program): Number of real, weakly primitive Dirichlet characters modulo n.
  • A114828 (program): Numbers n such that n-th octagonal number is 9-almost prime.
  • A114831 (program): Each term is previous term plus floor of harmonic mean of two previous terms.
  • A114832 (program): Each term is previous term plus ceiling of harmonic mean of two previous terms.
  • A114846 (program): Numbers of the form p^p - p!, where p is a prime.
  • A114853 (program): a(n) = floor(n^n/n!!).
  • A114855 (program): Expansion of q^(-1/3) * (eta(q) * eta(q^4))^2 / eta(q^2) in powers of q.
  • A114870 (program): a(n) = A002627(n+1) - A002627(n) - n!.
  • A114872 (program): Even numbers not representable as (p-1)p^k (where p is a prime and k>=0) in ascending order.
  • A114873 (program): Numbers representable in exactly one way as (p-1)p^k (where p is a prime and k>=0), in ascending order.
  • A114889 (program): a(1)=1 and, for n>1, a(n) is the smallest integer greater than a(n-1) such that a(n)+a(i) is not a power of 3, for i=1,…, n-1.
  • A114890 (program): First differences of A114889.
  • A114891 (program): Numbers that are the smallest element of a k-cycle (k > 1) of permutation A114861.
  • A114892 (program): a(n) is the cycle length corresponding to A114891(n).
  • A114900 (program): Number of compositions of n such that no two adjacent parts are equal, allowing 0.
  • A114912 (program): 2^a(n) divides A000009(n) but 2^(a(n)+1) does not.
  • A114913 (program): Numbers n such that A114912(n)=1. Numbers n such that A000009(n) == 2 (mod 4).
  • A114914 (program): Values in A114913 that are not in A111174.
  • A114938 (program): Number of permutations of the multiset {1,1,2,2,…,n,n} with no two consecutive terms equal.
  • A114945 (program): Number of monic irreducible polynomials over GF(3) of degree <= n.
  • A114946 (program): Number of monic irreducible polynomials over GF(4) of degree <= n.
  • A114947 (program): Number of monic irreducible polynomials over GF(5) of degree <= n.
  • A114948 (program): a(n) = n^2 + 10.
  • A114949 (program): a(n) = n^2 + 6.
  • A114955 (program): A 2/3-power Fibonacci sequence.
  • A114956 (program): a(0) = a(1) = 1, for n>1 a(n) = ceiling(a(n-1)^(3/4) + a(n-2)^(3/4)).
  • A114958 (program): a(n) = 6*2^(n+1) - 5*(n+1) - 4.
  • A114960 (program): Expansion of (-1+3*x-5*x^2+4*x^3) / ((1-2*x)*(2*x^2-1)*(x-1)^2).
  • A114962 (program): a(n) = n^2 + 14.
  • A114963 (program): a(n) = n^2 + 22.
  • A114964 (program): a(n) = n^2 + 30.
  • A114965 (program): n^2 + 34.
  • A114982 (program): Expansion of x(3-x^2)/(1-3x).
  • A114984 (program): Coefficients of cubic equations in the form w^2=4*x^3-g2*x-g3 Weierstrass elliptic form whose solutions approximate zeta zeros.
  • A114986 (program): Characteristic function of (A000201 prefixed with 0).
  • A114989 (program): Numbers whose sum of squares of distinct prime factors is prime.
  • A114990 (program): a(n) = a(n-2) + A000265(a(n-1)), a(0)=0, a(1)=1.
  • A114994 (program): Numbers whose binary representation has monotonically decreasing sizes of groups of zeros (including zero-length groups between adjacent ones).
  • A114997 (program): Number of ordered trees with n edges and no unary or binary nodes.
  • A115000 (program): a(n) = J_2(n) / 24.
  • A115001 (program): Sum_{k=1}^n J_2(k)/24.
  • A115002 (program): J_4(n)/240.
  • A115003 (program): Sum_{k=1}^n J_4(k)/240.
  • A115006 (program): Row 2 of array in A114999.
  • A115007 (program): Row 3 of array in A114999.
  • A115008 (program): a(n) = a(n-1)+a(n-3)+a(n-4).
  • A115012 (program): Sum_{i=1..n, gcd(5,i)=1} i.
  • A115013 (program): a(n) = difference between largest and smallest primes dividing the n-th squarefree integer (with a(1)=0).
  • A115014 (program): Sum_{i=1..n, gcd(6,i)=1} i.
  • A115015 (program): Sum_{i=1..n} (gcd(7,i)=1) i.
  • A115017 (program): a(n) = largest triangular number dividing n.
  • A115018 (program): Numbers n such that (n+1)*(n+2)^2 + 1 is prime.
  • A115020 (program): Count backwards from 100 in steps of 7.
  • A115022 (program): a(n) = F(n-th squarefree)/product{p=primes,p|(n-th squarefree)} F(p), where F(m) is m-th Fibonacci number.
  • A115024 (program): Natural numbers n such that the number of prime factors of n (counted with multiplicity) is equal to the number of decimal digits of n.
  • A115025 (program): a(n) = n-th element of n-th row of triangle shown below.
  • A115030 (program): Number of distinct sums of subsets of the first n prime numbers.
  • A115032 (program): Expansion of (5-14*x+x^2)/((1-x)*(x^2-18*x+1)).
  • A115034 (program): Alternately multiply and divide, with a(1)=1 and a(2)=2.
  • A115036 (program): Even terms of A116883.
  • A115048 (program): Count backwards from 100 in steps modulo n.
  • A115052 (program): Expansion of 1/(3*x^2 - 3*x + 1)^2.
  • A115053 (program): Series expansion of x*(x+3)^2/(3*x+1)^2.
  • A115055 (program): Lower level digraph derived from a voltage graph.
  • A115056 (program): a(n) = n*(n^2-1)*(3*n+2).
  • A115058 (program): Primes p such that 3p+2 is not prime.
  • A115059 (program): a(n+4) = a(n+3)+a(n+1)+a(n)+k(n), where k(n) = 0, 1, 0, or -1 according to n mod 4.
  • A115061 (program): a(n) is the number of occurrences of the n-th prime number in A051697.
  • A115065 (program): Number of points with integer coordinates inside the equilateral triangle with base [0,n].
  • A115066 (program): Chebyshev polynomial of the first kind T(n,x), evaluated at x=n.
  • A115067 (program): a(n) = (3*n^2 - n - 2)/2.
  • A115068 (program): Triangle read by rows: T(n,k) = number of elements in the Coxeter group D_n with descent set contained in {s_k}, for 0<=k<=n-1.
  • A115069 (program): a(n) = 3^b(n), where b(n) is #{primes p=1 mod 3 dividing n}.
  • A115070 (program): a(n) = phi(n)/3^b(n), where b(n) is #{primes p=1 mod 3 dividing n}.
  • A115074 (program): a(n) is the largest prime dividing the n-th nonsquarefree positive integer.
  • A115079 (program): Matrix log of triangle A051731, where nonzero elements in the matrix log are all unit fractions and represented here by the denominators, with zero elements remaining zero.
  • A115081 (program): Column 0 of triangle A115080.
  • A115082 (program): Column 1 of triangle A115080.
  • A115090 (program): a(n) = A115074(n) - A117183(n).
  • A115092 (program): The number of m such that prime(n) divides m!+1.
  • A115093 (program): Primes of the form p*q-2, where p and q are distinct primes.
  • A115098 (program): a(0)=2, a(n)=3*a(n-1)-3.
  • A115099 (program): a(0)=4, a(n) = 3*a(n-1) - 4.
  • A115102 (program): a(0)=2, a(1)=8, a(n)=a(n-1)+2*a(n-2).
  • A115104 (program): Numbers n such that 4*n^3 + 1 is prime.
  • A115107 (program): Numerator of q_n = -4*n + 2*(1+n)*HarmonicNumber(n).
  • A115110 (program): Expansion of q^(-1/24) * eta(q)^3 / eta(q^2) in powers of q.
  • A115112 (program): Number of different ways to select n elements from two sets of n elements under the precondition of choosing at least one element from each set.
  • A115113 (program): a(n) = 3*a(n-1) + 4*a(n-2), with a(0) = 2, a(1) = 6, a(2) = 10.
  • A115114 (program): Asymmetric rhythm cycles (patterns): binary necklaces of length 2n subject to the restriction that for any k if the k-th bead is of color 1 then the (k+n)-th bead (modulo 2n) is of color 0.
  • A115115 (program): Number of 3-asymmetric rhythm cycles: binary necklaces of length 3n subject to the restriction that for any k if the k-th bead is of color 1 then the (k+n)-th and (k+2n)-th beads (modulo 3n) are of color 0.
  • A115125 (program): A sequence related to Catalan numbers A000108.
  • A115126 (program): First (k=1) triangle of numbers related to totally asymmetric exclusion process (case alpha=1, beta=1).
  • A115128 (program): Row sums of triangle A115127.
  • A115129 (program): Partial sums of A005587. Fourth column of triangle A115127.
  • A115130 (program): Partial sums of A005557.
  • A115132 (program): Partial sums of A064059.
  • A115133 (program): Partial sums of A064061.
  • A115134 (program): Third diagonal sequence of triangle A115127.
  • A115136 (program): Row sums of triangle A113647.
  • A115137 (program): Second diagonal of triangle A113647 (called Y(2,1)).
  • A115138 (program): A sequence related to Catalan numbers A000108.
  • A115139 (program): Array of coefficients of polynomials related to integer powers of the generating function of Catalan numbers A000108.
  • A115140 (program): O.g.f. inverse of Catalan A000108 o.g.f.
  • A115141 (program): Convolution of A115140 with itself.
  • A115142 (program): Third convolution of A115140.
  • A115143 (program): a(n) = -4*binomial(2*n-5, n-4)/n for n > 0 and a(0) = 1.
  • A115144 (program): Fifth convolution of A115140.
  • A115145 (program): Sixth convolution of A115140.
  • A115146 (program): Seventh convolution of A115140.
  • A115147 (program): Eighth convolution of A115140.
  • A115148 (program): Ninth convolution of A115140.
  • A115149 (program): Tenth convolution of A115140.
  • A115150 (program): Third diagonal (M=3) sequence of triangle A113647, called Y(2,1).
  • A115158 (program): Number of divisors of A006558(n).
  • A115162 (program): Positive numbers that are not the sum of a triangular number, a square and a cube, all of them greater than or equal to 1.
  • A115164 (program): a(n) = 3*a(n-1) + 4*a(n-2), with a(0) = 3, a(1) = 7, a(3) = 9, for n > 2.
  • A115165 (program): Odd numbers k such that k-1 and k+1 have the same number of distinct prime divisors.
  • A115166 (program): Even numbers k such that k-2 and k+2 have the same number of distinct prime factors.
  • A115167 (program): Odd numbers k such that k-1 and k+1 have the same number of prime divisors with multiplicity.
  • A115178 (program): Expansion of c(x^2+x^3), c(x) the g.f. of A000108.
  • A115179 (program): Expansion of c(x*y*(1-x)), c(x) the g.f. of A000108.
  • A115180 (program): Beatty sequence for (Champernowne constant)*10 = 1.234567891011121314….
  • A115181 (program): Beatty sequence for (Cc/(Cc-1)) with Cc = 1.234567891011121314… = 10*(Champernowne constant).
  • A115193 (program): Generalized Catalan triangle of Riordan type, called C(1,2).
  • A115194 (program): A sequence related to A000108 (Catalan numbers).
  • A115197 (program): Convolution of generalized Catalan numbers A064062 (called C(n;2)).
  • A115202 (program): Fifth column of triangle A115193 (called C(1,2)).
  • A115203 (program): Sixth column of triangle A115193 (called C(1,2)).
  • A115204 (program): Seventh column of triangle A115193 (called C(1,2)).
  • A115205 (program): a(n) = binomial(n, 9) + 1.
  • A115216 (program): “Correlation triangle” for 2^n.
  • A115217 (program): Diagonal sums of “correlation triangle” for 2^n.
  • A115218 (program): Triangle read by rows: zeroth row is 0; to get row n >= 1, append next 2^n numbers to end of previous row.
  • A115219 (program): Expansion of 2*x^2*(1-x)/(1-3*x+2*x^2-2*x^3).
  • A115224 (program): Number of 3 X 3 symmetric matrices over Z(n) having determinant 1.
  • A115226 (program): Order of the group of invertible 3 X 3 symmetric matrices over Z(n).
  • A115228 (program): Nonsquarefree numbers n such that 2n+1 is also nonsquarefree (A013929).
  • A115232 (program): Primes p which can be written in the form 2^i + q^j where i >= 0, j >= 1, q = odd prime.
  • A115235 (program): Expansion of eta(q)^2*eta(q^9)*eta(q^18)/(eta(q^2)*eta(q^3)) in powers of q.
  • A115238 (program): Row sums of triangle A115237.
  • A115241 (program): Square array read by antidiagonals: T(n,p) is the number of linearly independent, homogeneous harmonic polynomials of degree n in p variables (n,p>=1).
  • A115243 (program): G.f.: (4*x^2 + 2*x)/(4*x^3 - x^2 - 4*x + 1).
  • A115246 (program): Number of different ways to select n elements from three sets of n elements such that there is at least one element from each set.
  • A115247 (program): 2^a(n) divides A001935(n) but 2^(a(n)+1) does not.
  • A115248 (program): Values such that A115247(a(n))=1. Values such that A001935(a(n))==2 (mod 4).
  • A115255 (program): “Correlation triangle” of central binomial coefficients A000984.
  • A115256 (program): Diagonal sums of correlation triangle of central binomial coefficients.
  • A115257 (program): Partial sums of binomial(2n,n)^2.
  • A115259 (program): Difference between the sum of digits in odd positions and the sum of digits in even positions of prime numbers.
  • A115262 (program): Correlation triangle for n+1.
  • A115264 (program): Diagonal sums of correlation triangle for floor((n+2)/2).
  • A115266 (program): Row sums of correlation triangle for floor((n+3)/3).
  • A115269 (program): Row sums of correlation triangle for floor((n+4)/4).
  • A115270 (program): Diagonal sums of correlation triangle for floor((n+4)/4).
  • A115271 (program): Partial sums of floor((n+4)/4)^2.
  • A115273 (program): Floor(n/3)*(n mod 3).
  • A115274 (program): a(n) = n + A115273(n), where A115273(n) = 0 for n = 1..3.
  • A115281 (program): Correlation triangle for the sequence 2-0^n.
  • A115282 (program): Correlation triangle for the sequence 3-2*0^n.
  • A115283 (program): Diagonal sums of correlation triangle for 3-2*0^n.
  • A115285 (program): Diagonal sums of correlation triangle for 1,3,4,4,4,…(A113311).
  • A115286 (program): a(n) = (1/6)*(n^6+3*n^4+12*n^3+8*n^2).
  • A115291 (program): Expansion of (1+x)^3/(1-x).
  • A115293 (program): Row sums of correlation triangle for (1+x)^3/(1-x).
  • A115294 (program): Diagonal sums of correlation triangle for (1+x)^3/(1-x).
  • A115295 (program): Partial sums of squares of A115291(n).
  • A115296 (program): Skew version of correlation triangle for constant sequence 1.
  • A115297 (program): Treillis triangle: a triangle read by rows showing the coefficients of sum formulas of Treillis numbers (A115298). The k-th row (k>=1) contains a(n,k) for n=1 to (k+1)/2 (odd rows) and for n=1 to k/2 (even rows), where a(n,k) satisfies Sum_{n=1..[(k+1)/2_odd, k/2_even]} a(n,k). The last term of each row (and its only odd number) equals Prime(k+1)-2.
  • A115299 (program): Greatest digit of n + least digit of n. Different from A088133.
  • A115300 (program): Greatest digit of n * least digit of n.
  • A115302 (program): Permutation of natural numbers generated by 3-rowed array shown below.
  • A115303 (program): a(n) = if n<3 then n else 3*a(floor(n/3)) + 2 - n mod 3.
  • A115305 (program): a(n) = if n<5 then n else 5*a(floor(n/5)) + 4 - n mod 5.
  • A115309 (program): a(n) = if n<9 then n else 9*a(floor(n/9)) + 8 - n mod 9.
  • A115311 (program): a(n) = gcd(Lucas(n)-1, Fibonacci(n)-1).
  • A115312 (program): a(n) = gcd(Lucas(n)-1, Fibonacci(n)+1).
  • A115313 (program): a(n) = gcd(Lucas(n)+1, Fibonacci(n)+1).
  • A115314 (program): a(n) = gcd(Lucas(n)+1, Fibonacci(n)-1).
  • A115315 (program): a(n) = floor(L^3*{phi^(3*n-2), phi^(3*n-1), phi^(3*n-2) + phi^(3*n-1)}) where L = (1 + sqrt(5))/(2*sqrt(5)) and phi = (1 + sqrt(5))/2.
  • A115318 (program): Inverse of A115316.
  • A115319 (program): a(n) = A115318(A115318(n)).
  • A115322 (program): Triangle of coefficients of Pell polynomials.
  • A115326 (program): E.g.f.: exp(x/(1-2*x))/sqrt(1-4*x^2).
  • A115327 (program): E.g.f.: exp(x + 3/2*x^2).
  • A115328 (program): E.g.f: exp(x/(1-3*x))/sqrt(1-9*x^2).
  • A115329 (program): E.g.f.: exp(x + 2*x^2).
  • A115330 (program): E.g.f: exp(x/(1-4*x))/sqrt(1-16*x^2).
  • A115331 (program): E.g.f.: exp(x+5/2*x^2).
  • A115332 (program): E.g.f: exp(x/(1-5*x))/sqrt(1-25*x^2).
  • A115333 (program): Sum of primes that do not divide n and are less than the largest prime dividing n.
  • A115334 (program): Numbers d > 0 such that 3+2d and 3+4d are primes.
  • A115335 (program): a(0) = 3, a(1) = 5, a(2) = 1, and a(n) = (2^(1 + n) - 11*(-1)^n)/3 for n > 2.
  • A115338 (program): a(n)=F([sqrt(n)]), where [k]=integer part of k and F(n) is the Fibonacci sequence.
  • A115339 (program): a(2n-1)=F(n+1), a(2n)=L(n), where F(n) and L(n) are the Fibonacci and the Lucas sequences.
  • A115341 (program): a(n) = abs(A154879(n+1)).
  • A115342 (program): 1 + (n-6)*2^(n-1).
  • A115346 (program): Triangle read by rows: T(n,k) = Fibonacci(k+2) - 1.
  • A115350 (program): Termination of the aliquot sequence starting at n.
  • A115352 (program): Concatenation of finite strings S_0, S_1, S_2, …, where S_0 = {0} and for k >= 1, S_k is obtained from S_{k-1} by inserting the numbers 2^(k-1) through 2^k-1 after the initial 0.
  • A115356 (program): Matrix (1,x)+(x,x^2) in Riordan array notation.
  • A115357 (program): Period 6: repeat [1,1,1,0,2,0].
  • A115358 (program): Inverse of matrix (1,x)+(x,x^2) (expressed in Riordan array notation).
  • A115359 (program): Matrix (1,x)-(x,x^2) in Riordan array notation.
  • A115360 (program): Period 6: repeat [1,-1,1,0,0,0].
  • A115361 (program): Inverse of matrix (1,x)-(x,x^2) (expressed in Riordan array notation).
  • A115362 (program): Row sums of ((1,x) + (x,x^2))^(-1)*((1,x)-(x,x^2))^(-1) (using Riordan array notation).
  • A115363 (program): ((1,x)-(x,x^2))^(-2) (using Riordan array notation).
  • A115364 (program): a(n) = A000217(A001511(n)), where A001511 is one more than the 2-adic valuation of n, and A000217(n) is the n-th triangular number, binomial(n+1, 2).
  • A115367 (program): Row sums of correlation triangle for Fredholm-Rueppel sequence A036987.
  • A115375 (program): <h[d,d],s[d,d]*s[d,d]*s[d,d]> where h[d,d] is a homogeneous symmetric function, s[d,d] is a Schur function indexed by two parts, * represents the Kronecker product and <, > is the standard scalar product on symmetric functions.
  • A115376 (program): <h[d+1,d-1],s[d,d]*s[d,d]*s[d,d]> where h[d+1,d-1] is a homogeneous symmetric function, s[d,d] is a Schur function indexed by two parts, * represents the Kronecker product and <, > is the standard scalar product on symmetric functions.
  • A115378 (program): a(n) = number of positive integers k < n such that n XOR k = (n+k).
  • A115379 (program): Number of positive integers k < n such that n XOR k < n and gcd(n,k) is odd.
  • A115383 (program): Row sums of Thue-Morse correlation triangle A115382.
  • A115384 (program): Partial sums of Thue-Morse numbers A010060.
  • A115388 (program): Numerator of rational part of raw moment n of the line point picking problem.
  • A115389 (program): Denominator of rational part of raw moment n of the line point picking problem.
  • A115390 (program): Binomial transform of tribonacci sequence A000073.
  • A115391 (program): a(0)=0; then a(4*k+1)=a(4*k)+(4*k+1)^2, a(4*k+2)=a(4*k+1)+(4*k+3)^2, a(4*k+3)=a(4*k+2)+(4*k+2)^2, a(4*k+4)=a(4*k+3)+(4*k+4)^2.
  • A115392 (program): First appearance of n-th prime as prime factor in list of semiprimes.
  • A115399 (program): Expansion of c(x^2-x^3), c(x) the g.f. of A000108.
  • A115400 (program): Number of n-colorings of the octahedral graph.
  • A115402 (program): Difference between 3-almostprime(n) and 3-almostprime(n+3).
  • A115403 (program): Numbers n such that n^3+1 is 3-almost prime (product of three primes).
  • A115405 (program): Numbers n such that n^k is deficient for all k>0.
  • A115411 (program): a(n) = least k such that semiprime(n) divides k-th triangular number.
  • A115412 (program): G.f.: (x - 1)/(x^5 - x^3 - x^2 - x - 1).
  • A115413 (program): Expansion of (x - 1)/(1 - x^2 + x^3 + x^4 - x^5).
  • A115415 (program): Real part of (n + i)^n, with i=sqrt(-1).
  • A115416 (program): Imaginary part of (n + i)^n, with i=sqrt(-1).
  • A115419 (program): Numbers having a 1 in position 3 of their binary expansion.
  • A115420 (program): Numbers having a 1 in position 4 of their binary expansion.
  • A115421 (program): Numbers having a 1 in position 5 of their binary expansion.
  • A115425 (program): The first four terms of the sequence are doubled, then those numbers are tripled and then those numbers are quadrupled, etc.
  • A115450 (program): Number triangle (1/((1-x)(1-2x)),-x)-(x/((1-x)(1-2x)),-x^2) (expressed in the notation of Riordan arrays).
  • A115451 (program): Expansion of 1/((1+x)*(1-2*x)*(1+x^2)).
  • A115454 (program): Composite positive integers written in base 2.
  • A115473 (program): Number of monic irreducible polynomials of degree 2 in GF(2)[x1,…,xn].
  • A115489 (program): Number of monic irreducible polynomials of degree 3 in GF(2^n)[x].
  • A115490 (program): Number of monic irreducible polynomials of degree 4 in GF(2^n)[x].
  • A115491 (program): Number of monic irreducible polynomials of degree 5 in GF(2^n)[x].
  • A115492 (program): Number of monic irreducible polynomials of degree 2 in GF(2^n)[x,y].
  • A115500 (program): Number of monic irreducible polynomials of degree 1 in GF(2^n)[x1,x2,x3,x4].
  • A115504 (program): Number of monic irreducible polynomials of degree 1 in GF(2^n)[x1,x2,x3,x4,x5].
  • A115512 (program): Number triangle (1,x)+(x,x^3) expressed in terms of Riordan arrays.
  • A115514 (program): Triangle read by rows: row n >= 1 lists first n positive members of A004526 (integers repeated) in decreasing order.
  • A115516 (program): The mode of the bits of n (using 0 if bimodal).
  • A115517 (program): The mode of the bits of n (using 1 if bimodal).
  • A115519 (program): n*(1+3*n+6*n^2)/2.
  • A115524 (program): Number triangle (1,-x)+(x,x)/2+(x,-x)/2-(x^2,x^2) (expressed using the notation of stretched Riordan arrays).
  • A115525 (program): Periodic {1,1,-2,0,1,0,-1,0,0,1,-1,-1}.
  • A115526 (program): Inverse of number triangle A115524.
  • A115535 (program): Numbers k such that the concatenation of k with 4*k gives a square.
  • A115536 (program): Numbers k such that the square of k is the concatenation of two numbers m and 4*m.
  • A115561 (program): a(n) = lpf((n/lpf(n))/lpf(n/lpf(n))), where lpf=A020639, least prime factor.
  • A115562 (program): a(n) = number of distinct squarefree ternary (cyclic) sequences uniquely containing every possible length-n substring.
  • A115565 (program): a(n) = 5*n^4 - 10*n^3 + 20*n^2 - 15*n + 11.
  • A115566 (program): Numbers k such that 2^k, 2^(k+1) and 2^(k+2) have the same number of digits.
  • A115567 (program): a(n) = C(n,6) + C(n,5) + C(n,4) + C(n,3) + C(n,2) + C(n,1).
  • A115568 (program): Maximal Fibonacci exponent in prime factorization of n, or 1 if there is no Fibonacci exponent.
  • A115588 (program): Number of distinct prime numbers necessary to represent a natural number n > 1.
  • A115591 (program): Primes p such that the multiplicative order of 2 modulo p is (p-1)/2.
  • A115594 (program): Triangle read by rows: number of isomorphism classes of series-parallel matroids of rank d on n elements.
  • A115598 (program): Consider all Pythagorean triples (X,X+1,Z) ordered by increasing Z; sequence gives Z-(X+1) values.
  • A115599 (program): Consider all Pythagorean triples (X,X+1,Z) ordered by increasing Z; sequence gives Z-X values.
  • A115601 (program): a(n) = numerator of b(n), where b(1) = 1, b(n+1) = Sum_{k=1..n} b(k)^((-1)^(n-k+1)).
  • A115602 (program): a(n) = denominator of b(n), where b(1) = 1, b(n+1) = Sum_{k=1..n} b(k)^((-1)^(n-k+1)).
  • A115605 (program): Expansion of -x^2*(2 + x - 2*x^2 - x^3 + 2*x^4) / ( (x-1)*(1+x)*(1 + x + x^2)*(x^2 - x + 1)*(x^2 + 4*x - 1)*(x^2 - x - 1) ).
  • A115607 (program): Sum of odd divisors of n times (-1)^(n+1).
  • A115618 (program): 1 + (n+6)*2^(n-1).
  • A115623 (program): Irregular triangle read by rows: row n lists numbers of distinct parts of partitions of n in Mathematica order.
  • A115634 (program): Expansion of (1-4*x^2)/(1-x^2).
  • A115635 (program): Periodic {1,1,-5,0,1,-3,-1,0,-3,1,-1,-4}.
  • A115637 (program): A divide-and-conquer sequence.
  • A115638 (program): A Jacobsthal-related divide-and-conquer sequence.
  • A115639 (program): First column of divide-and-conquer triangle A115636.
  • A115659 (program): Permutation of natural numbers generated by 2-rowed array shown below.
  • A115671 (program): Number of partitions of n into parts not congruent to 0, 2, 12, 14, 16, 18, 20, 30 (mod 32).
  • A115711 (program): Squares whose digit reversal is a semiprime (A001358).
  • A115716 (program): A divide-and-conquer sequence.
  • A115730 (program): a(n) = a(n-3) + A001654(n-1) with a(0)=0, a(1)=0 and a(2)=1.
  • A115731 (program): Permutation of natural numbers generated by 3-rowed array shown below.
  • A115732 (program): n-th prime p(n) repeated (p(n)-n) times.
  • A115733 (program): n-th prime minus n, p(n)-n, repeated (p(n)-n) times.
  • A115754 (program): Decimal expansion of sqrt(3/2).
  • A115767 (program): Integers i such that 2*i XOR 5*i = 3*i.
  • A115788 (program): a(n) = floor(n*Pi) mod 2.
  • A115789 (program): a(n) = (floor((n+1)*Pi) - floor(n*Pi)) mod 2.
  • A115790 (program): 1 - (Floor((n+1)*Pi)-Floor(n*Pi)) mod 2.
  • A115792 (program): A dihedial D1 elliptical transform on A000073.
  • A115793 (program): Integers i such that i XOR 10i = 11i.
  • A115794 (program): Sequence A115793 in binary.
  • A115809 (program): Integers i such that 17*i = 49 X i.
  • A115810 (program): Sequence A115809 in binary.
  • A115836 (program): Self-describing sequence. The n-th integer of the sequence indicates how many integers of the sequence are strictly < 2n.
  • A115837 (program): Self-describing sequence. The n-th integer of the sequence indicates how many integers of the sequence are strictly < 3n.
  • A115845 (program): Numbers n such that there is no bit position where the binary expansions of n and 8n are both 1.
  • A115846 (program): Sequence A115845 in binary.
  • A115851 (program): G.f. x^2*(-1+x+x^2)/((1-x)*(2*x-1)*(x+1)*(x^2+1)).
  • A115852 (program): Dihedral D3 elliptical invariant transform on A000045: a[n+1]/a[n]= Phi^4=((1+Sqrt[5])/2)^4.
  • A115864 (program): Legendre_P(n,2)*4^n.
  • A115865 (program): a(n) = Legendre_P(n,2)*6^n.
  • A115878 (program): a(n) is the number of positive solutions of the Diophantine equation x^2 = y(y+n).
  • A115880 (program): Largest positive x satisfying the Diophantine equation x^2 = y*(y+n), a(n)=0 if there are no solutions.
  • A115881 (program): a(n) is the largest positive y satisfying the Diophantine equation x^2=y(y+n). a(n)=0 if there are no solutions.
  • A115902 (program): Expansion of (1-8*x)^(-3/2).
  • A115903 (program): Expansion of (1-12*x)^(-3/2).
  • A115919 (program): Numbers k such that sigma(k) - phi(k) is a prime number.
  • A115944 (program): Number of partitions of n into distinct factorials.
  • A115945 (program): Numbers that cannot be written as a sum of distinct factorials.
  • A115948 (program): a(n) = (2^(semiprime(n)-1)) modulo (semiprime(n)^2).
  • A115951 (program): Expansion of 1/sqrt(1-4*x*y-4*x^2*y).
  • A115952 (program): Expansion of (1-x+x*y)/(1-x^2*y^2) - x^2/(1-x^2*y).
  • A115953 (program): Periodic {1,-1,0,0,1,-2,1,0,0,-1,1,-1}.
  • A115954 (program): Inverse of number triangle A115952.
  • A115955 (program): Product of A115952 and summing matrix (1/(1-x),x).
  • A115956 (program): Numbers n having exactly 2 distinct prime factors, the largest of which is greater than or equal to sqrt(n) (i.e., sqrt(n)-rough numbers with exactly 2 distinct prime factors).
  • A115960 (program): Numbers n having exactly 6 distinct prime factors, the largest of which is greater than or equal to sqrt(n) (i.e., sqrt(n)-rough numbers with exactly 6 distinct prime factors).
  • A115962 (program): Expansion of 1/sqrt(1-4*x^2-4*x^3).
  • A115963 (program): Numerator of Sum_{i=1..n} 1/prime(i)^3.
  • A115964 (program): Denominator of sum_{i=1..n} 1/prime(i)^3.
  • A115966 (program): Inverse permutation to sequence A094077.
  • A115967 (program): Expansion of 1/(2*sqrt(1-2*x-3*x^2) - 1).
  • A115969 (program): Expansion of 1/(2*sqrt(1-6*x+x^2) - 1).
  • A115970 (program): Expansion of 1/(4*sqrt(1-4*x) - 3).
  • A115971 (program): a(0) = 0. If a(n) = 0, then a(2^n) through a(2^(n+1)-1) are each equal to 1. If a(n) = 1, then a(m + 2^n) = a(m) for each m, 0 <= m <= 2^n -1.
  • A115974 (program): Number of Feynman diagrams (vanishing and non-vanishing) of order 2n for the proper self-energy function of quantum electrodynamics (QED).
  • A115975 (program): Numbers of the form p^k, where p is a prime and k is a Fibonacci number.
  • A115977 (program): Expansion of elliptic modular function lambda in powers of the nome q.
  • A115978 (program): Expansion of phi(-q) * phi(-q^3) in powers of q where phi() is a Ramanujan theta function.
  • A115979 (program): Expansion of (1 - theta_4(q)*theta_4(q^3))/2 in powers of q.
  • A115990 (program): Riordan array (1/sqrt(1-2*x-3*x^2), ((1-2*x-3*x^2)/(2*(1-3*x)) - sqrt(1-2*x-3*x^2)/2).
  • A115991 (program): Number triangle T(n,k) = Sum_{j=0..n} C(n-k,j-k)*C(j,n-j)*2^(n-j).
  • A116000 (program): phi(n) + sigma(n) gives a semiprime (A001358).
  • A116023 (program): The n-th prime plus n gives a semiprime (A001358).
  • A116024 (program): The n-th prime minus n gives a semiprime (A001358).
  • A116026 (program): phi(n) plus n gives a semiprime (A001358).
  • A116071 (program): Triangle T, read by rows, equal to Pascal’s triangle to the matrix power of Pascal’s triangle, so that T = C^C, where C(n,k) = binomial(n,k) and T(n,k) = A000248(n-k)*C(n,k).
  • A116072 (program): Central terms of triangle A116071, which equals Pascal’s triangle to the matrix power of Pascal’s triangle.
  • A116073 (program): Sum of the divisors of n that are not divisible by 5.
  • A116078 (program): Column 0 of triangle A116077.
  • A116081 (program): Final nonzero digit of n^n.
  • A116082 (program): a(n) = C(n,7) + C(n,6) + C(n,5) + C(n,4) + C(n,3) + C(n,2) + C(n,1).
  • A116083 (program): Numbers n such that phi(sigma(n))-sigma(phi(n))=1.
  • A116088 (program): Riordan array (1, x*(1+x)^2).
  • A116089 (program): Riordan array (1, x*(1+x)^3).
  • A116090 (program): Expansion of 1/(1-x^2*(1+x)^3).
  • A116091 (program): Expansion of 1/sqrt(1+4*x+16*x^2).
  • A116092 (program): Expansion of 1/sqrt(1+8*x+64*x^2).
  • A116093 (program): Expansion of 1/sqrt(1+4*x+12*x^2).
  • A116127 (program): Number of numbers that are congruent to {2, 4} mod 6 between prime(n) and prime(n+1) inclusive.
  • A116138 (program): a(n) = 3^n * n*(n + 1).
  • A116144 (program): a(n) = 4^n * n*(n+1).
  • A116149 (program): a(n) = sum of n consecutive cubes after n^3.
  • A116150 (program): a(n) = Sum_{j=1..n} (3^j + (-2)^j).
  • A116156 (program): a(n) = 5^n * n*(n + 1).
  • A116157 (program): a(n) = a(n-1) + 2*a(n-2) - 2*a(n-3) + a(n-5).
  • A116164 (program): a(n) = 6^n * n*(n+1).
  • A116165 (program): a(n) = 7^n * n*(n+1).
  • A116166 (program): a(n) = 8^n * n*(n+1).
  • A116176 (program): a(n) = 9^n * n*(n+1).
  • A116178 (program): Stewart’s choral sequence: a(3n) = 0, a(3n-1) = 1, a(3n+1) = a(n).
  • A116192 (program): Triangle T(n,k), 0<=k<=n : T(n,k)is smallest number such that T(n,k)>T(n-1,k-1), T(n,k)>T(n-1,k), T(n,k)and T(n-1,k-1)+T(n-1,k) have the same parity, T(0,0)=1 .
  • A116201 (program): a(n) = a(n-1) + a(n-2) + a(n-3) - a(n-4); a(0)=0, a(1)=1, a(2)=1, a(3)=1.
  • A116218 (program): If X_1,…,X_n is a partition of a 2n-set X into 2-blocks (or pairs) then a(n) is equal to the number of permutations f of X such that f(X_i) != X_i for all i=1,…n.
  • A116362 (program): Smallest m such that A116361(m) = n.
  • A116363 (program): a(n) = dot product of row n in Catalan triangle A033184 with row n in Pascal’s triangle.
  • A116364 (program): Row squared sums of Catalan triangle A033184.
  • A116366 (program): Triangle read by rows: even numbers as sums of two odd primes.
  • A116367 (program): Sums of rows of the triangle in A116366.
  • A116368 (program): Central terms of the triangle in A116366.
  • A116382 (program): Riordan array (1/sqrt(1-4*x^2), (1-2*x^2*c(x^2))*(x^2*c(x^2))/(x*(1-x-x^2*c(x^2))) where c(x) is the g.f. of A000108.
  • A116383 (program): Row sums of number triangle A116382.
  • A116384 (program): Diagonal sums of the Riordan array A116382.
  • A116385 (program): E.g.f. Bessel_I(2,2x)+2*Bessel_I(3,2x)+Bessel_I(4,2x).
  • A116386 (program): Number of calendar weeks in the year n (starting at n=0 for the year 2000).
  • A116387 (program): Expansion of 1/(sqrt(1-2*x-3*x^2)*(2-M(x))), where M(x) is the g.f. of the Motzkin numbers A001006.
  • A116390 (program): Expansion of 1/(2*sqrt(1-4*x^2)-x-1).
  • A116391 (program): Expansion of 1/((1+x)*(sqrt(1-4*x^2)-x)).
  • A116394 (program): Expansion of 1/((1+x)*sqrt(1-2*x-3*x^2) - x).
  • A116395 (program): Riordan array (1/sqrt(1-4*x), (1/sqrt(1-4*x)-1)/2).
  • A116396 (program): Expansion of 2/((2+x)*sqrt(1-4*x)-x).
  • A116399 (program): Triangle whose k-th column has e.g.f. sum{j=0..k, Bessel_I(k+j,2x)}.
  • A116400 (program): E.g.f. Bessel_I(2,2x)+Bessel_I(3,2x)+Bessel_I(4,2x).
  • A116404 (program): Expansion of (1-x)/((1-x)^2 - x^2*(1+x)^2).
  • A116405 (program): Triangle whose k-th column has e.g.f. sum{j=0..k, (-1)^j*Bessel_I(k+j,2x)}.
  • A116406 (program): Expansion of ((1 + x - 2x^2) + (1+x)*sqrt(1-4x^2))/(2(1-4x^2)).
  • A116408 (program): E.g.f. exp(x)*(Bessel_I(2,2*x) - Bessel_I(3,2*x) + Bessel_I(4,2*x)).
  • A116409 (program): Expansion of (1-x-2x^2+sqrt(1-2x-3x^2))/(2(1-x)(1-2x-3x^2)).
  • A116410 (program): Expansion of (1-x-2x^2+sqrt(1-2x-3x^2))/(2*(1-2x-3x^2)).
  • A116411 (program): Coefficient of x^n in the expansion of (1+x+x^3)^n.
  • A116412 (program): Riordan array ((1+x)/(1-2x),x(1+x)/(1-2x)).
  • A116413 (program): Expansion of (1+x)/(1-2x-x^2-x^3).
  • A116414 (program): Riordan array (1/((1-x)(1-3x)),x/((1-x)(1-3x))).
  • A116415 (program): a(n) = 5*a(n-1) - 3*a(n-2).
  • A116419 (program): Reduced numerators of 2*(2^(1+n)-1)/(1+n)/(2+n).
  • A116420 (program): Reduced denominators of 2(2^(1+n)-1)/(1+n)/(2+n).
  • A116421 (program): a(n) = 2^(n-1)*binomial(2n-1,n-1)^2.
  • A116423 (program): Binomial transform of A006053.
  • A116425 (program): Decimal expansion of 2 + 2*cos(2*Pi/7).
  • A116445 (program): Array read by antidiagonals: the binomial transform of the sequence (1,2,..n,0,0,0..) in row n.
  • A116447 (program): a(2n) = n, a(2n+1) = n!.
  • A116451 (program): Numbers having fewer prime factors than at least one smaller number.
  • A116452 (program): Number of prime factors of A116451.
  • A116453 (program): Third smallest number with exactly n prime factors.
  • A116454 (program): Smallest m such that A116452(m) = n.
  • A116466 (program): Unsigned row sums of triangle A114700.
  • A116468 (program): Permutation of natural numbers generated by 2-rowed array shown below.
  • A116470 (program): All distinct Fibonacci and Lucas numbers.
  • A116471 (program): Values 2*(n -+ 1)^2 sorted.
  • A116472 (program): a(n) = floor(exp(2*n)).
  • A116477 (program): a(n) = Sum_{1<=k<=n, gcd(k,n)=1} floor(n/k).
  • A116483 (program): Expansion of (1 + x) / (5*x^2 - 2*x + 1).
  • A116484 (program): Expansion of (-1+3*x)/(5*x^2 + 1 - 2*x).
  • A116487 (program): First digit after decimal point in decimal representation of (1+1/n)^n.
  • A116494 (program): Expansion of psi(q^5)/psi(q) in powers of q where psi() is a Ramanujan theta function.
  • A116508 (program): a(n) = C( C(n,2), n) for n >= 1.
  • A116509 (program): Values of c in a^2 + b^2 = c^2 where b - a = 31 and gcd(a,b)=1.
  • A116510 (program): a(0)=1. a(m +2^n) = a(m) - a(n), 0 <= m <= 2^n -1.
  • A116512 (program): a(n) = number of positive integers each of which is <= n and is divisible by exactly one prime dividing n (but is coprime to every other prime dividing n). a(1) = 0.
  • A116515 (program): a(n) = the period of the Fibonacci numbers modulo p divided by the smallest m such that p divides Fibonacci(m), where p is the n-th prime.
  • A116520 (program): a(0) = 0, a(1) = 1; a(n) = max { 4*a(k) + a(n-k) | 1 <= k <= n/2 }, for n > 1.
  • A116521 (program): Binomial transform of tetranacci sequence A000078.
  • A116522 (program): a(0)=1, a(1)=1, a(n)=7*a(n/2) for n=2,4,6,…, a(n)=6*a((n-1)/2)+a((n+1)/2) for n=3,5,7,….
  • A116523 (program): a(0)=1, a(1)=1, a(n) = 17*a(n/2) for n=2,4,6,…, a(n) = 16*a((n-1)/2) + a((n+1)/2) for n=3,5,7,….
  • A116524 (program): a(0)=1, a(1)=1, a(n) = 13*a(n/2) for n=2,4,6,…, a(n) = 12*a((n-1)/2) + a((n+1)/2) for n=3,5,7,….
  • A116525 (program): a(0)=1, a(1)=1, a(n) = 11*a(n/2) for even n, and a(n) = 10*a((n-1)/2) + a((n+1)/2) for odd n >= 3.
  • A116526 (program): a(0)=1, a(1)=1, a(n) = 9*a(n/2) for even n >= 2, and a(n) = 8*a((n-1)/2) + a((n+1)/2) for odd n >= 3.
  • A116528 (program): a(0)=0, a(1)=1, and for n>=2, a(2*n) = a(n), a(2*n+1) = 2*a(n) + a(n+1).
  • A116530 (program): a(n) = 3*a(n-1), with a(1) = 20.
  • A116533 (program): a(1)=1, a(2)=2, for n > 2 if a(n-1) is prime, then a(n) = 2*a(n-1), otherwise a(n) = a(n-1) - 1.
  • A116541 (program): Triangular numbers for which the number of divisors is also a triangular number.
  • A116543 (program): Number of terms in greedy representation of n in terms of the Lucas numbers.
  • A116544 (program): Triangular numbers for which the multiplicative digital root is also a triangular number.
  • A116545 (program): Sum of the largest Fibonacci exponent of prime factorizations of k, k=1..n.
  • A116549 (program): a(0) = 1. a(m + 2^n) = a(n) + a(m), for 0 <= m <= 2^n - 1.
  • A116551 (program): Permutation of natural numbers generated by 3-rowed array shown below.
  • A116556 (program): a(n) = 2*a(n-1) + 2*a(n-2), a(0)=0, a(1)=4.
  • A116558 (program): a(n) = 6*a(n-4) - a(n-8).
  • A116563 (program): a(n) is the genus of the modular curve X_0(p) for p = prime(n).
  • A116564 (program): Ono supersingular invariant power function.
  • A116568 (program): Difference between n and the absolute value of the difference between number of nonprimes not exceeding n and number of primes not exceeding n.
  • A116570 (program): a(2*n) = prime(n+1) * prime(n+2), a(2*n-1) = prime(n+1).
  • A116572 (program): a(n) = floor(prime(n)/5) for n > 2, a(1) = a(2) = 1.
  • A116576 (program): Number of distinct squares D(n) in the n-th iterate of the tribonacci morphism (a -> ab, b -> ac, c -> a) on the letter a.
  • A116579 (program): a(1) = a(2) = 1; a(n) = floor(prime(n)/6) for n > 2.
  • A116581 (program): Primes of the form k^3-k-1.
  • A116588 (program): Array read by antidiagonals: T(n,k) = max(2^(n - k), 2^(k - n)).
  • A116589 (program): a(n) = Sum{sqrt(n) < i <= n} i - Sum{1 <= i < sqrt(n)} i.
  • A116593 (program): a(n) = b(n+2) + b(n), where b(n) = A006046(n) is the sequence defined by b(0)=0, b(1)=1, b(n) = 2*b((n-1)/2) + b((n+1)/2) for n =3,5,7,… and b(n) = 3*b(n/2) for n =2,4,6,….
  • A116598 (program): Triangle read by rows: T(n,k) is the number of partitions of n having exactly k parts equal to 1 (n>=0, 0<=k<=n).
  • A116599 (program): Triangle read by rows: T(n,k) is the number of partitions of n having exactly k parts equal to 2 (n>=0, 0<=k<=floor(n/2)).
  • A116601 (program): a(0) = a(1) = 0; for n >= 2, a(n) = floor(sqrt(2^(n-2)-1)).
  • A116603 (program): Coefficients in asymptotic expansion of sequence A052129.
  • A116604 (program): Expansion of q^(-1/2) * eta(q)^3 * eta(q^4) * eta(q^12) / (eta(q^2)^2 * eta(q^3)) in powers of q.
  • A116607 (program): Sum of the divisors of n which are not divisible by 9.
  • A116609 (program): a(n) = 13^n modulo n.
  • A116621 (program): Positive integers n such that 13^n == 1 (mod n).
  • A116623 (program): a(0)=1, a(2n) = a(n)+A000079(A000523(2n)), a(2n+1) = 3*a(n) + A000079(A000523(2n+1)+1).
  • A116634 (program): Number of partitions of n having exactly one part that is a multiple of 3.
  • A116637 (program): G.f. satisfies: A(x) = x/series_reversion(x/G(x)) where A(x) + A(-x) = 2*G(x^2) and G(x) is the g.f. of A046646.
  • A116640 (program): a(n) = A116623(A059893(n)).
  • A116646 (program): Number of doubletons in all partitions of n. By a doubleton in a partition we mean an occurrence of a part exactly twice (the partition [4,(3,3),2,2,2,(1,1)] has two doubletons, shown between parentheses).
  • A116647 (program): Triangle of number of partitions that fit in an n X n box (but not in an (n-1) X (n-1) box) with Durfee square k.
  • A116661 (program): Integers in both sequences A114522 and A063989.
  • A116663 (program): Triangle read by rows: T(n,k) = number of partitions of n into odd parts and having exactly k parts equal to 1 (n>=0, 1<=k<=n).
  • A116666 (program): Triangle, row sums = number of edges in n-dimensional hypercubes.
  • A116667 (program): Greatest digit not used in n (or 10 if n is pandigital).
  • A116668 (program): a(n) = (5*n^2 + n + 2)/2.
  • A116669 (program): Triangle, rows tend to A001787, number of edges in n-dimensional hypercubes.
  • A116670 (program): Numbers with all but one decimal digit.
  • A116689 (program): Partial sums of dodecahedral numbers (A006566).
  • A116690 (program): a(n) = C(n,8) + C(n,7) + C(n,6) + C(n,5) + C(n,4) + C(n,3) + C(n,2) + C(n,1).
  • A116695 (program): Digit not appearing in A116670(n).
  • A116697 (program): a(n) = -a(n-1) - a(n-3) + a(n-4).
  • A116698 (program): Expansion of -(1-x+3*x^2+x^3) / ((x^2+x-1)*(2*x^2+1)).
  • A116699 (program): Number of permutations of length n which avoid the patterns 123 and 4312.
  • A116701 (program): Number of permutations of length n that avoid the patterns 132, 4321.
  • A116702 (program): Number of permutations of length n which avoid the patterns 123, 3241.
  • A116703 (program): Number of permutations of length n which avoid the patterns 231, 4123.
  • A116706 (program): Number of permutations of length n which avoid the patterns 2134, 3421.
  • A116707 (program): Number of permutations of length n which avoid the patterns 1342, 4213.
  • A116709 (program): Number of permutations of length n which avoid the patterns 2341, 4213.
  • A116710 (program): Number of permutations of length n which avoid the patterns 1423, 3421.
  • A116711 (program): Number of permutations of length n which avoid the patterns 123, 3214, 4312.
  • A116712 (program): Number of permutations of length n which avoid the patterns 231, 3214, 4312.
  • A116713 (program): Number of permutations of length n which avoid the patterns 123, 2431, 4132.
  • A116714 (program): Number of permutations of length n that avoid the patterns 321, 1342, 4123.
  • A116715 (program): Number of permutations of length n which avoid the patterns 312, 2341, 4321.
  • A116716 (program): Number of permutations of length n which avoid the patterns 321, 2341, 4123.
  • A116717 (program): Number of permutations of length n which avoid the patterns 231, 1423, 3214.
  • A116718 (program): Number of permutations of length n which avoid the patterns 321, 1342, 3124.
  • A116720 (program): Number of permutations of length n which avoid the patterns 213, 1234, 4312.
  • A116721 (program): Number of permutations of length n which avoid the patterns 123, 3142, 4312; or avoid the patterns 123, 3421, 4231.
  • A116722 (program): Number of permutations of length n which avoid the patterns 312, 1324, 3421; or avoid the patterns 312, 1324, 2341, etc.
  • A116723 (program): We have one bead labeled i for every i=1, 2, …; a(n) = number of necklaces that can be made using any subset of the first n beads.
  • A116725 (program): Number of permutations of length n which avoid the patterns 132, 3421, 4231.
  • A116726 (program): Number of permutations of length n which avoid the patterns 213, 1234, 2431.
  • A116727 (program): Number of permutations of length n which avoid the patterns 321, 2134, 3412.
  • A116728 (program): Number of permutations of length n which avoid the patterns 321, 1243, 2134.
  • A116730 (program): Number of permutations of length n which avoid the patterns 321, 1342, 1423.
  • A116731 (program): Number of permutations of length n which avoid the patterns 321, 2143, 3124; or avoid the patterns 132, 2314, 4312, etc.
  • A116732 (program): a(n) = a(n-1) + a(n-2) + a(n-3) - a(n-4).
  • A116733 (program): Number of permutations of length n which avoid the patterns 321, 1324, 2341.
  • A116734 (program): Number of permutations of length n which avoid the patterns 231, 1432, 4123.
  • A116735 (program): Number of permutations of length n which avoid the patterns 231, 1234, 4312; or avoid the patterns 312, 1234, 1432, etc.
  • A116736 (program): Number of permutations of length n which avoid the patterns 1432, 2314, 2413.
  • A116737 (program): Number of permutations of length n which avoid the patterns 3412, 4123, 4321.
  • A116738 (program): Number of permutations of length n which avoid the patterns 3214, 4123, 4132.
  • A116741 (program): Number of permutations of length n which avoid the patterns 1342, 2314, 4213.
  • A116742 (program): Number of permutations of length n which avoid the patterns 1342, 2341, 4132; or avoid the patterns 2431, 3124, 4231.
  • A116743 (program): Number of permutations of length n which avoid the patterns 3421, 4123, 4213.
  • A116744 (program): Number of permutations of length n which avoid the patterns 1243, 1432, 4213.
  • A116745 (program): Number of permutations of length n which avoid the patterns 2134, 3214, 4312.
  • A116746 (program): Number of permutations of length n which avoid the patterns 1243, 4123, 4213.
  • A116747 (program): Number of permutations of length n which avoid the patterns 1234, 2413, 3241.
  • A116751 (program): Number of permutations of length n which avoid the patterns 2314, 2431, 3124.
  • A116754 (program): Number of permutations of length n which avoid the patterns 2134, 2143, 4312.
  • A116755 (program): Number of permutations of length n which avoid the patterns 1234, 2431, 3412.
  • A116757 (program): Number of permutations of length n which avoid the patterns 1324, 2314, 4312.
  • A116758 (program): Number of permutations of length n which avoid the patterns 1234, 1432, 2341.
  • A116759 (program): Number of permutations of length n which avoid the patterns 2134, 3421, 4123.
  • A116760 (program): Number of permutations of length n which avoid the patterns 2341, 3214, 4213; or avoid the patterns 1324, 2341, 3214.
  • A116761 (program): Number of permutations of length n which avoid the patterns 2143, 3124, 3421.
  • A116763 (program): Number of permutations of length n which avoid the patterns 2134, 3241, 3421.
  • A116764 (program): Number of permutations of length n which avoid the patterns 1423, 2134, 3214.
  • A116768 (program): Number of permutations of length n which avoid the patterns 1342, 3214, 4213.
  • A116770 (program): Number of permutations of length n which avoid the patterns 1243, 1342, 4312.
  • A116773 (program): Number of permutations of length n which avoid the patterns 1432, 2134, 4132; or avoid the patterns 3124, 4123, 4321.
  • A116774 (program): Number of permutations of length n which avoid the patterns 2143, 2341, 4312; or avoid the patterns 1234, 1432, 3412.
  • A116776 (program): Number of permutations of length n which avoid the patterns 2134, 3142, 3421.
  • A116777 (program): Number of permutations of length n which avoid the patterns 2314, 3142, 4312.
  • A116778 (program): Number of permutations of length n which avoid the patterns 2431, 3124, 3421.
  • A116779 (program): Number of permutations of length n which avoid the patterns 2143, 2341, 3214.
  • A116781 (program): Number of permutations of length n which avoid the patterns 1234, 1243, 3214.
  • A116782 (program): Number of permutations of length n which avoid the patterns 3421, 4123, 4231; or avoid the patterns 1342, 3142, 4213.
  • A116784 (program): Number of permutations of length n which avoid the patterns 2314, 3241, 4312.
  • A116788 (program): Number of permutations of length n which avoid the patterns 1234, 3142, 4132.
  • A116790 (program): Number of permutations of length n which avoid the patterns 1423, 1432, 3241.
  • A116791 (program): Number of permutations of length n which avoid the patterns 1234, 1342, 4312.
  • A116793 (program): Number of permutations of length n which avoid the patterns 1432, 2143, 3124; or avoid the patterns 1432, 2314, 3142.
  • A116796 (program): Number of permutations of length n which avoid the patterns 2314, 3241, 4132.
  • A116798 (program): Number of permutations of length n which avoid the patterns 1234, 1342, 1432.
  • A116802 (program): Number of permutations of length n which avoid the patterns 1342, 3421, 4213.
  • A116805 (program): Number of permutations of length n which avoid the patterns 2134, 3214, 4123.
  • A116806 (program): Number of permutations of length n which avoid the patterns 2314, 4213, 4312.
  • A116809 (program): Number of permutations of length n which avoid the patterns 1432, 2134, 2143.
  • A116816 (program): Number of permutations of length n which avoid the patterns 2314, 3124, 4312.
  • A116817 (program): Number of permutations of length n which avoid the patterns 2341, 3241, 4132.
  • A116819 (program): Number of permutations of length n which avoid the patterns 2431, 4123, 4231.
  • A116820 (program): Number of permutations of length n which avoid the patterns 2341, 3241, 4213.
  • A116823 (program): Number of permutations of length n which avoid the patterns 1342, 3142, 4312; or avoid the patterns 3124, 3412, 3421.
  • A116826 (program): Number of permutations of length n which avoid the patterns 2143, 2431, 3124.
  • A116837 (program): Number of permutations of length n which avoid the patterns 3421, 4123, 4312; or avoid the patterns 2341, 3142, 3214.
  • A116844 (program): Number of permutations of length n which avoid the patterns 231, 12345.
  • A116845 (program): Number of permutations of length n which avoid the patterns 231, 12534.
  • A116847 (program): Number of permutations of length n which avoid the patterns 123, 51432.
  • A116848 (program): Number of permutations of length n which avoid the patterns 231, 51234.
  • A116849 (program): Number of permutations of length n which avoid the patterns 213, 51432.
  • A116850 (program): Number of permutations of length n which avoid the patterns 231, 12354.
  • A116851 (program): Number of permutations of length n which avoid the patterns 321, 31245.
  • A116852 (program): Number of partitions of n-th semiprime into 2 squares.
  • A116853 (program): Difference triangle of factorial numbers read by upward diagonals.
  • A116854 (program): First differences of the rows in the triangle of A116853, starting with 0.
  • A116855 (program): Triangle read by rows, constructed from binomial transforms of prefixes of A000255 (see Comments for precise definition).
  • A116862 (program): Row sums of triangle A116868 (called Y(1,3)).
  • A116866 (program): Generalized Catalan triangle of Riordan type, called C(1,3).
  • A116867 (program): Convolution of generalized Catalan sequence A064063 (named C(3;n)).
  • A116871 (program): Sixth column of triangle A067323.
  • A116873 (program): Generalized Catalan numbers C(2,3;n)=C(3,2;n).
  • A116879 (program): Row sums of triangle A116872.
  • A116881 (program): Row sums of triangle A116880 (generalized Catalan C(1,2)).
  • A116882 (program): A number n is included if (highest odd divisor of n)^2 <= n.
  • A116883 (program): A number k is included iff (highest odd divisor of k)^2 >= k.
  • A116891 (program): a(n) = gcd(n! + 1, n^n + 1).
  • A116895 (program): Least prime factor of n^n-1.
  • A116905 (program): Number of partitions of n-th 3-almost prime into 2 squares.
  • A116906 (program): Sum of squares of divisors of n!.
  • A116913 (program): Inverse Moebius transform of pentagonal numbers.
  • A116914 (program): Number of UUDD’s, where U=(1,1) and D=(1,-1), in all hill-free Dyck paths of semilength n (a hill in a Dyck path is a peak at level 1).
  • A116915 (program): Expansion of f(-x, -x^4)^2 / f(-x, -x^2) in powers of x where f(, ) is Ramanujan’s general theta function.
  • A116916 (program): Expansion of q^(-1/8) * (eta(q)^3 + 3 * eta(q^9)^3) in powers of q^3.
  • A116917 (program): a(1)=a(2)=1. a(n) = A006530(a(n-1)) + A006530(a(n-2)).
  • A116919 (program): a(0)=1. a(n) = A006530(a(n-1)) + n.
  • A116920 (program): a(0)=1. a(n) = A020639(a(n-1)) + n.
  • A116921 (program): a(n) = largest integer <= n/2 which is coprime to n.
  • A116922 (program): a(n) = smallest integer >= n/2 which is coprime to n.
  • A116924 (program): Triangle T(n,k) = B(k,n) - B(k-1,n) where B(n,m) = Sum_{i=0..n} binomial(m,i) (3*i+1).
  • A116928 (program): Number of 1’s in all self-conjugate partitions of n.
  • A116937 (program): Expansion of Pi^2 in base 2.
  • A116938 (program): Expansion of e^2 in base 2.
  • A116939 (program): Lexicographically earliest sequence such that each i occurs exactly i+1 times and succeeding terms differ exactly by -1 or +1.
  • A116940 (program): Greatest m such that A116939(m) = n.
  • A116941 (program): Permutation of the natural numbers in conjunction with A116939 and A003056.
  • A116942 (program): Permutation of the natural numbers in conjunction with A116939 and A003056.
  • A116943 (program): Number of 4s digits plus non-final 3s digits 3 base 5 expansion of 2^n.
  • A116948 (program): Riordan array ((1+2x^2)/(1-x^3),x).
  • A116949 (program): Riordan array ((1-x^3)/(1+2x^2),x).
  • A116952 (program): a(n) = 3*a(n-1) + 5 with a(0) = 1.
  • A116953 (program): a(n) = Floor[1/2((1-2/Sqrt[3])^n+(1-2/Sqrt[3])^n)]
  • A116954 (program): Numbers n such that 3*n^3 + 1 is prime.
  • A116955 (program): a(n+1) = a(n) + (if a(n) is odd then (next odd square) else (next even square)), a(0) = 1.
  • A116956 (program): Number of functions f:{1,2,…,n}->{1,2,…,n} with odd cycles only.
  • A116958 (program): Numbers k such that 2*k + 5 and 2*k + 7 are twin primes.
  • A116963 (program): Inverse Moebius transform of tetrahedral numbers.
  • A116966 (program): a(n) = n + {1,2,0,1} according as n == {0,1,2,3} mod 4.
  • A116969 (program): If n mod 2 = 0 then 3*2^(n-1)+n-1 else 3*2^(n-1)+n.
  • A116970 (program): a(n) = (3^n - 7)/2.
  • A116971 (program): a(n) = (35*2^((2*(3*n+2) + 2)/3) - 2*(3*n+2) - 46)/9.
  • A116972 (program): a(n) = 11*3^n - 2*n - 10.
  • A116973 (program): If n mod 2 = 0 then (3^(n+3)-19)/8 else (3^(n+3)-1)/8.
  • A116974 (program): Numbers n for which the sum of the proper divisors equals the product of the proper divisors.
  • A116975 (program): Number of compositions of n into parts of sizes == 1 mod 5 or 4 mod 5.
  • A116982 (program): Distance between prime neighbors of 4n.
  • A116995 (program): Pentagonal numbers with prime indices.
  • A116996 (program): Partial sums of A116966.
  • A116998 (program): Numbers having no fewer distinct prime factors than any predecessor; a(1) = 1.
  • A117000 (program): a(n) = Sum_{d|n} Jacobi(2,d)*d.
  • A117002 (program): a(n) = sigma(n) + 3*A079667(n).
  • A117003 (program): a(n) = sigma(n) + A079667(n).
  • A117004 (program): a(n) = sigma(n) - A079667(n).
  • A117013 (program): Decimal expansion of (sine of 1 radian)^2.
  • A117015 (program): Decimal expansion of (sine of 1 radian)^4.
  • A117030 (program): a(1) = a(2) = 1; a(n) = a(n-1)*a(n-2) - a(n-3) - a(n-4) - … - a(1) for n>2.
  • A117033 (program): Decimal expansion of (cos 1)^2.
  • A117035 (program): Decimal expansion of (cos 1)^4.
  • A117047 (program): Primes of the form 60*n+11.
  • A117049 (program): Primes of the form 22*(n^2)+1.
  • A117054 (program): Number of ordered ways of writing n = i + j, where i is a prime and j is of the form k*(k+1), k > 0.
  • A117060 (program): Mersenne numbers for which the product of the digits is not zero.
  • A117061 (program): Numbers n such that a(n) = (s(n-1))^2+n, with a(1) = 1.
  • A117062 (program): Hexagonal numbers for which the sum of the digits is also a hexagonal number.
  • A117066 (program): Partial sums of cupolar numbers (1/3)*(n+1)*(5*n^2+7*n+3) (A096000).
  • A117067 (program): Decimal value of binary number whose n-th 1 is followed by F(n) 0’s.
  • A117077 (program): Define binary strings S(0)=0, S(1)=1, S(n) = S(n-2)S(n-1); a(n) = S(n) converted to decimal.
  • A117079 (program): a(1) = 1; a(n) = 2*a(n-1) + (number of digits in a(n-1)).
  • A117080 (program): a(n) = 2a(n-1)+a(n-3)+1 with a(1)=1, a(2)=3, a(3)=8.
  • A117081 (program): a(n) = 36*n^2 - 810*n + 2753, producing the conjectured record number of 45 primes in a contiguous range of n for quadratic polynomials, i.e., abs(a(n)) is prime for 0 <= n < 44.
  • A117085 (program): Decimal value of binary number whose n-th 1 is followed by L(n) 0’s.
  • A117088 (program): a(n) = (11*5^n - 7)/4.
  • A117110 (program): The (1,1)-entry of the vector v[n]=Mv[n-1], where M is the 3 x 3 matrix [[0,-1/r,r],[ -1/r,-2/r,1],[r,1,2+2/r]], r being the golden ratio and v[0] is the column matrix [0,1,1].
  • A117119 (program): Number of partitions of 2*n into two odd prime powers.
  • A117120 (program): a(1)=1. a(n) is smallest positive integer not occurring earlier in the sequence where a(n) is congruent to -1 (mod a(n-1)).
  • A117123 (program): n minus the number of 0’s in binary expansion of n.
  • A117124 (program): Numbers that when multiplied by 37 produce a palindrome number.
  • A117131 (program): Remainder when n^n is divided by the n-th prime number.
  • A117142 (program): Number of partitions of n in which any two parts differ by at most 2.
  • A117143 (program): Number of partitions of n in which any two parts differ by at most 3.
  • A117149 (program): Trajectory of 4 under map k -> A094077(k).
  • A117150 (program): Retrograde trajectory of 4 under map k -> A094077(k).
  • A117152 (program): Sum of product of Fibonacci and triangular numbers.
  • A117157 (program): a(1)=a(2)=1; a(n) = a(n-1)*a(n-2) + a(n-3) + a(n-4) + … + a(1) for n>2.
  • A117178 (program): Riordan array (c(x^2)/sqrt(1-4*x^2), x*c(x^2)), c(x) the g.f. of A000108.
  • A117179 (program): Riordan array ((1-x^2)/(1+x^2)^2,x/(1+x^2)).
  • A117180 (program): Lowest prime-power dividing the n-th nonsquarefree positive integer.
  • A117181 (program): Highest prime-power dividing the n-th nonsquarefree positive integer.
  • A117183 (program): a(n) = smallest prime dividing n-th nonsquarefree positive integer.
  • A117184 (program): Riordan array ((1+x)c(x^2)/sqrt(1-4x^2),xc(x^2)), c(x) the g.f. of A000108.
  • A117186 (program): Expansion of (1+x)c(x^2)/((1-xc(x^2))*sqrt(1-4x^2)), c(x) the g.f. of A000108.
  • A117187 (program): Expansion of (1+x)c(x^2)/((1-x^2*c(x^2))sqrt(1-4x^2)), c(x) the g.f. of A000108.
  • A117188 (program): Expansion of (1-x^2)/(1+x^2+x^4).
  • A117189 (program): Binomial transform of the tribonacci sequence A000073 (shifted left twice).
  • A117197 (program): a(n) = (n^3 - 1)^3.
  • A117198 (program): Generalized Riordan array (1,x)+(x,x^2)+(x^2,x^3).
  • A117199 (program): Expansion of 1/(1-x^2) + x/(1-x^3) + x^2/(1-x^4).
  • A117202 (program): Binomial transform of n*F(n).
  • A117203 (program): Odd squarefree positive integers k such that (k-1)/2 is also squarefree.
  • A117204 (program): Squarefree positive integers k such that 2*k+1 is also squarefree.
  • A117205 (program): Odd squarefree positive integers k such that (k+1)/2 is also squarefree.
  • A117206 (program): Squarefree positive integers k such that 2*k-1 is also squarefree.
  • A117207 (program): Number triangle read by rows: T(n,k)=sum{j=0..n-k, C(n+j,j+k)C(n-j,k)}.
  • A117208 (program): G.f. A(x) satisfies (1-x) = product_{n>=1} A(x^n).
  • A117209 (program): G.f. A(x) satisfies 1/(1-x) = product_{n>=1} A(x^n).
  • A117210 (program): G.f. A(x) satisfies (1+x) = product_{n>=1} A(x^n).
  • A117211 (program): G.f. A(x) satisfies 1/(1+x) = product_{n>=1} A(x^n).
  • A117212 (program): Sum_{d|n} a(d)/d = (-1)^(n-1)/n for n>=1; equals the logarithmic g.f. of A117210.
  • A117213 (program): a(n) = smallest term of sequence A002110 divisible by n-th squarefree positive integer.
  • A117214 (program): a(n) = (A117213(n))/(n-th squarefree positive integer).
  • A117216 (program): Number of points in the standard root system version of the D_4 lattice having L_infinity norm n.
  • A117218 (program): Squares divisible by their number of digits.
  • A117220 (program): Number of partitions of 3-smooth numbers into parts not greater than 3.
  • A117229 (program): Number of decimal digits of n in {0,1,4,8,9}
  • A117230 (program): Start with 1 and repeatedly reverse the digits and add 1 to get the next term.
  • A117245 (program): Partial sums of A115975.
  • A117248 (program): Number of down steps at start of segment n of A079051.
  • A117251 (program): Column 0 of triangle A117250.
  • A117253 (program): Column 0 of triangle A117252.
  • A117255 (program): Column 0 of triangle A117254.
  • A117257 (program): Column 0 of triangle A117256.
  • A117259 (program): Column 0 of triangle A117258.
  • A117260 (program): Triangle T, read by rows, where matrix inverse T^-1 has -2^n in the secondary diagonal: T^-1 = -2^n, with all 1’s in the main diagonal and zeros elsewhere.
  • A117261 (program): Row sums of triangle A117260.
  • A117262 (program): Triangle T, read by rows, where matrix inverse T^-1 has -3^n in the secondary diagonal: T^-1 = -3^n, with all 1’s in the main diagonal and zeros elsewhere.
  • A117263 (program): Row sums of triangle A117262; also, self-convolution of A117264.
  • A117266 (program): Row sums of triangle A117265.
  • A117267 (program): Difference row triangle of A117189.
  • A117268 (program): Triangle, binomial transform of the tribonacci sequence.
  • A117274 (program): Triangle read by rows: T(n,k) is the number of partitions of n with no even part repeated and having k 1’s (n>=0, 0<=k<=n).
  • A117275 (program): Number of partitions of n with no even parts repeated and with no 1’s.
  • A117276 (program): Number of 1’s in all partitions of n with no even parts repeated.
  • A117277 (program): Number of partitions of n whose consecutive parts differ by 3.
  • A117284 (program): Numbers k for which the cototient k-phi(k) is a triangular number.
  • A117286 (program): Numbers k for which the cototient k-phi(k) is a hexagonal number.
  • A117290 (program): Numbers k for which the cototient k - phi(k) is a Fibonacci number.
  • A117291 (program): a(n) = phi(n)^(n-phi(n))
  • A117292 (program): a(n) = (n-phi(n))^phi(n).
  • A117295 (program): a(n) = phi(n)*(n - phi(n)).
  • A117298 (program): Number of partitions of n with unique smallest part and unique largest part.
  • A117302 (program): Number of cases in which the first player gets killed in a Russian roulette game when 7 players use a gun with n chambers and the number of the bullets can be from 1 to n. In the game they do not rotate the cylinder after the game starts.
  • A117303 (program): Self-inverse permutation of the natural numbers based on the bijection (2*x-1)*2^(y-1) <–> (2*y-1)*2^(x-1).
  • A117305 (program): Triangular numbers for which the sum of the digits is a pentagonal number.
  • A117309 (program): Triangular numbers for which the sum of the digits is a hexagonal number.
  • A117316 (program): Riordan array ((1-x)/(1-x-2x^2),x(1-x)/(1-x-2x^2)).
  • A117317 (program): Triangle related to partitions of n.
  • A117322 (program): a(n) = prime(n) modulo semiprime(n).
  • A117323 (program): Semiprime(n) modulo prime(n).
  • A117336 (program): Column 1 of triangle A117335.
  • A117338 (program): Row sums of triangle A117335.
  • A117339 (program): a(n)=a(n-1)+a(n-2); if a(n) is not prime divide a(n) by its largest prime factor.
  • A117352 (program): Riordan array (1/(1-2x), x(1-2x)/(1-x)).
  • A117353 (program): Expansion of (1-x)/(1-3x+x^2+4x^3-4x^4).
  • A117354 (program): Riordan array (1-x+sqrt(1-6x+x^2))/2, (1+x-sqrt(1-6x+x^2))/4).
  • A117360 (program): Numbers m such that m and 2*m+1 have the same number of prime factors.
  • A117362 (program): Riordan array (1-2x,x(1-x)).
  • A117363 (program): Expansion of (1-2x)/(1-x^2+x^3).
  • A117364 (program): a(n) = largest prime less than the largest prime dividing n (or 1 if there is no such prime).
  • A117365 (program): a(n) = largest prime less than the smallest prime dividing n (or 1 if there is no such prime).
  • A117366 (program): a(n) = smallest prime greater than the largest prime dividing n.
  • A117367 (program): a(n) = smallest prime greater than the smallest prime dividing n.
  • A117368 (program): a(n) = largest prime less than the smallest prime dividing (2n-1).
  • A117370 (program): Number of primes between smallest prime divisor of n and largest prime divisor of n.
  • A117372 (program): Riordan array (1-3x,x(1-x)).
  • A117373 (program): Expansion of (1 - 3x)/(1 - x + x^2).
  • A117374 (program): Expansion of (1-3x)/(1-x^2+x^3).
  • A117375 (program): Riordan array (1/(1-3x*c(x)),xc(x)), c(x) the g.f. of A000108.
  • A117377 (program): Riordan array (1-4x,x(1-x)).
  • A117378 (program): Expansion of (1-4*x)/(1-x+x^2).
  • A117379 (program): Expansion of (1-4x)/(1-x^2+x^3).
  • A117380 (program): Riordan array (1/(1-4*x*c(x)),xc(x)), c(x) the g.f. of A000108.
  • A117384 (program): Positive integers, each occurring twice in the sequence, such that a(n) = a(k) when n+k = 4*a(n), starting with a(1)=1 and filling the next vacant position with the smallest unused number.
  • A117385 (program): Positive integers, each occurring twice in the sequence, such that a(n) = a(k) when n+k = 5*a(n), starting with a(1)=1 and filling the next vacant position with the smallest unused number.
  • A117389 (program): A skew Delannoy number triangle read by rows.
  • A117394 (program): Product of the first F(n) primes, where F(n) is the n-th Fibonacci number.
  • A117396 (program): Triangle, read by rows, defined by: T(n,k) = (k+1)*T(n,k+1) - Sum_{j=1..n-k-1} T(j,0)*T(n,j+k+1) for n>k with T(n,n)=1 for n>=0.
  • A117397 (program): Column 3 of triangle A117396.
  • A117399 (program): Column 1 (divided by 2) of triangle A117398, which is the matrix log of A117396.
  • A117401 (program): Triangle T(n,k) = 2^(k*(n-k)), read by rows.
  • A117402 (program): Row sums of triangle A117401: a(n) = Sum_{k=0..n} 2^((n-k)*k) for n>=0.
  • A117403 (program): a(n) = Sum_{k=0..floor(n/2)} 2^((n-2*k)*k) for n>=0.
  • A117404 (program): Triangular numbers for which the sum of the digits is a square.
  • A117407 (program): a(n) = j if n is T(j), else a(n) = k if n is U(k), where T is a Beatty sequence based on (sqrt(5)+5)/2 (A054770) and U is its complement (A063732).
  • A117409 (program): Number of partitions of n into odd parts in which the largest part occurs only once.
  • A117410 (program): Expansion of q^(-5/24) * eta(q^2)^3 / eta(q) in powers of q.
  • A117411 (program): Skew triangle associated to the Euler numbers.
  • A117412 (program): Sum of the interior angles of an n-sided polygon, in gradians.
  • A117413 (program): Expansion of (1-x^2)/(1-2*x^2+4*x^3+x^4).
  • A117415 (program): E.g.f. (x*tan(x)-x^2)/8 (even powers only).
  • A117434 (program): Expansion of c(x*y(1+x)), c(x) the g.f. of A000108.
  • A117435 (program): Triangle related to exp(x)*cos(2*x).
  • A117436 (program): Triangle related to exp(x)*sec(2*x).
  • A117437 (program): Expansion of e.g.f.: exp(x)*sec(2*x).
  • A117438 (program): Triangle T(n, k) = binomial(2*n-k, k)*(-4)^(n-k), read by rows.
  • A117439 (program): Expansion of (1-x^2)/(1 -4*x -2*x^2 +x^4).
  • A117440 (program): A cyclically signed version of Pascal’s triangle.
  • A117441 (program): Periodic with repeating part {1,1,0,1,-1,0,-1,-1,0,-1,1,0}.
  • A117442 (program): Number triangle read by rows, related to exp(x)/(cos(x) + sin(x)).
  • A117443 (program): Expansion of e.g.f.: exp(x)/(cos(x) + sin(x)).
  • A117444 (program): Period 5: Repeat [0, 1, 2, -2, -1].
  • A117445 (program): Periodic {0,-1,1,4,-1,4,-4,-4,1,1,-4,-4,4,-1,4,1,-1} (period 17).
  • A117446 (program): Triangle T(n, k) = binomial(L(k/3), n-k) where L(j/p) is the Legendre symbol of j and p, read by rows.
  • A117447 (program): Expansion of (1 + 2*x + 3*x^2 + x^3)/(1 + x - x^3 - x^4).
  • A117448 (program): Diagonal sums of number triangle A117446.
  • A117450 (program): Expansion of (1-x+x^2+x^5)/((1-x)^2*(1-x^5)).
  • A117451 (program): Expansion of (1-x+x^2+x^5)/((1-x)*(1-x^5)).
  • A117452 (program): Periodic {2, -1, 1, 0, 0} - 0^n.
  • A117464 (program): Triangular numbers for which the product of the digits is a square.
  • A117472 (program): Values of c in a^2 + b^2 = c^2, where b - a = 17 and gcd(a,b,c)=1.
  • A117473 (program): The values of ‘a’ in a^2 + b^2 = c^2, where b - a = 17 and gcd(a, b, c) = 1.
  • A117474 (program): The values of ‘a’ in a^2 + b^2 = c^2 where b - a = 7 and gcd(a,b,c)=1.
  • A117475 (program): The values of c in a^2 + b^2 = c^2 where b - a = 23 and gcd(a,b,c) = 1.
  • A117476 (program): The values of a in a^2 + b^2 = c^2 where b - a = 23 and gcd(a,b,c)=1.
  • A117479 (program): Number of zeros in the maximal Fibonacci bit-representation of n (A104326).
  • A117481 (program): a(n) = n*(n-1)*(n-2)*(n-3)*…*(n-k) such that (n-k) is the largest prime smaller than n.
  • A117485 (program): Expansion of x^9/((1-x)*(1-x^2)*(1-x^3))^2.
  • A117490 (program): Number of primes between n and n^2 (with n and n^2 excluded).
  • A117494 (program): a(n) is the number of m’s, 1 <= m <= n, where gcd(m,n) is prime.
  • A117495 (program): Product of a prime number p and the number of primes smaller than p.
  • A117501 (program): Triangle generated from an array of generalized Fibonacci-like terms.
  • A117502 (program): Triangle, row sums = A001595.
  • A117507 (program): Numerators of partial sums of the Brun series divided by 4.
  • A117508 (program): Denominators of partial sums of the Brun series divided by 5.
  • A117512 (program): Triangular numbers for which the sum of the digits is a prime number.
  • A117513 (program): Number of ways of arranging 2*n tokens in a row, with 2 copies of each token from 1 through n, such that between every pair of tokens labeled i (i = 1..n-1) there is exactly one taken labeled i+1.
  • A117516 (program): Last entry (and high point) in segment n of A079051.
  • A117520 (program): Triangular numbers for which the digital root is also a triangular number.
  • A117521 (program): Start with 1 and repeatedly reverse the digits and add 2 to get the next term.
  • A117523 (program): Triangular numbers for which the sum of the digits is an octagonal number.
  • A117530 (program): Triangle read by rows: T(n,k) = k^2 - k + prime(n), 1<=k<=n.
  • A117535 (program): Number of ways of writing n as a sum of powers of 3, each power being used at most 4 times.
  • A117548 (program): Values of n for which there exist d(1),…,d(n), each in {0,1,2} and an r in {1,2} such that Sum[d(i)d(i+k),i=1,n-k]=r (mod 3) for all k=0,…,n-1. (Such a sequence is called a very(3,r) sequence. See the link.).
  • A117552 (program): Largest partial sum of the increasingly ordered divisors of n, not exceeding n.
  • A117553 (program): When adding some positive divisors of n in order from lowest divisor to highest divisor, a(n) is lowest sum achievable which is >= n.
  • A117560 (program): a(n) = n*(n^2 - 1)/2 - 1.
  • A117561 (program): Floor(n*(n^3-n-3)/(2*(n-1))).
  • A117567 (program): Riordan array ((1+x^2)/(1-x^3),x).
  • A117568 (program): Riordan array ((1-x^3)/(1+x^2),x).
  • A117569 (program): Expansion of (1+x+x^2)/(1+x^2).
  • A117571 (program): Expansion of (1+2*x^2)/((1-x)*(1-x^3)).
  • A117572 (program): Expansion of (1+2x^2)/((1-x^2)(1-x^3)).
  • A117573 (program): Expansion of (1+2x^2)/((1-x)(1-x^2)(1-x^3)).
  • A117575 (program): Expansion of (1-x^3)/((1-x)*(1+2*x^2)).
  • A117576 (program): Expansion of (1-x^3)/((1-x^2)(1+2x^2)).
  • A117584 (program): Generalized Pellian triangle.
  • A117585 (program): a(n) = 2*a(n-1) + a(n-2) + n.
  • A117589 (program): Periodic with period 8: repeat 0, 1, 3, 7, 15, 14, 12, 8.
  • A117590 (program): a(n) = ceiling(x(n)), where x(n) = 3*x(n-1)/2 and x(1) = 1.
  • A117591 (program): a(n) = 2^n + Fibonacci(n).
  • A117592 (program): a(n) = a(3n) = a(3n+1) = a(3n+2)/2 with a(0)=1.
  • A117596 (program): Start with x=6/5; repeatedly apply the map x -> x*ceiling(x); sequence gives numerators of the resulting sequence of fractions.
  • A117605 (program): Decimal expansion of the real solution to equation x^3 + 3*x = 2.
  • A117609 (program): Number of lattice points inside the ball x^2 + y^2 + z^2 <= n.
  • A117611 (program): Legendre-binomial transform of 10^n for p=3.
  • A117614 (program): a(0)=1, a(n)=4a(n-1)+2 for n odd, a(n)=4a(n-1) for n even.
  • A117615 (program): a(0)=0, a(1)=1, a(n)=4a(n-1)+2 for n =3,5,7,…, a(n)=4a(n-1) for n =2,4,6,….
  • A117616 (program): a(0)=0, a(n)=4a(n-1)+2 for n odd, a(n)=4a(n-1) for n even.
  • A117617 (program): a(n) = 5*a(n-1) + 3 with a(0) = 1.
  • A117619 (program): a(n) = n^2 + 7.
  • A117625 (program): Maximum number of regions defined by n zigzag-lines in the plane when a zigzag-line is defined as consisting of two parallel infinite half-lines joined by a straight line segment.
  • A117627 (program): Let f(n) = minimum of average number of comparisons needed for any sorting method for n elements and let g(n) = n!*f(n). Sequence gives a lower bound on g(n).
  • A117630 (program): Complement of A056576.
  • A117634 (program): a(0)=0. a(n) = a(n-1) + 1 + (number of positive integers which are <= n and are missing from {a(0),a(1),a(2),…a(n-1)}).
  • A117640 (program): Concatenation of first n numbers in base 4.
  • A117641 (program): Number of 3-Motzkin paths of length n with no level steps at height 0.
  • A117642 (program): a(n) = 3*n^3.
  • A117643 (program): a(n) = n*(a(n-1)-1) starting with a(0)=3.
  • A117644 (program): Number of distinct pairs a < b with nonzero decimal digits such that a + b = 10^n.
  • A117647 (program): a(2n) = A014445(n), a(2n+1) = A015448(n+1).
  • A117658 (program): Number of solutions to x^(k+1) = x^k mod n for some k >= 1.
  • A117662 (program): n*(n-1)*(n-2)*(n+3)/12.
  • A117663 (program): Heptagonal numbers for which the digital root is also a heptagonal number.
  • A117664 (program): Denominator of the sum of all elements in the n X n Hilbert matrix M(i,j) = 1/(i+j-1), where i,j = 1..n.
  • A117665 (program): n times the n-th n-gonal number.
  • A117666 (program): Expansion of (1-3*x+x^2)*(1-x-x^2)/((1+x+x^2)*(1-x+x^2)*(1-x)^2).
  • A117667 (program): a(n) = n^n-n^(n-1)-n^(n-2)-n^(n-3)-…-n^3-n^2-n.
  • A117670 (program): Triangle read by rows: partial sums of the Pascal triangle minus 1.
  • A117671 (program): a(n) = binomial(3*n+1, n+1).
  • A117672 (program): Numbers n such that |cos(n)*cos(n+2)| < (cos(n+1))^2.
  • A117673 (program): a(n) is the least k such that k*2*prime(n) + 1 is prime.
  • A117676 (program): Squares for which the digital root is also a square.
  • A117677 (program): a(n) = number of divisors of n^2 (excluding 1 and n^2).
  • A117678 (program): Squares for which the multiplicative digital root is also a square.
  • A117681 (program): Floor of exp(n^2).
  • A117686 (program): Squares for which the product of the digits are cubes.
  • A117689 (program): Cubes for which the product of the digits is a square.
  • A117691 (program): Expansion of -(x^7+x^6+x^5-2*x^3-3*x^2-3*x-4) / ((x-1)^2*(x+1)^2*(x^2+1)^2).
  • A117694 (program): (n^n + n)/2.
  • A117704 (program): Least refined sequence that can be grouped to sum to either natural numbers or odd numbers.
  • A117714 (program): a(n) = (A034962(n) - A152470(n))/2.
  • A117715 (program): Triangle T(n,m) containing the value of the Fibonacci polynomial F(n,x) at x=m.
  • A117717 (program): Maximal number of regions obtained by a straight line drawing of the complete bipartite graph K_{n,n}.
  • A117718 (program): Number of heptagonal numbers with n digits.
  • A117719 (program): a(2n) = A001653(n) (Numbers n such that 2*n^2 - 1 is a square), a(2n+1) = A038725(n+1).
  • A117722 (program): a(n) = A000045(A003622(n)).
  • A117727 (program): Partial sums of A051109.
  • A117731 (program): Numerator of the fraction n*Sum_{k=1..n} 1/(n+k).
  • A117733 (program): Sum of the n-th primorial and the n-th compositorial number.
  • A117734 (program): Absolute difference between the n-th primorial and the n-th compositorial number.
  • A117735 (program): a(n) = n! - primorial(n).
  • A117736 (program): factorial(n) - A049614(n).
  • A117748 (program): Triangular numbers divisible by 3.
  • A117756 (program): Squares for which the reversed sum of the digits is also a square.
  • A117760 (program): Expansion of 1/(1 - x - x^3 - x^5 - x^7).
  • A117761 (program): a(n) = a(n-1) + a(n-3) + a(n-5) + a(n-7) for n >= 7.
  • A117762 (program): a(1)=6; for n>1, a(n) = prime(n)*(prime(n)^2-1)/2.
  • A117767 (program): a(n) is the differences between the smallest square greater than prime(n) and the largest square less than prime(n), where prime(n) = A000040(n) is the n-th prime number.
  • A117768 (program): Number of Lucas numbers with n digits.
  • A117791 (program): Expansion of 1/(1 - x - x^2 + x^4 - x^6).
  • A117792 (program): First entry of the vector (M^n)w, where M is the 6x6 matrix [[0, 1, 0, 0, 0, 0, ], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 1], [1, 0, -1, 0, 1, 1]] and w is the column vector [0, 1, 1, 2, 3, 5].
  • A117793 (program): Pentagonal numbers divisible by 5.
  • A117794 (program): Hexagonal numbers divisible by 6.
  • A117795 (program): Heptagonal numbers divisible by 7.
  • A117796 (program): Enneagonal numbers divisible by 9.
  • A117797 (program): Decagonal numbers divisible by 10.
  • A117798 (program): Icosagonal numbers divisible by 20.
  • A117800 (program): Start with 1 and repeatedly reverse the digits and add 5 to get the next term.
  • A117802 (program): Numbers with an “a” in Dutch.
  • A117804 (program): Natural position of n in the string 12345678910111213….
  • A117806 (program): n appears {a(1)+a(2)+…+a(n-1)} times (with a(1)=1).
  • A117807 (program): Start with 1015 and repeatedly reverse the digits and add 4 to get the next term.
  • A117812 (program): a(n) = n^(2*n) - 1.
  • A117813 (program): Consider 1-D random walk with jumps up to the third neighbor, i.e., set of possible jumps is {-3,-2,-1,+1,+2,+3}. Sequence gives number of paths of length n ending at origin.
  • A117814 (program): a(n) = 1 if at least one of decimal digits of n is a prime, otherwise a(n)=0.
  • A117818 (program): a(n) = n if n is 1 or a prime, otherwise a(n) = n divided by the least prime factor of n (A032742(n)).
  • A117824 (program): a(0) = 0, a(1) = 1; for n >= 2, a(n) = a(n-1) + a(n-2) - (n-1) if that number is positive and not already in the sequence, otherwise a(n) = a(n-1) + a(n-2) + (n-1).
  • A117826 (program): First four terms of the sequence are doubled, then those numbers are tripled and then those numbers are quadrupled, etc.
  • A117828 (program): Start with 1 and repeatedly reverse the decimal digits and add 4 to get the next term.
  • A117829 (program): Start with 3 and repeatedly reverse the digits and add 4 to get the next term.
  • A117830 (program): Let S_m be the infinite sequence formed by starting with m and repeatedly reversing the digits and adding 4 to get the next term. For all m < 1015, S_m enters the cycle of length 54 whose terms are shown here.
  • A117841 (program): Start with 1 and repeatedly reverse the digits and add 10 to get the next term.
  • A117842 (program): Partial sum of smallest prime >= n (A007918).
  • A117849 (program): a(n) =(A001359[n]^2-1)/2
  • A117852 (program): Mirror image of A098473 formatted as a triangular array.
  • A117854 (program): Let p(n) be the n-th-prime. Sequence gives primes of the form | p(n)*p(n+2) - p(n+1)*p(n+3)| +1.
  • A117855 (program): Number of nonzero palindromes of length n (in base 3).
  • A117856 (program): Number of palindromes of length n (in base 4).
  • A117857 (program): Number of palindromes of length n (in base 5).
  • A117858 (program): Number of palindromes of length n (in base 6).
  • A117859 (program): Number of palindromes of length n (in base 7).
  • A117860 (program): Number of palindromes of length n (in base 8).
  • A117861 (program): Number of palindromes of length n (in base 9).
  • A117862 (program): Number of palindromes (in base 3) below 3^n.
  • A117863 (program): Number of palindromes (in base 4) below 4^n.
  • A117864 (program): Number of palindromes (in base 5) below 5^n.
  • A117865 (program): Number of palindromes (in base 6) below 6^n.
  • A117866 (program): Number of palindromes (in base 7) below 7^n.
  • A117867 (program): Number of palindromes (in base 8) below 8^n.
  • A117868 (program): Number of palindromes (in base 9) below 9^n.
  • A117869 (program): Partial sums of floor(e^n).
  • A117880 (program): a(1) = 4; a(n) is smallest semiprime > 2*a(n-1).
  • A117886 (program): Expansion of q^(-2/3)eta(q)eta(q^10)^2/eta(q^5) in powers of q.
  • A117887 (program): Number of labeled trees on <= n nodes.
  • A117890 (program): Numbers n such that number of non-leading 0’s in binary representation of n divides n.
  • A117892 (program): Add up the positive integers which are coprime to n in order (starting at 1). a(n) is the largest such partial sum that is <= n.
  • A117893 (program): Add up the positive integers that are coprime to n in order (starting at 1). a(n) is the smallest such partial sum that is >= n.
  • A117894 (program): Triangle, row sums = Pell numbers, A000129.
  • A117895 (program): Triangle T(n, k) = (k-n)*A000129(k+1) + (3*n-3*k+1)*A000129(k) with T(n,0) = 1, for 0 <= k <= n-1, read by rows.
  • A117897 (program): Number of labeled trees on prime numbers of nodes through n-th prime.
  • A117898 (program): Number triangle 2^abs(L(C(n,2)/3) - L(C(k,2)/3))*[k<=n] where L(j/p) is the Legendre symbol of j and p.
  • A117899 (program): Expansion of (1 + 2*x + 5*x^2 + 3*x^3 + 2*x^4)/(1-x^3)^2.
  • A117900 (program): Expansion of (1 + 2*x + 4*x^2 + 4*x^3 + 2*x^4)/((1+x)*(1-x^3)^2).
  • A117902 (program): Expansion of (1-x^2-2x^3)/(1-4x^3).
  • A117904 (program): Number triangle [k<=n]*0^abs(L(C(n,2)/3) - L(C(k,2)/3)) where L(j/p) is the Legendre symbol of j and p.
  • A117905 (program): Expansion of (1+2*x+2*x^2)/((1+x)*(1-x^3)^2).
  • A117906 (program): Inverse of number triangle A117904.
  • A117907 (program): Expansion of x + (1-x)^2/(1-x^6).
  • A117908 (program): Chequered (or checkered) triangle for odd prime p=3.
  • A117909 (program): Count, inserting 0 after every even number.
  • A117910 (program): Expansion of (1 + x + x^2 + x^4)/((1-x^3)*(1-x^6)).
  • A117916 (program): a(1) = 4; a(n) is smallest semiprime > 3*a(n-1).
  • A117917 (program): a(n) = 3*a(n-1) + a(n-2) + n.
  • A117918 (program): Difference row triangle of the Pell sequence.
  • A117919 (program): Triangle read by rows: T(n, k) = 2^floor((k-1)/2)*binomial(n-1, k-1).
  • A117926 (program): a(n) = n^floor(sqrt(n)).
  • A117927 (program): a(n) = binomial(s(n), n) where s(n) = n-th semiprime.
  • A117929 (program): Number of partitions of n into 2 distinct primes.
  • A117935 (program): Triangle, row terms converge to the Pell sequence.
  • A117938 (program): Triangle, columns generated from Lucas Polynomials.
  • A117940 (program): a(0)=1, thereafter a(3n) = a(3n+1)/3 = a(n), a(3n+2)=0.
  • A117942 (program): a(n) = a(3n) = -a(3n+1) = -a(3n+2)/2.
  • A117943 (program): a(1) = 0, a(2) = 1; a(3n) = a(n); if every third term (a(3), a(6), a(9), …) is deleted, this gives back the original sequence.
  • A117944 (program): Triangle related to powers of 3 partitions of n.
  • A117945 (program): Triangle related to powers of 3 partitions of n.
  • A117946 (program): a(3n)=0, a(3n+1)/a(1)=a(3n+2)/a(2)=A059151(n).
  • A117947 (program): T(n,k)=L(C(n,k)/3) where L(j/p) is the Legendre symbol of j and p.
  • A117948 (program): Sum of the divisors of pentagonal numbers.
  • A117950 (program): a(n) = n^2 + 3.
  • A117951 (program): a(n) = n^2 + 5.
  • A117956 (program): Number of partitions of n into exactly 2 types of parts: one odd and one even.
  • A117957 (program): Number of partitions of n into parts larger than 1 and congruent to 1 mod 4.
  • A117960 (program): Triangular numbers with only odd digits.
  • A117961 (program): Hexagonal numbers with prime indices.
  • A117962 (program): Partial sums of hexagonal numbers with prime indices.
  • A117963 (program): Antidiagonal sums of a Legendre-binomial triangle for p = 3.
  • A117964 (program): A117963 mod 2.
  • A117966 (program): Balanced ternary enumeration (based on balanced ternary representation) of integers; write n in ternary and then replace 2’s with (-1)’s.
  • A117967 (program): Positive part of inverse of A117966; write n in balanced ternary and then replace (-1)’s with 2’s.
  • A117968 (program): Negative part of inverse of A117966; write -n in balanced ternary and then replace (-1)’s with 2’s.
  • A117972 (program): Numerator of zeta’(-2n), n >= 0.
  • A117973 (program): a(n) = 2^(wt(n)+1), where wt() = A000120().
  • A117976 (program): Legendre-binomial transform of 2^n for p=3.
  • A117977 (program): Legendre-binomial transform of 3^n for p=3.
  • A117980 (program): Legendre-binomial transform of (-1)^n for p=3.
  • A117981 (program): A modified Legendre-binomial transform of 2^n for p=3.
  • A117982 (program): Trisection of A117981.
  • A117983 (program): A modified Legendre-binomial transform of 2^n for p=3.
  • A117984 (program): A modified Legendre-binomial transform of 4^n for p=3.
  • A117985 (program): Pentagonal numbers with only odd digits.
  • A117989 (program): Number of partitions of n such that the least part occurs at least twice.
  • A117993 (program): Heptagonal numbers with only odd digits.
  • A117995 (program): Number of partitions of n in which both smallest and largest part occur only once.
  • A117997 (program): Sum_{d|n} a(d) = n for n = 3^m (m >= 0) and for other n the sum is zero; i.e., the Möbius transform of [1, 0, 3, 0, 0, 0, 0, 0, 9, 0,…].
  • A117998 (program): Decimal number generated by the binary bits of the n-th generation of the Rule 102 elementary cellular automaton.
  • A117999 (program): Decimal number generated by the binary bits of the n-th generation of the Rule 110 elementary cellular automaton.
  • A118000 (program): a(0) = 0. a(n) = a(n-1) + (smallest integer >= n which is coprime to a(n-1)).
  • A118001 (program): a(n) = smallest integer >= n which is coprime to A118000(n-1). a(n) = A118000(n) - A118000(n-1).
  • A118002 (program): a(0) = 0. a(n) = a(n-1) + (largest integer <= n which is coprime to a(n-1)).
  • A118003 (program): a(n) = largest integer <= n which is coprime to A118002(n-1). a(n) = A118002(n) - A118002(n-1).
  • A118004 (program): a(n) = 9^n - 4^n.
  • A118005 (program): a(n) = ((-1)^n*5^(n+1) + 9^(n+1))/14.
  • A118006 (program): Define a sequence of binary words by w(1) = 01 and w(n+1) = w(n)w(n)Reverse[w(n)]. Sequence gives the limiting word w(infinity).
  • A118007 (program): Triangle, diagonals generated from Lucas polynomials.
  • A118010 (program): Difference row triangle of A118009.
  • A118011 (program): Complement of the Connell sequence (A001614); a(n) = 4*n - A001614(n).
  • A118012 (program): a(n) = 4*A117384(n) - n; a self-inverse permutation of the natural numbers.
  • A118013 (program): Triangle read by rows: T(n,k) = floor(n^2/k), 1<=k<=n.
  • A118014 (program): Sum_{k=1..n} floor(n^2/k).
  • A118015 (program): a(n) = floor(n^2/5).
  • A118057 (program): a(n) = 8*n^2 - 4*n - 3.
  • A118058 (program): a(n) = 49n^2 - 28n - 20.
  • A118059 (program): 288*n^2 - 168*n - 119.
  • A118060 (program): a(n) = 1681*n^2 - 984*n - 696.
  • A118061 (program): 9800*n^2-5740*n-4059
  • A118070 (program): Numbers with exactly one even decimal digit.
  • A118071 (program): Primes which are the sum of a twin prime pair + 1.
  • A118074 (program): Start with 1 and repeatedly reverse the digits and add 41 to get the next term.
  • A118075 (program): Start with 1 and repeatedly reverse the digits and add 42 to get the next term.
  • A118081 (program): Even numbers that can’t be represented as the sum of two odd composite numbers.
  • A118083 (program): Number of partitions of n such that largest part k occurs at least floor(k/2) times.
  • A118087 (program): Start with 1 and repeatedly reverse the digits and add 43 to get the next term.
  • A118088 (program): a(0) = 0, a(n) = (1+2*0^(n mod 3))*a(floor(n/3)) + n mod 3.
  • A118090 (program): Start with 1 and repeatedly reverse the digits and add 44 to get the next term.
  • A118091 (program): Start with 1 and repeatedly reverse the digits and add 46 to get the next term.
  • A118093 (program): Numbers of rooted hypermaps on the torus with n darts (darts are semi-edges in the particular case of ordinary maps).
  • A118101 (program): Decimal representation of n-th iteration of the Rule 94 elementary cellular automaton starting with a single ON cell.
  • A118102 (program): Triangle read by rows giving successive states of cellular automaton generated by “Rule 94” initiated with a single ON (black) cell.
  • A118108 (program): Decimal representation of n-th iteration of the Rule 54 elementary cellular automaton starting with a single black cell.
  • A118109 (program): Binary representation of n-th iteration of the Rule 54 elementary cellular automaton starting with a single black cell.
  • A118110 (program): State of one-dimensional cellular automaton ‘sigma’ (Rule 150): 000,001,010,011,100,101,110,111 -> 0,1,1,0,1,0,0,1 at generation n, when started with a single ON cell, regarded as a binary number.
  • A118111 (program): Binary representation of n-th iteration of the Rule 190 elementary cellular automaton starting with a single black cell.
  • A118112 (program): a(n) = binomial(3n,n) mod (n+1).
  • A118113 (program): Even Fibbinary numbers + 1; also 2*Fibbinary(n) + 1.
  • A118114 (program): a(n) = binomial(3n,n) mod((n+1)(n+2)).
  • A118115 (program): Partial sums of n concatenated n times.
  • A118117 (program): Concatenate n F(n) times.
  • A118124 (program): Triangle T(n,m) = (n+m)^2+n+m+41, read by rows.
  • A118136 (program): 2 + (2*n! mod n+1).
  • A118137 (program): Sum of decimal digits of two successive natural numbers.
  • A118138 (program): Sum of factorials of prime factors, with multiplicity.
  • A118139 (program): Numbers expressible as the sum of two triangular numbers in at least two different ways.
  • A118140 (program): Index of A005846(n) in the primes.
  • A118144 (program): Numbers of prime factors of l, where l is defined in A118534.
  • A118145 (program): Start with 1 and repeatedly reverse the digits and add 47 to get the next term.
  • A118146 (program): Start with 1 and repeatedly reverse the digits and add 49 to get the next term.
  • A118147 (program): Start with 1 and repeatedly reverse the digits and add 50 to get the next term.
  • A118148 (program): Start with 1 and repeatedly reverse the digits and add 51 to get the next term.
  • A118149 (program): Start with 1 and repeatedly reverse the digits and add 52 to get the next term.
  • A118150 (program): Start with 1 and repeatedly reverse the digits and add 53 to get the next term.
  • A118151 (program): Start with 1 and repeatedly reverse the digits and add 54 to get the next term.
  • A118152 (program): Start with 1 and repeatedly reverse the digits and add 56 to get the next term.
  • A118153 (program): Start with 1 and repeatedly reverse the digits and add 57 to get the next term.
  • A118154 (program): Start with 1 and repeatedly reverse the digits and add 58 to get the next term.
  • A118155 (program): Start with 1 and repeatedly reverse the digits and add 59 to get the next term.
  • A118156 (program): Start with 1 and repeatedly reverse the digits and add 61 to get the next term.
  • A118157 (program): Start with 1 and repeatedly reverse the digits and add 62 to get the next term.
  • A118158 (program): Start with 1 and repeatedly reverse the digits and add 63 to get the next term.
  • A118159 (program): Start with 1 and repeatedly reverse the digits and add 64 to get the next term.
  • A118160 (program): Start with 1 and repeatedly reverse the digits and add 48 to get the next term.
  • A118161 (program): Start with 1 and repeatedly reverse the digits and add 55 to get the next term.
  • A118162 (program): Start with 1 and repeatedly reverse the digits and add 60 to get the next term.
  • A118163 (program): Start with 1 and repeatedly reverse the digits and add 65 to get the next term.
  • A118170 (program): x for which abs(n^n-x!) is minimal for given n.
  • A118171 (program): Decimal representation of n-th iteration of the Rule 158 elementary cellular automaton starting with a single black cell.
  • A118173 (program): Decimal representation of n-th iteration of the Rule 188 elementary cellular automaton starting with a single black cell.
  • A118175 (program): Binary representation of n-th iteration of the Rule 220 elementary cellular automaton starting with a single black cell.
  • A118180 (program): Triangle T(n, k) = 3^(k*(n-k)), read by rows.
  • A118181 (program): Row sums of triangle A118180: a(n) = Sum_{k=0..n} (3^k)^(n-k) for n>=0.
  • A118182 (program): Antidiagonal sums of triangle A118180: a(n) = Sum_{k=0..[n/2]} (3^k)^(n-2*k) for n>=0.
  • A118185 (program): Triangle T(n,k) = 4^(k*(n-k)) for n>=k>=0, read by rows.
  • A118186 (program): Row sums of triangle A118185: a(n) = Sum_{k=0..n} 4^(k*(n-k)) for n>=0.
  • A118187 (program): Antidiagonal sums of triangle A118185: a(n) = Sum_{k=0..[n/2]} 4^(k*(n-2*k)) for n>=0.
  • A118190 (program): Triangle T(n,k) = 5^(k*(n-k)) for n >= k >= 0, read by rows.
  • A118191 (program): Row sums of triangle A118190: a(n) = Sum_{k=0..n} 5^(k*(n-k)) for n>=0.
  • A118192 (program): Antidiagonal sums of triangle A118190: a(n) = Sum_{k=0..floor(n/2)} 5^(k*(n-2*k)) for n>=0.
  • A118200 (program): Start with 1 and repeatedly reverse the digits and add 66 to get the next term.
  • A118205 (program): Euler transform of the negative of the Liouville function.
  • A118206 (program): Euler transform of the Liouville function.
  • A118207 (program): Expansion of Product_{k>=1}(1 + x^k)^lambda(k) where lambda(k) is the Liouville function, A008836.
  • A118208 (program): G.f.: A(x) = product_{k>=1}(1 + x^k)^(-lambda(k)) where lambda(k) is the Liouville function, A008836.
  • A118209 (program): Expansion of Sum_{k>=1} lambda(k) * k * x^k/(1 + x^k) where lambda(k) is the Liouville function, A008836.
  • A118210 (program): Numerators of the coefficients of (x-1)(x-2)… in the interpolating polynomial through the first n primes.
  • A118211 (program): Denominator of the coefficients of (x-1)(x-2)… in the interpolating polynomial through the first n primes.
  • A118214 (program): Start with 1 and repeatedly reverse the digits and add 67 to get the next term.
  • A118215 (program): Start with 1 and repeatedly reverse the digits and add 68 to get the next term.
  • A118216 (program): Start with 1 and repeatedly reverse the digits and add 69 to get the next term.
  • A118217 (program): Start with 1 and repeatedly reverse the digits and add 70 to get the next term.
  • A118218 (program): Start with 1 and repeatedly reverse the digits and add 71 to get the next term.
  • A118220 (program): Start with 1 and repeatedly reverse the digits and add 72 to get the next term.
  • A118221 (program): Start with 1 and repeatedly reverse the digits and add 73 to get the next term.
  • A118225 (program): Start with 1 and repeatedly reverse the digits and add 74 to get the next term.
  • A118226 (program): Start with 1 and repeatedly reverse the digits and add 76 to get the next term.
  • A118235 (program): Smallest positive number starting an interval of consecutive integers with element sum n.
  • A118237 (program): Start with 14 and repeatedly reverse the digits and add 1 to get the next term.
  • A118238 (program): Start with 15 and repeatedly reverse the digits and add 1 to get the next term.
  • A118239 (program): Engel expansion of cosh(1).
  • A118243 (program): Triangle generated from Pell polynomials.
  • A118254 (program): Start with 16 and repeatedly reverse the digits and add 1 to get the next term.
  • A118255 (program): a(1)=1, then a(n)=2*a(n-1) if n is prime, a(n)=2*a(n-1)+1 if n not prime.
  • A118256 (program): Concatenation for i=1 to n of A005171(i); also A118255 in base 2.
  • A118259 (program): Numbers of strongly carefree couples (a,b) with a,b <= n.
  • A118263 (program): a(3n) = 2^n, a(3n+1) = 3^n, a(3n+2) = 4^n.
  • A118264 (program): Coefficient of q^n in (1-q)^3/(1-3q); dimensions of the enveloping algebra of the derived free Lie algebra on 3 letters.
  • A118265 (program): Coefficient of q^n in (1-q)^4/(1-4q); dimensions of the enveloping algebra of the derived free Lie algebra on 4 letters.
  • A118266 (program): Coefficient of q^n in (1-q)^5/(1-5q); dimensions of the enveloping algebra of the derived free Lie algebra on 5 letters.
  • A118271 (program): Expansion of (9 * theta_4(q^3)^4 - theta_4(q)^4) / 8 in powers of q.
  • A118272 (program): Expansion of q^(-2/3) * (eta(q) * eta(q^3) * eta(q^6) / eta(q^2))^2 in powers of q.
  • A118273 (program): Decimal expansion of (4/3)^(3/2).
  • A118277 (program): Generalized 9-gonal (or enneagonal) numbers: m*(7*m - 5)/2 with m = 0, 1, -1, 2, -2, 3, -3, …
  • A118286 (program): Numbers n such that n == 0 (mod 4) or n == 2 (mod 12).
  • A118293 (program): Start with 18 and repeatedly reverse the digits and add 1 to get the next term.
  • A118294 (program): Start with 19 and repeatedly reverse the digits and add 1 to get the next term.
  • A118295 (program): Start with 20 and repeatedly reverse the digits and add 1 to get the next term.
  • A118296 (program): Start with 21 and repeatedly reverse the digits and add 1 to get the next term.
  • A118297 (program): Start with 22 and repeatedly reverse the digits and add 1 to get the next term.
  • A118298 (program): Start with 23 and repeatedly reverse the digits and add 1 to get the next term.
  • A118299 (program): Start with 24 and repeatedly reverse the digits and add 1 to get the next term.
  • A118301 (program): Number of partitions of n into distinct parts with largest part congruent to n modulo 2.
  • A118302 (program): Number of partitions of n into distinct parts with largest part not congruent to n modulo 2.
  • A118304 (program): Start with 25 and repeatedly reverse the digits and add 1 to get the next term.
  • A118309 (program): Decimal expansion of (1/2)*(-9*sqrt(3) + 5*Pi).
  • A118310 (program): a(n) = gcd(n,m(n)), where m(n) is the n-th nonprime positive integer (1 or composite).
  • A118312 (program): Number of squares on infinite chessboard that a knight can reach in n moves from a fixed square.
  • A118319 (program): a(n) = (highest power of 2 dividing n)th integer among those positive integers not occurring in {a(1),a(2),a(3),…,a(n-1)}.
  • A118321 (program): Decimal expansion of 8/105.
  • A118335 (program): a(n)= smallest multiple of (prime(n+1)-p(n)) which is >= prime(n+1), where prime(m) is the m-th prime.
  • A118336 (program): a(n) = greatest multiple of (p(n+1) - p(n)) which is < p(n), where p(m) is the m-th prime.
  • A118341 (program): Self-convolution square of A108447.
  • A118342 (program): Self-convolution cube of A108447.
  • A118346 (program): Central terms of pendular triangle A118345.
  • A118347 (program): Semi-diagonal (one row below central terms) of pendular triangle A118345 and equal to the self-convolution of the central terms (A118346).
  • A118348 (program): Semi-diagonal (two rows below central terms) of pendular triangle A118345 and equal to the self-convolution cube of the central terms (A118346).
  • A118351 (program): Central terms of pendular triangle A118350.
  • A118352 (program): Semi-diagonal (one row below central terms) of pendular triangle A118350 and equal to the self-convolution of the central terms (A118351).
  • A118353 (program): Semi-diagonal (two rows below central terms) of pendular triangle A118350 and equal to the self-convolution cube of the central terms (A118351).
  • A118358 (program): Records in A086793.
  • A118359 (program): Primes for which the weight as defined in A117078 is 7 and the gap as defined in A001223 is 6.
  • A118360 (program): Start with 1; repeatedly reverse the digits when the number is written in binary and add 2 to get the next term.
  • A118362 (program): a(1)=1; for n>1, a(n) = “n AND a(n-1)” if that number is positive and not already in the sequence, otherwise a(n) = “n OR a(n-1)”.
  • A118363 (program): Factorial base Niven (or Harshad) numbers: numbers that are divisible by the sum of their factorial base digits.
  • A118373 (program): Product of decimal digits of two successive natural numbers.
  • A118375 (program): Minimum over all permutations b of 1..n of sum b(i)*b^{-1}(i).
  • A118376 (program): Number of all trees of weight n, where nodes have positive integer weights and the sum of the weights of the children of a node is equal to the weight of the node.
  • A118381 (program): Largest 3-smooth number dividing n!.
  • A118384 (program): Gaussian column reduction of Hankel matrix for central Delannoy numbers.
  • A118391 (program): Numerator of sum of reciprocals of first n tetrahedral numbers A000292.
  • A118392 (program): Denominator of sum of reciprocals of first n tetrahedral numbers A000292.
  • A118393 (program): Eigenvector of triangle A059344. E.g.f.: exp( Sum_{n>=0} x^(2^n) ).
  • A118395 (program): Expansion of e.g.f. exp(x + x^3).
  • A118396 (program): Eigenvector of triangle A118394; E.g.f.: exp( Sum_{n>=0} x^(3^n) ).
  • A118402 (program): Row sums of triangle A118401.
  • A118403 (program): Unsigned row sums of triangle A118401; a(n) = A118402(n^2-n+2), where A118402 is the row sums of triangle A118400.
  • A118405 (program): Row sums of triangle A118404.
  • A118406 (program): Unsigned row sums of triangle A118404.
  • A118408 (program): Row sums of triangle A118407.
  • A118412 (program): Denominator of sum of reciprocals of first n pentatope numbers A000332.
  • A118413 (program): Triangle read by rows: T(n,k) = (2*n-1)*2^(k-1), 0<k<=n.
  • A118414 (program): a(n) = (2*n - 1) * (2^n - 1).
  • A118415 (program): a(n) = (4*n - 3) * 2^(n - 1).
  • A118416 (program): Triangle read by rows: T(n,k) = (2*k-1)*2^(n-1), 0<k<=n.
  • A118417 (program): a(n) = (2*n + 1) * 2^(n + 1).
  • A118421 (program): Number of integer solutions to n = x^2 + (2y)^2 + z(z+1)/2.
  • A118425 (program): Number of binary sequences of length n containing exactly one subsequence 001.
  • A118430 (program): Number of binary sequences of length n containing exactly one subsequence 010.
  • A118431 (program): Numerator of sum of reciprocals of first n 5-simplex numbers A000389.
  • A118432 (program): Denominator of sum of reciprocals of first n 5-simplex numbers A000389.
  • A118433 (program): Self-inverse triangle H, read by rows; a nontrivial matrix square-root of identity: H^2 = I, where H(n,k) = C(n,k)*(-1)^(floor((n+1)/2) - floor(k/2) + n - k) for n >= k >= 0.
  • A118434 (program): Row sums of self-inverse triangle A118433.
  • A118437 (program): Row sums of triangle A118435.
  • A118440 (program): Row sums of triangle A118438.
  • A118442 (program): Column 0 of triangle A118441, which is the matrix log of triangle A118435.
  • A118443 (program): Row sums of triangle A118441, which is the matrix log of triangle A118435.
  • A118444 (program): a(n) = A118443(n)/(n+1), where A118443 is the row sums of triangle A118441.
  • A118445 (program): Number of tree-rooted maps of genus 1 with n edges: rooted maps on the torus with a distinguished spanning tree.
  • A118447 (program): Number of rooted n-edge one-vertex maps on the Klein bottle (dually: one-face maps).
  • A118455 (program): a(1)=1, a(n) = Product_{k=2..n} P(k), where P(k) is the largest prime <= k.
  • A118456 (program): a(n) = Product_{k=1..n} P(k), where P(k) is the smallest prime >= k.
  • A118458 (program): Lengths of partitions into distinct parts in Abramowitz and Stegun order.
  • A118459 (program): Lengths of partitions into distinct parts in Mathematica order.
  • A118465 (program): a(n) = 8*n^3 + n.
  • A118469 (program): Triangle read by rows: a(n,m) = If(n = 1, then 1, else Prime(n) - 1 + Sum_{k=n..m} (Prime(k + 1) - Prime(k))/2.
  • A118475 (program): Write numbers from n down to 1 in decreasing order, then move the 1 to the front.
  • A118480 (program): (n-th 4k+1 prime minus n-th 4k+3 prime less two)/4.
  • A118486 (program): a(n) is the smallest prime occurring in the prime factorization of n! to an odd power.
  • A118488 (program): Squares for which the sum of the digits is a triangular number.
  • A118489 (program): Squares for which the product of the digits is a triangular number.
  • A118491 (program): Product of first n Chen primes.
  • A118498 (program): a(n) = 11*n^20 + 11*n^2 + 152821.
  • A118512 (program): Define sequence S_m by: initial term = m, reverse digits and add 1 to get next term. Entry shows S_11. This reaches a cycle of length 9 in 18 steps.
  • A118513 (program): Define sequence S_m by: initial term = m, reverse digits and add 1 to get next term. Entry shows S_13. This reaches a cycle of length 9 in 15 steps.
  • A118517 (program): Define sequence S_m by: initial term = m, reverse digits and add 3 to get next term. Entry shows S_1. This reaches a cycle of length 3 in 1 step.
  • A118518 (program): Define sequence S_m by: initial term = m, reverse digits and add 3 to get next term. Entry shows S_2. This reaches a cycle of length 6 in 3 steps.
  • A118519 (program): Define sequence S_m by: initial term = m, reverse digits and add 3 to get next term. Entry shows S_3. This reaches a cycle of length 6 in 3 steps.
  • A118520 (program): Define sequence S_m by: initial term = m, reverse digits and add 3 to get next term. Entry shows S_5. This reaches a cycle of length 6 in 2 steps.
  • A118521 (program): Define sequence S_m by: initial term = m, reverse digits and add 3 to get next term. Entry shows S_6. This reaches a cycle of length 6 in 2 steps.
  • A118525 (program): Start with 1 and repeatedly reverse the digits and add 6 to get the next term.
  • A118526 (program): Start with 1 and repeatedly reverse the digits and add 7 to get the next term.
  • A118527 (program): Start with 1 and repeatedly reverse the digits and add 8 to get the next term.
  • A118528 (program): Start with 1 and repeatedly reverse the digits and add 11 to get the next term.
  • A118529 (program): Start with 1 and repeatedly reverse the digits and add 12 to get the next term.
  • A118530 (program): Start with 1 and repeatedly reverse the digits and add 13 to get the next term.
  • A118531 (program): Start with 1 and repeatedly reverse the digits and add 14 to get the next term.
  • A118532 (program): Start with 1 and repeatedly reverse the digits and add 15 to get the next term.
  • A118533 (program): Start with 1 and repeatedly reverse the digits and add 16 to get the next term.
  • A118534 (program): a(n) is the largest k such that prime(n+1) = prime(n) + (prime(n) mod k), or 0 if no such k exists.
  • A118535 (program): Start with 1 and repeatedly reverse the digits and add 20 to get the next term.
  • A118536 (program): Start with 1 and repeatedly reverse the digits and add 36 to get the next term.
  • A118537 (program): Number of functions f: {1, 2, …, n} –> {1, 2, …, n} such that f(1) != f(2), f(2) != f(3), …, f(n-1) != f(n), f(n) != f(1).
  • A118538 (program): a(n) = A000040(n+1) - 6.
  • A118543 (program): Start with 1 and repeatedly reverse the digits and add 25 to get the next term.
  • A118547 (program): Squares which are divisible by the sum of their digits.
  • A118550 (program): a(0)=1; a(n) = a(n-1) + n if n is in the sequence, a(n) = a(n-1) + 1 if n is missing from the sequence.
  • A118557 (program): Numbers beginning with a vowel in French.
  • A118558 (program): a(n) = (2^n-1)^4 - 2.
  • A118586 (program): Numbers whose binary expansion contains group of at least two 1’s followed by a nonempty group of 0’s.
  • A118587 (program): Expansion of (17-25*x-23*x^2+133*x^3)/(1-x)^4.
  • A118589 (program): E.g.f.: A(x) = exp(x + x^2 + x^3).
  • A118593 (program): Larger component of twin prime pairs whose sum is a square.
  • A118594 (program): Palindromes in base 3 (written in base 3).
  • A118595 (program): Palindromes in base 4 (written in base 4).
  • A118596 (program): Palindromes in base 5 (written in base 5).
  • A118597 (program): Palindromes in base 6 (written in base 6).
  • A118598 (program): Palindromes in base 7 (written in base 7).
  • A118599 (program): Palindromes in base 8 (written in base 8).
  • A118600 (program): Palindromes in base 9 (written in base 9).
  • A118602 (program): Start with 1 and repeatedly reverse the digits and add 21 to get the next term.
  • A118603 (program): Start with 1 and repeatedly reverse the digits and add 22 to get the next term.
  • A118606 (program): Start with 1 and repeatedly reverse the digits and add 17 to get the next term.
  • A118607 (program): Start with 1 and repeatedly reverse the digits and add 18 to get the next term.
  • A118608 (program): Start with 1 and repeatedly reverse the digits and add 19 to get the next term.
  • A118609 (program): Start with 1 and repeatedly reverse the digits and add 23 to get the next term.
  • A118610 (program): Start with 1 and repeatedly reverse the digits and add 24 to get the next term.
  • A118613 (program): Start with 1 and repeatedly reverse the digits and add 27 to get the next term.
  • A118614 (program): Start with 1 and repeatedly reverse the digits and add 28 to get the next term.
  • A118615 (program): Start with 1 and repeatedly reverse the digits and add 26 to get the next term.
  • A118616 (program): Start with 1 and repeatedly reverse the digits and add 29 to get the next term.
  • A118617 (program): Start with 1 and repeatedly reverse the digits and add 31 to get the next term.
  • A118618 (program): Start with 1 and repeatedly reverse the digits and add 32 to get the next term.
  • A118619 (program): Start with 1 and repeatedly reverse the digits and add 33 to get the next term.
  • A118620 (program): Start with 1 and repeatedly reverse the digits and add 45 to get the next term.
  • A118631 (program): Start with 1 and repeatedly reverse the digits and add 34 to get the next term.
  • A118632 (program): Start with 1 and repeatedly reverse the digits and add 35 to get the next term.
  • A118633 (program): Start with 1 and repeatedly reverse the digits and add 37 to get the next term.
  • A118634 (program): Start with 1 and repeatedly reverse the digits and add 38 to get the next term.
  • A118635 (program): Start with 1 and repeatedly reverse the digits and add 39 to get the next term.
  • A118636 (program): Start with 1 and repeatedly reverse the digits and add 40 to get the next term.
  • A118637 (program): Start with 1 and repeatedly reverse the digits and add 30 to get the next term.
  • A118639 (program): Smallest number expressible using the next Roman-numeral symbol.
  • A118640 (program): Result of left concatenation of the next Roman-numeral symbol.
  • A118644 (program): Number of distinct (n red, n blue, n green)-bead necklaces.
  • A118645 (program): Number of binary strings of length n such that there exist three consecutive digits where at least two of them are 1’s.
  • A118646 (program): a(n) is the number of binary strings of length n such that there exists a subsequence of length 4 containing 3 or more ones.
  • A118647 (program): a(n) is the number of binary strings of length n such that no subsequence of length 4 contains 3 or more ones.
  • A118648 (program): a(n) is the number of binary strings of length n+3 such that there exists a subsequence of length 4 with 2 ones in it.
  • A118649 (program): Row sums for A106597.
  • A118654 (program): Square array T(n,k) read by antidiagonals: T(n,k) = 2^n*Fibonacci(k) - Fibonacci(k-2).
  • A118658 (program): a(n) = 2*F(n-1) = L(n) - F(n), where F(n) and L(n) are Fibonacci and Lucas numbers respectively.
  • A118659 (program): Minimum number of unit faces required to construct n unit cubes.
  • A118663 (program): Index of the least prime dividing the n-th composite number: A000720(A020639(A002808(n))).
  • A118666 (program): Binary polynomials p(x) that are fixed points of the map p(x) -> p(x+1), evaluated as polynomials over Z at x=2.
  • A118667 (program): a(n) = a(n-1)+ ((abs(2^a(n-1)*a(n-1)) mod 10).
  • A118672 (program): Numbers divisible by prime(i)^i for some i.
  • A118679 (program): Absolute value of numerator of determinant of n X n matrix with M(i,j) = i/(i+1) if i=j otherwise 1.
  • A118680 (program): Numerator of determinant of n X n matrix with M(i,j) = (i+1)/i if i=j otherwise 1.
  • A118688 (program): Semiprimes for which the sum of the digits is also a semiprime.
  • A118691 (program): Semiprimes for which the digital root is also a semiprime.
  • A118701 (program): Largest prime (or power of prime) that divides the average of twin-prime pairs.
  • A118714 (program): Determinant of n X n matrix whose diagonal contains the first n tetrahedral numbers and all other elements are 1’s.
  • A118717 (program): Sum of two consecutive semiprimes.
  • A118719 (program): Cubes for which the digital root is also a cube.
  • A118726 (program): a(n)=sum(k=0,n,F(n+k)*binomial(n+k,k)) where F=A000045.
  • A118729 (program): Infinite square array which contains the 8 numbers 4*r^2 - 3*r, 4*r^2 - 2*r, …, 4*r^2 + 4*r in row r.
  • A118730 (program): Numbers n such that 2^n has even digit sum.
  • A118731 (program): Numbers n such that 2^n has odd digit sum.
  • A118732 (program): Numbers n such that 3^n has odd digit sum.
  • A118733 (program): Numbers n such that 3^n has even digit sum.
  • A118736 (program): Number of zeros in binary expansion of 3^n.
  • A118737 (program): Number of zeros in binary expansion of 5^n.
  • A118738 (program): Number of ones in binary expansion of 5^n.
  • A118742 (program): Numbers n for which the expression n!/(n+1) is an integer.
  • A118745 (program): Triangle of coefficients of polynomials giving the n-anacci constants.
  • A118747 (program): a(n) = product[k=1..n] P(k), where P(k) is the largest prime <= 2*k. a(n) = product[k=1..n] A060308(k).
  • A118748 (program): a(n) = product[k=1..n] P(k), where P(k) is the smallest prime >= 2*k.
  • A118749 (program): Largest prime <= 3*n.
  • A118750 (program): a(n) = product[k=1..n] P(k), where P(k) is the largest prime <= 3*k. a(n) = product[k=1..n] A118749(k).
  • A118751 (program): Smallest prime >= 3*n.
  • A118752 (program): a(n) = product[k=0..n] P(k), where P(k) is the smallest prime > 3*n. a(n) = product[k=0..n] A118751(k).
  • A118753 (program): First prime after 4n. Smallest prime >= 4*n. Bisection of A060264.
  • A118754 (program): Smallest prime >= 5*n.
  • A118755 (program): Smallest prime >= 6*n.
  • A118759 (program): A118757(A118757(n)).
  • A118760 (program): A118758(A118758(n)).
  • A118767 (program): Fixed points of permutations A118763, A118764, A118765 and A118766.
  • A118777 (program): a(0) = 1; n > 0: a(n) = a(n-1) + d, d = -/+1 if n is prime/nonprime.
  • A118800 (program): Triangle read by rows: T satisfies the matrix products: C*T*C = T^-1 and T*C*T = C^-1, where C is Pascal’s triangle.
  • A118801 (program): Triangle T that satisfies the matrix products: C*[T^-1]*C = T and T*[C^-1]*T = C, where C is Pascal’s triangle.
  • A118802 (program): Row squared sums of triangle A118801: a(n) = Sum_{k=0..n} A118801(n,k)^2.
  • A118816 (program): A fractal sequence based upon powers of 3.
  • A118819 (program): Start with 1 and repeatedly place the first digit at the end of the number and add 6.
  • A118821 (program): 2-adic continued fraction of zero, where a(n) = 2 if n is odd, -A006519(n/2) otherwise.
  • A118822 (program): Numerators of the convergents of the 2-adic continued fraction of zero given by A118821.
  • A118823 (program): Denominators of the convergents of the 2-adic continued fraction of zero given by A118821.
  • A118824 (program): 2-adic continued fraction of zero, where a(n) = -2 if n is odd, A006519(n/2) otherwise.
  • A118825 (program): Numerators of the convergents of the 2-adic continued fraction of zero given by A118824.
  • A118826 (program): Denominators of the convergents of the 2-adic continued fraction of zero given by A118824.
  • A118827 (program): 2-adic continued fraction of zero, where a(n) = 1 if n is odd, otherwise -2*A006519(n/2).
  • A118828 (program): Numerators of the convergents of the 2-adic continued fraction of zero given by A118827.
  • A118829 (program): Denominators of the convergents of the 2-adic continued fraction of zero given by A118827.
  • A118830 (program): 2-adic continued fraction of zero, where a(n) = -1 if n is odd, 2*A006519(n/2) otherwise.
  • A118831 (program): Numerators of the convergents of the 2-adic continued fraction of zero given by A118830.
  • A118832 (program): Denominators of the convergents of the 2-adic continued fraction of zero given by A118830.
  • A118835 (program): Numerators of n-th convergent to continued fraction with semiprime terms.
  • A118836 (program): Denominators of n-th convergent to continued fraction with semiprime terms.
  • A118870 (program): Number of binary sequences of length n with no subsequence 0101.
  • A118879 (program): Let T(S,Q) be the sequence obtaining by starting with S and repeatedly reversing the digits and adding Q to get the next term. This is T(1016,5), the first S for which T(S,5) reaches a cycle of length 36.
  • A118880 (program): a(n) is the cube of the sum of digits of n.
  • A118881 (program): Square of sum of decimal digits of n.
  • A118882 (program): Numbers which are the sum of two squares in two or more different ways.
  • A118885 (program): Number of binary sequences of length n containing exactly one subsequence 0011.
  • A118886 (program): Numbers expressible as x^2 + x*y + y^2, 0 <= x <= y, in 2 or more ways.
  • A118892 (program): Number of binary sequences of length n containing exactly one subsequence 0110.
  • A118898 (program): Number of binary sequences of length n containing exactly one subsequence 0000.
  • A118904 (program): Perimeters of rectangles with integer sides and diagonal.
  • A118905 (program): Sum of legs of Pythagorean triangles (without multiple entries).
  • A118916 (program): Number of inequivalent primes in ring of integers Z[sqrt(2)] of successive norms (indexed by A055029).
  • A118917 (program): Number of inequivalent primes in ring of integers Z[sqrt(2)] with absolute value of norm = n.
  • A118919 (program): Triangle read by rows: T(n,k) is the number of Grand Dyck paths of semilength n that cross downwards the x-axis k times. (A Grand Dyck path of semilength n is a path in the half-plane x>=0, starting at (0,0), ending at (2n,0) and consisting of steps u=(1,1) and d=(1,-1)).
  • A118920 (program): Triangle read by rows: T(n,k) is the number of Grand Dyck paths of semilength n that cross the x-axis k times (n>=1, k>=0).
  • A118921 (program): Triangle read by rows: T(n,k) is the number of Grand Dyck paths of semilength n having first return to the x-axis at (2k,0) (n,k >= 1). (A Grand Dyck path of semilength n is a path in the half-plane x >= 0, starting at (0,0), ending at (2n,0) and consisting of steps u=(1,1) and d=(1,-1)).
  • A118922 (program): Primes for which the weight as defined in A117078 is 9 and the gap as defined in A001223 is 8.
  • A118923 (program): Triangle T(n,k) built by placing T(n,0)=A000012(n) in the left edge, T(n,n)=A079978(n) on the right edge and filling the body with the Pascal recurrence T(n,k) = T(n-1,k) + T(n-1,k-1).
  • A118930 (program): E.g.f.: A(x) = exp( Sum_{n>=0} x^(2^n)/2^(2^n-1) ).
  • A118934 (program): E.g.f.: exp(x + x^4/4).
  • A118939 (program): Primes p such that (p^2+3)/4 is prime.
  • A118940 (program): Primes p such that (p^2+7)/8 is prime.
  • A118941 (program): Primes p such that (p^2-5)/4 is prime.
  • A118944 (program): n-th (starting from the right) decimal digit of 11^n.
  • A118946 (program): n-th (starting from the right) decimal digit of 12^n.
  • A118948 (program): n-th (starting from the right) decimal digit of 13^n.
  • A118950 (program): Numbers containing at least one prime digit.
  • A118951 (program): Numbers containing at least one composite digit.
  • A118952 (program): Characteristic function of numbers that can be written as p+2^k, where p is prime and p less than 2^k (A118957).
  • A118953 (program): Number of ways to write the n-th prime as 2^k + p, where p is prime and p < 2^k.
  • A118954 (program): Numbers that cannot be written as 2^k + prime.
  • A118955 (program): Numbers of the form 2^k + prime.
  • A118956 (program): Numbers that cannot be written as 2^k + p with p prime < 2^k.
  • A118957 (program): Numbers of the form 2^k + p, where p is a prime less than 2^k.
  • A118958 (program): Primes that cannot be written as 2^k + p with p prime < 2^k.
  • A118963 (program): Triangle read by rows: T(n,k) is the number of Grand Dyck paths of semilength n that have k double rises (n >= 1, k >= 0).
  • A118966 (program): a(n) = (n+1)/2 if n occurs among the first n-1 terms of the sequence, otherwise a(n) = 2*n - 1.
  • A118967 (program): If n doesn’t occur among the first (n-1) terms of the sequence, then a(n) = 2n. If n occurs among the first (n-1) terms of the sequence, then a(n) = n/2.
  • A118968 (program): a(4n+k)=(k+1)*binomial(5n+k,n)/(4n+k+1), k=0,..3.
  • A118969 (program): a(n) = 2*binomial(5*n+1,n)/(4*n+2).
  • A118970 (program): a(n) = 3*binomial(5n+2,n)/(4n+3).
  • A118971 (program): a(n) = binomial(5*n+3,n)/(n+1).
  • A118973 (program): Number of hill-free Dyck paths of semilength n+2 and having length of first descent equal to 2 (a hill in a Dyck path is a peak at level 1).
  • A118974 (program): Sum of the lengths of the first descents in all hill-free Dyck paths of semilength n (a hill in a Dyck path is a peak at level 1).
  • A118977 (program): a(0)=0, a(1)=1; a(2^i+j) = a(j) + a(j+1) for 0 <= j < 2^i.
  • A118978 (program): Array read by antidiagonals: the n-th row contains the binomial transform of row n-1 of A014410.
  • A118979 (program): O.g.f: -12*x^3/(-1+x)/(-1+2*x)/(-1+3*x) = -2-2/(-1+3*x)-6/(-1+x)+6/(-1+2*x) .
  • A118981 (program): Triangle read by rows: T(n,k) = abs( A104509(n-1,n-k) ).
  • A119002 (program): Maximal determinant of real n X n symmetric (0,1) matrices.
  • A119012 (program): Number of valleys strictly above the x-axis in all hill-free Dyck paths of semilength n (a hill in a Dyck path is a peak at level 1).
  • A119016 (program): Numerators of “Farey fraction” approximations to sqrt(2).
  • A119029 (program): Numerator of Sum_{k=1..n} n^(k-1)/k!.
  • A119030 (program): Difference between numerator and denominator of the sum of all matrix elements of n X n Hilbert matrix M(i,j)=1/(i+j-1) (i,j = 1..n), A117731[n] - A117664[n].
  • A119031 (program): Add and Reverse: a(n) = the reversal of (a(n-1)+d), case a(1)=1 and d=4.
  • A119032 (program): a(n+2)=18a(n+1)-a(n)+8.
  • A119245 (program): Triangle, read by rows, defined by: T(n,k) = (4*k+1)*binomial(2*n+1, n-2*k)/(2*n+1) for n >= 2*k >= 0.
  • A119248 (program): a(n) is the difference between denominator and numerator of the n-th alternating harmonic number Sum_{k=1..n} (-1)^(k+1)/k = A058313(n)/A058312(n).
  • A119251 (program): Positive integers each with exactly 1 unitary prime divisor (i.e., n is included if and only if A056169(n) = 1).
  • A119257 (program): A permutation of the positive integers formed by reversing the order of the composites within each run of composites (1 and primes are left alone).
  • A119258 (program): Triangle read by rows: T(n,0) = T(n,n) = 1 and for 0<k<n: T(n,k) = 2*T(n-1, k-1) + T(n-1,k).
  • A119259 (program): Central terms of the triangle in A119258.
  • A119260 (program): Numbers with even decimal digits in increasing order.
  • A119261 (program): Numbers with even decimal digits in decreasing order.
  • A119262 (program): Number of B-trees of order infinity with n leaves, where a(n) = Sum_{k=1..floor(n/2)} a(k)*C(n-k-1,n-2*k) for n >= 2, with a(0)=0, a(1)=1.
  • A119272 (program): Product of numerator and denominator in Stern-Brocot tree.
  • A119274 (program): Triangle of coefficients of numerators in Padé approximation to exp(x).
  • A119275 (program): Inverse of triangle related to Padé approximation of exp(x).
  • A119281 (program): Number of counting rods to represent n in the ancient Chinese rod numeral system.
  • A119282 (program): Alternating sum of the first n Fibonacci numbers.
  • A119283 (program): Alternating sum of the squares of the first n Fibonacci numbers.
  • A119284 (program): Alternating sum of the cubes of the first n Fibonacci numbers.
  • A119285 (program): Alternating sum of the fourth powers of the first n Fibonacci numbers.
  • A119286 (program): Alternating sum of the fifth powers of the first n Fibonacci numbers.
  • A119287 (program): Alternating sum of the sixth powers of the first n Fibonacci numbers.
  • A119288 (program): a(n) is the second smallest prime factor of n, or 1 if n is a prime power.
  • A119301 (program): Number triangle binomial(3n-k,n-k).
  • A119302 (program): Inverse of number triangle binomial(3n-k,n-k).
  • A119303 (program): Expansion of (1 - 3x)/(1 - x + 2x^2 - x^3).
  • A119304 (program): Triangle read by rows: T(n,k) = binomial(4n-k,n-k), 0 <= k <= n.
  • A119305 (program): Riordan array (1-4x, x(1-x)^3).
  • A119306 (program): Expansion of (1-4*x)/(1-x*(1-x)^3).
  • A119307 (program): Number triangle T(n,k)=sum{j=0..n, C(j,k)C(j,n-k)}.
  • A119308 (program): Triangle for first differences of Catalan numbers.
  • A119309 (program): a(n) = binomial(2*n,n) * 6^n.
  • A119313 (program): Numbers with a prime as third-smallest divisor.
  • A119314 (program): Complement of A119313.
  • A119315 (program): Numbers with composite numbers as third divisors.
  • A119316 (program): Complement of A119315.
  • A119327 (program): Expansion of (1-4x+12x^2-16x^3+8x^4)/(1-x)^5.
  • A119328 (program): Number triangle T(n,k)=sum{i=0..n, (-1)^(n-i)*C(n,i)*sum{j=0..i-k, C(k,2j)*C(i-k,2j)}}.
  • A119330 (program): Expansion of (1-x)^2/((1-x)^4-2x^4).
  • A119332 (program): Expansion of (1+x)/(1-2x^4).
  • A119336 (program): Expansion of (1-x)^4/((1-x)^6 - x^6).
  • A119345 (program): Numbers having exactly one representation as sum of two triangular numbers.
  • A119346 (program): Sequence of nim-values for the game in which two players alternately cut off one inch or root two inches from a piece of string of length n. Player who runs out of string loses.
  • A119352 (program): Smallest base b > 1 such that n in base b uses no digit b-1.
  • A119356 (program): Square pyramidal number (A000330) n(n+1)(2n+1)/6 is squarefree.
  • A119358 (program): Number of n-element subsets of [2n] having an even sum.
  • A119359 (program): Central coefficients of number triangle A119326.
  • A119360 (program): a(n) = Sum_{i=1..n, j=1..n} i! mod j.
  • A119363 (program): a(n) = Sum_{k=0..n} C(n,3k)^2.
  • A119364 (program): Central coefficients of number triangle A119335.
  • A119365 (program): Generalized Catalan numbers for triangle A119335.
  • A119366 (program): Number of rooted planar n-trees whose number of leaves is equal to 1 modulo 3.
  • A119367 (program): Number of rooted planar n-trees whose number of leaves is equal to 2 modulo 3.
  • A119370 (program): G.f. satisfies: A(x) = 1 + x*A(x)^2 + x^2*(A(x)^2 - A(x)).
  • A119380 (program): Remainder when the integer part of e^n is divided by the n-th prime number.
  • A119384 (program): Ten’s complement of the factorials.
  • A119387 (program): a(n) is the number of binary digits (1’s and nonleading 0’s) which remain unchanged in their positions when n and (n+1) are written in binary.
  • A119389 (program): Numerator of (1^2/n + 2^2/(n-1) + … + k^2/(n-k+1) + … + (n-1)^2/2 + n^2/1).
  • A119394 (program): a(n) = Sum_{k=0..n} (-1)^(n-k)*(n!/k!)^2*binomial(n-1,k-1).
  • A119395 (program): Number of nonnegative integer solutions to the equation x^2 + 3y^2 = n.
  • A119399 (program): a(n) = Sum_{k=0..n} (n!/k!)^2*binomial(n-1,k-1).
  • A119400 (program): a(n) = Sum_{k=0..n} (n!/k!)^2*binomial(n,k).
  • A119401 (program): a(n) = Sum_{k=0..n} (-1)^(n-k)*(n!/k!)^2*binomial(n,k).
  • A119406 (program): Years in which there are five Sundays in the month of February.
  • A119407 (program): Number of nonempty subsets of {1,2,…,n} with no gap of length greater than 4 (a set S has a gap of length d if a and b are in S but no x with a < x < b is in S, where b-a=d).
  • A119408 (program): Decimal equivalent of the binary string generated by the n X n identity matrix.
  • A119409 (program): Numbers n such that 235*n + 1 is prime.
  • A119411 (program): Product of the first prime(n) primes.
  • A119412 (program): a(n) = n*(n+11).
  • A119413 (program): 16*n-12.
  • A119416 (program): n * (smallest prime greater than largest prime factor of n).
  • A119428 (program): G.f.: A(x) = 1 + Sum_{n>=0} (-1)^n* Sum_{k=1..4} x^(5n+k)/(1-x^(5n+k)).
  • A119440 (program): Triangle read by rows: T(n,k) is the number of binary sequences of length n that start with exactly k 01’s (0 <= k <= floor(n/2)).
  • A119449 (program): Primes with even digit sum.
  • A119450 (program): Primes with odd digit sum.
  • A119454 (program): Start with 34 and repeatedly reverse the digits and add 16 to get the next term.
  • A119455 (program): Start with 1027 and repeatedly reverse the digits and add 16 to get the next term.
  • A119457 (program): Triangle read by rows: T(n,1)=n, T(n,2)=(n-1)*2 for n>1 and T(n,k)=T(n-1,k-1)+T(n-2,k-2) for 2<k<=n.
  • A119462 (program): Triangle read by rows: T(n,k) is the number of circular binary words of length n having k occurrences of 01 (0 <= k <= floor(n/2)).
  • A119467 (program): A masked Pascal triangle.
  • A119468 (program): Triangle read by rows: T(n,k) = Sum_{j=0..n-k} binomial(n,2j)*binomial(n-2j,k).
  • A119473 (program): Triangle read by rows: T(n,k) is number of binary words of length n and having k runs of 0’s of odd length, 0 <= k <= ceiling(n/2). (A run of 0’s is a subsequence of consecutive 0’s of maximal length.)
  • A119476 (program): a(1)=1, a(n)=a((n+1)/2)+1 if n is odd, a(n)=a(n/2)+2 if n is even.
  • A119477 (program): a(1)=1, a(n) = a((n+1)/2) + 2 if n is odd, a(n) = a(n/2) + 1 if n is even.
  • A119485 (program): Number of children for which any subset can be generated by a counting-out game.
  • A119486 (program): Numbers of children for which there is a subset which cannot be generated by a counting-out game.
  • A119487 (program): Primes of the form i*prime(i) + (i+1)*prime(i+1).
  • A119489 (program): Sum of the absolute values in row n of A118686.
  • A119490 (program): Sum of the absolute values in row n of A118687.
  • A119502 (program): Triangle read by rows, T(n,k) = (n-k)!, for n>=0 and 0<=k<=n.
  • A119505 (program): The Pi-th digit of Pi where the digit value of 0 is interpreted as decimal 10.
  • A119506 (program): The e-th digit of e where the digit value of 0 is interpreted as decimal 10.
  • A119522 (program): Determinant of n X n matrix of first n^2 nonzero terms of triangular numbers.
  • A119536 (program): 3*n^3 + 3*n.
  • A119538 (program): Fixed point of the morphism a -> {a, a + 1, 2a + 2} beginning with 0.
  • A119548 (program): 10-gonal numbers which are divisible by the sum of their digits.
  • A119549 (program): Binomial( Catalan(n), 4).
  • A119552 (program): Binomial(binomial(2*n,n)*n,n).
  • A119557 (program): a(1)=0,a(2)=0,a(3)=1 then a(n)=abs(a(n-1)-a(n-2))-a(n-3).
  • A119558 (program): a(1)=0,a(2)=0,a(3)=1 then a(n)=abs(a(n-1)-a(n-2))+(-1)^n*a(n-3).
  • A119565 (program): a(0)=1, a(1)=2, a(2)=3, a(3)=5, a(4)=7, a(5)=10; a(n) = floor(a(n-1) + 1 + a(n-2)/6) for n>=6.
  • A119570 (program): Primes p such that p^2 - p - 1 is not prime.
  • A119574 (program): a(n) = binomial(2*n,n)*(n+2)^2/(n+1).
  • A119575 (program): Binomial(2*n,n)*(n+3)^2/(n+1).
  • A119576 (program): (n+n^2+n^3)*(binomial(2*n,n)).
  • A119577 (program): (n+n^2+n^3)*(binomial(2*n,n))/2.
  • A119578 (program): a(n) = (n + n^2)*binomial(2*n,n)/2.
  • A119579 (program): a(n) = (n + n^2)*(binomial(2*n, n)).
  • A119580 (program): a(n) = (n^2+n^3)*binomial(2*n,n).
  • A119581 (program): a(n) = (2*n+n^2)*(binomial(2*n,n))/2.
  • A119582 (program): a(n) = (n^2+n^3)*(binomial(2*n,n))/2.
  • A119584 (program): Sum{k=1 to phi(n)-1} t(n,k)*t(n,k+1), where t(n,k) is the k-th positive integer which is coprime to n and phi(n) is the number of positive integers which are <= n and are coprime to n.
  • A119587 (program): 2^n + 1 - 2*Fibonacci(n+1).
  • A119592 (program): a(0)=1, a(1)=2, a(2)=3, a(3)=5, a(4)=7, a(5)=10; a(n) = floor(a(n-1) + 1 + (a(n-2) + 1)/6) for n>=6.
  • A119600 (program): a(n) = 4*Product_{i=1..n-1} (3^i+1)^2.
  • A119605 (program): Numbers n such that all groups of order n are Con-Cos groups.
  • A119608 (program): Let b(1)=0, b(2)= 1. b(2^m +k) = (b(2^m+1-k) + b(k))/2, 1 <= k <= 2^m, m >= 0. a(n) is numerator of b(n).
  • A119609 (program): p^2-p-1 that is not prime, where p is prime.
  • A119610 (program): Number of cases in which the first player is killed in a Russian roulette game where 5 players use a gun with n chambers and the number of bullets can be from 1 to n. Players do not rotate the cylinder after the game starts.
  • A119613 (program): Numbers n such that the difference between the largest distinct prime divisor and the smallest distinct prime divisor is a prime.
  • A119614 (program): a(1)=1. a(2^m +k) = a(2^m + 1 - k)*a(k) + 1, where 1 <= k <= 2^m, m>=0.
  • A119616 (program): Second elementary symmetric function of divisors of n.
  • A119617 (program): Integers of the form c(n)/b(n) where c(n+1)=c(n)+(n+1)^4 with c(0)=1 and b(n+1)=b(n)+(n+1)^2 with b(0)=1.
  • A119619 (program): a(n) = Product_{i=1..n} i / gcd(i,n).
  • A119620 (program): Number of partitions of floor(3n/2) into n parts each from {1,2,…,n}.
  • A119622 (program): Numbers n such that no group of order n is a Con-Cos group.
  • A119623 (program): Composite numbers for which the second elementary symmetric function of divisors (s2) is prime.
  • A119625 (program): Start with 17 and repeatedly reverse the digits and add 1 to get the next term.
  • A119633 (program): a(n) = (A046717(n))^3.
  • A119634 (program): a(n) = lcm(1,…,2n+2)/2.
  • A119635 (program): a(n) = n*(1 + n^2)*2^n.
  • A119647 (program): Fixed point of the morphism 1->{1,2}, 2->{1,3}, 3->{1}.
  • A119651 (program): Number of different values of exactly n standard American coins (pennies, nickels, dimes and quarters).
  • A119652 (program): Number of different values of <= n standard American coins (pennies, nickels, dimes and quarters).
  • A119653 (program): Denominator of BernoulliB[2p] divided by 6, where p=Prime[n].
  • A119658 (program): Area of consecutive Prime-Indexed Prime rectangles.
  • A119664 (program): Sign in term (2p +/- 1) for triangular numbers of the form p * (2p +/- 1), where the two factors are both primes.
  • A119671 (program): a(0)=1. a(2^m +k) = a(m) + k, where 0 <= k <= 2^m -1, m >= 0.
  • A119672 (program): Number of prime factors (with multiplicity) of n^4 + 3*n^2 + 1 (A057721).
  • A119673 (program): T(n, k) = 3*T(n-1, k-1) + T(n-1, k) for k < n and T(n, n) = 1, T(n, k) = 0, if k < 0 or k > n; triangle read by rows.
  • A119674 (program): Number of states of the minimal deterministic finite automaton that accepts binary strings that represent numbers that are divisible by n.
  • A119675 (program): Natural numbers n such that the number of prime factors of n (counted with multiplicity) is a Fibonacci number.
  • A119677 (program): a(n) is the number of complete squares that fit inside the circle with radius n, drawn on squared paper.
  • A119681 (program): Odd numbers n such that 2n-1 is prime.
  • A119682 (program): Numerator of Sum_{k=1..n} (-1)^(k+1)/k^2.
  • A119685 (program): G.f. satisfies: A(x) = x + A(x^2/(1-x)^2).
  • A119688 (program): a(n) = n!! mod (n+1).
  • A119689 (program): Numbers n such that the sum of the largest distinct prime divisor and the smallest distinct prime divisor is a prime.
  • A119690 (program): n! mod n*(n+1)/2.
  • A119692 (program): a(n) = binomial(2*n,n) * Fibonacci(n).
  • A119693 (program): a(n) = binomial(2*n,n) * Fibonacci(n)/2.
  • A119694 (program): a(n) = Fibonacci(n) * Catalan(n).
  • A119695 (program): Fib(n)*n^2*(binomial(2*n, n))^2/(n+1).
  • A119696 (program): Fib(n)*n^3*(binomial(2*n, n))^2/(n+1).
  • A119697 (program): a(n) = Fibonacci(n)*n*binomial(2*n,n)/(n+1).
  • A119698 (program): n^3*binomial(2*n, n)*Fibonacci(n)^2.
  • A119699 (program): n^2*binomial(2*n, n)*Fibonacci(n)^2.
  • A119700 (program): n*binomial(2*n, n)*Fibonacci(n)^2.
  • A119701 (program): n*binomial(2*n, n)*Fibonacci(n).
  • A119702 (program): n^2*binomial(2*n, n)*Fibonacci(n).
  • A119703 (program): n^3*binomial(2*n, n)*Fibonacci(n).
  • A119707 (program): Number of distinct primes appearing in all partitions of n into prime parts.
  • A119713 (program): First differences are 2, 5, 5, 9, 9, 9, 14, 14, 14, 14, …, that is, A000096 with m-th term repeated m times (m>=1).
  • A119721 (program): Numbers n such that 4*n^4 + 7 is prime.
  • A119733 (program): Offsets of the terms of the nodes of the reverse Collatz function.
  • A119737 (program): a(n) = Sum{k=1..n} Fibonacci(floor(n/k)).
  • A119741 (program): A008279, with the first and last of each row removed.
  • A119743 (program): Triangle read by rows: row n gives number of matchings of size 0<=k<=n (edges) in the complete graph on 2*n >= 2 vertices.
  • A119746 (program): Sum of previous term and preceding relatively prime terms.
  • A119749 (program): Number of compositions of n into odd blocks with one element in each block distinguished.
  • A119750 (program): Let k=binomial(n-1,2); a(n) = n*(n-1)*k!/(k-n+1)! for n >= 4, with a(1)=a(2)=a(3)=0.
  • A119758 (program): Numerator of Sum_{k=1..n} k^n/n^k.
  • A119771 (program): Product of n^2 and n-th tetrahedral number: n^3*(n+1)*(n+2)/6.
  • A119785 (program): Numerator of the product of the n-th square pyramidal number and the n-th generalized harmonic number in power 2.
  • A119786 (program): Numerator of the product of the n-th triangular number and the n-th harmonic number.
  • A119787 (program): Numerator of the product of n and the n-th alternating harmonic number, Sum_{k=1..n} (-1)^(k+1)/k.
  • A119789 (program): Fibonacci Logarithms used to get a triangular array.
  • A119791 (program): a(1) = 1, a(n) = number of divisors of n*a(n-1).
  • A119795 (program): a(1) = a(2) = 1. a(n) = a(n-2) + (largest power of 2 dividing a(n-1)).
  • A119800 (program): Array of coordination sequences for cubic lattices (rows) and of numbers of L1 forms in cubic lattices (columns) (array read by antidiagonals).
  • A119826 (program): Number of ternary words of length n with no 000’s.
  • A119827 (program): Number of ternary words of length n with exactly one 000.
  • A119828 (program): Number triangle T(n,k)=(2n)!/(2k)!.
  • A119829 (program): Diagonal sum of number triangle A119828.
  • A119830 (program): Bi-diagonal inverse of (2n)!/(2k)!.
  • A119831 (program): Number triangle (3n)!/(3k)!.
  • A119837 (program): a(n)=(2n)!/n!-(2n)!/(n-1)!.
  • A119852 (program): Number of ternary words with exactly one 012.
  • A119863 (program): Numbers k such that k^3 + k^2 + 1 is prime.
  • A119874 (program): Sizes of successive clusters in f.c.c. lattice centered at an octahedral hole.
  • A119879 (program): Exponential Riordan array (sech(x),x).
  • A119880 (program): E.g.f. exp(2x)*sech(x).
  • A119881 (program): Expansion of e.g.f. exp(3*x)*sech(x).
  • A119882 (program): E.g.f.: (1+x)*sech(x).
  • A119883 (program): Expansion of E.g.f. (1 + 2*x + x^2/2) * sech(x).
  • A119884 (program): E.g.f. sech(x)/(1-x).
  • A119899 (program): Integers i such that bigomega(i) (A001222) and tau(i) (A000005) are both even.
  • A119900 (program): Triangle read by rows: T(n,k) is the number of binary words of length n with k strictly increasing runs, for 0<=k<=n.
  • A119901 (program): Difference between two consecutive squares enclosing 3^(2n+1).
  • A119905 (program): Numbers k such that gcd(k, R_k) = 1, where R_k is the repunit (10^k -1)/9 = A002275(k).
  • A119907 (program): Number of partitions of n such that if k is the largest part, then k-2 occurs as a part.
  • A119910 (program): Period 6: repeat [1, 3, 2, -1, -3, -2].
  • A119912 (program): Scan A076368, discard any nonprimes.
  • A119913 (program): Number of directed simple cycles in the complete graph K_n.
  • A119915 (program): Number of ternary words of length n and having exactly one run of 0’s of odd length.
  • A119916 (program): Number of runs of 0’s of odd length in all ternary words of length n.
  • A119917 (program): Number of rationals in [0, 1) consisting just of repeating bits of period at most n.
  • A119919 (program): Table read by antidiagonals: number of rationals in [0, 1) having at most n preperiodic bits, then at most k periodic bits (read up antidiagonals).
  • A119920 (program): Number of rationals in [0, 1) having exactly n preperiodic bits, then exactly n periodic bits.
  • A119921 (program): Number of rationals in [0, 1) having at most n preperiodic bits, then at most n periodic bits.
  • A119930 (program): Sum of the numbers of the matrix A111490 along a boustrophedon path: a11, a11+a12, a11+a12+a21, etc.
  • A119931 (program): Sum of the numbers of the matrix A111490 along a boustrophedon path: a11, a11+a21, a11+a21+a21, etc.
  • A119936 (program): Least common multiple (LCM) of denominators of the rows of the triangle of rationals A119935/A119932.
  • A119938 (program): Row sums of triangle A119937.
  • A119939 (program): Main diagonal of triangle A119937.
  • A119944 (program): First differences of A003418(n) = lcm(1..n).
  • A119951 (program): Numerators of partial sums of a convergent series with value 4, involving scaled Catalan numbers A000108.
  • A119956 (program): Numbers n such that n^3+1=p*q*r where p,q,r are distinct primes.
  • A119959 (program): p^2-p+1 central polygonal numbers with prime indices A002061(prime(n)).
  • A119963 (program): Triangle T(n,k), 0 <= k <= n, read by rows, with T(2n,2k) = T(2n+1,2k) = T(2n+1,2k+1) = T(2n+2,2k+1) = binomial(n,k).
  • A119967 (program): A transform of the central binomial coefficients C(n,floor(n/2)).
  • A119968 (program): Binomial transform of Fredholm-Rueppel sequence.
  • A119969 (program): Sum{k>=0, C(2^k-1,n-2*(2^k-1))}.
  • A119970 (program): Binomial transform of A119969.
  • A119971 (program): G.f. sum{k>=0, (x^2/(1-x)^3)^(2^k-1)}.
  • A119972 (program): Flag n when the first difference of the decimal encoding of the Gray code is negative.
  • A119975 (program): E.g.f. exp(x)*(Bessel_I(0,2*sqrt(2)x) + Bessel_I(1,2*sqrt(2)x)/sqrt(2)).
  • A119976 (program): E.g.f. exp(2x)*(Bessel_I(0,2*sqrt(2)x) + Bessel_I(1,2*sqrt(2)x)/sqrt(2)).
  • A119979 (program): a(n+1)=(2^a(n) mod n)+1, with a(0)=1.
  • A119992 (program): a(n) = n-th positive integer which is coprime to n!.
  • A119993 (program): a(n) = n-th prime from among those primes which are coprime to n.
  • A119996 (program): Numerator of Sum_{k=1..n} 1/(Fibonacci(k)*Fibonacci(k+2)).
  • A119997 (program): Sum of all matrix elements of n X n matrix M[i,j] = (-1)^(i+j)*Fibonacci[i+j-1].
  • A120007 (program): Mobius transform of sum of prime factors of n with multiplicity (A001414).
  • A120009 (program): G.f.: A(x) = (x-x^2) o x/(1-x) o (1-sqrt(1-4*x))/2, a composition of functions involving the Catalan function and its inverse.
  • A120010 (program): G.f.: A(x) = (1-sqrt(1-4*x))/2 o x/(1-x) o (x-x^2), a composition of functions involving the Catalan function and its inverse.
  • A120011 (program): Decimal expansion of sqrt(3)/4.
  • A120012 (program): The third self-composition of A120009; g.f.: A(x) = G(G(G(x))), where G(x) = g.f. of A120009.
  • A120017 (program): The 2nd self-composition of A120010; g.f.: A(x) = G(G(x)), where G(x) = g.f. of A120010.
  • A120018 (program): The third self-composition of A120010; g.f.: A(x) = G(G(G(x))), where G(x) = g.f. of A120010.
  • A120027 (program): Triangle, generated from (3^(n-k) * 5^k) table.
  • A120030 (program): Expansion of theta_4(q)^2*theta_4(q^2)^4 in powers of q.
  • A120031 (program): Numerators of reduced forms of fractions obtained by performing the first n divisions shown below.
  • A120032 (program): Denominators associated with A120031.
  • A120054 (program): a(n) = binomial(n+3,4)*4^4.
  • A120058 (program): Coefficients for obtaining A120057 from Bell numbers.
  • A120068 (program): Numbers n such that n-th prime + 1 is squarefree.
  • A120069 (program): Denominators of partial sums of a convergent series involving scaled Catalan numbers A000108.
  • A120070 (program): Triangle of numbers used to compute the frequencies of the spectral lines of the hydrogen atom.
  • A120071 (program): a(n) = n*(n+20).
  • A120072 (program): Numerator triangle for hydrogen spectrum rationals.
  • A120074 (program): Row sums of triangle A120072 (numerator triangle for H atom spectrum).
  • A120076 (program): Numerators of row sums of rational triangle A120072/A120073.
  • A120077 (program): Denominators of row sums of rational triangle A120072/A120073.
  • A120080 (program): Numerators of expansion of original Debye function D(3,x).
  • A120081 (program): Denominators of expansion for original Debye function (n=3).
  • A120082 (program): Numerators of expansion for Debye function for n=1: D(1,x).
  • A120083 (program): Denominators of expansion for Debye function for n=1: D(1,x).
  • A120084 (program): Numerators of expansion for Debye function for n=2: D(2,x).
  • A120085 (program): Denominators of expansion for Debye function for n=2: D(2,x).
  • A120086 (program): Numerators of expansion of Debye function for n=4: D(4,x).
  • A120088 (program): Numerators of partial sums of a series for sqrt(2).
  • A120096 (program): a(n) = (A046717(n))^2 (starting with n=1).
  • A120105 (program): Number triangle T(n,k) = lcm(1,..,2n+2)/lcm(1,..,2k+2).
  • A120106 (program): a(n) = Sum_{k=0..n} lcm(1..2n+2)/lcm(1..2k+2).
  • A120108 (program): Number triangle T(n,k) = lcm(1,..,n+1)/lcm(1,..,k+1).
  • A120109 (program): Row sums of number triangle A120108.
  • A120111 (program): Bi-diagonal inverse matrix of A120108.
  • A120112 (program): Row sums of number triangle A120111.
  • A120114 (program): a(n) = lcm(1, …, 2n+4)/lcm(1, …, 2n+2).
  • A120134 (program): a(1)=4; a(n) = floor((8 + Sum_{k=1..n-1} a(k))/2).
  • A120135 (program): a(1)=5; a(n)=floor((11+sum(a(1) to a(n-1)))/2).
  • A120136 (program): a(1)=7; a(n)=floor((14+sum(a(1) to a(n-1)))/2).
  • A120137 (program): a(1)=8; a(n)=floor((17+sum(a(1) to a(n-1)))/2).
  • A120138 (program): a(1)=10; a(n)=floor((20+sum(a(1) to a(n-1)))/2).
  • A120139 (program): a(1)=11; a(n)=floor((23+sum(a(1) to a(n-1)))/2).
  • A120140 (program): a(1)=13; a(n)=floor((26+sum(a(1) to a(n-1)))/2).
  • A120141 (program): a(1)=14; a(n)=floor((29+sum(a(1) to a(n-1)))/2).
  • A120142 (program): a(1)=16; a(n)=floor((32+sum(a(1) to a(n-1)))/2).
  • A120143 (program): a(1)=17; a(n)=floor((35+sum(a(1) to a(n-1)))/2).
  • A120144 (program): a(1)=19; a(n)=floor((38+sum(a(1) to a(n-1)))/2).
  • A120145 (program): a(1)=20; a(n)=floor((41+sum(a(1) to a(n-1)))/2).
  • A120146 (program): a(1)=22; a(n)=floor((44+sum(a(1) to a(n-1)))/2).
  • A120147 (program): a(1)=23; a(n)=floor((47+sum(a(1) to a(n-1)))/2).
  • A120148 (program): a(1)=25; a(n)=floor((50+sum(a(1) to a(n-1)))/2).
  • A120149 (program): a(1)=2; a(n)=floor((7+sum(a(1) to a(n-1)))/3).
  • A120150 (program): a(1)=3; a(n)=floor((11+sum(a(1) to a(n-1)))/3).
  • A120151 (program): a(1)=5; a(n)=floor((15+sum(a(1) to a(n-1)))/3).
  • A120152 (program): a(1)=6; a(n)=floor((19+sum(a(1) to a(n-1)))/3).
  • A120153 (program): a(1)=7; a(n)=floor((23+sum(a(1) to a(n-1)))/3).
  • A120154 (program): a(1) = 9, a(n) = floor( (27 + Sum_(a(1) to a(n-1))) / 3 ).
  • A120155 (program): a(1)=10; a(n)=floor((31+sum(a(1) to a(n-1)))/3).
  • A120156 (program): a(1)=11; a(n)=floor((35+sum(a(1) to a(n-1)))/3).
  • A120157 (program): a(1)=13; a(n)=floor((39+sum(a(1) to a(n-1)))/3).
  • A120158 (program): a(1)=14; a(n)=floor((43+sum(a(1) to a(n-1)))/3).
  • A120159 (program): a(1)=15; a(n)=floor((47+sum(a(1) to a(n-1)))/3).
  • A120160 (program): a(n) = ceiling(Sum_{i=1..n-1} a(i)/4) for n >= 2 starting with a(1) = 1.
  • A120161 (program): a(1)=2; a(n)=floor((9+sum(a(1) to a(n-1)))/4).
  • A120162 (program): a(1)=3; a(n)=floor((14+sum(a(1) to a(n-1)))/4).
  • A120163 (program): a(1)=4; a(n)=floor((19+sum(a(1) to a(n-1)))/4).
  • A120164 (program): a(1)=6; a(n)=floor((24+sum(a(1) to a(n-1)))/4).
  • A120165 (program): a(1)=7; a(n)=floor((29+sum(a(1) to a(n-1)))/4).
  • A120166 (program): a(1)=8; a(n)=floor((34+sum(a(1) to a(n-1)))/4).
  • A120167 (program): a(1)=9; a(n)=floor((39+sum(a(1) to a(n-1)))/4).
  • A120168 (program): a(1)=11; a(n)=floor((44+sum(a(1) to a(n-1)))/4).
  • A120169 (program): a(1)=12; a(n)=floor((49+sum(a(1) to a(n-1)))/4).
  • A120170 (program): a(n) = ceiling( Sum_{i=1..n-1} a(i)/5 ), a(1)=1.
  • A120171 (program): a(1)=2; a(n)=floor((11+sum(a(1) to a(n-1)))/5).
  • A120172 (program): a(1)=3; a(n)=floor((17+sum(a(1) to a(n-1)))/5).
  • A120173 (program): a(1)=4; a(n)=floor((23+sum(a(1) to a(n-1)))/5).
  • A120174 (program): a(1)=5; a(n)=floor((29+sum(a(1) to a(n-1)))/5).
  • A120175 (program): a(1)=7; a(n)=floor((35+sum(a(1) to a(n-1)))/5).
  • A120176 (program): a(1)=8; a(n)=floor((41+sum(a(1) to a(n-1)))/5).
  • A120177 (program): a(1)=9; a(n)=floor((47+sum(a(1) to a(n-1)))/5).
  • A120178 (program): a(n)=ceiling( sum_{i=1..n-1} a(i)/6), a(1)=1.
  • A120179 (program): a(1)=2; a(n)=floor((13+sum(a(1) to a(n-1)))/6).
  • A120180 (program): a(1)=3; a(n)=floor((20+sum(a(1) to a(n-1)))/6).
  • A120181 (program): a(1)=4; a(n)=floor((27+sum(a(1) to a(n-1)))/6).
  • A120182 (program): a(1)=5; a(n)=floor((34+sum(a(1) to a(n-1)))/6).
  • A120183 (program): a(1)=6; a(n)=floor((41+sum(a(1) to a(n-1)))/6).
  • A120184 (program): a(1)=8; a(n)=floor((48+sum(a(1) to a(n-1)))/6).
  • A120185 (program): a(1)=9; a(n)=floor((55+sum(a(1) to a(n-1)))/6).
  • A120186 (program): a(n) = ceiling( Sum_{i=1..n-1} a(i)/7 ), a(1) = 1.
  • A120187 (program): a(1)=2; a(n)=floor((15+sum(a(1) to a(n-1)))/7).
  • A120188 (program): a(1)=3; a(n)=floor((23+sum(a(1) to a(n-1)))/7).
  • A120189 (program): a(1)=4; a(n)=floor((31+sum(a(1) to a(n-1)))/7).
  • A120190 (program): a(1)=5; a(n)=floor((39+sum(a(1) to a(n-1)))/7).
  • A120191 (program): a(1)=6; a(n)=floor((47+sum(a(1) to a(n-1)))/7).
  • A120192 (program): a(1)=7; a(n)=floor((55+sum(a(1) to a(n-1)))/7).
  • A120193 (program): a(1)=9; a(n)=floor((63+sum(a(1) to a(n-1)))/7).
  • A120194 (program): a(n) = ceiling( Sum_{i=1..n-1} a(i)/8 ), a(1)=1.
  • A120195 (program): a(1)=2; a(n)=floor((17+sum(a(1) to a(n-1)))/8).
  • A120196 (program): a(1)=3; a(n) = floor((26 + Sum_{j=1..n-1} a(j))/8).
  • A120197 (program): a(1)=4; a(n)=floor((35+sum(a(1) to a(n-1)))/8).
  • A120198 (program): a(1)=5; a(n)=floor((44+sum(a(1) to a(n-1)))/8).
  • A120199 (program): a(1)=6; a(n)=floor((53+sum(a(1) to a(n-1)))/8).
  • A120200 (program): a(1)=7; a(n)=floor((62+sum(a(1) to a(n-1)))/8).
  • A120201 (program): a(1)=8; a(n)=floor((71+sum(a(1) to a(n-1)))/8).
  • A120202 (program): a(n) = ceiling( sum_{i=1..n-1} a(i)/9), a(1)=1.
  • A120203 (program): a(1) = 2; a(n) = floor( (19 + Sum_{i=1..n-1} a(i)) /9).
  • A120204 (program): a(1)=3; a(n)=floor((29+sum(a(1) to a(n-1)))/9).
  • A120205 (program): a(1)=4; a(n)=floor((39+sum(a(1) to a(n-1)))/9).
  • A120206 (program): a(1)=5; a(n)=floor((49+sum(a(1) to a(n-1)))/9).
  • A120207 (program): a(1)=6; a(n)=floor((59+sum(a(1) to a(n-1)))/9).
  • A120208 (program): a(1)=7; a(n)=floor((69+sum(a(1) to a(n-1)))/9).
  • A120209 (program): a(1)=8; a(n)=floor((79+sum(a(1) to a(n-1)))/9).
  • A120212 (program): “a” values providing solution x = b in A120211 (i.e., y^2 = b^2*(a^2 - b)*(b + 1) with a, b legs in primitive Pythagorean triangles).
  • A120214 (program): Start with 1013 and repeatedly reverse the digits and add 2 to get the next term.
  • A120215 (program): Start with 1057 and repeatedly reverse the digits and add 2 to get the next term.
  • A120226 (program): Numbers n such that a+n and a*n+1 are prime, case a=4.
  • A120227 (program): Numbers n such that a+n and a*n+1 are prime, case a=5.
  • A120228 (program): Numbers n such that a+n and a*n+1 are prime, case a=8.
  • A120229 (program): Split-floor-multiplier sequence (SFMS) using multipliers 1/3 and 3. The SFMS using multipliers r and s is here introduced: for every positive integer n and positive real number r, let [rn] abbreviate floor(rn). Then SFMS(r, s), where max {r, s} > 1, is the sequence a defined by a(n)=[rn] if [rn] > 0 and is not already in a and a(n) = [sn] otherwise.
  • A120230 (program): Split-floor-multiplier sequence (SFMS) using multipliers 1/4 and 4. (SFMS is defined at A120229.)
  • A120242 (program): Inverse permutation to permutation sequence A120241.
  • A120243 (program): Numbers k such that {k*sqrt(2)} < 1/2, where { } = fractional part.
  • A120246 (program): a(1) = 1. a((m(m+1)/2 +k) = m + a(k), 1 <= k <= m+1, m >= 1.
  • A120248 (program): a(n)=Product{k=0..n, C(n+k+2, n+2)}.
  • A120249 (program): Numerator of cfenc[n] (see definition in comments).
  • A120250 (program): Denominator of cfenc[n] (see definition in comments).
  • A120263 (program): Ratio of the numerator of n*HarmonicNumber[n] to the numerator of HarmonicNumber[n]: A096617(n)/A001008(n).
  • A120264 (program): Numerator of Sum[ (-1)^(k+1)/k^k, {k,1,n} ].
  • A120265 (program): a(n) = numerator(Sum_{k=1..n} 1/k!).
  • A120266 (program): Numerator of Sum_{k=0..n} n^k/k!.
  • A120267 (program): Numerator of Sum_{k=1..n} n^k/k!.
  • A120268 (program): Numerator of Sum_{k=1..n} 1/(2*k-1)^2.
  • A120269 (program): Numerator of Sum_{k=1..n} 1/(2k-1)^4.
  • A120275 (program): Smallest prime factor of the odd Catalan number A038003(n).
  • A120277 (program): Sum of all matrix elements of n X n matrix M[i,j]=(2n+i+j)!/(n+i)!/(n+j)!, i,j=1..n.
  • A120278 (program): Sum[Sum[C(2k,k),{k,1,m}],{m,1,n}], where C(2k,k)=(2k)!/(k!)^2=A000984[k].
  • A120279 (program): a(n) = Sum[Sum[(i+j)!/i!/j!,{i,1,j}],{j,1,n}].
  • A120281 (program): Logarithmic numbers A002104[p+1] divided by p=Prime[n].
  • A120284 (program): Numerator of absolute value of Sum[(-1)^(k+1)*(2k+1)*Sum[1/i,{i,1,k}],{k,1,n}]]].
  • A120286 (program): Numerator of 1/n^2 + 2/(n-1)^2 + 3/(n-2)^2 +…+ (n-1)/2^2 + n.
  • A120287 (program): Numerator of 1/n^3 + 2/(n-1)^3 + 3/(n-2)^3 +…+ (n-1)/2^3 + n.
  • A120288 (program): Numerator of 1/n^4 + 2/(n-1)^4 + 3/(n-2)^4 +…+ (n-1)/2^4 + n.
  • A120291 (program): Numerator of determinant of n X n matrix with elements M[i,j] = (1+Prime[i])/Prime[i] if i=j and 1 otherwise.
  • A120293 (program): Absolute value of numerator of determinant of n X n matrix with M(i,j) = (i+1)/(i+2) if i=j otherwise 1.
  • A120294 (program): Numerator of determinant of n X n matrix with elements M[j,j] = (i+j)/(i+j-1).
  • A120296 (program): Numerator of Sum_{k=1..n} (-1)^(k+1)/k^4.
  • A120297 (program): Sum of all matrix elements of n X n matrix M(i,j) = Fibonacci(i+j-1).
  • A120303 (program): Largest prime factor of Catalan number A000108(n).
  • A120304 (program): Catalan numbers minus 2.
  • A120305 (program): a(n) = Sum_{i=0..n} Sum_{j=0..n} (-1)^(i+j) * (i+j)!/(i!j!).
  • A120307 (program): Inverse determinant of n X n matrix M[i,j] = i*j/(i+j-1).
  • A120309 (program): Numbers k such that pi(k) == 0 (mod 4), where pi() = A000720.
  • A120321 (program): RF(7): refactorable numbers with 7 as smallest prime factor.
  • A120323 (program): Periodic sequence 0, 3, 1, 0, 1, 3.
  • A120324 (program): Periodic sequence 0, 1, 0, 4, 0, 1.
  • A120325 (program): Period 6: repeat [0, 0, 1, 0, 1, 0].
  • A120326 (program): Cumulative sum of the remainders when dividing primes by 3.
  • A120327 (program): Smallest nonsquarefree number >= n.
  • A120328 (program): Sum of three consecutive squares: a(n) = n^2 + (n + 1)^2 + (n + 2)^2.
  • A120344 (program): Numbers k such that 23*k + 1 is a prime.
  • A120347 (program): Numerator of Sum[ 1/k^n, {k,1,n-1} ].
  • A120348 (program): Number of labeled simply-rooted 2-trees with n labeled vertices (i.e., n+2 vertices altogether; a simply-rooted 2-tree is an externally rooted 2-tree whose root edge belongs to exactly one triangle).
  • A120351 (program): Even numbers k such that the number of odd divisors r and the number of even divisors s are both divisors of k.
  • A120353 (program): Sum of 5 consecutive powers of 3, starting with a power of 9.
  • A120354 (program): a(n) = 11*3^n.
  • A120367 (program): a(1) = 1. a(n) = a(n-1) + (maximum number of 1’s occurring in the binary representation of any of the sequence’s earlier terms).
  • A120368 (program): a(n) = number of sequences (a_1, a_2, …, a_n) in {1,2,…,n} such that the range {a_1, a_2, …, a_n} is an interval.
  • A120370 (program): a(1) = 2. a(n) = a(n-1) + (maximum number of distinct primes dividing any earlier terms).
  • A120382 (program): Even numbers n such that 3*n-1 and 3*n+1 are not prime.
  • A120385 (program): If a(n-1) = 1 then largest value so far + 1, otherwise floor(a(n-1)/2); or table T(n,k) with T(n,0) = n, T(n,k+1) = floor(T(n,k)/2).
  • A120387 (program): c(n) mod b(n) where c(n) = (n-1)! and b(n) = Sum_{i=1..n} i.
  • A120390 (program): Sum of digits of double factorial numbers.
  • A120397 (program): Minimal number of steps needed to represent a prime >=5 as a sum of at most 3 primes such that all the previous odd primes are represented.
  • A120400 (program): Expansion of 1/(1-x-x^2-x^6).
  • A120405 (program): a(n) = 1, a(2) = 1, then append the dot product of (1,2) and (1,1) = 1*1, 1*2 = 1, 2; to the right of 1, 1; getting (1, 1, 1, 2). The next operation uses the dot product of (1, 2, 3, 4) and (1, 1, 1, 2), getting (1, 2, 3, 8) which we append to the right of (1, 1, 1, 2), getting (1, 1, 1, 2, 1, 2, 3, 8) and so on.
  • A120408 (program): a(n) = n^1*(n+1)^2*(n+2)^3*(n+3)^4*(n+4)^5/(1!*2!*3!*4!*5!).
  • A120409 (program): a(n) = n^1*(n+1)^2*(n+2)^3*(n+3)^4*(n+4)^5*(n+5)^6/(1!*2!*3!*4!*5!*6!).
  • A120410 (program): a(n) = n^1*(n+1)^2*(n+2)^3*(n+3)^4*(n+4)^5*(n+5)^6*(n+6)^7/(1!*2!*3!*4!*5!*6!*7!).
  • A120413 (program): Largest even number strictly less than n^2.
  • A120415 (program): Expansion of 1/(1-x-x^3-x^6).
  • A120423 (program): a(n) = maximum value among all k where 1<=k<=n of gcd(k,floor(n/k)).
  • A120424 (program): Having specified two initial terms, the “Half-Fibonacci” sequence proceeds like the Fibonacci sequence, except that the terms are halved before being added if they are even.
  • A120425 (program): a(n) = maximum value among all k where 1<=k<=n of GCD(k,ceiling(n/k)).
  • A120427 (program): For each y >= 1 there are only finitely many values of x >= 1 such that x-y and x+y are both squares; list all such pairs (x,y) with gcd(x,y) = 1 ordered by values of y; sequence gives y values.
  • A120433 (program): Numbers n with property that Roman numeral for n uses the subtractive notation.
  • A120434 (program): Triangle read by rows: counts permutations by number of big descents.
  • A120435 (program): Triangle read by rows: T(n,k) = lcm(1,2,3,4,…,n)/k (1 <= k <= n).
  • A120437 (program): Differences of A037314 (sum of base-3 digits of n = sum of base-9 digits of n).
  • A120438 (program): Average of twin-prime pairs modulo 10 (least absolute residue).
  • A120439 (program): Average of twin-prime pairs modulo 5.
  • A120440 (program): Nearest integer to twin-prime pair averages divided by 10.
  • A120444 (program): First differences of A004125.
  • A120446 (program): Expansion of 1/(1-x-x^4-x^6).
  • A120452 (program): Number of partitions of n-1 boys and one girl with no couple.
  • A120454 (program): a(n) = ceiling(GPF(n)/LPF(n)) where GPF is greatest prime factor, LPF is least prime factor.
  • A120458 (program): Triangle read by rows: row 0 is 1; for n>0, row n gives 1^n, prime(1)^n, prime(2)^n, …, prime(n)^n.
  • A120459 (program): Row sums of A120458.
  • A120460 (program): Primes p such that (3*p^2+1)/4 is prime.
  • A120461 (program): Expansion of x*(4-x)/( (2x-1)*(x^2-x-1)).
  • A120462 (program): Expansion of -2*x*(-3-2*x+4*x^2) / ((x-1)*(2*x+1)*(2*x-1)*(1+x)).
  • A120463 (program): Expansion of x*(1+x+2*x^3) / ( (x-1)*(1+x)*(3*x^2-1) ).
  • A120464 (program): a(n) = 5*a(n-1)+a(n-2)-2*a(n-3).
  • A120465 (program): a(0)=1, a(1)=36, a(n)=204*a(n-2).
  • A120468 (program): Expansion of -2*x*(-8-12*x+9*x^2) / ( (x-1)*(3*x-1)*(3*x+1)*(1+x) )
  • A120470 (program): 2*4^n +(-1)^n*2^(n-1).
  • A120471 (program): a(n) = 6 * A015518(n).
  • A120474 (program): Second differences of A004001.
  • A120476 (program): Triangle read by rows: a(n,m)=(2*n-1)*(n-m)*(n+m+1)/2, where n is the column and m the row index.
  • A120477 (program): Apply partial sum operator 5 times to partition numbers.
  • A120478 (program): Binomial(n+6,5)-binomial(n,5).
  • A120479 (program): Primes of the form k^3 + k^2 + 1.
  • A120484 (program): a(n) = Sum(Sum p_i, {Sum p_i=prime(n)}, p_i is prime).
  • A120485 (program): a(n) = n^n - (n-1)^n + (n-2)^n - … + (-1)^(k+n)*k^n + … + (-1)^(2+n)*2^n + (-1)^(1+n)*1^n = Sum_{k=1..n} (-1)^(k+n)*k^n.
  • A120486 (program): Partial sums of A000188.
  • A120487 (program): Denominator of 1^n/n + 2^n/(n-1) + 3^n/(n-2) + … + (n-1)^n/2 + n^n/1.
  • A120489 (program): Number of nonisomorphic perfect 1-factorizations of complete bipartite graph K_{n,n}.
  • A120490 (program): 1 + Sum[ k^(n-1), {k,1,n}].
  • A120492 (program): 1 + Sum[ Prime[k]^(n-1), {k,1,n}].
  • A120493 (program): Triangle T(n,k) read by rows ; multiply row n of Pascal’s triangle (A007318) by A024175(n).
  • A120497 (program): Positive integers whose number of divisors is a perfect power.
  • A120501 (program): Meta-Fibonacci sequence a(n) with parameters s=2.
  • A120502 (program): Meta-Fibonacci sequence a(n) with parameters s=3.
  • A120503 (program): Generalized meta-Fibonacci sequence a(n) with parameters s=0 and k=3.
  • A120504 (program): Generalized meta-Fibonacci sequence a(n) with parameters s=1 and k=3.
  • A120505 (program): Generalized meta-Fibonacci sequence a(n) with parameters s=2 and k=3.
  • A120506 (program): Generalized meta-Fibonacci sequence a(n) with parameters s=3 and k=3.
  • A120507 (program): Generalized meta-Fibonacci sequence a(n) with parameters s=0 and k=4.
  • A120508 (program): Generalized meta-Fibonacci sequence a(n) with parameters s=1 and k=4.
  • A120509 (program): Generalized meta-Fibonacci sequence a(n) with parameters s=2 and k=4.
  • A120510 (program): Generalized meta-Fibonacci sequence a(n) with parameters s=3 and k=4.
  • A120511 (program): a(n) = min{j>0 : A006949(j) = n}.
  • A120512 (program): a(n) = min{j : A120501(j) = n}.
  • A120513 (program): a(n) = min{j : A120502(j) = n}.
  • A120514 (program): a(n) = min{j : A120503(j) = n}.
  • A120515 (program): a(n) = min{j : A120504(j) = n}.
  • A120516 (program): a(n) = min{j : A120505(j) = n}.
  • A120517 (program): a(n) = min{j : A120506(j) = n}.
  • A120518 (program): a(n) = min{j : A120507(j) = n}.
  • A120519 (program): a(n) = min{j : A120508(j) = n}.
  • A120520 (program): a(n) = min{j : A120509(j) = n}.
  • A120521 (program): a(n) = min{j : A120510(j) = n}.
  • A120522 (program): First differences of successive meta-Fibonacci numbers A006949.
  • A120523 (program): First differences of successive meta-Fibonacci numbers A120501.
  • A120524 (program): First differences of successive meta-Fibonacci numbers A120502.
  • A120525 (program): First differences of successive generalized meta-Fibonacci numbers A120503.
  • A120526 (program): First differences of successive generalized meta-Fibonacci numbers A120504.
  • A120527 (program): First differences of successive generalized meta-Fibonacci numbers A120505.
  • A120528 (program): First differences of successive generalized meta-Fibonacci numbers A120506.
  • A120529 (program): First differences of successive generalized meta-Fibonacci numbers A120507.
  • A120530 (program): First differences of successive generalized meta-Fibonacci numbers A120508.
  • A120531 (program): First differences of successive generalized meta-Fibonacci numbers A120509.
  • A120532 (program): First differences of successive generalized meta-Fibonacci numbers A120510.
  • A120533 (program): Primes having a prime number of digits.
  • A120537 (program): Sum of all matrix elements of n X n matrix M[i,j] = Lucas[i+j-1], (i,j = 1..n), where Lucas[n] = A000032[n] = Fibonacci[n-1] + Fibonacci[n+1].
  • A120539 (program): Sequence that except for initial 1 is the complement of its inverse binomial transform.
  • A120562 (program): Sum of binomial coefficients binomial(i+j, i) modulo 2 over all pairs (i,j) of positive integers satisfying 3i+j=n.
  • A120565 (program): Maximum over all planar partitions of n of the number of ways the partition can be shrunk by removing a single element.
  • A120571 (program): 2n^4+6n^2+4 = 2(n^2+1)(n^2+2).
  • A120573 (program): a(n) = n^5 + 3n^3 + 2n = n(n^2+1)(n^2+2).
  • A120580 (program): Hankel transform of sum{k=0..n, C(2k,k)}.
  • A120581 (program): Hankel transform of sum{k=0..n, C(2k,k)*2^k}.
  • A120582 (program): Hankel transform of Sum_{k=0..floor(n/2)} binomial(2*k, k).
  • A120588 (program): G.f. is 1 + x*c(x), where c(x) is the g.f. of the Catalan numbers (A000108).
  • A120589 (program): Self-convolution of A120588, such that a(n) = 3*A120588(n) for n >= 2.
  • A120590 (program): G.f. satisfies: 4*A(x) = 3 + x + A(x)^3, starting with [1,1,3].
  • A120592 (program): G.f. satisfies: 5*A(x) = 4 + 4*x + A(x)^3, starting with [1,2,6].
  • A120609 (program): Primes among the absolute value of numbers of the form f(x)= x^2 + x - 1354363.
  • A120612 (program): For n>1, a(n) = 2*a(n-1) + 15*a(n-2); a(0)=1, a(1)=1.
  • A120613 (program): a(n) = floor(phi*floor(n/phi)) where phi=(1+sqrt(5))/2.
  • A120614 (program): a(n) = g(n+1) - g(n) where g(k) = floor(phi*floor(k/phi)) and phi = (1+sqrt(5))/2.
  • A120615 (program): a(n) = Sum_{k=0..n} floor(phi*floor(n/phi)) where phi = (1+sqrt(5))/2.
  • A120616 (program): Generalized Riordan array (1/sqrt(1+4x^2),(1-sqrt(1+4x^2))/(2x)).
  • A120617 (program): Hankel transform of g.f. 1/sqrt(1+4x^2).
  • A120624 (program): Numbers n such that the n-th Catalan number C(2n,n)/(n+1) is divisible by 2n.
  • A120628 (program): Primes such that their double is 1 away from a prime number.
  • A120630 (program): Dirichlet inverse of A002654.
  • A120632 (program): Number of numbers >1 up to 2*prime(n) which are divisible by primes up to prime(n).
  • A120634 (program): Decimal equivalent of A066335.
  • A120640 (program): Primes such that their quadruple is not 1 away from a prime number.
  • A120645 (program): Numbers not in A121644.
  • A120656 (program): 6 X 6 trigonal prism bonding graph matrix Markov: this molecular structure is the major symmetry between the tetrahedron and cube: characteristic polynomial:12 x^2 - 4 x^3 - 9 x^4 + x^6.
  • A120664 (program): Expansion of 2*x*(1-6*x+12*x^2)/(1-8*x+19*x^2-12*x^3).
  • A120665 (program): a(n) = 6*a(n-1) - 9*a(n-2) + 2*a(n-3) for n>3, a(1)=0, a(2)=-1, a(3)=0,
  • A120666 (program): Triangle read by rows: T(m,n) = (n*m)!/(m!)^n.
  • A120672 (program): a(n) = 2 * A285917(n) for n >=2, a(0) = a(1) = 0.
  • A120675 (program): Number of prime factors of odd squarefree numbers A056911.
  • A120676 (program): Number of prime factors of even squarefree numbers A039956.
  • A120679 (program): a(1)=1. a(n) = a(n-1) + d(a(k)), where d(m) is the number of positive divisors of m and d(a(k)) is the maximum value over the k’s where 1<=k <=n-1.
  • A120680 (program): a(n) = number of positive divisors of A120679(n).
  • A120683 (program): Decimal expansion of secant of 15 degrees (cosecant of 75 degrees).
  • A120689 (program): a(n) = 10*a(n-1) - 16*a(n-2), n>0.
  • A120691 (program): First differences of coefficients in the continued fraction for e.
  • A120694 (program): Sequence demonstrating the Pythagorean theorem.
  • A120699 (program): Lengths of set partitions.
  • A120700 (program): a(n) is the least refactorable number k having the n-th prime as its greatest prime factor.
  • A120701 (program): Number of unit circles which fit touching a circle of radius n-1, i.e., with their centers on a circle of radius n.
  • A120718 (program): Expansion of 3*x/(1 - 2*x^2 - 2*x + x^3).
  • A120721 (program): Partial sums of A079645.
  • A120723 (program): Let M be the 8 X 8 matrix M = {{0, 1, 1, 0, 0, 1, 0, 0}, {1, 0, 0, 1, 1, 0, 0, 0}, {1, 0, 0, 1, 0, 1, 1, 0}, {0, 1, 1, 0, 1, 0, 1, 0}, {0, 1, 0, 1, 0, 1, 0, 1}, {1, 0, 1, 0, 1, 0, 0, 1}, {0, 0, 1, 1, 0, 0, 0, 1}, {0, 0, 0, 0, 1, 1, 1, 0}}; let v[1] = [Fibonacci[1], …, Fibonacci[8]]; let v[n] = M.v[n - 1]; then a(n) = v[n][[1]].
  • A120727 (program): a(n) = a(n-1) + a(n-2), starting with 110, 211.
  • A120728 (program): Floor of e^n, reduced modulo 3.
  • A120730 (program): Another version of Catalan triangle A009766.
  • A120731 (program): Decimal expansion of 3 + sqrt(2)/10.
  • A120736 (program): Numbers n such that every prime p that divides d(n) (A000005) also divides n.
  • A120738 (program): a(n) = 4*n - A000120(n).
  • A120739 (program): a(n) = Sum_{k=0..n} floor(C(n,k)/2).
  • A120740 (program): Numbers n such that n = Sum_digits[k*abs(n-k)] for some k>=0.
  • A120741 (program): a(n) = (7^n - 1)/2.
  • A120743 (program): a(n) = (1/2)*(1 + 3*i)^n + (1/2)*(1 - 3*i)^n where i = sqrt(-1).
  • A120747 (program): Sequence relating to the hendecagon (11-gon).
  • A120748 (program): Expansion of x^2*(1 + 2*x - x^2)/(1 - x - 3*x^2 - x^3 + x^4).
  • A120749 (program): Numbers k such that {k* sqrt(2)} > 1/2, where { } = fractional part.
  • A120752 (program): Numbers k such that {rk} <= c, where r = (1/2)^(1/2), c = 1/2 and { } denotes fractional part.
  • A120753 (program): Numbers k such that {rk} > c, where r = (1/2)^(1/2), c = 1/2 and { } denotes fractional part.
  • A120757 (program): Expansion of x^2*(2+x)/(1-3*x-4*x^2-x^3).
  • A120758 (program): The (1,3)-entry in the matrix M^n, where M is the 3 X 3 matrix [0,2,1; 2,1,2; 1,2,2] (n>=1).
  • A120765 (program): E.g.f.: -exp(-x)*log(1-2*x)/2.
  • A120767 (program): 2^(n^2)+3^n.
  • A120768 (program): Partial sums of A120405.
  • A120769 (program): Starting from a(0)=1, recursively a(2^k+r) = (2^k-r)*a(2^k-1-r), 0<=r < 2^(k+1).
  • A120770 (program): Partial sums of A120769.
  • A120772 (program): Triangular array, permutation of A119973. a(r,r) = A084109(r); a(r+1,c) = 2*a(r,c).
  • A120773 (program): a(n) = 2^(n^2) - 3^n.
  • A120775 (program): The (3,1)-entry of the matrix M^n, where M is the 3 X 3 matrix [0,1,1; 2,1,2; 1,2,2] (n>=1).
  • A120777 (program): One half of denominators of partial sums of a series for sqrt(2).
  • A120778 (program): Numerators of partial sums of Catalan numbers scaled by powers of 1/4.
  • A120780 (program): Numerators of partial sums of Catalan numbers scaled by powers of 1/8.
  • A120781 (program): Denominators of partial sums of Catalan numbers scaled by powers of 1/8.
  • A120782 (program): Numerators of partial sums of Catalan numbers scaled by powers of 1/12.
  • A120783 (program): Denominators of partial sums of Catalan numbers scaled by powers of 1/12.
  • A120784 (program): Numerators of partial sums of Catalan numbers scaled by powers of 1/16.
  • A120785 (program): Denominators of partial sums of Catalan numbers scaled by powers of 1/16.
  • A120786 (program): Numerators of partial sums of Catalan numbers scaled by powers of 1/20.
  • A120787 (program): Denominators of partial sums of Catalan numbers scaled by powers of 1/20.
  • A120788 (program): Numerators of partial sums of Catalan numbers scaled by powers of -1/4.
  • A120789 (program): Numerators of partial sums of Catalan numbers scaled by powers of -1/8.
  • A120791 (program): Numerators of partial sums of Catalan numbers scaled by powers of -1/20.
  • A120792 (program): Numerators of partial sums of Catalan numbers scaled by powers of -1/12.
  • A120793 (program): Denominators of partial sums of Catalan numbers scaled by powers of -1/12.
  • A120794 (program): Numerators of partial sums of Catalan numbers scaled by powers of -1/16.
  • A120796 (program): Denominators of partial sums of Catalan numbers scaled by powers of -1/20.
  • A120797 (program): a(0) = 1. a(n) = n + (largest noncomposite {1 or prime} occurring earlier in the sequence).
  • A120798 (program): 3^(n^2)+2^n.
  • A120799 (program): 3^(n^2)-2^n.
  • A120800 (program): a(n) = 3^(n^2) + 2^(n^2).
  • A120801 (program): a(n) = 3^(n^2) - 2^(n^2).
  • A120817 (program): 10-adic integer x=…07839804103263499879186432 satisfying x^5 = x; also x^3 = -x = A120818; (x^2)^3 = x^2 = A091664; (x^4)^2 = x^4 = A018248.
  • A120818 (program): 10-adic integer x=…92160195896736500120813568 satisfying x^5 = x; also x^3 = -x = A120817; (x^2)^3 = x^2 = A091664; (x^4)^2 = x^4 = A018248.
  • A120831 (program): Numerators of partial sums of (p+q)/p*q, where p and q are primes.
  • A120832 (program): Denominators of partial sums of (p+q)/p*q, where p and q are primes.
  • A120835 (program): Integer parts of partial sums of (p+q)/p*q, with primes p and q.
  • A120842 (program): a(n) = the (number of positive divisors of n)th positive integer which is coprime to n.
  • A120845 (program): 2^n+3^n+5*n.
  • A120846 (program): a(n) = 3^n + 2^n + n.
  • A120848 (program): 2^n+3^n-n.
  • A120849 (program): 5n+3^n-2^n.
  • A120855 (program): Row sums of triangle A120854, which is the matrix log of triangle A117939.
  • A120864 (program): a(n) is the number j for which there exists a unique pair (j,k) of positive integers such that (j + k + 1)^2 - 4*k = 12*n^2.
  • A120865 (program): a(n) is the number k for which there exists a unique pair (j,k) of positive integers such that (j + k + 1)^2 - 4*k = 12*n^2.
  • A120866 (program): a(n) is the number j for which there exists a unique pair (j,k) of positive integers such that (j + k + 1)^2 - 4*k = 20*n^2.
  • A120867 (program): a(n) is the number k for which there exists a unique pair (j,k) of positive integers such that (j + k + 1)^2 - 4*k = 20*n^2.
  • A120868 (program): a(n) is the number k for which there exists a unique pair (j,k) of positive integers such that (j + k + 1)^2 - 4*k = 5*n^2.
  • A120869 (program): a(n) is the number j for which there exists a unique pair (j,k) of positive integers such that (j + k + 1)^2 - 4*k = 13*n^2.
  • A120870 (program): a(n) is the number k for which there exists a unique pair (j,k) of positive integers such that (j + k + 1)^2 - 4*k = 13*n^2.
  • A120872 (program): a(n) is the value of k for row n of the fixed-k dispersion for Q = 8.
  • A120873 (program): Fractal sequence of the Wythoff difference array (A080164).
  • A120874 (program): Fractal sequence of the Fraenkel array (A038150).
  • A120875 (program): Product of twin primes minus 1.
  • A120876 (program): (Product of twin primes - 1)/2.
  • A120879 (program): G.f. satisfies: A(x) = A(x^3)*(1 + 3*x + 2*x^2).
  • A120880 (program): G.f. satisfies: A(x) = A(x^3)*(1 + 2*x + x^2); thus a(n) = 2^A062756(n), where A062756(n) is the number of 1’s in the ternary expansion of n.
  • A120881 (program): a(n) = number of k’s, for 1 <= k <= n, where GCD(k,floor(n/k)) > 1.
  • A120882 (program): a(n) is the number of k’s, for 1 <= k <= n, where gcd(k,floor(n/k)) = 1.
  • A120883 (program): (1/4)*number of lattice points with odd indices in a square lattice inside a circle around the origin with radius 2*n.
  • A120885 (program): Triangle read by rows where t(n,m) = ceiling(n/m).
  • A120886 (program): a(n) = number of k’s with 1 <= k <= n where gcd(k,ceiling(n/k)) > 1.
  • A120887 (program): a(n) is the number of k’s in 1..n such that gcd(k,ceiling(n/k)) = 1.
  • A120888 (program): Triangle read by rows: T(n,k) = gcd(k,floor(n/k)) (1 <= k <= n).
  • A120889 (program): Triangle read by rows: T(n,k) = gcd(k,ceiling(n/k)) (1 <= k <= n).
  • A120890 (program): Ordered odd leg of primitive Pythagorean triangles.
  • A120891 (program): Number of primitive Pythagorean triangles with odd leg 2n-1.
  • A120892 (program): a(n)=3*a(n-1)+3*a(n-2)-a(n-3);a(0)=1,a(1)=0,a(2)=3. a(n)=4*{a(n-1)+(-1)^n}-a(n-2);a(0)=1,a(1)=0.
  • A120893 (program): a(n) = 3*a(n-1) + 3*a(n-2) - a(n-3); a(0)=1, a(1)=1, a(2)=5.
  • A120908 (program): Sum of the lengths of the drops in all ternary words of length n on {0,1,2}. The drops of a ternary word on {0,1,2} are the subwords 10,20 and 21, their lengths being the differences 1, 2 and 1, respectively.
  • A120909 (program): Triangle read by rows: T(n,k) is the number of ternary words of length n having k runs (i.e., subwords of maximal length) of identical letters (1 <= k <= n).
  • A120910 (program): Triangle read by rows: T(n,k) is the number of ternary words of length n having k levels (n >= 1, 0 <= k <= n-1). A level is a pair of identical consecutive letters).
  • A120925 (program): Number of ternary words on {0,1,2} having no isolated 0’s.
  • A120926 (program): Number of isolated 0’s in all ternary words of length n on {0,1,2}.
  • A120927 (program): a(n) = floor(semiprime(n)/n).
  • A120928 (program): Number of “ups” and “downs” in the permutations of [n] if either a previous counted “up” (“down”) or a “void” precedes an “up” (“down”) which then will be counted also.
  • A120933 (program): Triangle read by rows: T(n,k) is the number of binary words of length n for which the length of the maximal leading nondecreasing subword is k (1<=k<=n).
  • A120940 (program): Alternating sum of the Fibonacci numbers multiplied by their (combinatorial) indices.
  • A120944 (program): Composite squarefree numbers.
  • A120947 (program): a(n) = smallest m such that n-th prime divides Pell(m).
  • A120948 (program): 8n+3^n+5^n.
  • A120949 (program): 2n+3^n+5^n.
  • A120950 (program): 3^n+5^n-2n.
  • A120960 (program): Pythagorean prime powers.
  • A120962 (program): Final digit (in decimal system) of n^(n^n), i.e., n^(n^n) mod 10.
  • A120969 (program): 8n+5^n-3^n.
  • A120978 (program): 2n+5^n-3^n.
  • A120984 (program): Number of ternary trees with n edges and having no vertices of degree 1. A ternary tree is a rooted tree in which each vertex has at most three children and each child of a vertex is designated as its left or middle or right child.
  • A120985 (program): Number of ternary trees with n edges and having no vertices of degree 2. A ternary tree is a rooted tree in which each vertex has at most three children and each child of a vertex is designated as its left or middle or right child.
  • A120986 (program): Triangle read by rows: T(n,k) is the number of ternary trees with n edges and having k middle edges (n >= 0, k >= 0).
  • A120987 (program): Triangle read by rows: T(n,k) is the number of ternary words of length n with k strictly increasing runs (0 <= k <= n; for example, the ternary word 2|01|12|02|1|1|012|2 has 8 strictly increasing runs).
  • A120989 (program): Level of the first leaf (in preorder traversal) of a binary tree, summed over all binary trees with n edges. A binary tree is a rooted tree in which each vertex has at most two children and each child of a vertex is designated as its left or right child.
  • A120990 (program): 5^n-3^n-2n.
  • A120992 (program): Number of integers in n-th run of squarefree positive integers.
  • A120994 (program): Numerators of rationals related to John Wallis’ product formula for Pi/2 from his ‘Arithmetica infinitorum’ from 1659.
  • A120995 (program): Denominators of rationals related to John Wallis’ product formula for Pi/2 (from his ‘Arithmetica infinitorum’ from 1659).
  • A120996 (program): Numerators of partial sums of Catalan numbers scaled by powers of 1/9.
  • A120997 (program): Denominators of partial sums of Catalan numbers scaled by powers of 1/9.
  • A120998 (program): Numerators of partial sums of Catalan numbers scaled by powers of 1/7^2 = 1/49.
  • A120999 (program): Denominators of partial sums of Catalan numbers scaled by powers of 1/7^2 = 1/49.
  • A121000 (program): Numerators of partial sums of Catalan numbers scaled by powers of 1/18^2 = 1/324.
  • A121001 (program): Denominators of partial sums of Catalan numbers scaled by powers of 1/18^2 = 1/324.
  • A121002 (program): Numerators of partial sums of Catalan numbers scaled by powers of 1/5.
  • A121003 (program): Denominators of partial sums of Catalan numbers scaled by powers of 1/5.
  • A121004 (program): Numerators of partial sums of Catalan numbers scaled by powers of 1/(5*5^2)=1/125.
  • A121005 (program): Denominators of partial alternating sums of Catalan numbers scaled by powers of 1/125.
  • A121006 (program): Numerators of partial alternating sums of Catalan numbers scaled by powers of 1/5.
  • A121007 (program): Denominators of partial alternating sums of Catalan numbers scaled by powers of 1/5.
  • A121008 (program): Numerators of partial alternating sums of Catalan numbers scaled by powers of 1/(5*3^2) = 1/45.
  • A121009 (program): Denominators of partial alternating sums of Catalan numbers scaled by powers of 1/(5*3^2) = 1/45.
  • A121010 (program): Numerators of partial alternating sums of Catalan numbers scaled by powers of 1/(5*8^2) = 1/320.
  • A121011 (program): Denominators of partial alternating sums of Catalan numbers scaled by powers of 1/(5*8^2) = 1/320.
  • A121012 (program): Numerators of partial alternating sums of Catalan numbers scaled by powers of 1/(11^2) = 1/121.
  • A121013 (program): Denominators of partial alternating sums of Catalan numbers scaled by powers of 1/(11^2) = 1/121.
  • A121017 (program): Stirling transform of A104600.
  • A121022 (program): Even numbers containing a 2 in their decimal representation.
  • A121023 (program): Multiples of 3 containing a 3 in their decimal representation.
  • A121024 (program): Multiples of 4 containing a 4 in their decimal representation.
  • A121025 (program): Multiples of 5 containing a 5 in their decimal representation.
  • A121026 (program): Multiples of 6 containing a 6 in their decimal representation.
  • A121027 (program): Multiples of 7 containing a 7 in their decimal representation.
  • A121028 (program): Multiples of 8 containing an 8 in their decimal representation.
  • A121029 (program): Multiples of 9 containing a 9 in their decimal representation.
  • A121048 (program): a(n) = n + phi(n), for Euler totient function phi(n).
  • A121049 (program): Let p_n be the polynomial of degree n-1 that interpolates the first n primes (i.e., p_n(i) = prime(i) for 1 <= i <= n.) Then a(n) = p_n(n+1)/2.
  • A121051 (program): Semiprimes which are sums of 4 but no fewer nonzero squares.
  • A121054 (program): Sizes of successive clusters in f.c.c. lattice centered at a tetrahedral hole.
  • A121055 (program): Sizes of successive clusters in b.c.c. lattice centered at midpoint of a short edge.
  • A121062 (program): Partition numbers mod 4.
  • A121068 (program): Numbers k such that 8*k^2 + 7 is prime.
  • A121069 (program): Conjectured sequence for jumping champions greater than 1 (most common prime gaps up to x, for some x).
  • A121079 (program): a(n) = Sum_{i=0..n} C(n,i)^2*i!*4^i + 2^n*n!.
  • A121081 (program): Number of partitions of n into parts with at most one 1 and at most one 2.
  • A121101 (program): Catapolyoctagons (see Cyvin et al. for precise definition).
  • A121102 (program): Catapolyoctagons (see Cyvin et al. for precise definition).
  • A121104 (program): a(n) = Fibonacci(n - 1) modulo the n-th prime number.
  • A121112 (program): Edge-rooted tree-like octagonal systems (see the Cyvin et al. reference for precise definition).
  • A121123 (program): Unbranched a-4-catapolynonagons (see Brunvoll reference for precise definition).
  • A121142 (program): Numbers of isomers of unbranched a-4-catapolydecagons - see Brunvoll reference for precise definition.
  • A121149 (program): Minimal number of vertices in a planar connected n-polyhex.
  • A121150 (program): Minimal number of vertices in an n-polyomino.
  • A121151 (program): Minimal number of vertices in an n-polytrimino (or n-polyiamond).
  • A121152 (program): Dimension of the space spanned by the symmetric functions L_lambda of Gessel and Reutenauer, where lambda ranges over all partitions of n.
  • A121173 (program): Sequence S with property that for n in S, a(n) = a(1) + a(2) +…+ a(n-1) and for n not in S, a(n) = n+1.
  • A121177 (program): Catapolyoctagons (see Cyvin et al. for precise definition).
  • A121179 (program): Related to enumeration of alkane systems - see reference for precise definition.
  • A121190 (program): Number of non-overlapping unbranched staggered conformers of alkanes with 2n-1 nodes and symmetry point group C_s.
  • A121199 (program): 12n+7^n+5^n.
  • A121200 (program): 2n+7^n+5^n.
  • A121201 (program): 7^n+5^n-2n.
  • A121202 (program): a(n) = 12*n + 7^n - 5^n.
  • A121203 (program): 2n+7^n-5^n.
  • A121204 (program): -2n+7^n-5^n.
  • A121205 (program): “666” in bases 7 and higher rewritten in base 10.
  • A121206 (program): a(n) = (2n)! mod n(2n+1).
  • A121213 (program): 7^n-5^n.
  • A121218 (program): a(n) = (n-th prime)th positive integer which is coprime to n.
  • A121224 (program): Decimal expansion of 1/(2*tan(1/2)).
  • A121238 (program): a(n) = (-1)^(1+n+A088585(n)).
  • A121239 (program): Decimal expansion of 10-e.
  • A121240 (program): Numerator of sum_{k=1..n} 1/2^prime(k).
  • A121241 (program): Change 0 to -1 in A090678.
  • A121242 (program): Number of 2’s in first n primes.
  • A121245 (program): (Floor(n*Pi))^n.
  • A121250 (program): Numbers n such that n^2 + 14 is prime.
  • A121251 (program): Number of labeled graphs without isolated vertices and with n edges.
  • A121252 (program): Number of labeled digraphs without isolated vertices and with n arcs.
  • A121253 (program): a(n) = a(n-1)*a(n-3)+1 with a(0)=a(1)=a(2)=0.
  • A121254 (program): Number of conjugated cycles composed of six carbons in (n,n)-nanotubes in terms of the number of naphthalene units.
  • A121255 (program): Number of conjugated cycles composed of ten carbons in (n,n)-nanotubes in terms of the number of naphthalene units.
  • A121256 (program): a(n) = a(n-1)*a(n-3) - 1, starting with a(0)=a(1)=a(2)=2.
  • A121257 (program): Number of conjugated cycles composed of six carbons in (1,1)-nanotubes in terms of the number of naphthalene units.
  • A121258 (program): a(n) = a(n-1)*a(n-2)*a(n-3) - 1 with a(0)=a(1)=a(2)=2.
  • A121259 (program): Numbers n such that (3n^2+1)/4 is prime.
  • A121260 (program): Beginning with a(1)=0, take a(n) to be the smallest number not equal to the product of two consecutive (not distinct) earlier terms.
  • A121262 (program): The characteristic function of the multiples of four.
  • A121273 (program): Number of different n-dimensional convex regular polytopes that can tile n-dimensional space.
  • A121275 (program): (Ceiling(n*Pi))^n.
  • A121277 (program): Row sums of triangle A062993.
  • A121282 (program): a(n) = ceiling(n*Pi*e).
  • A121283 (program): a(n) = floor(n*Pi*e).
  • A121289 (program): a(n) = n/(largest triangular number dividing n).
  • A121290 (program): a(n) = (2^prime(n) - 8)/24 for n>=2.
  • A121292 (program): a(n) = Bell(3*n+1).
  • A121293 (program): a(n) = Bell(3*n+2).
  • A121294 (program): a(m^2) = m^3; a(m^2+k) = m^3 + km, 0 <= k <= m; a(m(m+1)) = (m+1)m^2; a(m(m+1)+k) = (m+1)m^2 + k(2m+1), 0 <= k <= m+1; a((m+1)^2) = (m+1)^3.
  • A121302 (program): Number of directed column-convex polyominoes having at least one 1-cell column.
  • A121311 (program): a(0) = 1, a(1) = 2, a(2) = 5; for n >= 3, a(n) = a(n - 1) - 2*a(n - 2) + a(n - 3).
  • A121314 (program): Triangle T(n,k), 0 <= k <= n, read by rows given by [0, 1, 0, 0, 0, 0, …] DELTA [1, 0, 1, 0, 0, 0, 0, 0, 0, 0, …] where DELTA is the operator defined in A084938.
  • A121315 (program): Products of two consecutive prime powers.
  • A121318 (program): Molecular topological indices of the path graphs P_n
  • A121320 (program): Number of vertices in all ordered (plane) trees with n edges that are at distance two from all the leaves above them.
  • A121323 (program): a(n) = (2*n+1)*a(n-1) - a(n-2) starting a(0)=0, a(1)=1.
  • A121324 (program): Number of digits in quotient {R_(n*R_n)}/(R_n)^2, where R_n=A002275(n),n*R_n=A053422(n).
  • A121326 (program): Primes of the form 4*k^2 + 1.
  • A121334 (program): Triangle, read by rows, where T(n,k) = C( n*(n+1)/2 + n-k, n-k), for n>=k>=0.
  • A121335 (program): Triangle, read by rows, where T(n,k) = C( n*(n+1)/2 + n-k + 1, n-k), for n>=k>=0.
  • A121336 (program): Triangle, read by rows, where T(n,k) = C( n*(n+1)/2 + n-k + 2, n-k), for n>=k>=0.
  • A121340 (program): List of triples {1^(2^k), 2^(2^k), 3^(2^k)} for k>0.
  • A121343 (program): a(n) = Fibonacci(n) mod n(n+1)/2.
  • A121347 (program): Largest number whose factorial is less than (n!)^2.
  • A121349 (program): a(n) = round(Pi*2^(n-1)) for n >= 1, a(0) = 1.
  • A121351 (program): a(n] = (3*n+1)*a(n-1) - a(n-2), starting a(0)=0, a(1)=1.
  • A121353 (program): a(n) = (3*n - 2)*a(n-1) - a(n-2) starting a(0)=0, a(1)=1.
  • A121354 (program): a(n) = (3*n-1)*a(n-1) - a(n-2).
  • A121357 (program): Number of different, not necessarily connected, labeled trivalent diagrams of size n.
  • A121358 (program): Least prime factor of pyramidal number A000292(n), a(1) = 1.
  • A121359 (program): Greatest prime factor of pyramidal number A000292(n).
  • A121361 (program): Expansion of f(x^1, x^5) * psi(x^2) in powers of x where psi(), f() are Ramanujan theta functions.
  • A121362 (program): Expansion of eta(q)*eta(q^6)*eta(q^10)*eta(q^15)/(eta(q^3)*eta(q^5)) in powers of q.
  • A121363 (program): Expansion of q^(-1/4)(eta(q)*eta(q^6)*eta(q^9)/eta(q^3))^2/(eta(q^2)eta(q^18)) in powers of q.
  • A121364 (program): Convolution of A066983 with the double Fibonacci sequence A103609.
  • A121365 (program): a(n) = 6*a(n-1) - 9*a(n-2) + n + 1.
  • A121366 (program): a(n) = 2^(n*(3n+5)/2)= 2^A115067(n+1).
  • A121367 (program): a(1) = a(2) = 1, a(n) = a(n-1) + A007947(a(n-2)) for n >= 3, i.e., a(n) = a(n-1) plus the largest squarefree divisor of a(n-2).
  • A121373 (program): Expansion of f(x) = f(x, -x^2) in powers of x where f(, ) is Ramanujan’s general theta function.
  • A121377 (program): ASCII codes for decimal digits.
  • A121378 (program): EBCDIC codes for decimal digits.
  • A121381 (program): a(n) = Ceiling(n*Pi).
  • A121384 (program): a(n) = ceiling(n*e).
  • A121387 (program): Semiprimes p*q with p and q primes of the form 4k+1 (A002144).
  • A121389 (program): a(n) = 10^Fibonacci(n) - 1.
  • A121401 (program): a(n)=((sqrt(3)+1)^n+(sqrt(3)-1)^n)^2/2^(n+1).
  • A121406 (program): a(1) = a(2) = 0; a(3) = 2; for n >= 4, a(n) = (prime(n-1)-2)*a(n-1), where prime(n) is the n-th prime.
  • A121442 (program): Expansion of (1-x^2)/(1-x-9*x^2+x^3).
  • A121443 (program): Sum of divisors d of n which are odd and n/d is not divisible by 3.
  • A121444 (program): Expansion of f(x^3, x^9) * f(x, x^2) in powers of x where f(, ) is Ramanujan’s general theta functions.
  • A121446 (program): Number of ternary trees with n edges and such that the first leaf in the preorder traversal is at level 1.
  • A121448 (program): Triangle read by rows: T(n,k) is the number of binary trees with n edges and having k vertices of outdegree 1 (n>=0, k>=0). A binary tree is a rooted tree in which each vertex has at most two children and each child of a vertex is designated as its left or right child.
  • A121449 (program): Expansion of (1-3*x+2*x^2)/(1-4*x+3*x^2+x^3).
  • A121450 (program): Expansion of (theta_4(q^3)^2 - theta_4(q)^2)/4 in powers of q.
  • A121451 (program): Maximum product over partitions into parts of the form 3k+2.
  • A121453 (program): Numbers m such that (m mod k) > (m+2 mod k) with least value of k = 5.
  • A121454 (program): Expansion of q * psi(-q) * psi(-q^7) in powers of q where psi(q) is a Ramanujan theta function.
  • A121455 (program): Expansion of q*(phi(-q)psi(q^4))^2 in powers of q where phi(), psi() are Ramanujan theta functions.
  • A121456 (program): Expansion of q*(psi(-q)psi(-q^3))^2 in powers of q where psi() is a Ramanujan theta function.
  • A121458 (program): Expansion of (1+x-2*x^2)/(1-21*x^2-7*x^3).
  • A121460 (program): Triangle read by rows: T(n,k) is the number of nondecreasing Dyck paths of semilength n, having k returns to the x-axis (1<=k<=n).
  • A121461 (program): Triangle read by rows: T(n,k) is the number of nondecreasing Dyck paths of semilength n, having last ascent of length k (1 <= k <= n).
  • A121462 (program): Triangle read by rows: T(n,k) is the number of nondecreasing Dyck paths of semilength n, having pyramid weight k (1 <= k <= n).
  • A121463 (program): Triangle read by rows: T(n,k) is the number of nondecreasing Dyck paths of semilength n, having k distinct valley levels (n>=1, k>=0).
  • A121464 (program): Triangle read by rows: T(n,k) is the number of nondecreasing Dyck paths of semilength n, having k triangles (0<=k<=n). A triangle in a Dyck path is a subpath of the form U^h D^h, starting at the x-axis; here U=(1,1), D=(1,-1), h being the height of the triangle.
  • A121466 (program): Triangle read by rows: T(n,k) = is the number of directed column-convex polyominoes of area n having along the lower contour exactly k reentrant corners, i.e., a vertical step that is followed by a horizontal step (n >= 1, k >= 0).
  • A121470 (program): Expansion of x*(1+5*x+2*x^2+x^3)/((1+x)*(1-x)^3).
  • A121471 (program): a(n) = 9*n^2/4 -4*n +19/8 -3*(-1)^n/8.
  • A121478 (program): Triangular numbers with three distinct prime factors.
  • A121482 (program): Number of nondecreasing Dyck paths of semilength n and having no peaks at odd level (n>=0). A nondecreasing Dyck path is a Dyck path for which the sequence of the altitudes of the valleys is nondecreasing.
  • A121485 (program): Number of nondecreasing Dyck paths of semilength n and having no peaks at even level (n>=0). A nondecreasing Dyck path is a Dyck path for which the sequence of the altitudes of the valleys is nondecreasing.
  • A121487 (program): Triangle read by rows: T(n,k) is the number of nondecreasing Dyck paths of semilength n and having abscissa of first return equal to 2k (1<=k<=n). A nondecreasing Dyck path is a Dyck path for which the sequence of the altitudes of the valleys is nondecreasing.
  • A121488 (program): a(n) = 8*n^2 - floor(n*sqrt(8))^2.
  • A121489 (program): Diagonal of array A121490.
  • A121496 (program): Run lengths of successive numbers in A068225.
  • A121497 (program): Binomial transform of the characteristic function of the prime numbers (A010051).
  • A121498 (program): Numerators of partial alternating sums of Catalan numbers scaled by powers of 1/(29^2) = 1/841.
  • A121499 (program): Denominators of partial alternating sums of Catalan numbers scaled by powers of 1/(29^2) = 1/841.
  • A121500 (program): Minimal polygon values for a certain polygon problem leading to an approximation of Pi.
  • A121505 (program): Hit triangle for unit circle area (Pi) approximation problem described in A121500.
  • A121509 (program): a(n) = 5*n^2/2 - 5*n + 13/4 - (-1)^n/4.
  • A121511 (program): a(n) = a(n-1) + a(n-4) - a(n-5).
  • A121512 (program): a(n) = a(n-1) + a(n-3) - a(n-4) for n>4, with a(1)=1, a(2)=4, a(3)=10, a(4)=4.
  • A121517 (program): a(n) = 4*a(n-1) + 4*a(n-2) - a(n-3); a(0)=1, a(1)=1, a(2)=7.
  • A121527 (program): a(0)=1. a(n) = n-th integer from among those positive integers which are coprime to the sum of the previous terms of this sequence.
  • A121528 (program): a(1)=1. a(n) = n-th integer from among those positive integers which are coprime to the sum of the previous terms of this sequence.
  • A121536 (program): Smallest m such that m^3>=n^2.
  • A121538 (program): Increasing sequence: “if n appears then a*n+b doesn’t”, case a(1)=1, a=2, b=1.
  • A121539 (program): Numbers whose binary expansion ends in an even number of 1’s.
  • A121540 (program): Increasing sequence: “if n appears a*n+b does not”, case a(1)=3, a=2, b=1.
  • A121541 (program): Increasing sequence: “if n appears a*n+b does not”, case a(1)=4, a=2, b=1.
  • A121542 (program): Increasing sequence: “if n appears a*n+b does not”, case a(1)=5, a=2, b=1.
  • A121543 (program): “If n appears then n-th prime doesn’t”, with a(1)=1.
  • A121544 (program): Sum of all proper base 4 numbers with n digits (those not beginning with 0).
  • A121545 (program): Coefficients of Taylor series expansion of the operad Prim L.
  • A121546 (program): a(n) = dimension of the space in which the sphere of radius n is of maximum volume.
  • A121553 (program): Total area of all deco polyominoes of height n. A deco polyomino is a directed column-convex polyomino in which the height, measured along the diagonal, is attained only in the last column.
  • A121555 (program): Number of 1-cell columns in all deco polyominoes of height n. A deco polyomino is a directed column-convex polyomino in which the height, measured along the diagonal, is attained only in the last column.
  • A121559 (program): Final result (0 or 1) under iterations of {r mod (max prime p <= r)} starting at r = n.
  • A121560 (program): Lengths of blocks of zeros in sequence A121559.
  • A121561 (program): The number of iterations of “subtract the largest prime less than or equal to the current value” to go from n to the limiting value 0 or 1.
  • A121563 (program): Numerator of Sum[i=1..n] i!/(i^i).
  • A121564 (program): Denominator of Sum[i=1..n] i!/(i^i).
  • A121566 (program): a(n) is the denominator of Sum_{i=1..n} i!/(i^2).
  • A121567 (program): Fibonacci[ (p - 1) ], where p = Prime[n].
  • A121568 (program): Fibonacci[ (p - 1)/2 ], where p = Prime[n].
  • A121569 (program): a(n) = Fibonacci((prime(n)+3)/2) - 1.
  • A121570 (program): Decimal expansion of cosecant of 36 degrees = csc(Pi/5) = 1/sin(Pi/5).
  • A121572 (program): Subprimorials: inverse binomial transform of primorials (A002110).
  • A121573 (program): Prime-gap race; difference of the cumulative sums of gaps above and below prime(2n).
  • A121574 (program): Riordan array (1/(1-2*x), x*(1+x)/(1-2*x)).
  • A121575 (program): Riordan array (-sqrt(4*x^2+8*x+1)+2*x+2), (sqrt(4*x^2+8*x+1)-2*x-1)/2).
  • A121576 (program): Riordan array (2-2*x-sqrt(1-8*x+4*x^2), (1-2*x-sqrt(1-8*x+4*x^2))/2).
  • A121578 (program): Values m of number pairs (m,n) which yield associated matching times on the clock with interchanged hour and minute hands for corresponding n in A121577.
  • A121580 (program): Number of cells in column 1 of all deco polyominoes of height n. A deco polyomino is a directed column-convex polyomino in which the height, measured along the diagonal, is attained only in the last column.
  • A121582 (program): Number of cells in column 2 of all deco polyominoes of height n. A deco polyomino is a directed column-convex polyomino in which the height, measured along the diagonal, is attained only in the last column.
  • A121584 (program): Number of cells in columns 1 and 2 of all deco polyominoes of height n. A deco polyomino is a directed column-convex polyomino in which the height, measured along the diagonal, is attained only in the last column.
  • A121586 (program): Number of columns in all deco polyominoes of height n. A deco polyomino is a directed column-convex polyomino in which the height, measured along the diagonal, is attained only in the last column.
  • A121589 (program): Series expansion of (eta(q^9) / eta(q))^3 in powers of q.
  • A121590 (program): Expansion of (eta(q^3) / eta(q))^12 in powers of q.
  • A121591 (program): Expansion of (eta(q^5) / eta(q))^6 in powers of q.
  • A121592 (program): Expansion of (eta(q)eta(q^9)/eta(q^3)^2)^6 in powers of q.
  • A121596 (program): Expansion of q^(-1/2)(eta(q^3)/eta(q))^6 in powers of q.
  • A121597 (program): Expansion of (eta(q^13) / eta(q))^2 in powers of q.
  • A121601 (program): Decimal expansion of cosecant of 22.5 degrees = csc(Pi/8).
  • A121607 (program): (n^3+n)*3^n.
  • A121613 (program): Expansion of psi(-x)^4 in powers of x where psi() is a Ramanujan theta function.
  • A121621 (program): Real part of (2 + 3i)^n.
  • A121622 (program): Real part of (3 + 2i)^n.
  • A121623 (program): Floor((prime(n)/n)^n).
  • A121625 (program): Real part of (n + n*i)^n.
  • A121626 (program): Real part of (1 + n*i)^n, where i=sqrt(-1).
  • A121627 (program): Real part of a complex operation analogous to the factorials.
  • A121628 (program): Nonnegative k such that 3*k + 1 is a perfect cube.
  • A121629 (program): Finite sum involving signless Stirling numbers of the first kind and the Bell numbers. Appears in the process of normal ordering of n-th power of (a)^2*(a+*a), where a+ and a are boson creation and annihilation operators, respectively.
  • A121633 (program): Sum of the bottom levels of the last column over all deco polyominoes of height n. A deco polyomino is a directed column-convex polyomino in which the height, measured along the diagonal, is attained only in the last column.
  • A121635 (program): Number of deco polyominoes of height n, having no 2-cell columns starting at level 0. A deco polyomino is a directed column-convex polyomino in which the height, measured along the diagonal, is attained only in the last column.
  • A121636 (program): Number of 2-cell columns starting at level 0 in all of deco polyominoes of height n. A deco polyomino is a directed column-convex polyomino in which the height, measured along the diagonal, is attained only in the last column.
  • A121638 (program): Number of deco polyominoes of height n, having no 2-cell columns. A deco polyomino is a directed column-convex polyomino in which the height, measured along the diagonal, is attained only in the last column.
  • A121639 (program): Number of 2-cell columns in all deco polyominoes of height n. A deco polyomino is a directed column-convex polyomino in which the height, measured along the diagonal, is attained only in the last column.
  • A121640 (program): a(1) = 1. a(n) = a(n-1) + (n-th integer from among those positive integers which are coprime to a(n-1)).
  • A121641 (program): a(0) = 1. a(n) = a(n-1) + (n-th integer from among those positive integers which are coprime to a(n-1)).
  • A121644 (program): Slowest increasing sequence with squarefree cumulative sums.
  • A121646 (program): a(n) = Fibonacci(n-1)^2 - Fibonacci(n)^2.
  • A121658 (program): Primes neither of the n^2+1 nor n^2+n+1 form.
  • A121659 (program): Number of partitions of n into parts with at most one part not greater than 2.
  • A121660 (program): Numerator of fraction equal to the continued fraction [4, 6, 9, …, semiprime(n)].
  • A121662 (program): Triangle read by rows: T(i,j) for the recurrence T(i,j) = (T(i-1,j) + 1)*i.
  • A121663 (program): a(0) = 1; if n = 2^k, a(n) = k+2, otherwise a(n)=(A000523(n)+2)*a(A053645(n)).
  • A121665 (program): McKay-Thompson series of class 6B for the Monster group with a(0) = 12.
  • A121667 (program): McKay-Thompson series of class 6D for the Monster group with a(0) = -4.
  • A121668 (program): Products of consecutive Apery numbers, cf. A006221.
  • A121670 (program): a(n) = n^3 - 3*n.
  • A121671 (program): Real part of (1 + n*i)^5.
  • A121672 (program): Real part of (n + i)^5.
  • A121673 (program): a(n) = [x^n] (1 + x*(1+x)^(n-1) )^n.
  • A121674 (program): a(n) = [x^n] (1 + x*(1+x)^n )^n.
  • A121675 (program): a(n) = [x^n] (1 + x*(1+x)^(n+1) )^n.
  • A121676 (program): a(n) = [x^n] (1 + x*(1+x)^(n-1) )^(n+1).
  • A121677 (program): a(n) = A121676(n)/(n+1) = [x^n] (1 + x*(1+x)^(n-1) )^(n+1) / (n+1).
  • A121678 (program): a(n) = [x^n] (1 + x*(1+x)^n )^(n+1).
  • A121679 (program): a(n) = A121678(n)/(n+1) = [x^n] (1 + x*(1+x)^n )^(n+1) / (n+1).
  • A121680 (program): a(n) = [x^n] (1 + x*(1+x)^(n+1) )^(n+1).
  • A121681 (program): a(n) = A121680(n)/(n+1) = [x^n] (1 + x*(1+x)^(n+1) )^(n+1) / (n+1).
  • A121682 (program): Triangle read by rows: T(i,j) = (T(i-1,j) + i)*i.
  • A121686 (program): Number of branches in all binary trees with n edges. A binary tree is a rooted tree in which each vertex has at most two children and each child of a vertex is designated as its left or right child.
  • A121688 (program): G.f.: Sum_{n>=0} x^n * (1+x)^(2^n).
  • A121689 (program): G.f.: Sum_{n>=0} x^n * (1+x)^(n^2).
  • A121690 (program): G.f.: A(x) = Sum_{k>=0} x^k * (1+x)^(k*(k+1)/2).
  • A121693 (program): Number of deco polyominoes of height n and vertical height 3 (i.e., having 3 rows).
  • A121695 (program): Number of odd-length first columns in all deco polyominoes of height n. A deco polyomino is a directed column-convex polyomino in which the height, measured along the diagonal, is attained only in the last column.
  • A121696 (program): Number of even-length first columns in all deco polyominoes of height n. A deco polyomino is a directed column-convex polyomino in which the height, measured along the diagonal, is attained only in the last column.
  • A121699 (program): Floor((prime(n+1)/prime(n))^n).
  • A121701 (program): Lexicographically earliest sequence such that a(m)<>a(n) for all m with m<>n except either for m=2*n or n=2*m.
  • A121706 (program): a(n) = Sum_{k=1..n-1} k^n.
  • A121708 (program): Numerator of Sum/Product of first n Fibonacci numbers A000045[n].
  • A121709 (program): Numerator of Sum/Product of first n Lucas numbers A000032[n].
  • A121718 (program): Write 0, 1, …, n in base 3 and add as if they were decimal numbers.
  • A121720 (program): a(n)= 4*a(n-2) -2*a(n-4).
  • A121722 (program): Triangle T(n,k) = 1 + k*n*(n+1)/2, read by rows.
  • A121723 (program): a(n) = A098916(n+2) + (1-n) * A067318(n).
  • A121724 (program): Generalized central binomial coefficients for k=2.
  • A121725 (program): Generalized central coefficients for k=3.
  • A121726 (program): Sum sequence A000522 then subtract 0,1,2,3,4,5,…
  • A121740 (program): Solutions to the Pell equation x^2 - 17y^2 = 1 (y values).
  • A121744 (program): Numbers n such that (1 + Sum[Prime[k],{k,1,n}]) = (1 + A007504[n]) divides primorial number p(n)# = Product[Prime[k],{k,1,n}] = A002110[n].
  • A121746 (program): Number of deco polyominoes of height n, consisting only of columns of even length. A deco polyomino is a directed column-convex polyomino in which the height, measured along the diagonal, is attained only in the last column.
  • A121749 (program): Number of deco polyominoes of height n, consisting only of columns of odd length. A deco polyomino is a directed column-convex polyomino in which the height, measured along the diagonal, is attained only in the last column.
  • A121751 (program): Number of deco polyominoes of height n in which all columns end at an even level. A deco polyomino is a directed column-convex polyomino in which the height, measured along the diagonal, is attained only in the last column.
  • A121753 (program): Number of deco polyominoes of height n in which all columns end at an odd level. A deco polyomino is a directed column-convex polyomino in which the height, measured along the diagonal, is attained only in the last column.
  • A121755 (program): Numerator of Sum/Product of first n primes = Numerator[ A007504[n] / A002110[n] ].
  • A121757 (program): Triangle read by rows: multiply Pascal’s triangle by 1,2,6,24,120,720,… = A000142.
  • A121758 (program): In decimal number system, take odd digits of n with negative sign.
  • A121759 (program): In decimal number system, take even digits of n with negative sign.
  • A121762 (program): Single (or isolated or non-twin) primes of form 6n-1.
  • A121763 (program): Numbers n such that 6*n-1 is prime while 6*n+1 is composite.
  • A121764 (program): Single (or isolated or non-twin) primes of form 6n + 1.
  • A121765 (program): Numbers n such that 6*n-1 is composite while 6*n+1 is prime.
  • A121775 (program): T(n, k) = Sum_{d|n} phi(n/d)*binomial(d,k) for n>0, T(0, 0) = 1. Triangle read by rows, for 0 <= k <= n.
  • A121776 (program): Antidiagonal sums of triangle A121775.
  • A121782 (program): Series expansion for mean-squared radius of gyration of rectangles on square lattice.
  • A121801 (program): Expansion of 2*x^2*(3-x)/((1+x)*(1-3*x+x^2)).
  • A121807 (program): Partial sums of A004676.
  • A121810 (program): a(n) = a(n - 1)*a(n - 2) + a(n - 2)*a(n - 3) + a(n - 1)*a(n - 3).
  • A121816 (program): Conjectured chromatic number of the square of an outerplanar graph G^2 as a function of the maximum degree of a vertex of G.
  • A121817 (program): Numbers m such that 23 + 36*m*(m+1) is prime.
  • A121822 (program): Number of closed walks of length 2*n on the 5-cube.
  • A121823 (program): (3^p+p)/(p+1) with (p + 1) odd prime > 3.
  • A121826 (program): a(n) = Product_{k=1..n} D(k), where D() are the doublets, A020338.
  • A121827 (program): Ceiling ((Pi+e)n).
  • A121828 (program): Ceiling((Pi-e)n).
  • A121830 (program): a(n) = floor((Pi - e)*n).
  • A121832 (program): Expansion of 1/(1-x-x^5-x^6).
  • A121833 (program): Expansion of 1/(1-x^2-x^3-x^6).
  • A121839 (program): Decimal expansion of Sum_{k>=1} 1/C(k), where C(k) is a Catalan Number (A000108).
  • A121842 (program): Difference between n^3 and next prime.
  • A121844 (program): Excess of n^3 over previous prime.
  • A121853 (program): Cumulative product of A000120.
  • A121854 (program): a(n) = floor(Pi*(sqrt(n))).
  • A121855 (program): a(n) = ceiling(Pi*sqrt(n)).
  • A121858 (program): Smallest odd number having prime(n) divisors, where prime(n) is the n-th prime=A000040(n).
  • A121867 (program): Let A(0) = 1, B(0) = 0; A(n+1) = Sum_{k=0..n} binomial(n,k)*B(k), B(n+1) = Sum_{k=0..n} -binomial(n,k)*A(k); entry gives A sequence (cf. A121868).
  • A121868 (program): Let A(0) = 1, B(0) = 0; A(n+1) = Sum_{k=0..n} binomial(n,k)*B(k), B(n+1) = Sum_{k=0..n} -binomial(n,k)*A(k); entry gives B sequence (cf. A121867).
  • A121869 (program): Monthly Problem 10791, first expression.
  • A121872 (program): Triangle T(n, k) = (k*ChebyshevU(n, (k+2)/2) + 2*ChebyshevT(n+1, (k+2)/2))/2.
  • A121873 (program): Number of non-crossing plants in the (n+1)-sided regular polygon (contains non-crossing trees).
  • A121875 (program): Triangular array read by rows: see Comments for definition.
  • A121879 (program): a(n) = Fibonacci(n-1)*a(n-1) - a(n-2), with a(1)=0, a(2)=1.
  • A121881 (program): a(n) = (4*a(n-1)*a(n-3) + a(n-2)^2)/a(n-4), with a(1)=…=a(4)=1.
  • A121882 (program): Numbers k such that k + D(k) + 1 is prime, where D() are the doublets, A020338.
  • A121883 (program): a(n) = (2*a(n-1)*a(n-3) + a(n-2)^2)/a(n-4), with a(1)=..=a(4)=1.
  • A121884 (program): Excess of n-th semiprime over previous prime.
  • A121892 (program): Row sums of triangle in A066094.
  • A121893 (program): Composite integers not equal to k*[k or k+1 or k+2] where k is a natural number.
  • A121896 (program): Let M be the matrix defined in A111490. Sequence gives M(1,1), M(1,2)+M(1,2)+M(2,2), M(1,3)+M(2,3)+M(3,1)+M(3,2)+M(3,3), etc.
  • A121899 (program): a(n) = ceiling((Pi + e)*sqrt(n)).
  • A121901 (program): a(n) = floor((Pi + e)*sqrt(n)).
  • A121906 (program): Excess of n-th 3-almost prime A014612 over previous prime.
  • A121907 (program): Expansion of g.f.: (1 + x + x^2)/(1 - 2*x - 2*x^2).
  • A121911 (program): First four terms are decimal digits of 1979. Rest are found by adding four previous terms modulo 10.
  • A121924 (program): Number of splitting steps that one can take with a sequence of n 2’s.
  • A121925 (program): a(n) = floor(n*(Pi^e + e^Pi)).
  • A121926 (program): a(n) = prime(n) + n!.
  • A121928 (program): a(n) = ceiling(n*(e^Pi - Pi^e)).
  • A121929 (program): a(n) = ceiling(n*(e^Pi + Pi^e)).
  • A121930 (program): a(n) = floor(n*(e^Pi - Pi^e)).
  • A121934 (program): Smallest positive number m such that m == i (mod i+1) for all 1<=i<=n.
  • A121935 (program): Decimal expansion of 1/log(3).
  • A121937 (program): a(n) = least m >= 2 such that (n mod m) > (n+2 mod m).
  • A121940 (program): Product of the first n primes of the form 6k+1.
  • A121944 (program): Composite number of the form 4n^2+1.
  • A121945 (program): a(n) is the sum of the first n factorials in decreasing powers from n to 1. a(n) = Sum_{k = 1..n} k!^(n-k+1).
  • A121946 (program): Let r be the matrix {{1,1},{0,1}} and b={{1,0},{1,0}}. Let A be the semigroup generated by r and b. a(n) is the number of words of length n in A.
  • A121948 (program): Floor of n-th 3-almost prime / n.
  • A121953 (program): a(n) = (n-2)*a(n-2) + a(n-3), with a(1)=0, a(2)=1, a(3)=1.
  • A121955 (program): Expansion of x^2*(9 + 8*x - 8*x^2)/((1+x-x^2)*(1-2*x-4*x^2)).
  • A121956 (program): a(n) = a(n-1) + (n-2)*a(n-2) + a(n-3) starting a(0)=0, a(1)=a(2)=1.
  • A121958 (program): a(n) = a(n-2) + (n^2 - 3*n + 1)*a(n-1) with a(1)=0, a(2)=1, a(3)=1.
  • A121963 (program): Expansion of x^2*(1 + 2*x + 7*x^2 - 3*x^3 + x^4)/(1 - 26*x^3 - x^6).
  • A121965 (program): a(n) = (n-1)*a(n-1)-a(n-2), a(0)=0, a(1)=1.
  • A121966 (program): a(n) = a(n-1) - (n-1)*a(n-2), with a(0) = 1, a(1) = 2.
  • A121968 (program): a(n) = 2*a(n-1) - a(n-2) + n + 1.
  • A121982 (program): Numbers n such that n^2 + 15 is prime.
  • A121986 (program): Expansion of x*(-1+2*x-3*x^3+x^4)/((x^3+x^2+x-1) * (x-1)^2).
  • A121987 (program): a(n + 4) = (n + 2)*(a(n + 3) - a(n) + 1) for n > 3, a(0) = a(1) = a(2) = a(3) = 1.
  • A121988 (program): Number of vertices of the n-th multiplihedron.
  • A121989 (program): a(n) = (n - 1)*(a(n - 2) - a(n - 3) + 1), a(0) = a(1) = a(2) = 1.
  • A121990 (program): Expansion of x*(1+9*x+2*x^2)/((1-x)*(1-3*x+x^2)).
  • A121991 (program): a(n) = 3*a(n-1) - a(n-2) - a(n-3) + 12.
  • A121996 (program): Sums of two squares mod 100.
  • A121997 (program): Count up to n, n times.
  • A121998 (program): Table, n-th row gives numbers between 1 and n that have a common factor with n.
  • A122002 (program): a(0)=5; otherwise a(n) = (n mod 4) if n is odd, a(n) = h + 4, where h = (highest odd divisor of n) mod 4 if n is even.
  • A122006 (program): Expansion of x^2*(1-x)/((1-3*x)*(1-3*x^2)).
  • A122007 (program): Expansion of 2*x^2*(1-2*x) / ((3*x-1)*(3*x^2-1)).
  • A122008 (program): Expansion of (2*x-1)*(x-1)*x / ((3*x-1)*(3*x^2-1)).
  • A122009 (program): G.f. x*(1-11*x+6*x^2)/(1-12*x+15*x^2-2*x^3).
  • A122010 (program): G.f. x^2*(1-5*x)/(1-12*x+15*x^2-2*x^3).
  • A122011 (program): G.f. x^2*(1+x)/(1-12*x+15*x^2-2*x^3).
  • A122012 (program): G.f.: x^2*(3+3*x-2*x^2)/ ( (x^2-x-1) * (x^2+x-1)).
  • A122016 (program): Riordan array(1, x*(1+2*x)/(1-x)).
  • A122020 (program): Sum[k=0..n] Eulerian[n,k]*n^k.
  • A122021 (program): a(n) = a(n-2) - (n-1)*a(n-3), with a(0) = 0, a(1) = 1, a(2) = 2.
  • A122022 (program): a(n) = a(n-1) - (n-1)*a(n-4), with a(0) = 0, a(1) = 1, a(2) = 2, a(3) = 1.
  • A122025 (program): a(n) = (3*a(n-1)*a(n-4) - a(n-2)*a(n-3)) / a(n-5).
  • A122027 (program): Largest integer m such that every n-tournament contains a transitive (i.e., acyclic) sub-tournament with at least m vertices.
  • A122031 (program): a(n) = a(n - 1) + (n - 1)*a(n - 2).
  • A122033 (program): a(n) = 2*a(n-1) - 2*(n-2)*a(n-2), with a(0)=1, a(1)=2.
  • A122037 (program): Largest prime factor of number equal to the arithmetic mean of four successive primes.
  • A122038 (program): a(n) = 1*3^(3*n) + 2*3^(2*n) - 3*3^(1*n).
  • A122041 (program): a(n) = 2*a(n-1) - 1 for n>1, a(1)=23.
  • A122044 (program): a(n) = a(n-2) - (n-3)*a(n-3), with a(0)=0, a(1)=1, a(2)=2.
  • A122045 (program): Euler (or secant) numbers E(n).
  • A122046 (program): Partial sums of floor(n^2/8).
  • A122047 (program): Degree of the polynomial P(n,x), defined by a Somos-6 type sequence: P(n,x)=(x^(n-1)*P(n-1,x)*P(n-5,x) + P(n-2,x)*P(n-4,x))/P(n-6,x), initialized with P(n,x)=1 at n<0.
  • A122048 (program): a(n) = (n-2)*a(n-2) - a(n-3), with a(0)=0, a(1)=1, a(2)=2.
  • A122049 (program): a(n) = a(n-1) - (n-4)*a(n-4), with a(0)=0, a(1)=1, a(2)=2, a(3)=1.
  • A122053 (program): Triangle T(n, k) = 2*(-1 + 2*k)*T(n-1, k) - T(n-2, k) with T(-2, k) = T(-1, k) = 1, read by rows.
  • A122056 (program): A Somos 9-Hone exponent type recursion: a(n) = (x^(n-1)*a(n - 1)a(n - 8) - a(n - 4)*a(n - 5))/a(n - 9).
  • A122057 (program): a(n) = (n+1)! * (H(n+1) - H(2)), where H(n) are the harmonic numbers.
  • A122058 (program): Expansion of x*(1 + 4*x + 6*x^2 + 6*x^3)/((1-x)*(1 - 11*x^2 - 12*x^3)).
  • A122061 (program): First pentagonal number, 2nd hexagonal number, 3rd heptagonal number, 4th octagonal number and then repeat the same pattern: 5th pentagonal, 6th hexagonal, 7th heptagonal, 8th octagonal, etc.
  • A122062 (program): Numbers n such that n^2 + 16 is prime.
  • A122063 (program): a(1) = 17, a(n) = sum of digits of all previous terms.
  • A122067 (program): a(n) = 2^A014105(n).
  • A122068 (program): Expansion of x*(1-3*x)*(1-x)/(1-7*x+14*x^2-7*x^3).
  • A122069 (program): a(n) = 3*a(n-1) + 9*a(n-2) for n > 1, with a(0)=1, a(1)=3.
  • A122070 (program): Triangle given by T(n,k) = Fibonacci(n+k+1)*binomial(n,k) for 0<=k<=n.
  • A122071 (program): Sum over divisors d of 2n+1 of Kronecker(-18/d).
  • A122072 (program): Greatest prime less than 10n.
  • A122074 (program): a(0)=1, a(1)=6, a(n) = 7*a(n-1) - 2*a(n-2).
  • A122075 (program): Coefficients of a generalized Pell-Lucas polynomial read by rows.
  • A122076 (program): Coefficients of a generalized Jaco-Lucas polynomial (even indices) read by rows.
  • A122088 (program): Add 10, subtract 5, add 10, subtract 5, ad infinitum.
  • A122089 (program): a(1)=a(2)=1. a(n) = smallest integer which is greater than a(n-1) and is coprime to (a(n-1)+a(n-2)).
  • A122092 (program): a(n) = (n-2)*a(n-1) - (n-1)*a(n-2), with a(0)=1, a(1)=1.
  • A122098 (program): Smallest number, different from 1, which when multiplied by “n” produces a number with “n” as its rightmost digits.
  • A122099 (program): a(n) = -3*a(n-1) + a(n-3) for n>2, with a(0)=1, a(1)=1, a(2)=0.
  • A122100 (program): a(n) = 3*a(n-1) - a(n-3) for n>2, with a(0)=1, a(1)=-1, a(2)=0.
  • A122101 (program): T(n,k) = Sum_{i=0..k} (-1)^(k-i)*binomial(k,i)*A000670(n-k+i).
  • A122102 (program): a(n) = Sum_{k=1..n} prime(k)^4.
  • A122103 (program): Sum of the fifth powers of the first n primes.
  • A122105 (program): Sum of the bottom levels of all columns in all deco polyominoes of height n. A deco polyomino is a directed column-convex polyomino in which the height, measured along the diagonal, is attained only in the last column.
  • A122109 (program): a(n) = 9*a(n-2) - 4*a(n-3) for n > 2 with a(0)=1, a(1)=2.
  • A122111 (program): Self-inverse permutation of the positive integers induced by partition enumeration in A112798 and partition conjugation.
  • A122112 (program): a(n) = 4*a(n-2) - a(n-1), with a(0)=1, a(1)=-2.
  • A122114 (program): Primes of the form 2n^2 + 26n + 1.
  • A122117 (program): a(n) = 3*a(n-1) + 4*a(n-2), with a(0)=1, a(1)=2.
  • A122120 (program): a(n) = 4*a(n-1) + 9*a(n-2), for n>1, with a(0)=1, a(1)=3.
  • A122122 (program): a(0) = 1; for n>0, a(n) = 2*(n+2)*4^(n-2)-(n/4)*((3-4*n)/(1-2*n))*binomial(2*n,n).
  • A122123 (program): Product of the first n 5-almost primes (A014614).
  • A122124 (program): Numbers n such that 25 divides Sum[ Prime[k]^n, {k,1,n}].
  • A122132 (program): Squarefree numbers multiplied by binary powers.
  • A122144 (program): Numbers n such that q(n)=M(n) where q(n) is the largest prime divisor of n and M(n) is the largest prime power divisor of n.
  • A122145 (program): Numbers n such that q(n) < M(n) where q(n) is the largest prime divisor of n and M(n) is the largest prime power divisor of n.
  • A122150 (program): Numerator of Sum[ (-1)^(k+1) * 1/2^Prime[k], {k,1,n} ].
  • A122155 (program): Simple involution of natural numbers: List each block of (2^k)-1 numbers (from (2^k)+1 to 2^(k+1) - 1) in reverse order and fix the powers of 2.
  • A122161 (program): Expansion of x*(1 - 3*x + x^2) / (1 - x - 2*x^2 + x^3).
  • A122162 (program): Coefficient of q-series for constant term of Tate curve.
  • A122163 (program): Expansion of f(-q)^2*P(q) in powers of q.
  • A122165 (program): Continued fraction expansion of constant x = Sum_{n>=0} 1/5^(2^n).
  • A122167 (program): Expansion of x*(-1+5*x-6*x^2+x^3) / ( (2*x-1)*(x^3-3*x^2+1) )
  • A122173 (program): Expansion of -x * (x^5+x^4-15*x^3+19*x^2-8*x+1) / (x^6-12*x^5+34*x^4-30*x^3+6*x^2+3*x-1).
  • A122174 (program): First row sum of the matrix M^n, where M is the 5 X 5 matrix {{0,-1,-1,-1,-1}, {-1,0,-1,-1,0}, {-1,-1,0,0,0}, {-1,-1,0,1,0}, {-1,0,0,0,1}}.
  • A122175 (program): Triangle, read by rows, where T(n,k) = C( k*(k+1)/2 + n-k, n-k) for n>=k>=0.
  • A122176 (program): Triangle, read by rows, where T(n,k) = C( k*(k+1)/2 + n-k + 1, n-k) for n>=k>=0.
  • A122177 (program): Triangle, read by rows, where T(n,k) = C( k*(k+1)/2 + n-k + 2, n-k) for n>=k>=0.
  • A122178 (program): Triangle, read by rows, where T(n,k) = C( n*(n+1)/2 + n-k - 1, n-k), for n>=k>=0.
  • A122181 (program): Numbers n that can be written as n = x*y*z with 1<x<y<z (A122180(n)>0).
  • A122184 (program): Numerator of Sum_{k=0..2n} (-1)^k/C(2n,k)^3.
  • A122186 (program): First row sum of the 4 X 4 matrix M^n, where M={{10, 9, 7, 4}, {9, 8, 6, 3}, {7, 6, 4, 2}, {4, 3, 2, 1}}.
  • A122187 (program): First row sum of the matrix M^n, where M is the 3 X 3 matrix [[6, 5, 3], [5, 4, 2], [3, 2, 1]] (n>=0).
  • A122188 (program): Triangle read by rows, formed from the coefficients of characteristic polynomials of the following sequence of matrices: 2 X 2 {{0, 1}, {1, 1}}, 3 X 3 {{0, 1, 0}, {0, 0, 1}, {1, 1, 1}}, 4 X 4 {{0, 1,0, 0}, {0, 0, 1, 0}, {0, 0, 0, 1}, {1, 1, 1, 1}}, 5 X 5 {{0, 1, 0, 0, 0}, {0, 0, 1, 0, 0}, {0, 0, 0, 1, 0}, {0, 0, 0, 0, 1}, {1, 1, 1, 1, 1}}, …
  • A122189 (program): Heptanacci numbers: each term is the sum of the preceding 7 terms, with a(0),…,a(6) = 0,0,0,0,0,0,1.
  • A122190 (program): Expansion of q^(-1/4) * eta(q^2) * eta(q^5)^3 / (eta(q) * eta(q^10)) in powers of q.
  • A122194 (program): Numbers that are the sum of exactly two sets of Fibonacci numbers.
  • A122196 (program): Fractal sequence: count down by 2’s from successive integers.
  • A122197 (program): Fractal sequence: count up to successive integers twice.
  • A122198 (program): Permutation of natural numbers: a recursed variant of A122155.
  • A122199 (program): Permutation of natural numbers: a recursed variant of A122155.
  • A122213 (program): a(n) = (sum of the divisors of n)th integer from among those positive integers which are coprime to n.
  • A122218 (program): Pascal array A(n,p,k) for selection of k elements from two sets L and U with n elements in total whereat the nl = n - p elements in L are labeled and the nu = p elements in U are unlabeled and (in this example) with p = 2 (read by rows).
  • A122219 (program): Period 9: repeat 5, 4, 5, 4, 3, 4, 5, 4, 5.
  • A122220 (program): a(n) = (prime(n)^6-prime(n)^2))/20.
  • A122229 (program): a(n) = A014486(A122228(n)).
  • A122230 (program): a(n) = A007088(A122229(n)).
  • A122247 (program): Partial sums of A005187.
  • A122248 (program): a(n) - a(n-1) = A113474(n).
  • A122249 (program): Numerators of Hankel transform of 1/(2n+1).
  • A122250 (program): Partial sums of A004128.
  • A122257 (program): Characteristic function of Pierpont primes (A005109).
  • A122258 (program): Number of Pierpont primes <= n.
  • A122259 (program): Primes p such that p - 1 is not 3-smooth.
  • A122260 (program): Multiplicative closure of Pierpont primes.
  • A122263 (program): a(n) = 2*a(n-1)-a(n-2)+2*(Prime[n+1]-Prime[n]).
  • A122264 (program): 2 X 2 vector matrix Markov of a Prime gap affine type.
  • A122278 (program): Records in A122277.
  • A122299 (program): Expansion of x * (1-x) / ( 1 - 2*x - 3*x^2 + x^3 ).
  • A122365 (program): The (1,6)-entry of the matrix M^n, where M is the 6 X 6 matrix {{1, 1, 1, 1, 1, 1},{1, 0, 0, 0, 1, 0},{1, 0, 0, 1, 0, 0},{1, 0, 1, 0, 0, 0},{1, 1, 0, 0, 0, 0}, {1, 0, 0, 0, 0, 0}}.
  • A122366 (program): Triangle read by rows: T(n,k) = binomial(2*n+1,k), 0 <= k <= n.
  • A122367 (program): Dimension of 3-variable non-commutative harmonics (twisted derivative). The dimension of the space of non-commutative polynomials in 3 variables which are killed by all symmetric differential operators (where for a monomial w, d_{xi} ( xi w ) = w and d_{xi} ( xj w ) = 0 for i != j).
  • A122368 (program): Dimension of 4-variable non-commutative harmonics (twisted derivative). The dimension of the space of non-commutative polynomials in 4 variables which are killed by all symmetric differential operators (where for a monomial w, d_{xi} ( xi w ) = w and d_{xi} ( xj w ) = 0 for i/=j).
  • A122369 (program): Dimension of 5-variable non-commutative harmonics (twisted derivative). The dimension of the space of non-commutative polynomials in 5 variables which are killed by all symmetric differential operators (where for a monomial w, d_{xi} ( xi w ) = w and d_{xi} ( xj w ) = 0 for i/=j).
  • A122373 (program): Expansion of (c(q)^3 + c(q^2)^3) / 27 in powers of q where c() is a cubic AGM theta function.
  • A122377 (program): a(n) is the n-th term in periodic sequence repeating the divisors of n in increasing order.
  • A122383 (program): a(n) = m-th positive integer which is coprime to n, where phi(n) is number of positive integers which are <= n and are coprime to n and m = phi(n) if phi(n)|n, else m = n mod phi(n)..
  • A122391 (program): Dimension of 2-variable non-commutative harmonics (Hausdorff derivative). The dimension of the space of non-commutative polynomials in 2 variables which are killed by all symmetric differential operators (where for a monomial w, d_{xi} ( w ) = sum over all subwords of w deleting xi once).
  • A122392 (program): Dimension of 3-variable non-commutative harmonics (Hausdorff derivative). The dimension of the space of non-commutative polynomials in 3 variables which are killed by all symmetric differential operators (where for a monomial w, d_{xi} ( w ) = sum over all subwords of w deleting xi once).
  • A122410 (program): a(n) = sum of j’s for those k’s, 1 <= k <= n, where gcd(k,n) = p^j, p = prime.
  • A122411 (program): a(n) is the sum of primes p for those k’s, 2 <= k <= n, where gcd(k,n) = p^j > 1. (a(1) = 0.)
  • A122414 (program): Triangle T(n,k) for 1 <= k <= n read by rows, where T(n,k) = 1 if gcd(n,k) is prime, 0 otherwise.
  • A122415 (program): Triangle T(n,k) for 1 < k < n read by rows, where T(n,k) = 1 if gcd(n,k) is prime, 0 otherwise.
  • A122416 (program): Numbers from an irrationality measure for e, with a(1) = 2.
  • A122417 (program): Factorials from an irrationality measure for e, with a(1) = 2.
  • A122430 (program): Primes of the form 1+2*n+3*n^2.
  • A122431 (program): Riordan array ((1+x)^3,x).
  • A122432 (program): Riordan array (1/(1+x)^3,x).
  • A122433 (program): Riordan array ((1+x)^2,x/(1+x)).
  • A122434 (program): Expansion of (1+x)^3/(1+x+x^2).
  • A122437 (program): Allowable values of the “dropping time” of the Collatz (3x+1) iteration.
  • A122438 (program): Riordan array (1/(1-2x), x(1+2x)).
  • A122439 (program): Expansion of 1/(1-2x-x^2+4x^4).
  • A122441 (program): Expansion of 2*(sqrt(1+8x)-3)/(sqrt(1+8x)-5).
  • A122446 (program): G.f. satisfies: A(x) = 1 + x*A(x)^2 + 2*x^2*(A(x)^2 - A(x)); equals the base sequence of pendular trinomial triangle A122445.
  • A122461 (program): Repetitions of even numbers four times.
  • A122466 (program): Semiprimes written in base 2.
  • A122467 (program): Write n-th semiprime in binary, sum as if decimal numbers.
  • A122471 (program): a(n)=7*a(n-1)-n for n> 0, a(0)=1.
  • A122481 (program): a(n) = if n < 10 then n else a(digitsum(n)) + digitsum(n), where digitsum(n)=A007953(n), the sum of digits in decimal representation of n.
  • A122485 (program): Values of A083097(k) such that A083097(k) = A083097(k+1) - 1.
  • A122487 (program): 2 together with odd primes p that divide Fibonacci[(p+1)/2].
  • A122488 (program): Numbers k such that 1 + 2k + 3k^2 is semiprime.
  • A122489 (program): Partial sums of A111939 (= number of primes < semiprime(n)).
  • A122491 (program): a(n) = n * Fibonacci(n) - Sum_{i=0..n} Fibonacci(i).
  • A122496 (program): Triangle, read by rows, defined by f[i, k, l] = binomial(k-l, i - Min(k, l))/2^(k-l), then T(n, m) = f(n, 0, m).
  • A122497 (program): Let f(S) denote the interchange of 1’s and 2’s in S. Let S_0 = 1, S_{N+1} = f(S_N).S_N, where the dot indicates concatenation. Sequence gives S_0.S_1.S_2.S_3….
  • A122504 (program): a(n) = -a(n-6) + 3*a(n-5) + a(n-4) - 7*a(n-3) + a(n-2) + 3*a(n-1).
  • A122507 (program): Triangle in which row n contains the first n terms of A018805.
  • A122508 (program): G.f.: 1/[(1-2x)(1+2x+3x^2)].
  • A122509 (program): Expansion of x/(1 - 2*x^2 - 21*x^3).
  • A122512 (program): Expansion of 1/(1 - x^2 - 2 x^3 + x^4).
  • A122513 (program): Numbers n such that 1+2n+3n^2 is a triangular number.
  • A122514 (program): Expansion of x/(1 - 2*x^2 - x^3 + x^4).
  • A122515 (program): a(n) = A007504(n)-A046992(n).
  • A122517 (program): G.f.: 1/(1 - x^3 - 2 x^4 + x^5)
  • A122518 (program): G.f.: 1/(1 -2 x^3 - x^4 + x^5)
  • A122519 (program): Expansion of x * (x+1) * (x^3-x^2-1) / ((x^2+1) * (x^3+x^2-1)).
  • A122520 (program): Expansion of -x * (4*x^4+4*x^3+3*x^2+2*x+1) / (x^5-x^3-x^2-x-1).
  • A122521 (program): Recursion: a(n) = a(n - 6) + a(n - 8).
  • A122522 (program): a(n) = a(n - 2) + a(n - 8).
  • A122523 (program): Coefficients of series giving the best rational approximations to e.
  • A122525 (program): Triangle read by rows: G(s, rho) = ((s-1)!/s)*Sum_{i=0..s-1} ((s-i)/i!)*(s*rho)^i.
  • A122533 (program): Coefficients of the series giving the best rational approximations to 1/e.
  • A122538 (program): Riordan array (1, x*f(x)) where f(x)is the g.f. of A006318.
  • A122542 (program): Triangle T(n,k), 0 <= k <= n, read by rows, given by [0, 2, -1, 0, 0, 0, 0, 0, …] DELTA [1, 0, 0, 0, 0, 0, 0, 0, …] where DELTA is the operator defined in A084938.
  • A122551 (program): Denominators of the coefficients of the series for InverseErf(x).
  • A122552 (program): a(0)=a(1)=a(2)=1, a(n) = a(n-1) + a(n-2) + 2*a(n-3) for n > 2.
  • A122553 (program): a(0)=1, a(n)=3 for n > 0.
  • A122554 (program): Let S(1) = {1} and, for n>1 let S(n) be the smallest set containing x, 2x and x+2 for each element x in S(n-1). a(n) is the number of elements in S(n).
  • A122558 (program): a(0)=1, a(1)=3, a(n) = 4*a(n-1) + 3*a(n-2) for n > 1.
  • A122562 (program): a(n) = n^3 + 114 * n.
  • A122564 (program): Twin primes of form 4k-1, 4k+1.
  • A122565 (program): Twin primes of form 4k+1, 4k+3.
  • A122566 (program): Primes with index k^2+k+1.
  • A122567 (program): Twin primes modulo 4.
  • A122571 (program): a(1)=a(2)=1, a(n) = 14*a(n-1) - a(n-2).
  • A122572 (program): a(1)=a(2)=1, a(n) = -14a(n-1) - a(n-2).
  • A122573 (program): Expansion of x*(1 + x)*(1 - 3*x^2)/(1 - 4*x^2 + x^4).
  • A122574 (program): a(1) = a(2) = 1, a(n) = -11*a(n-1) + a(n-2).
  • A122576 (program): G.f.: (1 - 2*x + 6*x^2 - 2*x^3 + x^4)/((x-1)^3*(x+1)^4).
  • A122581 (program): a(n) = a(n - 1) - 2*a(n - 2) + a(n - 3) - 4*a(n - 4) + 2*a(n - 5).
  • A122582 (program): a(n) = a(n - 1) - 2*a(n - 2) + a(n - 3) - 2*a(n - 4) + a(n - 5).
  • A122583 (program): a(n) = a(n - 1) - 2*a(n - 2) + a(n - 3) - 6*a(n - 4) + 3*a(n - 5).
  • A122584 (program): Expansion of x*(1+x)*(1-2*x)/(1 - 2*x - x^2 + 2*x^3 - x^4).
  • A122585 (program): Reciprocal of n modulo smallest prime greater than n.
  • A122586 (program): Leading digit of n expressed in base 3.
  • A122587 (program): Leading digit of n in base 4.
  • A122588 (program): Expansion of x/(1 - 9*x + 28*x^2 - 35*x^3 + 15*x^4 - x^5).
  • A122590 (program): a(n) = 2*a(n-1) - a(n-2) - (a(n-1)^2 + a(n-2)^2).
  • A122591 (program): a(n) = 2*a(n-1) - a(n-2) + (a(n-1)^2 + a(n-2)^2).
  • A122592 (program): a(n) = - a(n-1) + a(n-3) + (a(n-1) - a(n-2))^2 + (a(n-2) - a(n-3))^2.
  • A122593 (program): a(n) = -a(n-1) - a(n-3) - (a(n-1) - a(n-2))^2 + (a(n-2) - a(n-3))^2.
  • A122595 (program): Expansion of x/(1 - 3*x + x^2 + x^3 - x^4).
  • A122598 (program): a[0] = 0; a[1] = 1; if n is odd then a[n] = 2*a[n - 1] - ( n - 1)*a[n - 2] otherwise a[n] = 2*(a[n - 1] - (n - 2)*a[n - 2])].
  • A122600 (program): Expansion of 1/(1 + 3*x - 4*x^2 + x^3).
  • A122601 (program): a(n)=(n-th prime +1) modulo 7.
  • A122606 (program): n^(n+1) mod 7.
  • A122608 (program): a(1) = 1; a(2) = 1; a(3) = 1; a(4) = 1; a(5) = 1; a(n) = a(n-1)+4a(n-2)-3a(n-3)-3a(n-4)+a(n-5) for n >= 6.
  • A122610 (program): Triangle read by rows: T(n,k) is coefficient of x^k in Sum_{m=0..n} x^m*(1-x)^(n-m)*(-1)^[(m+1)/2]*binomial(m-[(m+1)/2],[m/2]).
  • A122618 (program): a(n) = n_n, where “N_b” denotes “N read in base b”: if N = Sum c_i 10^i then N_b = Sum c_i b^i.
  • A122619 (program): n_{2n}.
  • A122620 (program): n_{n+1}.
  • A122621 (program): a(n) = n_prime(n).
  • A122622 (program): a(n) = prime(n)_prime(n).
  • A122623 (program): {2^n}_{2^n}.
  • A122624 (program): n_{2^n}.
  • A122625 (program): n_{n^2}.
  • A122626 (program): a(n) = {n^2}_{n^2}.
  • A122627 (program): a(n) = n_t(n) where t() = triangular numbers A000217.
  • A122628 (program): a(n) = t(n)_t(n) where t() = triangular numbers A000217.
  • A122630 (program): a(n) = F(n)_F(n) where F() = Fibonacci numbers A000045.
  • A122634 (program): t(n)_n where t() = triangular numbers A000217.
  • A122635 (program): {n^2}_n.
  • A122636 (program): {2^n}_n.
  • A122638 (program): {n+1}_n.
  • A122639 (program): n_{2n+1}.
  • A122640 (program): a(n) = {2n}_n.
  • A122641 (program): {2n+1}_n.
  • A122642 (program): {2n}_{2n}.
  • A122643 (program): {2n+1}_{2n+1}.
  • A122644 (program): n_phi(n) where phi() = A000010.
  • A122645 (program): a(n) = phi(n)_phi(n) where phi() = A000010.
  • A122646 (program): phi(n)_n where phi() = A000010.
  • A122648 (program): Expansion of e.g.f.: exp(x^2)*(exp(2*x)+1)/2.
  • A122649 (program): Difference between the double factorial of the n-th nonnegative odd number and the double factorial of the n-th nonnegative even number.
  • A122650 (program): Fibonacci numbers starting at F(23).
  • A122651 (program): Number of partitions of n into distinct parts, with each part divisible by the next.
  • A122652 (program): a(0) = 0, a(1) = 4; for n > 1, a(n) = 10*a(n-1) - a(n-2).
  • A122653 (program): a(n) = 10*a(n-1) - a(n-2) with a(0)=0, a(1)=6.
  • A122656 (program): n*floor(n/2)^2.
  • A122657 (program): a(n) = if n mod 2 = 1 then (n^2-1)*n^3/4 else n^5/4.
  • A122658 (program): a(n) = if n mod 2 = 1 then n^3*(n-1)^2/2 else n^5/2.
  • A122666 (program): a(n) = n_d(n) where d() = A000005.
  • A122667 (program): a(n) = d(n)_d(n) = A122618(d(n)), where d = A000005, and A122618 = “n read in base n”.
  • A122668 (program): d(n)_n where d() = A000005.
  • A122670 (program): If n mod 4 = 2 or n mod 4 = 3 then a(n) = 0 else let m=floor(n/4), then a(n) = (2*m)!/m!.
  • A122678 (program): Related to number of n-circum-C_5 H_5 systems.
  • A122679 (program): Related to number of n-circum-C_5 H_5 systems.
  • A122685 (program): a(n) = n! except that a(2) = -2 and a(2n) = 0 for n > 2.
  • A122690 (program): a(n) = 5*a(n-1) + 4*a(n-2) with a(0)=1, a(1)=4.
  • A122693 (program): Bishops on an n X n board (see Robinson paper for details).
  • A122695 (program): Number of edges in the n-th Mycielski graph.
  • A122698 (program): a(1)=a(2)=1 then a(n) = Sum_{d|n, 1<d<n} a(d)*a(n/d).
  • A122701 (program): a(0)=0, a(n) = 2*a(floor(n/2)) + n - 1 for n > 0.
  • A122704 (program): a(n) = Sum_{k=0..n} 3^(n-k)*A123125(n, k).
  • A122708 (program): Number of connected parking functions of length n. This is the number of independent algebraic generators in degree n of the Hopf algebra of parking functions.
  • A122709 (program): a(0)=1; thereafter a(n) = 9*n - 3.
  • A122725 (program): a(n) = A000670(n)^2.
  • A122737 (program): Expansion of 1 - 3*x - sqrt(1 - 6*x + 5*x^2).
  • A122743 (program): Number of normalized polynomials of degree n in GF(2)[x,y].
  • A122746 (program): G.f.: 1/((1-2*x)*(1-2*x^2)).
  • A122747 (program): Bishops on an n X n board (see Robinson paper for details).
  • A122750 (program): Triangle T(n,k) = (-1)^(k+1) if n is odd, = (-1)^k if n and k are even, = 2*(-1)^k if n is even and k is odd, 0<=k<=n.
  • A122751 (program): Number of essentially different semi-magic squares of order 3 with semimagic sum n.
  • A122752 (program): a(0) = 1; a(1) = 1; a(2) = 1; a(n) = (n-1)*a(n-1) + (n-2)*a(n-2) + (n-3)*a(n-3) for n >= 3.
  • A122754 (program): a(n) = 10*n - A101306(n).
  • A122756 (program): Odd-indexed terms, a(n) = 2^n. Even-indexed terms, a(n) = floor(2^n+2^(n-1)).
  • A122757 (program): Process number as a vertex through put triangular product function: m (In)-> {n-states}->m (Out) T(n,m)=m^2*g(n): g(n)=A084221[n].
  • A122758 (program): Triangle read by rows: T(n,m) = 2*n^2*A084221(n) (n>=0, 0 <= m <= n).
  • A122759 (program): Triangle T(n,m) read by rows: 3^n if m is odd, 0 if m is even.
  • A122760 (program): Triangle read by rows: t(n,m) = 2*3^m*(n mod 2).
  • A122761 (program): “Completed” Cantor based power of three triangular array: t(n,m) = 3^m*(1+Mod[n,2]): power sets as {1,0} set + {0,2} set = {1,2} set.
  • A122765 (program): Triangle read by rows, based on the coefficients of derivatives of the polynomials in A130777. Let p(k, x) = x*p(k - 1, x) - p(k - 2, x). Then T(k,x) = dp(k,x)/dx.
  • A122766 (program): Triangle read by rows, based on the coefficients of the second derivatives of the polynomials in A130777. Let p(k, x) = x*p(k - 1, x) - p(k - 2, x). Then T(k,x)=d^2 p(k,x)/dx^2.
  • A122768 (program): Number of combinations which can be taken from the integer partitions of n. Total number of cases in the (n,m)-fragmentation process.
  • A122769 (program): Numbers k such that k^2 is of the form 3*m^2 + 2*m + 1 (A056109).
  • A122770 (program): Numbers k such that A056109(k) is a square.
  • A122772 (program): Numbers k, excluding powers of 2, such that a regular k-sided polygon can be constructed with a ruler and compass.
  • A122774 (program): Triangle of bifactorial numbers, n B m = (2(n-m)-1)!! (2(n-1))!! / (2(n-m))!!, read by rows.
  • A122778 (program): a(n) = Sum_{k=0..n} A(n,k)*n^k where A(n,k) are Eulerian numbers.
  • A122788 (program): (1,3)-entry of the 3 X 3 matrix M^n, where M = {{0, -1, 1}, {1, 1, 0}, {0, 1, 1}}.
  • A122789 (program): The (1,4)-entry in the matrix M^n, where M is the 4 X 4 matrix {{0, -1, -1, 1}, {1, -1, 0, 0}, {0, 1, 1, 0}, {0, 0, 1, 1 }}.
  • A122792 (program): Expansion of eta(q^2)^2/(eta(q)eta(q^3)) in powers of q.
  • A122793 (program): Connell sum sequence (partial sums of the Connell sequence).
  • A122794 (program): Connell (3,2)-sum sequence (partial sums of the (3,2)-Connell sequence).
  • A122795 (program): Connell (5,3)-sum sequence (partial sums of the (5,3)-Connell sequence)
  • A122796 (program): Connell (3,5)-sum sequence (partial sums of the (3,5)-Connell sequence)
  • A122797 (program): A P_3-stuttered arithmetic progression with a(n+1) = a(n) if n is a triangular number, a(n+1) = a(n) + 1 otherwise.
  • A122798 (program): A P_5-stuttered arithmetic progression with a(n+1) = a(n) if n is a pentagonal number, a(n+1) = a(n)+4 otherwise.
  • A122799 (program): A P_7-stuttered arithmetic progression with a(n+1)=a(n) if n is not a heptagonal number, a(n+1)=a(n)+2 otherwise.
  • A122800 (program): A P_4-stuttered arithmetic progression with a(n+1)=a(n) if n is square, a(n+1)=a(n)+2 otherwise.
  • A122801 (program): Number of labeled bipartite graphs on 2n vertices having equal parts and no isolated vertices.
  • A122803 (program): Powers of -2.
  • A122822 (program): The (1,4) entry in the matrix M^n, where M is the 4 X 4 matrix [[0,-1,1,0],[0,0,-1,1],[1,1,1,0],[0,1,1,1]].
  • A122825 (program): a(n) = n + number of previous prime terms, a(1) = 1.
  • A122827 (program): Number of independent generators of degree n of the algebra of Free quasi-symmetric functions (or Malvenuto-Reutenauer algebra of permutations) as a dendriform dialgebra (i.e., number of totally primitive elements).
  • A122830 (program): Expansion of c(q) * c(q^6) / c(q^2)^2 in powers of q where c() is a cubic AGM theta function.
  • A122831 (program): Expansion of b(q^3)b(q^2)^2/(b(q)b(q^6)^2) in powers of q where b(q) is a cubic AGM function.
  • A122832 (program): Exponential Riordan array (e^(x(1+x)),x).
  • A122833 (program): Exponential Riordan array (e^(-x(1+x)),x).
  • A122835 (program): Number of topologies on n labeled elements in which no element belongs to any pair of noncomparable members of the topology.
  • A122840 (program): a(n) is the number of 0’s at the end of n when n is written in base 10.
  • A122841 (program): Greatest k such that 6^k divides n.
  • A122842 (program): a(n) = k such that A038547[2n-1] = k^2.
  • A122844 (program): Triangle read by rows: T[n,k] = the number of ascending runs of length at least k in the permutations of [n] for k <= n.
  • A122848 (program): Exponential Riordan array (1, x(1+x/2)).
  • A122850 (program): Exponential Riordan array (1, sqrt(1+2x)-1).
  • A122851 (program): Number triangle T(n,k) = C(k,n-k)*(n-k)!.
  • A122852 (program): Row sums of number triangle A122851.
  • A122854 (program): Expansion of phi(q)^2*psi(q)^4 in powers of q where phi(),psi() are Ramanujan theta functions.
  • A122855 (program): Expansion of (phi(q^3)phi(q^5) + phi(q)phi(q^15))/2 in powers of q where phi(q) is a Ramanujan theta function.
  • A122856 (program): Expansion of f(x, x^5)^2 in powers of x where f(, ) is Ramanujan’s general theta function.
  • A122857 (program): Expansion of (phi(q)^2 + phi(q^3)^2) / 2 in powers of q where phi() is a Ramanujan theta function.
  • A122858 (program): Expansion of E(k) * K(k) * (2/Pi)^2 in powers of q^2 where E(), K() are complete elliptic integrals and the nome q = exp( -Pi * K(k’) / K(k)).
  • A122859 (program): Expansion of phi(-q)^3 / phi(-q^3) in powers of q where phi() is a Ramanujan theta function.
  • A122860 (program): Expansion of (1 - phi(-q)^3 / phi(-q^3)) / 6 in powers of q where phi() is a Ramanujan theta function.
  • A122861 (program): Expansion of phi(-q)chi(-q)psi(q^3) in powers of q where phi(),chi(),psi() are Ramanujan theta functions.
  • A122864 (program): Expansion of eta(q^3)^2 * eta(q^4) * eta(q^6)^2 * eta(q^36) / (eta(q) * eta(q^9) * eta(q^12)^2) in powers of q.
  • A122865 (program): Expansion of chi(x) * phi(x^3) * psi(-x^3) in powers of x where chi(), phi(), psi() are Ramanujan theta functions.
  • A122868 (program): Expansion of 1/sqrt(1-6x-3x^2).
  • A122869 (program): Primes p that divide Lucas((p-1)/2), where Lucas is A000032.
  • A122870 (program): Primes p that divide Lucas[(p+1)/2] = A000032[(p+1)/2].
  • A122871 (program): Expansion of (1 - 2*x - sqrt(1 - 4*x - 8*x^2))/(6*x^2).
  • A122872 (program): Table by antidiagonals, T(n,k) is k-th number that starts with n in binary representation.
  • A122874 (program): List of pairs n+7, 13-n, n >= 0.
  • A122876 (program): a(0)=1, a(1)=1, a(2)=2, a(n) = a(n-1) - a(n-2) for n>2.
  • A122877 (program): Expansion of (1-2*x-3*x^2-(1-x)*sqrt(1-2*x-7*x^2))/(8*x^3).
  • A122878 (program): Periodic sequence of period 21 related to a simple scheduling problem.
  • A122879 (program): Periodic sequence of period 21.
  • A122880 (program): Catalan numbers minus odd-indexed Fibonacci numbers.
  • A122882 (program): Array of T(n,m)=1*5*…*(4n-3)*3*7*…*(4m-1)*2^(n+m)/(n+m)! by antidiagonals.
  • A122883 (program): The (1,3)-entry in the 3 X 3 matrix M^n, where M = [1,1,1 / 4,2,1 / 9,3,1].
  • A122884 (program): The (2,3)-entry in the n-th power of the 3 X 3 matrix M = [1,1,1; 4,2,1; 9,3,1].
  • A122885 (program): The (3,3)-entry in the n-th power of the 3 X 3 matrix M = [1,1,1; 4,2,1; 9,3,1].
  • A122895 (program): Characteristic function of natural numbers with number of divisors equal to a Fibonacci number.
  • A122896 (program): Riordan array (1, (1 - x - sqrt(1 - 2*x - 3*x^2)) / (2*x)), a Riordan array for directed animals. Triangle read by rows.
  • A122897 (program): Riordan array (1/(1-x), c(x)-1) where c(x) is the g.f. of A000108.
  • A122898 (program): Expansion of (sqrt(21*x^2 - 10*x + 1) + 7*x - 1) / (2*x*(1 - 7*x)).
  • A122899 (program): Triangle with row sums counting directed animals.
  • A122908 (program): A central binomial scaling of the Riordan array (1+x,x) (A097806).
  • A122909 (program): F(n+1)F(2n+2)+F(n)F(2n).
  • A122917 (program): Riordan array (1/(1+x+x^2),x/(1+x)^2).
  • A122918 (program): Expansion of (1+x)^2/(1+x+x^2)^2.
  • A122919 (program): Inverse of Riordan array (1/(1+x+x^2),x/(1+x)^2).
  • A122920 (program): Diagonal sums of number triangle A122919.
  • A122928 (program): Coefficients of a q-series inspired by Andrews and Ramanujan.
  • A122931 (program): Row sums of triangular array A122930.
  • A122932 (program): a(n) = A000085(n) - A000079(n-1).
  • A122935 (program): Triangle T(n,k), 0 <= k <= n, read by rows given by [0, 1, 0, 1, 0, 0, 0, 0, 0, …] DELTA [1, 0, 1, 0, 0, 0, 0, 0, 0, …] where DELTA is the operator defined in A084938.
  • A122943 (program): Odd numbers n ordered by n/2^BigOmega(n), where BigOmega(n) is the number of prime divisors of n with repetition.
  • A122946 (program): a(0)=a(1)=0, a(2)=a(3)=2, for n>=3 a(n)=a(n-1)+4*a(n-3).
  • A122948 (program): First row sum of the 5 X 5 matrix M^n, where M = {{0, -1, 0, 0, 0}, {-1, 1, -1, 0, 0}, {0, -1, 1, -1, 0}, {0, 0, -1, 1, -1}, {0, 0, 0, -1, 1}}, n>=0.
  • A122949 (program): Number of ordered pairs of permutations generating a transitive group.
  • A122952 (program): Decimal expansion of 3*Pi.
  • A122958 (program): a(0)=1, a(n) = 2 - 2^(n-1) for n>0.
  • A122959 (program): a(0) = 1, a(n) = (-1)^n*(2-2^(n-1)) for n>0.
  • A122960 (program): Triangle T(n,k), 0 <= k <= n, read by rows given by [0, 1, -1, -1, 1, 0, 0, 0, 0, 0, 0, …] DELTA [1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, …] where DELTA is the operator defined in A084938.
  • A122961 (program): Alternately form product and sum of all previous terms.
  • A122963 (program): Triangular numbers with semiprime indices.
  • A122964 (program): Semiprimes with triangular indices.
  • A122968 (program): 27th powers: a(n) = n^27.
  • A122969 (program): 28th powers: a(n) = n^28.
  • A122970 (program): 29th powers: a(n) = n^29.
  • A122972 (program): a(1) = 1, a(2) = 2; for n>2, a(n+1) = a(n)*(n-1) + a(n-1)*n.
  • A122973 (program): Number of vertices on the surface of an icosahedron.
  • A122975 (program): Numbers containing no successive even ternary digits.
  • A122983 (program): a(n) = (2 + (-1)^n + 3^n)/4.
  • A122994 (program): a(n) = a(n-1)+9*a(n-2) initialized with a(0)=1, a(1)=3.
  • A122995 (program): Expansion of x*(1+4*x)/(1-x-25*x^2).
  • A122996 (program): Expansion of (1+6*x)/(1-x-49*x^2).
  • A122997 (program): Pentanacci numbers for following initial values: a(0) = 1, a(1) = -1, a(2) = 1, a(3) = -1, a(4) = 1.
  • A122999 (program): G.f.: 1/(1 - x - 25*x^2).
  • A123001 (program): Binary numbers that start 10…
  • A123003 (program): Expansion of g.f.: (8-29*x+24*x^2)/((1-4*x)*(1-3*x)*(1-2*x)^2*(1-x)^2).
  • A123004 (program): Expansion of g.f. x^2/(1 - 2*x - 25*x^2).
  • A123005 (program): Expansion of g.f. x^2/(1-2*x-49*x^2).
  • A123006 (program): Expansion of x^2/(1 -2*x -121*x^2).
  • A123007 (program): Expansion of x*(1+x)/(1 -2*x -9*x^2).
  • A123008 (program): Expansion of x*(1 + 3*x)/(1 - 2*x - 25*x^2).
  • A123009 (program): Expansion of x*(1 + 5*x)/(1 - 2*x - 49*x^2).
  • A123010 (program): a(n) = 5*a(n-1) + a(n-2) - 5*a(n-3), for n>4, with a(1)=1, a(2)=0, a(3)=4, a(4)=16.
  • A123011 (program): a(n) = 2*a(n-1) + 5*a(n-2) for n > 1; a(0) = 1, a(1) = 5.
  • A123012 (program): Expansion of 1/(1 - 2*x - 21*x^2).
  • A123014 (program): E.g.f.: ((1+x)/(1-x))^(1/3)*((1+x+x^2)/(1-x+x^2))^(1/6).
  • A123015 (program): Grow a binary tree using the following rules. Initially there is a single node labeled 1. At each step we add 1 to all labels less than 3. If a node has label 3 and zero or one descendants we add a new descendant labeled 1. Sequence gives sum of all labels at step n.
  • A123016 (program): a(1)=1, a(2)=1, a(3)=4, a(4)=0; a(n)=12a(n-2)-16a(n-3) for n>=5.
  • A123017 (program): Semiprimes k such that k+3 is also a semiprime.
  • A123018 (program): Triangle read by rows: row n gives the coefficients of x^k (0 <= k <= n) in the expansion of Sum_{j=0..n} A320508(n,j)*x^j*(1 - x)^(n - j).
  • A123020 (program): Expansion of (1 -5*x +5*x^2)/((1 -2*x)*(1 -4*x +x^2)).
  • A123022 (program): a(n) = n!*b(n) where b(n) = (n-4)*b(n-2)/(n*(n-1)) and b(0) = b(1) = 1.
  • A123023 (program): a(n) = (n-1)*a(n-2), a(0)=1, a(1)=0.
  • A123024 (program): a(n) = n!*b(n) where b(n) = (b(n-2) + b(n-3))/(n*(n-1)), b(0) = b(1) = b(2) = 1.
  • A123025 (program): a(n) = n!*b(n), where b(n) = (1 + n - n^2)*b(n-2)/(n*(n-1)), b(0) = b(1) = 1.
  • A123026 (program): a(n) = n!*b(n), where b(n) = ((n-1)^2 - 2)*b(n-2)/(n*(n-1)) and b(0) = b(1) = 1.
  • A123028 (program): a(n) = (3*n^2 + 3*n + 1)*a(n-2), for n>2, with a(0) = a(1) = 1.
  • A123029 (program): a(2*n-1) = Product_{i=1..n} Fibonacci(2*i-1) and a(2*n) = Product_{i=1..n} Fibonacci(2*i).
  • A123030 (program): Partial sums of A038538.
  • A123051 (program): a(2*n-1) = (4*n-3)^(4*n-2) and a(2*n) = (4*n)^(4*n-1), n=1,2,…
  • A123056 (program): Values of X satisfying the equation (X-Y)^4 - 2*X*Y = 0 with integer X >= Y >= 0.
  • A123057 (program): Values x of solutions (x, y) to the Diophantine equation (x-y)^4 - 8*x*y = 0 with x >= y.
  • A123059 (program): Primes of the form 1 + 2n + 3n^2 + 4n^3.
  • A123065 (program): Numbers primitively represented by the quadratic form 2 x^2 + xy + 4 y^2.
  • A123066 (program): (Number of numbers <= n with an odd number of distinct prime factors) - (number of numbers <= n with an even number of distinct prime factors).
  • A123068 (program): Numbers represented by the “Little Methuselah” quadratic form x^2 + 2*y^2 + y*z + 4*z^2.
  • A123070 (program): Hofstadter Flip-G-sequence.
  • A123071 (program): Bishops on a 2n+1 X 2n+1 board (see Robinson paper for details).
  • A123072 (program): Bishops on an 8n+1 X 8n+1 board (see Robinson paper for details).
  • A123073 (program): Number of ordered triples of primes (p,q,r) such that pqr = n-th 3-almost prime A014612(n).
  • A123074 (program): Number of ordered triples of primes (p,q,r) such that pqr = n.
  • A123076 (program): Numbers n such that p=1+2n+3n^2+4n^3 is prime.
  • A123079 (program): Twin primes of form 4k+1.
  • A123080 (program): Twin primes of form 4k+3.
  • A123081 (program): Infinite square array read by antidiagonals: T(n,k) = Bell(n+k) = A000110(n+k).
  • A123087 (program): Sequence of numbers such that a(2*n) + a(n) = n and a(n) is the smallest number such that a(n) >= a(n-1).
  • A123088 (program): a(1)=1. For n>=2, a(n) = n + (largest integer which is <= n and is missing from the earlier terms of the sequence).
  • A123091 (program): Numbers k such that k divides 5^k - 5.
  • A123092 (program): Decimal expansion of Sum_{k=1..inf.} 1/((2k-1)^2(2k+1)^2) = (Pi^2-8)/16.
  • A123094 (program): Sum of first n 12th powers.
  • A123095 (program): Sum of first n 11th powers.
  • A123097 (program): Triangle read by rows: T(n,k) = binomial(n-2, k-1) + n*binomial(n-1, k-1), 1 <= k <= n, starting with T(1, 1) = 1.
  • A123102 (program): a(0)=1, a(1)=0, a(2)=1, a(n) = a(n-1) + a(n-2) + 3*a(n-3).
  • A123108 (program): a(n) = a(n-1) + a(n-2) - a(n-3), for n > 3, with a(0)=1, a(1)=0, a(2)=1, a(3)=1.
  • A123109 (program): a(0) = 1, a(1) = 3, a(n) = 3*a(n-1) + 3 for n > 1.
  • A123110 (program): Triangle T(n,k), 0 <= k <= n, read by rows given by [0,1,0,0,0,0,0,0,0,0,…] DELTA [1,0,-1,1,0,0,0,0,0,0,…] where DELTA is the operator defined in A084938.
  • A123111 (program): 1+n^2+n^3+n^5+n^7; 10101101 in base n.
  • A123115 (program): Values of Y satisfying the equation (X-Y)^4 - 2*X*Y = 0 with integer X >= Y >= 0.
  • A123116 (program): Values y of solutions (x, y) to the Diophantine equation (x-y)^4 - 8*x*y = 0 with x >= y.
  • A123119 (program): Number of digits in sum of first n primes (A007504).
  • A123121 (program): Length of the n-th Zimin word (A082215(n)).
  • A123122 (program): Numbers of the form 5i + 7j for some nonnegative integers i and j.
  • A123123 (program): Numbers m such that m mod k = 2 for only one integer k in 2..m.
  • A123125 (program): Triangle of Eulerian numbers T(n,k), 0 <= k <= n, read by rows.
  • A123128 (program): Add n to the n-th difference between consecutive primes.
  • A123129 (program): a(n) = ( n + prime(n+1) - prime(n) )^(n-1).
  • A123130 (program): a(n) = 2^(n-1)*((2*n)!/n!) * Integral_{t=0..Pi/3} sin(t)^(2*n-1) dt.
  • A123134 (program): a(n) = prime(n)*(prime(n+1) + 1).
  • A123135 (program): a(n) = n^3 plus sum of digits of n^3.
  • A123137 (program): a(n) = a(n-1)^2 + Sum of the digits of a(n-1), with a(1)=1.
  • A123138 (program): The n-th digit of a(n-1) gives the position of digit n in a(n), a(1)=263514.
  • A123144 (program): a(n) = if mod[n, 3] - 1 == 0 then a(n - 1) else n*a(n - 1).
  • A123145 (program): a(1)=1, a(n) = a(n-1) if n == 1 (mod 4), otherwise a(n) = n * a(n-1) for n >= 2.
  • A123146 (program): Sum of integers triangular array based on trinomial: trinomial[n,k,m]=(n*(n+1)/2)!/(k!*m!*Abs[k+m-(n*(n+1)/2)]!) where k=1.
  • A123149 (program): Triangle T(n,k), 0<=k<=n, read by rows given by [1, 0, -1, 0, 0, 0, 0, 0, …] DELTA [0, 1, 0, -1, 0, 0, 0, 0, …] where DELTA is the operator defined in A084938.
  • A123152 (program): a(n) = (n-th decimal digit of Pi) + 1.
  • A123153 (program): a(n) = (n-th digit of Pi) times (the n-th prime number).
  • A123157 (program): Sum of digits of the squares of prime numbers.
  • A123160 (program): Triangle read by rows: T(n,k) = n!*(n+k-1)!/((n-k)!*(n-1)!*(k!)^2) for 0 <= k <= n, with T(0,0) = 1.
  • A123162 (program): Triangle read by rows: T(n,k) = binomial(2*n - 1, 2*k - 1) for 0 < k <= n and T(n,0) = 1.
  • A123163 (program): Triangle read by rows: binomial[(n-m)^2,m^2].
  • A123164 (program): Row sums of A123160.
  • A123165 (program): Row sums of A123163.
  • A123166 (program): Row sums of A123162.
  • A123167 (program): Continued fraction for c=sqrt(2)*(exp(sqrt(2))+1)/(exp(sqrt(2))-1). a(2*n-1) = 8*n-6, a(2*n) = 4*n-1.
  • A123168 (program): Continued fraction for c = sqrt(2)*(exp(sqrt(2))-1)/(exp(sqrt(2))+1).
  • A123169 (program): Continued fraction for sqrt(1/2)*(exp(sqrt(1/2))-1)/(exp(sqrt(1/2))+1).
  • A123183 (program): a(1)=-1; a(2)=-1; a(3)=-2; a(n) = 4*a(n-1) - 3*a(n-2) for n >= 4.
  • A123187 (program): Triangle of coefficients in expansion of (1+13x)^n.
  • A123189 (program): a(1)=1; a(2)=1; a(3)=6; a(n)=3a(n-1)+3a(n-2)-4a(n-3) for n >=4.
  • A123191 (program): Triangle read by rows: T(n,k) is the coefficient of x^k in the polynomial P[n] defined by P[0]=1, P[1]=x-1, P[n]=(1-x)P[n-1]+xP[n-2] for n>=2. Alternatively, P[n]=-1-(-x)^n-3*Sum((-x)^k,k=1..n-1).
  • A123193 (program): Natural numbers with number of divisors equal to a Fibonacci number.
  • A123194 (program): a(n) = (n+1)*Fibonacci(n+2) + 3.
  • A123197 (program): (2*n+1)*(n+1)*(2*n^2+3*n-1).
  • A123198 (program): a(n)=[(n+1)(2n-1)]^2.
  • A123199 (program): Irregular triangle read by rows: row n is the expansion of (1 + 2*x - x^2)^n.
  • A123203 (program): A007318 * [1, 1, 4, 4, 4, …].
  • A123208 (program): Start with 1, then alternately add 2 or double.
  • A123219 (program): Expansion of -x*(x^4 + 52*x^3 - 122*x^2 - 28*x + 1) / ((x-1)*(x^2 - 34*x + 1)*(x^2 + 6*x + 1)).
  • A123222 (program): Expansion of -x * (x-1) * (3*x^2-1) / (9*x^4-8*x^3+4*x-1).
  • A123224 (program): a(n) = the first row sum of M^(n-1), where M = matrix(4,4, [1,1,1,1;0,1,2,3;0,1,3,6;0,1,4,10]).
  • A123225 (program): Triangle read by rows: T(n,d) = (n!/d!)*(n+1)*binomial(2n-d+1,n+1)/(n-d+1) (0 <= d <= n).
  • A123227 (program): Expansion of e.g.f.: 2*exp(2*x) / (3 - exp(2*x)).
  • A123229 (program): Triangle read by rows: T(n, m) = n - (n mod m).
  • A123231 (program): Row sums of A123230.
  • A123232 (program): Numbers n such that (2*n)^2 + 1 and (2*n)^2 + 3 are both prime.
  • A123240 (program): Natural numbers with number of divisors not equal to a Fibonacci number.
  • A123241 (program): Number of squares < lesser of twin primes.
  • A123246 (program): a(n) = PrimePi(n) + (-1)^(PrimePi(n) + 1) (cf. A000720).
  • A123249 (program): a(1) = 1. For n >= 2, a(n) = n + (smallest integer which is >= n and is missing from among the earlier terms of the sequence).
  • A123251 (program): Continued fraction for sqrt(2)*tan(1/sqrt(2)).
  • A123252 (program): a(n) = smallest prime of the form 2^k + 2n - 1, k = 0, 1, …, or 0 if there is none.
  • A123253 (program): Sum of 7th powers of digits of n.
  • A123265 (program): Fibonacci-Lucas triangle read by rows.
  • A123268 (program): X-values of solutions to the equation 3(X-Y)^4 - X*Y = 0 with X >= Y.
  • A123270 (program): a(0)=1, a(1)=1, a(n) = 5*a(n-1) + 4*a(n-2).
  • A123273 (program): a(0) = 1; a(n) = the number of earlier terms, a(k), where gcd(a(k), a(floor(k/2))) = 1.
  • A123274 (program): a(0)=a(1)=a(2) = 1. a(n) = (a(n-1) +a(n-2)) /GCD(a(n-1)+a(n-2),a(n-3)), for n >= 3.
  • A123275 (program): Square array A(n,m) = largest divisor of m which is coprime to n, read by upwards antidiagonals.
  • A123278 (program): X-values of solutions to the equation 3(X-Y)^4 - 2*X*Y = 0 with X >= Y.
  • A123279 (program): a(n) = product of the first n integers from among those positive integers which are coprime to n.
  • A123282 (program): X-values of solutions to the equation 3(X-Y)^4 - 4*X*Y = 0 with X >= Y.
  • A123283 (program): X-values of solutions to the equation 3(X-Y)^4 - 8*X*Y = 0 with X >= Y.
  • A123290 (program): Number of distinct binomial(n,2)-tuples of zeros and ones that are obtained as the collection of all 2 X 2 minor determinants of a 2 X n matrix over GF(2).
  • A123291 (program): Numbers that are sum of a square and a nonnegative cube (with repetition).
  • A123293 (program): Number of permutations of n distinct letters (ABCD…) each of which appears 4 times and having n-3 fixed points.
  • A123296 (program): Number of permutations of n distinct letters (ABCD…) each of which appears 5 times and having n-2 fixed points.
  • A123302 (program): a(0) = 1. a(n) = the n-th integer from among those positive integers coprime to a(n-1).
  • A123316 (program): Triangle read by rows: T(n,k)=(k+1)*n!/2 (1<=k<=n).
  • A123323 (program): Number of integer-sided triangles with maximum side n, with sides relatively prime.
  • A123324 (program): Number of integer-sided triangles with all sides <= n and sides relatively prime.
  • A123326 (program): Let M be the matrix defined in A111490. Sequence gives the sum of the elements of the submatrices (from the upper left element): M(1,1); M(1,1)+M(1,2)+M(1,2)+M(2,2); M(1,1)+M(1,2)+M(1,3)+M(2,1)+M(2,2)+M(2,3)+M(3,1)+M(3,2)+M(3,3), etc.
  • A123327 (program): a(n) = A000203(n) + A004125(n).
  • A123328 (program): Let M be the matrix defined in A111490. Sequence gives M(1,1), M(1,2)+M(1,2)+M(2,2), M(1,3)+M(2,3)+M(3,1)+M(3,2)+M(3,3), etc.
  • A123329 (program): Let M be the matrix defined in A111490. Sequence gives M(2,1)-M(1,2), M(2,1)+M(3,1)+M(3,2)-M(1,2)-M(1,3)-M(2,3), etc.
  • A123330 (program): Expansion of eta(q^2) * eta(q^3)^6 / (eta(q)^2 * eta(q^6)^3) in powers of q.
  • A123331 (program): Expansion of (c(q)^2/(3c(q^2))-1)/2 in powers of q where c(q) is a cubic AGM function.
  • A123332 (program): a(n) = 2^n*(Gamma(n+1/2)/Gamma(1/2) + (n-1)!).
  • A123333 (program): a(n) = 3^n*(Gamma(n+1/3)/Gamma(1/3) + (n-1)!).
  • A123334 (program): a(n) = 4^n*(Gamma(n+1/4)/Gamma(1/4) + (n-1)!).
  • A123335 (program): a(n) = -2*a(n-1) + a(n-2) for n>1, a(0)=1, a(1)=-1.
  • A123336 (program): Values X satisfying the equation 3(X-Y)^4-16XY=0, where X>=Y.
  • A123344 (program): Expansion of (1+3*x)/(1+2*x).
  • A123346 (program): Mirror image of the Bell triangle A011971, which is also called the Pierce triangle or Aitken’s array.
  • A123347 (program): Number of words of length n over the alphabet {1,2,3,4,5} such that 1 is not followed by an odd letter.
  • A123348 (program): Kekulé numbers for certain benzenoids (see the Cyvin-Gutman book for details).
  • A123349 (program): Square array of Kekulé numbers for the mirror-symmetrical chevrons Ch(m,n), read by antidiagonals (m,n >= 0).
  • A123350 (program): a(n) = (n^4 + 2n^3 + 5n^2 + 4)/4.
  • A123351 (program): Kekulé numbers for certain benzenoids (see the Cyvin-Gutman book for details).
  • A123357 (program): Kekulé numbers for certain benzenoids (see the Cyvin-Gutman book for details).
  • A123358 (program): Kekulé numbers for certain benzenoids (see the Cyvin-Gutman book for details).
  • A123362 (program): a(0) = 1, a(1) = 1, a(n) = 6*a(n-1) + 5*a(n-2) for n > 1.
  • A123363 (program): a(n) = n^3 + (-1)^(n+1).
  • A123365 (program): Values of k such that A046530(k) = (k+2)/3, where A046530(k) is the number of distinct residues of cubes mod k.
  • A123367 (program): a(n) = (n! - 2^n)/8, n >= 4.
  • A123377 (program): Values X satisfying the equation 5(X-Y)^4 - XY = 0, where X >= Y.
  • A123378 (program): Values x of the solutions (x,y) of the Diophantine equation 5*(X-Y)^4 - 2*X*Y = 0 with X >= Y.
  • A123379 (program): Values x of the solutions (x,y) of the Diophantine equation 5*(X-Y)^4 - 4*X*Y = 0 with X >= Y.
  • A123380 (program): Values x of the solutions (x,y) of the Diophantine equation 5*(X-Y)^4 - 8*X*Y = 0 with X >= Y.
  • A123381 (program): Values x of the solutions (x,y) of the Diophantine equation 5*(X-Y)^4 - 16*X*Y = 0 with X >= Y.
  • A123384 (program): Number of bits in binary expansion of 10^n.
  • A123385 (program): a(n) = (n!)^2/2.
  • A123387 (program): Number of triangular numbers <= n-th prime.
  • A123390 (program): Triangle read by rows: n-th row starts with n and continues with half the previous value as long as that is even.
  • A123392 (program): a(-3) = a(-2) = a(-1) = 0, a(0) = 1, a(n) = a(n-1) + 2*a(n-2) + 2*a(n-3) + a(n-4), for n>0.
  • A123393 (program): Values X satisfying the equation 7(X-Y)^4-2XY=0, where X>=Y.
  • A123394 (program): Values X satisfying the equation 7(X-Y)^4-8XY=0, where X>=Y.
  • A123395 (program): Values X satisfying the equation 7(X-Y)^4-16XY=0, where X>=Y.
  • A123397 (program): Values X satisfying the equation 9(X-Y)^4-2XY=0, where X>=Y.
  • A123401 (program): Number of maximal chains in the Stanley lattice of order n.
  • A123476 (program): a(n) = (n!)^2/phi(n!), where phi is Euler’s totient function.
  • A123477 (program): Expansion of (1 - b(q)) / 3 in powers of q where b(q) is a cubic AGM theta function.
  • A123478 (program): Coefficients of series giving the best rational approximations to sqrt(7).
  • A123479 (program): Coefficients of series giving the best rational approximations to sqrt(6).
  • A123480 (program): Coefficients of the series giving the best rational approximations to sqrt(3).
  • A123482 (program): Coefficients of the series giving the best rational approximations to sqrt(11).
  • A123484 (program): Expansion of eta(q)^2 * eta(q^6)^4 * eta(q^8) * eta(q^24) / (eta(q^2) * eta(q^3) * eta(q^12))^2 in powers of q.
  • A123486 (program): Riordan array (1/(1-2*x), x/(1-4*x^2)).
  • A123490 (program): Triangle whose k-th column satisfies a(n) = (k+3)*a(n-1)-(k+2)*a(n-2).
  • A123491 (program): Diagonal sums of number triangle A123490.
  • A123504 (program): Sequence generated from the first nontrivial zero of the Riemann zeta function.
  • A123505 (program): Lengths of bit runs in A123504.
  • A123509 (program): Rohrbach’s problem: a(n) is the largest integer such that there exists a set of n integers that is a basis of order 2 for (0, 1, …, a(n)-1).
  • A123510 (program): Arises in the normal ordering of functions of a*(a+)*a, where a and a+ are the boson annihilation and creation operators, respectively.
  • A123511 (program): Arises in the normal ordering of functions of a*(a+)*a, where a and a+ are the boson annihilation and creation operators, respectively.
  • A123512 (program): Arises in the normal ordering of functions of a*(a+)*a, where a and a+ are the boson annihilation and creation operators, respectively.
  • A123513 (program): Triangle read by rows: T(n,k) is the number of permutations of [n] having k small descents (n >= 1; 0 <= k <= n-1). A small descent in a permutation (x_1,x_2,…,x_n) is a position i such that x_i - x_(i+1) = 1.
  • A123515 (program): Triangle read by rows: T(n,k) is the number of involutions of {1,2,…,n} with exactly k fixed points and which contain the pattern 231 exactly once (n>=4, 2<=k<=n-2).
  • A123517 (program): Triangle read by rows: T(n,k) = floor(n/k + 1/2) - floor(n/(k + 1/2)) (1<=k<=n).
  • A123519 (program): Triangle read by rows: T(n,k) number of tilings of a 2n X 3 grid by dominoes, 2k of which are in a vertical position (0<=k<=n).
  • A123520 (program): Number of vertical dominoes in all possible tilings of a 2n X 3 grid by dominoes.
  • A123521 (program): Triangle read by rows: T(n,k)=number of tilings of a 2 X n grid with k pieces of 1 X 2 tiles (in horizontal position) and 2n-2k pieces of 1 X 1 tiles (0<=k<=n).
  • A123522 (program): Not of the form n + [log_10 n].
  • A123525 (program): Arises in the normal ordering of functions of a*(a+)*a, where a and a+ are the boson annihilation and creation operators, respectively.
  • A123526 (program): Octanacci numbers.
  • A123528 (program): Numerator of average of prime factors of n.
  • A123529 (program): Denominator of average of prime factors of n.
  • A123530 (program): Expansion of q^(-1/2)*eta(q)^2*eta(q^6)^3/(eta(q^2)*eta(q^3)^2) in powers of q.
  • A123532 (program): Expansion of (eta(q) * eta(q^6))^7 / (eta(q^2) * eta(q^3))^5 in powers of q.
  • A123533 (program): Primes in A001855.
  • A123552 (program): Expansion of 1/(1 - x - x^3 + x^5).
  • A123554 (program): Triangle read by rows: T(n,k) = number of labeled loopless digraphs with n nodes and k arcs (n >= 1, 0 <= k <= n*(n-1)).
  • A123555 (program): Number of standard Young tableaux of type (n+1,n,n-1).
  • A123562 (program): Pascal-(1,-3,1) array, read by antidiagonals.
  • A123564 (program): The infinite Fibonacci word reencoded by writing successive non-overlapping pairs of bits as decimal numbers.
  • A123565 (program): a(n) is the number of positive integers k which are <= n and where k, k-1 and k+1 are each coprime to n.
  • A123567 (program): Recursive sum of 2*Omega(n), where Omega(n) is the sequence A001222.
  • A123572 (program): The Kruskal-Macaulay function K_3(n).
  • A123573 (program): The Kruskal-Macaulay function K_4(n).
  • A123574 (program): The Kruskal-Macaulay function K_5(n).
  • A123575 (program): The Kruskal-Macaulay function L_3(n).
  • A123576 (program): The Kruskal-Macaulay function L_4(n).
  • A123578 (program): The Kruskal-Macaulay function M_2(n).
  • A123579 (program): The Kruskal-Macaulay function M_3(n).
  • A123580 (program): The Kruskal-Macaulay function M_4(n).
  • A123581 (program): a(1) = 3, a(n) = a(n-1) + greatest prime factor of a(n-1).
  • A123582 (program): Values of k associated with A123728.
  • A123594 (program): Unique sequence of 0’s and 1’s which are either repeated or not repeated with the following property: when the sequence is ‘coded’ in writing down a 1 when an element is repeated and a 0 when it is not repeated and by putting the initial element in front of the sequence thus obtained, the above sequence appears.
  • A123596 (program): Squares alternating with triangular numbers.
  • A123608 (program): Numbers k such that k, k+1 and 2*k+1 are composite.
  • A123611 (program): Row sums of triangle A123610.
  • A123613 (program): Column 3 of triangle A123610.
  • A123617 (program): Central terms of triangle A123610: a(n) = A123610(2*n,n).
  • A123618 (program): a(n) = A123610(2*n+2,n).
  • A123619 (program): a(n) = A123610(2*n+2,n)/(n+1) = A123618(n)/(n+1).
  • A123620 (program): Expansion of (1 + x + x^2) / (1 - 3*x - 3*x^2).
  • A123629 (program): Expansion of b(q^2) * c(q^6) / (b(q) * c(q^3)) in powers of q where b(), c() are cubic AGM theta functions.
  • A123633 (program): Expansion of (c(q^2)/c(q))^3 in powers of q where c() is a cubic AGM theta function.
  • A123635 (program): Residue mod 3 of average of n-th and (n+1)st odd primes.
  • A123636 (program): a(n) = 1 + 1*n + 1*n*2 + 1*n*2*(n-1) + 1*n*2*(n-1)*3 + 1*n*2*(n-1)*3*(n-2) + … + n!.
  • A123637 (program): a(n) = 1 + 1*n + 1*n*2 + 1*n*2*(n-1) + 1*n*2*(n-1)*3 + 1*n*2*(n-1)*3*(n-2) + … + n!*(n+1)!.
  • A123640 (program): Consider the 2^n compositions of n per row and mark only those ending in an odd part.
  • A123641 (program): Triangular array related to sequence A123640 with row sum A001045.
  • A123642 (program): a(n) = n! - 2^n.
  • A123647 (program): Expansion of (eta(q^4) * eta(q^12) / (eta(q) * eta(q^3)))^2 in powers of q.
  • A123649 (program): Expansion of c(q^4) / c(q) in powers of q where c() is a cubic AGM theta function.
  • A123650 (program): a(n) = 1 + n^2 + n^3 + n^5.
  • A123653 (program): Expansion of (eta(q^2)eta(q^6)/(eta(q)eta(q^3)))^6 in powers of q.
  • A123655 (program): Expansion of q * psi(q^8) / phi(-q) in powers of q where psi(), phi() are Ramanujan theta functions.
  • A123656 (program): a(n) = 1 + n^4 + n^6.
  • A123657 (program): a(n) = 1 + n^4 + n^6 + n^9.
  • A123658 (program): a(n) = 1 + n^4 + n^6 + n^9 + n^10.
  • A123659 (program): a(n) = 1 + n^4 + n^6 + n^9 + n^10 + n^14.
  • A123663 (program): Number of shared edges in a spiral of n unit squares.
  • A123666 (program): Numbers with an even number of prime factors, at least half of which are 2.
  • A123667 (program): a(n) = n * 2^bigomega(n).
  • A123671 (program): Number of nonisomorphic Camina groups of order n.
  • A123672 (program): a(1) = 1; for n > 1, a(n) = (2^n-1)*a(n-1) + (-1)^n.
  • A123679 (program): a(n) = 2*n - A123088(n).
  • A123680 (program): a(n) = Sum_{k=0..n} C(n+k-1,k)*k!.
  • A123681 (program): a(n) = (1/(n+1)) * Sum_{k=0..n} C(n+k-1,k)*k! = A123680(n)/(n+1).
  • A123682 (program): First in an infinite series of triangular arrays which, when taken together, sum to 1,1,3,5,11,21,43,85,… cf. A001045.
  • A123684 (program): Alternate A016777(n) with A000027(n).
  • A123687 (program): E.g.f.: (1-x^2)^(-1/2)*exp(x^2/(1-x^2))*BesselI(0,x^2/(x^2-1)) (since this is an even function, we do not give the intercalating 0’s).
  • A123691 (program): a(n) = number of standard Young tableaux of type (n,n-1,n-1).
  • A123702 (program): a(1)=a(2)=1. For n >= 3, a(n) = (product{k=1 to n-1} a(k)) - (sum{j=1 to n-1} a(j)).
  • A123707 (program): a(n) = Sum_{k=1..n} A123706(n,k)*2^(k-1).
  • A123710 (program): Indices n such that 4 = A123709(n) = number of nonzero terms in row n of triangle A123706.
  • A123711 (program): Indices n such that A123709(n) = 8 = number of nonzero terms in row n of triangle A123706.
  • A123712 (program): Indices n such that 16 = A123709(n) = number of nonzero terms in row n of triangle A123706.
  • A123720 (program): a(n) = 2^n + 2^(n-1) - n.
  • A123721 (program): a(n) = A123249(n) - 2*n.
  • A123725 (program): Numerators of fractional partial quotients appearing in a continued fraction for the power series Sum_{n>=0} x^(2^n - 1)/(n+1)^s.
  • A123726 (program): Denominators of fractional partial quotients appearing in a continued fraction for the power series Sum_{n>=0} x^(2^n - 1)/(n+1)^s.
  • A123731 (program): The Kruskal-Macaulay function M_5(n).
  • A123736 (program): Triangle T(n,k) = Sum_{j=0..k/2} binomial(n-j-1,k-2*j), read by rows.
  • A123737 (program): Partial sums of (-1)^floor(n*sqrt(2)).
  • A123739 (program): Partial sums of (-1)^floor(n*e).
  • A123740 (program): Characteristic sequence for Wythoff AB-numbers A003623.
  • A123741 (program): A second version of Fibonacci factorials besides A003266.
  • A123742 (program): Certain Vandermonde determinants with Fibonacci numbers.
  • A123746 (program): Numerators of partial sums of a series for 1/sqrt(2).
  • A123747 (program): Numerators of partial sums of a series for sqrt(5).
  • A123748 (program): Denominators of partial sums of a series for sqrt(5).
  • A123749 (program): Numerators of partial sums of a series for 3/sqrt(5) = (3/5)*sqrt(5).
  • A123750 (program): Number of distinct resistances possible with at most n arbitrary resistors connected in series or in parallel.
  • A123752 (program): a(n) = 7*a(n-2), a(0) = 1, a(1) = 2.
  • A123753 (program): Partial sums of A070941.
  • A123754 (program): Positive numbers of the form 4*n^2 - 1 which are not semiprimes.
  • A123760 (program): Numbers whose binary expansion is 1xy100…0 where x,y = 0 or 1.
  • A123837 (program): Number of ways to build a contiguous building with n LEGO blocks of size 3 X 3 on top of a fixed block of the same size so that the building is symmetric after a rotation by 90 degrees.
  • A123854 (program): Denominators in an asymptotic expansion for the cubic recurrence sequence A123851.
  • A123858 (program): Expansion of q^(-1/3) * eta(q^2)^2 * eta(q^5)/eta(q) in powers of q.
  • A123860 (program): a(n) = ceiling( (7 + sqrt(49+24*n))/2 ).
  • A123861 (program): Expansion of (f(q) * f(q^3) / (f(-q) * f(-q^3)))^2 in powers of q where f() is a Ramanujan theta function.
  • A123863 (program): Expansion of (c(q^3) - c(q^6) - 2*c(q^12)) / 3 in powers of q where c(q) is a cubic AGM theta function.
  • A123864 (program): Expansion of (eta(q^3) * eta(q^5))^2 / (eta(q) * eta(q^15)) in powers of q.
  • A123865 (program): a(n) = n^4 - 1.
  • A123866 (program): a(n) = n^6 - 1.
  • A123867 (program): a(n) = n^10 - 1.
  • A123868 (program): a(n) = n^12 - 1.
  • A123869 (program): Order of minimal triangulation of the orientable closed surface of genus n (S_n).
  • A123870 (program): Order of minimal triangulation of nonorientable closed surface with n cross-caps (N_n).
  • A123871 (program): Expansion of g.f.: (1+x+x^2)/(1-4*x-4*x^2).
  • A123876 (program): Riordan array (1/(1+2*x), x*(1+x)/(1+2*x)^2).
  • A123877 (program): Expansion of (1+2*x)/(1+3*x+3*x^2).
  • A123878 (program): Product of signed and unsigned Morgan-Voyce triangles.
  • A123879 (program): Expansion of (1-2*x+2*x^2-x^3)/(1-3*x+5*x^2-3*x^3+x^4).
  • A123884 (program): Expansion of phi(x) * phi(-x^6) / chi(-x^2) in powers of x where phi(), chi() are Ramanujan theta functions.
  • A123887 (program): Expansion of g.f.: (1+x+x^2)/(1-5*x-5*x^2).
  • A123888 (program): Expansion of g.f.: x/((1-x^2)^3 -1+x).
  • A123889 (program): Expansion of g.f.: x/((1-x^2)^4 -1+x).
  • A123891 (program): Expansion of (1-3*x^2+x^3)/(1-3*x+x^3).
  • A123892 (program): Expansion of g.f.: (1+x^2)*(1+2*x^2)/(1-3*x+3*x^2-6*x^3+2*x^4-2*x^5).
  • A123901 (program): a(n) = (n+3)/gcd(d(n), d(n+2)) where d(n) = cancellation factor in reducing Sum_{k=0..n} 1/k! to lowest terms.
  • A123903 (program): Total number of “Emperors” in all tournaments on n labeled nodes.
  • A123908 (program): Number of sequences with terms 1, 2 or 3 summing to n with no three consecutive 1’s.
  • A123914 (program): a(n) = prime(n)^2 - prime(n^2). Commutator of (primes, squares) at n.
  • A123916 (program): Number of binary words whose (unique) decreasing Lyndon decomposition is into Lyndon words each with an odd number of 1’s; EULER transform of A000048.
  • A123919 (program): Number of numbers congruent to 2 or 4 mod 6 and <= n.
  • A123920 (program): Number of numbers congruent to 2 or 4 mod 6 between n and 2n inclusive.
  • A123922 (program): Number of 2143-avoiding Dumont paths of the 2nd kind of length 2n.
  • A123931 (program): a(n) = H(n)*n!/(floor(n/2))! (mod (n+1)), where H(n) = sum{k=1 to n} 1/k, the n-th harmonic number.
  • A123932 (program): a(0) = 1, a(n) = 4 for n > 0.
  • A123934 (program): Triangle T(n,k), 1<=k<=n :forms the odd-indexed trinomial coefficients (A027907).
  • A123938 (program): Ramsey number r(K_{2,2}, K_{2,n}).
  • A123941 (program): The (1,2)-entry in the 3 X 3 matrix M^n, where M = {{2, 1, 1}, {1, 1, 0}, {1, 0, 0}}.
  • A123942 (program): The (1,4)-entry in the 4 X 4 matrix M^n, where M={{3, 2, 1, 1}, {2, 1, 1, 0}, {1, 1, 0, 0}, {1, 0, 0, 0}} (n>=0).
  • A123947 (program): Expansion of x^2*(1+x-x^2)/(1-2*x-4*x^2+x^3+x^4).
  • A123950 (program): Expansion of g.f.: x^2*(1-2*x) / (1-3*x-3*x^2+2*x^3).
  • A123952 (program): Sum of first row of the 5 X 5 matrix M^n, where M = {{5,-1,0,0,0}, {-1,5,-1,0,0}, {0,-1,5,-1,0}, {0,0,-1,5,-1}, {0,0,0,-1,5}}.
  • A123957 (program): Expansion of g.f.: x^4/((1+2*x) * (1-2*x+x^2+2*x^3)).
  • A123958 (program): Expansion of x^3 / ( 1+2*x^2+2*x^3 ).
  • A123959 (program): Expansion of 1/(8*x^5+8*x^4-8*x^3-4*x^2+1)
  • A123961 (program): Triangle T(n, k) = k^2*(1+n)^2 - 4*n, read by rows.
  • A123965 (program): Triangle read by rows: T(0,0)=1; T(n,k) is the coefficient of x^k in the polynomial (-1)^n*p(n,x), where p(n,x) is the characteristic polynomial of the n X n tridiagonal matrix with 3’s on the main diagonal and -1’s on the super- and subdiagonal (n >= 1; 0 <= k <= n).
  • A123967 (program): Triangle read by rows: T(0,0)=1; for n >= 1 T(n,k) is the coefficient of x^k in the monic characteristic polynomial of the tridiagonal n X n matrix with main diagonal 5,5,5,… and sub- and superdiagonals 1,1,1,… (0 <= k <= n).
  • A123968 (program): a(n) = n^2 - 3.
  • A123970 (program): Triangle read by rows: T(0,0)=1; T(n,k) is the coefficient of x^(n-k) in the monic characteristic polynomial of the n X n matrix (min(i,j)) (i,j=1,2,…,n) (0 <= k <= n, n >= 1).
  • A123971 (program): Triangle T(n,k), read by rows, defined by T(n,k)=3*T(n-1,k)-T(n-1,k-1)-T(n-2,k), T(0,0)=1, T(1,0)=2, T(1,1)=-1, T(n,k)=0 if k<0 or if k>n.
  • A123972 (program): a(n) = n^3 - n^2 - 2*n + 1.
  • A123973 (program): Sequence of tridiagonal matrices with one center zero terminal that give a triangular sequence from the characteristic polynomials based on the 3 X 3 matrix type: {{1, -1, 0}, {-1, 1, -1}, {0, -1, 0}}.
  • A123976 (program): Numbers n such that Fibonacci(n-1) is divisible by n.
  • A123977 (program): Complement of A061909 (skinny numbers).
  • A123979 (program): Numbers k such that 12*k+1, 12*k+5 and 12*k+7 are primes.
  • A123980 (program): Numbers k for which 8*k+1, 8*k+5 and 8*k+7 are primes.
  • A123986 (program): Numbers n for which 4n+1 and 4n+3 are primes.
  • A123989 (program): a(n) = H(2n)*(2n)!/n! where H(n) = sum{k=1 to n} 1/k, the n-th harmonic number.
  • A123998 (program): Numbers k such that 2k+1 and 4k+1 are primes.
  • A124007 (program): Number of permutations of n distinct letters (ABCD…) each of which appears thrice with n-3 fixed points.
  • A124008 (program): Number of permutations of n distinct letters (ABCD…) each of which appears thrice with n-4 fixed points.
  • A124011 (program): Add three, add six, add nine, ….
  • A124019 (program): Triangle read by rows: T(0,0)=1; for n>=1 T(n,k) is the coefficient of x^k in the monic characteristic polynomial of the n X n band matrix with main diagonal 2,3,3,…, subdiagonal -3,-3,-3,…, sub-subdiagonal 1,1,1,… and superdiagonal -1,-1,-1,… (0<=k<=n).
  • A124020 (program): New tetradiagonal form matrix as triangular sequence from solution of : X(n,m)=Steinbach(n,m)^(-1).tri-Antidiagonal_1(n,n).
  • A124023 (program): G.f.: 1/(1-2*x-6*x^2+4*x^3).
  • A124024 (program): G.f.: 1/(1+2*x-9*x^2-10*x^3+5*x^4).
  • A124025 (program): Recursive polynomial from a tridiagonal matrix version of A123965: p(k, x) = ((x - b(k - 1))*p(k - 1, x) - a(k - 2) *p(k - 2, x))/a(n - 1); a(n)=-1;b(n)=3;.
  • A124026 (program): Let M = {{0, -1, 2}, {-1, 2, -1}, {2, -1, 0}}; v[1] = {0, 0, 1}; v[n] = M.v[n - 1]; then a(n) = v[n][[1]]
  • A124027 (program): G. J. Chaitin’s numbers of s-expressions of size n are given by the coefficients of polynomials p(k, x) satisfying p(k, x) = Sum[p(j, x)*p(k - j, x), {j, 2, k - 1}]. The coefficients of these polynomials give the triangle shown here.
  • A124038 (program): Determinants of tridiagonal matrices in y with upper diagonal y-2: m(n,n,d)=If[ n == m && n > 1 && m > 1, y, If[n == m - 1 || n == m + 1, -1, If[n == m == 1, y - 2, 0]]] Det(m,n,m,d)=P(d,y).
  • A124044 (program): Number of ways to express 4n+3 as the sum of an odd square and twice a prime.
  • A124051 (program): Quasi-mirror of A062196 formatted as a triangular array.
  • A124052 (program): a(n) = sigma(lcm(1,2,…,n)) = A000203(A003418(n)).
  • A124062 (program): Number of ways to write n as an ordered sum of 1’s, 2’s and 3’s such that no 2 precedes any 1.
  • A124065 (program): Numbers k such that 8*k - 1 and 8*k + 1 are twin primes.
  • A124071 (program): a(1)=1. a(n) = GCD(n,a(n-1)) + GCD(n+1,a(n-1)).
  • A124072 (program): First differences of A129819.
  • A124078 (program): a(n) = H(n)*n!/(floor(n/2))!, where H(n) = sum{k=1 to n} 1/k, the n-th harmonic number.
  • A124079 (program): a(n) = H(2n+1)*(2n+1)!/n!, where H(n) = Sum_{k=1..n} 1/k, the n-th harmonic number.
  • A124080 (program): 10 times triangular numbers: a(n) = 5*n*(n + 1).
  • A124087 (program): 9th column of Catalan triangle A009766.
  • A124088 (program): 10th column of Catalan triangle A009766.
  • A124089 (program): Binomial(n,6)-1.
  • A124090 (program): C(n,7)-1.
  • A124093 (program): Triangular numbers alternating with squares.
  • A124099 (program): Sum_(x^i*y^j*z^k) with i + j + k = m and (x, y, z) = the primitive Pythagorean triple (5, 12, 13).
  • A124100 (program): Sum_(x^i*y^j*z^k) with i + j + k = m and (x, y, z) = the primitive Pythagorean triple (8, 15, 17).
  • A124101 (program): Sum_(x^i*y^j*z^k) with i + j + k = m and (x, y, z) = the primitive Pythagorean triple (7, 24, 25).
  • A124102 (program): a(n) = C(2n,n)*Bell(n).
  • A124103 (program): C(2*n,n)*stirling2(2*n,n).
  • A124106 (program): Octagonal numbers equal to S*(3S - 2) with 3S - 2 = k^2 and S semiprime.
  • A124107 (program): Numbers n such that n is the sum of the augmenting factorials of the digits of n, e.g. 733 = 7 + 3! + (3!)!.
  • A124108 (program): Replace each 1 with 10 in binary representation of n.
  • A124114 (program): Subsequence of primes in sequence b(n) = 2*prime(n) - prime(n+1) + 2 (A124115).
  • A124115 (program): a(n) = 2*prime(n) - prime(n+1) + 2.
  • A124124 (program): Nonnegative integers n such that 2n^2 + 2n - 3 is square.
  • A124127 (program): Numbers k such that 17k + 1 is prime.
  • A124131 (program): a(n)=((-1)^n/2)*sum_{i1+i2+i3=2n} ((2*n)!/(i1! i2! i3!))*B(i1+i2) where B are the Bernoulli numbers.
  • A124133 (program): a(n) = (-1/2)*Sum_{i1 + i2 + i3 = 2*n} ((2*n)!/(i1! i2! i3!))*B(i1), where B are the Bernoulli numbers (with i1, i2, i3 >= 1).
  • A124148 (program): Fibonacci triangle read by rows; the triangles below read by rows. Analog of A124171.
  • A124152 (program): a(n) = Fibonacci(6, n).
  • A124156 (program): Thickness of complete graph K_n.
  • A124158 (program): Maximal number of edges in a rectangle visibility graph with n nodes.
  • A124161 (program): a(n) = n*(n-1)*(n^3 + 21*n^2 - 4*n + 96)/120.
  • A124162 (program): Number of quadruples [i,j,k,l] with all entries between 1 and n such that gcd(i,j) = gcd(k,l).
  • A124166 (program): 100*(10^n-1)/9.
  • A124167 (program): a(n) = 10*(10^n-1).
  • A124171 (program): Sequence obtained by reading the triangles shown below by rows.
  • A124174 (program): Sophie Germain triangular numbers tr: 2*tr+1 is also a triangular number.
  • A124179 (program): Prime(R(p)) where Prime(i) is the i-th prime and R(p) is the value of the reverse of the digits of prime p.
  • A124180 (program): Prime(R(n)) where Prime(i) is the i-th prime and R(n) is the value of the reverse of the digits of n.
  • A124182 (program): A skewed version of triangular array A081277.
  • A124191 (program): a(n) = ((2 + 3*sqrt(2))^n - (2 - 3*sqrt(2))^n)/(2*sqrt(2)).
  • A124192 (program): Numbers k for which 8*k + 3 and 8*k + 5 are twin primes.
  • A124195 (program): a(1)=1. a(n) = n - GCD(a(n-1),n).
  • A124197 (program): Number of subsets S of {1,2,3,…,n}, including the empty subset, such that if x and y are in S with x<y and x+y even, then (x+y)/2 is also in S.
  • A124198 (program): Numbers k such that 21*k + 1 is prime.
  • A124199 (program): Primes of the form k(k+1)/2-2 (i.e., two less than triangular numbers).
  • A124203 (program): a(n) = 2n + “reverse of n-written-in-binary” + 2.
  • A124204 (program): Numbers k such that 20*k + 1 is prime.
  • A124212 (program): E.g.f.: exp(x)/sqrt(2-exp(2*x)).
  • A124217 (program): Expansion of (1-x-x^2)/(1-2x-x^2+x^4).
  • A124218 (program): a(n) is the m-th positive integer which is coprime to n, where phi(n) is number of positive integers which are <= n and are coprime to n, d(n) is the number of positive divisors of n and m = phi(n) if phi(n)|d(n), else m = d(n) mod phi(n).
  • A124219 (program): a(n)= m-th positive divisor of n, where phi(n) is number of positive integers which are <= n and are coprime to n, d(n) is the number of positive divisors of n and m = d(n) if d(n)|phi(n), else m = phi(n) mod d(n).
  • A124226 (program): Number of partitions of n with even crank minus number of partitions of n with odd crank.
  • A124227 (program): Number of partitions of n with even crank.
  • A124228 (program): Number of partitions of n with odd crank.
  • A124229 (program): Numerator of g(n) defined by g(1)=1, g(2n)=1/g(n)+1, g(2n+1)=g(2n).
  • A124230 (program): Denominator of g(n) defined by g(1)=1, g(2n)=1/g(n)+1, g(2n+1)=g(2n).
  • A124233 (program): Expansion of psi(q) * phi(-q^10) * chi(-q^5) / chi(-q^2) in powers of q where phi(), psi(), chi() are Ramanujan theta functions.
  • A124234 (program): Riordan array (1/(1-x), x(1+x)^2).
  • A124237 (program): Riordan array (1/(1-2x), x/((1-x)(1-2x))).
  • A124239 (program): a(n) = Sum_{k=1..n} Sum_{m=1..n} (2*k - 1)^m.
  • A124240 (program): Numbers n such that lambda(n) divides n, where lambda is Carmichael’s function (A002322).
  • A124243 (program): Expansion of q*psi(q^9)/psi(q) in powers of q.
  • A124252 (program): 10 times A007623.
  • A124258 (program): Triangle whose rows are sequences of increasing and decreasing squares: 1; 1,4,1; 1,4,9,4,1; …
  • A124268 (program): Primes indexed by 3-almost primes.
  • A124269 (program): 3-almost primes indexed by primes.
  • A124279 (program): Riordan array (1/(1-x),x(1-x+x^2)/(1-x)).
  • A124280 (program): Expansion of 1/(1-x-x^2+x^3-x^4).
  • A124281 (program): Expansion of 1/(1-x-2*x^2+2*x^3-2*x^4).
  • A124282 (program): Primes indexed by 4-almost primes.
  • A124283 (program): 4-almost primes indexed by primes.
  • A124292 (program): Number of free generators of degree n of symmetric polynomials in 4 noncommuting variables.
  • A124293 (program): Number of free generators of degree n of symmetric polynomials in 5-noncommuting variables.
  • A124294 (program): Number of free generators of degree n of symmetric polynomials in 6-noncommuting variables.
  • A124295 (program): Number of free generators of degree n of symmetric polynomials in 7-noncommuting variables.
  • A124296 (program): a(n) = 5*F(n)^2 - 5*F(n) + 1, where F(n) = Fibonacci(n).
  • A124297 (program): a(n) = 5*F(n)^2 + 5*F(n) + 1, where F(n) = Fibonacci(n).
  • A124302 (program): Number of set partitions with at most 3 blocks; number of Dyck paths of height at most 4; dimension of space of symmetric polynomials in 3 noncommuting variables.
  • A124303 (program): Number of set partitions of length <= 4; sum of first 4 columns of triangle of Stirling numbers of 2nd kind; dimension of space of symmetric polynomials in 4 noncommuting variables.
  • A124304 (program): Riordan array (1,x(1-x^2)).
  • A124305 (program): Riordan array (1, 2*sqrt(3)*sin(arcsin(3*sqrt(3)*x/2)/3)/3).
  • A124308 (program): Primes indexed by 5-almost primes.
  • A124309 (program): 5-almost primes indexed by primes.
  • A124311 (program): a(n) = Sum_{i=0..n} (-2)^i*B(i)*binomial(n,i) where B(n) = Bell numbers A000110(n).
  • A124312 (program): G.f.: (x^3 - x^4)/(1 - x - x^2 - x^3 - x^4 - x^5).
  • A124313 (program): Pentanacci numbers: a(n) = a(n-1) + a(n-2) + a(n-3) + a(n-4) + a(n-5), starting 1,0,0,0,1.
  • A124314 (program): Expansion of 1/(-1 - x - x^2 - x^3 - x^4 + x^5).
  • A124315 (program): a(n) = Sum_{ d divides n } tau(gcd(d,n/d)), where tau = sigma_0 = A000005.
  • A124316 (program): a(n) = Sum_{ d divides n } sigma(gcd(d,n/d)), where sigma is the sum of divisors function, A000203.
  • A124317 (program): Semiprimes indexed by 3-almost primes.
  • A124318 (program): 3-almost primes indexed by semiprimes.
  • A124320 (program): Triangle read by rows: T(n,k) = k!*binomial(n+k-1,k) (n >= 0, 0 <= k <= n), rising factorial power, Pochhammer symbol.
  • A124323 (program): Triangle read by rows: T(n,k) is the number of partitions of an n-set having k singleton blocks (0<=k<=n).
  • A124325 (program): Number of blocks of size >1 in all partitions of an n-set.
  • A124326 (program): T(n,m) = A007318(n,m) - A077028(n,m).
  • A124329 (program): Number of ordered trees with n edges, with thinning limbs and with root of degree 2. An ordered tree with thinning limbs is such that if a node has k children, all its children have at most k children.
  • A124330 (program): a(n)= ((d(n) mod phi(n)) +1)th positive integer which is coprime to n, where phi(n) is number of positive integers which are <= n and are coprime to n and d(n) is the number of positive divisors of n.
  • A124331 (program): a(n) is the ((phi(n) mod d(n)) + 1)-th positive divisor of n, where phi(n) is number of positive integers which are <= n and are coprime to n and d(n) is the number of positive divisors of n.
  • A124332 (program): a(n) = ((n mod d(n)) +1)th divisor of n, where d(n) is number of positive divisors of n.
  • A124333 (program): a(n) = ((n mod phi(n)) +1)th positive integer which is coprime to n, where phi(n) is number of positive integers which are <= n and are coprime to n.
  • A124340 (program): Number of solutions to n = x^2 + 2*y^2 + 4*(T(z) + T(w)) + 1 where x and y are integers, z and w are nonnegative integers and T(x) = (x^2+x)/2.
  • A124341 (program): Riordan array (1/(1+x), x(1+2x)/(1+x)^2).
  • A124342 (program): Expansion of (1+x)/(1+2x-2x^3).
  • A124349 (program): Numbers of directed Hamiltonian cycles on the n-prism graph.
  • A124350 (program): a(n) = 4*n*(floor(n^2/2)+1). For n>=3, this is the number of directed Hamiltonian paths on the n-prism graph.
  • A124351 (program): Order of the automorphism group of the n-prism graph.
  • A124353 (program): Number of (directed) Hamiltonian circuits on the n-antiprism graph.
  • A124354 (program): Orders of the automorphisms groups of the n-antiprism graph.
  • A124355 (program): Number of (directed) Hamiltonian cycles on the complete graph K_n.
  • A124356 (program): Number of (directed) Hamiltonian cycles on the Moebius ladder graph M_n (for n>=4).
  • A124363 (program): a(n) = n^3 + 71*n + 1
  • A124369 (program): Riordan array (1/((1-x-x^2)(1+x+x^2)),x(1+x)/((1-x-x^2)(1+x+x^2))).
  • A124370 (program): Expansion of 1/(1-2x^2-3x^3-x^4).
  • A124377 (program): Riordan array (1/(1-x-x^2),x/(1+x)).
  • A124379 (program): Numbers n such that 120n-1, 120n+1 are twin primes.
  • A124387 (program): Largest prime < 2*a[n-1] written in binary, a[1]=2.
  • A124388 (program): 27*n+18.
  • A124392 (program): A Fine number related number triangle.
  • A124394 (program): Inverse of Fine number renewal array.
  • A124395 (program): Expansion of (1-2*x)/(1-2*x+2*x^3).
  • A124396 (program): Denominators of partial sums of a series for 3/sqrt(5) = (3/5)*sqrt(5).
  • A124397 (program): Numerators of partial sums of a series for sqrt(5)/3.
  • A124398 (program): Denominators of partial sums of a series for sqrt(5)/3.
  • A124399 (program): a(n) = 4^(n - bitcount(n)) where bitcount(n) = A000120(n).
  • A124400 (program): a(n) = a(n-1) + 3*a(n-2) - a(n-4), with a(0)=1, a(1)=1, a(2)=4, a(3)=7.
  • A124403 (program): a(n) = -1 + Sum_{i=1..n} Sum_{j=1..n} i^j.
  • A124405 (program): a(n) = 1 + Sum_{i=1..n} Sum_{j=1..n} i^j.
  • A124419 (program): Number of partitions of the set {1,2,…n} having no blocks that contain both odd and even entries.
  • A124426 (program): Product of two successive Bell numbers.
  • A124427 (program): Sum of the sizes of the blocks containing the element 1 in all set partitions of {1,2,…,n}.
  • A124428 (program): Triangle, read by rows: T(n,k) = binomial(floor(n/2),k)*binomial(floor((n+1)/2),k).
  • A124431 (program): a(n) = Sum_{k=0..n} 2^k*C([(n+k)/2],k)*C([(n+k+1)/2],k)) where [x]=floor(x).
  • A124434 (program): LCM (least common multiple) of A001043 (sum of consecutive primes) and A001223 (difference of consecutive primes).
  • A124437 (program): Experience Points thresholds for levels in the pen and paper role-playing game “Das Schwarze Auge” (DSA, a.k.a. “The Dark Eye”).
  • A124440 (program): a(n) = Sum_{n/2<=k<=n, gcd(k,n)=1} k.
  • A124441 (program): a(n) = Product_{1<=k<=n/2, gcd(k,n)=1} k.
  • A124442 (program): a(n) = Product_{ceiling(n/2) <= k <= n, gcd(k,n)=1} k.
  • A124443 (program): a(1)=1, a(n) = LCM of the integers, from 1 to n/2, which are coprime to n.
  • A124445 (program): Expansion of 1/(1-x-x*y+x^2*y-x^3*y^2).
  • A124448 (program): Riordan array (sqrt(1+4x^2)-2x, (1+2x-sqrt(1+4x^2))/2).
  • A124449 (program): Expansion of (phi(-q^3)^4 - phi(-q)^4)/8 in powers of q where phi() is a Ramanujan theta function.
  • A124458 (program): Triangular array resulting from summing three repeated Pascal sequences; (related to the generalized pentagonal sequence (A001318) and the classical modular tessellation (cf. A054886).
  • A124459 (program): Square array resulting from the bisection of array A124458. (The other array is A093560.)
  • A124479 (program): From the game of Quod: number of “squares” on an n X n array of points with the four corner points deleted.
  • A124485 (program): Numbers n such that 2n-1 and 4n-1 are primes.
  • A124493 (program): Numbers k for which 2*k-1, 4*k-1 and 8*k-1 are primes.
  • A124495 (program): G.f.: A(x) = 1/[1-x - Sum_{n>=1} A001147(n)*x^(2n) ] where A001147(n) = (2n)!/(n!*2^n) is the double factorials.
  • A124502 (program): a(1)=a(2)=1; thereafter, a(n+1) = a(n) + a(n-1) + 1 if n is a multiple of 5, otherwise a(n+1) = a(n) + a(n-1).
  • A124508 (program): 2^BigO(n) * 3^omega(n), where BigO=A001222 and omega=A001221, the numbers of prime factors of n with and without repetitions.
  • A124511 (program): A124508(A124508(n)).
  • A124512 (program): a(n) = A124508(A124508(A124508(n))).
  • A124518 (program): Numbers k such that 10k-1 and 10k+1 are twin primes.
  • A124519 (program): Numbers k such that 12*k - 1 and 12*k + 1 are twin primes.
  • A124520 (program): Numbers k such that 14*k - 1 and 14*k + 1 are twin primes.
  • A124521 (program): Numbers k such that 16*k - 1 and 16*k + 1 are twin primes.
  • A124522 (program): a(n) = smallest k such that 2nk-1 and 2nk+1 are primes.
  • A124574 (program): Triangle read by rows: row n is the first row of the matrix M[n]^(n-1), where M[n] is the n X n tridiagonal matrix with main diagonal (3,4,4,…) and super- and subdiagonals (1,1,1,…).
  • A124582 (program): Primes p such that q-p >= 6, where q is the next prime after p.
  • A124583 (program): Duplicate of A083371.
  • A124584 (program): Primes p such that q-p >= 10, where q is the next prime after p.
  • A124585 (program): Primes p such that q-p >= 12, where q is the next prime after p.
  • A124586 (program): Primes p such that q-p >= 14, where q is the next prime after p.
  • A124587 (program): Primes p such that q-p >= 16, where q is the next prime after p.
  • A124588 (program): Primes p such that q - p <= 2, where q is the next prime after p.
  • A124589 (program): Primes p such that q-p <= 4, where q is the next prime after p.
  • A124590 (program): Primes p such that q-p <= 6, where q is the next prime after p.
  • A124594 (program): Primes p such that q-p = 26, where q is the next prime after p.
  • A124595 (program): Primes p such that q-p = 28, where q is the next prime after p.
  • A124596 (program): Primes p such that q-p = 30, where q is the next prime after p.
  • A124610 (program): a(n) = 5*a(n-1) + 2*a(n-2), n > 1; a(0) = a(1) = 1.
  • A124625 (program): Even numbers sandwiched between 1’s.
  • A124642 (program): Antidiagonal sums of A096465.
  • A124644 (program): Mirror image of A098474 formatted as a triangular array.
  • A124645 (program): Triangle T(n,k), 0<=k<=n, read by rows given by [1,-1,0,0,0,0,0,…] DELTA [ -1,2,-1,0,0,0,0,0,0,…] where DELTA is the operator defined in A084938 .
  • A124647 (program): a(n) = (2n + 1)*3^n.
  • A124657 (program): Factorials that are abundant numbers.
  • A124659 (program): Twin prime products minus 2.
  • A124669 (program): Product of successive primes minus 2.
  • A124671 (program): Row sums of A126277 = binomial transform of (1, 2, 2, 3, 4, 4, 4, …)
  • A124672 (program): Oblong (promic) abundant numbers = abundant numbers of the form k(k+1).
  • A124678 (program): Number of conjugacy classes in PSL_2(p), p = prime(n).
  • A124679 (program): a(n) = number of conjugacy classes in PSL_3(prime(n)).
  • A124691 (program): a(n) = lcm(prime(n)+1, prime(n+1)+1) / 2.
  • A124696 (program): Number of base-3 circular n-digit numbers with adjacent digits differing by 1 or less.
  • A124697 (program): Number of base 4 circular n-digit numbers with adjacent digits differing by 1 or less.
  • A124698 (program): Number of base 5 circular n-digit numbers with adjacent digits differing by 1 or less.
  • A124720 (program): Number of ternary Lyndon words of length n with exactly two 1’s.
  • A124724 (program): a(n) = (4/(n + 1)) * C(5*n, n).
  • A124725 (program): Triangle read by rows: T(n,k) = binomial(n,k) + binomial(n,k+2) (0 <= k <= n).
  • A124727 (program): Triangle read by rows: T(n,k)=k*binomial(n-1,k-1)+binomial(n-1,k) (1<=k<=n).
  • A124732 (program): Triangle P*M, where P is the Pascal triangle written as an infinite lower triangular matrix and M is the infinite bidiagonal matrix with (1,2,1,2,…) in the main diagonal and (2,1,2,1,…) in the subdiagonal.
  • A124733 (program): Triangle read by rows: row n is the first row of the matrix M[n]^(n-1), where M[n] is the n X n tridiagonal matrix with main diagonal (2,3,3,…) and super- and subdiagonals (1,1,1,…).
  • A124736 (program): Table where row n has k C(n,k-1) times.
  • A124737 (program): Table where row n has k C(n,k) times.
  • A124739 (program): a(n) = sum of those positive integers which are coprime to both n and n+1 and which are <= n.
  • A124740 (program): a(n) = product of those positive integers which are coprime to both n and n+1 and which are <= n.
  • A124741 (program): a(n) = largest of those positive integers which are coprime to both n and n+1 and which are <= n.
  • A124744 (program): Expansion of (1+x*y)/(1-x^2*y^2+x^3*y^2).
  • A124745 (program): Expansion of (1+x)/(1-x^2+x^3).
  • A124746 (program): Expansion of (1+x^2)/(1-x^4+x^5).
  • A124748 (program): Table where row n has k C(n,k) times, in reverse order.
  • A124749 (program): Expansion of (1+x*y+x^2*y^2)/(1-x^3*y^3+x^4*y^3).
  • A124750 (program): Expansion of (1 + x + x^2)/(1 - x^3 + x^4).
  • A124751 (program): Expansion of (1+x^2+x^4)/(1-x^6+x^7).
  • A124753 (program): a(3n+k) = (k+1)*binomial(4n+k, n)/(3n+k+1), where k is n reduced mod 3.
  • A124754 (program): Alternating sum of compositions in standard order.
  • A124757 (program): Zero-based weighted sum of compositions in standard order.
  • A124758 (program): Product of the parts of the compositions in standard order.
  • A124759 (program): Sum of products of consecutive terms for compositions in standard order.
  • A124760 (program): Number of rises for compositions in standard order.
  • A124761 (program): Number of falls for compositions in standard order.
  • A124762 (program): Number of levels for compositions in standard order.
  • A124763 (program): Number of non-rises (levels or falls) for compositions in standard order.
  • A124764 (program): Number of non-falls (levels or rises) for compositions in standard order.
  • A124765 (program): Number of monotonically decreasing runs for compositions in standard order.
  • A124766 (program): Number of monotonically increasing runs for compositions in standard order.
  • A124767 (program): Number of level runs for compositions in standard order.
  • A124768 (program): Number of strictly increasing runs for compositions in standard order.
  • A124769 (program): Number of strictly decreasing runs for compositions in standard order.
  • A124772 (program): Number of set partitions associated with compositions in standard order.
  • A124773 (program): Number of permutations associated with compositions in standard order.
  • A124774 (program): Multinomial coefficients for compositions in standard order.
  • A124775 (program): Number of unlabeled partially ordered sets associated with compositions in standard order.
  • A124778 (program): Number of unlabeled unordered rooted forests associated with compositions in standard order.
  • A124779 (program): a(n) = gcd(A(n), A(n+2))/gcd(d(n), d(n+2)) where A(n) = Sum_{k=0..n} n!/k! and d(n) = gcd(A(n), n!).
  • A124780 (program): a(n) = gcd(A(n), A(n+2)) where A(n) = A000522(n) = Sum_{k=0..n} n!/k!.
  • A124781 (program): a(n) = gcd(A093101(n), A093101(n+2)) where A093101(n) = gcd(n!, A(n)) and A(n) = A000522(n) = Sum_{k=0..n} n!/k!).
  • A124782 (program): a(n) = (n+3)/gcd(A(n), A(n+2)) where A(n) = A000522(n) = Sum_{k=0..n} n!/k!.
  • A124785 (program): Semiprime sopfr of semiprimes A115585.
  • A124788 (program): Triangle read by rows: expansion of (1+x*y)/(1-x^2*y^2-x^3*y^2).
  • A124789 (program): Expansion of (1+x^2)/(1-x^4-x^5).
  • A124791 (program): Row sums of number triangle A124790.
  • A124793 (program): Numbers in a perpendicular plane intersecting a 3D clockwise spiral produced by powers of 2.
  • A124797 (program): Sum of cyclic permutations of 123…n seen as number written in base n+1: ((n+1)^n-1)*(n+1)/2.
  • A124800 (program): Let M be a diagonal matrix with A007442 on the diagonal and P = Pascal’s triangle as an infinite lower triangular matrix. Now read the triangle P*M by rows.
  • A124802 (program): Triangle, row sums = Fibonacci numbers in two ways, companion to A124801.
  • A124805 (program): Number of base 4 circular n-digit numbers with adjacent digits differing by 2 or less.
  • A124808 (program): Number of numbers k <= n such that k^2 + 1 is squarefree.
  • A124809 (program): Numbers of the form (square + 1) that are not squarefree.
  • A124810 (program): Number of 4-ary Lyndon words of length n with exactly two 1s.
  • A124815 (program): Expansion of q * psi(q)^2 * psi(-q^3)^2 * phi(-q^6) / phi(-q^2) in powers of q where phi(), psi() are Ramanujan theta functions.
  • A124817 (program): Interpolation of A001764(n+1) and A006629(n).
  • A124819 (program): Number triangle T(n,k)=C(n+2k+1,3k+1).
  • A124820 (program): Expansion of (1-x)/(1-4*x+3*x^2-x^3).
  • A124821 (program): Number triangle T(n,k)=(-1)^(n-k)*(3k+2)*C(3n+1, n-k)/(2n+k+2).
  • A124822 (program): a(n) = the n-th integer from among those positive integers which are coprime to n(n+1).
  • A124823 (program): a(n) = n-th integer from among those positive integers which are coprime to n(n+1)/2.
  • A124824 (program): LambertW analog of the Bell numbers: a(n) = (1/e)*Sum_{k>=0} k*(n+k)^(n-1)/k! for n > 0 with a(0)=1.
  • A124826 (program): Primes congruent to 1 mod 21.
  • A124827 (program): Order of Galois groups of irreducible Chebyshev polynomials of order n.
  • A124830 (program): Number of distinct prime factors of A055932(n).
  • A124831 (program): Number of prime factors of A055932(n) with repetition.
  • A124833 (program): A055932(n) divided by product of all primes less than the greatest prime factor of A055932(n).
  • A124837 (program): Numerators of third order harmonic numbers (defined by Conway and Guy, 1996).
  • A124838 (program): Denominators of third-order harmonic numbers (defined by Conway and Guy, 1996).
  • A124839 (program): Inverse binomial transform of the Moebius sequence {mu(k), k >= 1}, A008683.
  • A124841 (program): Inverse binomial transform of A005614, the rabbit sequence: (1, 0, 1, 1, 0, …).
  • A124842 (program): Triangle, row sums = A005614, the rabbit sequence.
  • A124844 (program): Triangle T(n,k)=binomial(n,k)*A061084(k), 0<=k<=n, read by rows.
  • A124845 (program): Triangle read by rows: T(n,k) = (3 - (-1)^k)*binomial(n,k)/2 (0 <= k <= n).
  • A124846 (program): Triangle read by rows: T(n,k) = (2 - (-1)^k)*binomial(n,k) (0 <= k <= n).
  • A124847 (program): Triangle read by rows: T(n,k) = k(k+1)*binomial(n-1, k-1)/2 (1 <= k <= n).
  • A124848 (program): Triangle read by rows: T(n,k) = (k+1)*(k+2)*(k+3)*binomial(n,k)/6 (0 <= k <= n).
  • A124853 (program): Numbers k such that 5k + 3 and 3k + 5 are primes.
  • A124855 (program): Numbers k such that 3k + 4 and 4k + 3 are primes.
  • A124859 (program): Multiplicative with p^e -> primorial(e), p prime and e > 0.
  • A124860 (program): A Jacobsthal-Pascal triangle.
  • A124861 (program): Expansion of 1/(1-x-3x^2-4x^3-2x^4).
  • A124862 (program): a(n)=J(2n+1)*C(2n,n), J(n)=A001045(n).
  • A124863 (program): Expansion of 1 / chi(q)^12 in powers of q where chi() is a Ramanujan theta function.
  • A124867 (program): Numbers that are the sum of 3 distinct primes.
  • A124868 (program): Natural numbers that are not the sum of 3 distinct primes.
  • A124871 (program): Numerator of imaginary part of (2*omega)^(-n) where omega = (-1 + i*3)/ 2.
  • A124895 (program): Triangle read by rows, 1<=k<=n: T(n,k) = mu(n^2 + k^2) with mu=A008683.
  • A124896 (program): Number of squarefree numbers of the form n^2 + k^2, 1<=k<=n.
  • A124897 (program): a(n) = mu(n^2 + 1), mu = A008683.
  • A124899 (program): Sierpinski quotient ((2n-1)^(2n-1) + 1)/(2n) = A014566(2n-1)/(2n).
  • A124922 (program): Second in a series of triangular arrays providing index numbers for subsequences of A060351.
  • A124923 (program): a(n) = n^(n-1) + 1.
  • A124925 (program): Interlaced triples: a(3n+1)=1, a(3n+2) = 2n+3, a(3n+3)= A028387(n).
  • A124926 (program): Triangle read by rows: T(n,k) = binomial(n,k)*r(k), where r(k) are the Riordan numbers (r(k) = A005043(k); 0 <= k <= n).
  • A124927 (program): Triangle read by rows: T(n,0)=1, T(n,k)=2*binomial(n,k) if k>0 (0<=k<=n).
  • A124928 (program): Triangle read by rows: T(n,0) = 1, T(n,k) = 3*binomial(n,k) if k>=0 (0<=k<=n).
  • A124929 (program): Triangle read by rows: T(n,k) = (2^k-1)*binomial(n-1,k-1) (1<=k<=n).
  • A124931 (program): Triangle read by rows: T(n,k) = (2*k-1)*binomial(n,k) (1 <= k <= n).
  • A124932 (program): Triangle read by rows: T(n,k) = k*(k+1)*binomial(n,k)/2 (1 <= k <= n).
  • A124934 (program): Numbers of the form 4mn - m - n, where m, n are positive integers.
  • A124936 (program): Numbers k such that k - 1 and k + 1 are semiprimes.
  • A124959 (program): Triangle read by rows: T(n,k) = a(k)*binomial(n,k) (0 <= k <= n), where a(0)=1, a(1)=2, a(k) = a(k-1) + 3*a(k-2) for k >= 2 (a(k) = A006138(k)).
  • A124965 (program): Odd values of 2^n mod n corresponding to the n’s given in A015911.
  • A124972 (program): Expansion of Fricke’s 32*tau_4(z) in powers of q = exp(2*Pi*i*z).
  • A124981 (program): Odd numbers that are not the sum of 2 squares.
  • A124999 (program): Number of base 5 circular n-digit numbers with adjacent digits differing by 3 or less.
  • A125018 (program): Numbers == 1 (mod 4) with a unique partition as a sum of 2 squares x^2 + y^2.
  • A125021 (program): Even numbers with a unique partition as the sum of 2 squares x^2 + y^2.
  • A125022 (program): Numbers with a unique partition as the sum of 2 squares x^2 + y^2.
  • A125026 (program): Triangle read by rows: T(n,k) = k*binomial(n,k) + binomial(n-1,k) (1 <= k <= n).
  • A125028 (program): a(1)=2, a(n)=2*a(n-1)-floor(sqrt(a(n-1))).
  • A125046 (program): Partial sums of A003095.
  • A125047 (program): Infinite word generated by mapping 1->12, 2->13, 3->43, 4->42 starting at 1.
  • A125048 (program): 2^(10n) - 10^(3n).
  • A125049 (program): a(1) = 1. If a(n) is prime, a(n+1) = 2*a(n); otherwise, a(n+1) = 2*a(n) + 1.
  • A125050 (program): a(1) = 1. If a(n) is composite, a(n+1) = 2*a(n)+1; otherwise, a(n+1) = 2*a(n).
  • A125054 (program): Central terms of triangle A125053.
  • A125055 (program): Diagonal of symmetric triangle A125053 located immediately below the central terms (A125054).
  • A125059 (program): Number of digits in n!!.
  • A125061 (program): Expansion of psi(q) * psi(q^2) * chi(q^3) * chi(-q^6) in powers of q where psi(), chi() are Ramanujan theta functions.
  • A125062 (program): Number of increasing trees with hills of height 1.
  • A125070 (program): a(n) = number of nonzero exponents in the prime-factorization of n which are not primes.
  • A125076 (program): Triangle with trigonometric properties,
  • A125078 (program): Fifth in an infinite set of generalized Pascal’s triangles, with trigonometric properties.
  • A125079 (program): Excess of number of divisors of 2n+1 of form 12k+1, 12k+5 over those of form 12k+7, 12k+11.
  • A125082 (program): a(n) = n^4 - n^3 - n^2 - n - 1.
  • A125083 (program): a(n) = n^5-n^4-n^3-n^2-n-1.
  • A125084 (program): Cubes which have a partition as the sum of 3 squares.
  • A125086 (program): Even numbers not in A036990.
  • A125089 (program): First nonzero digit of solution to log_n(z) = -z, where log_n stands for the base-n logarithm.
  • A125090 (program): Triangle read by rows: T(0,0)=1; for 0<=k<=n, n>=1, T(n,k) is the coefficient of x^(n-k) in the monic characteristic polynomial of the tridiagonal n X n matrix with diagonal (0,1,1,…) and super- and subdiagonals (1,1,1,…).
  • A125091 (program): Triangle read by rows: T(n,k) = (1/6)*k*(k+1)*(k+2)*binomial(n,k) (1 <= k <= n).
  • A125092 (program): Triangle read by rows: T(n,k) = (k+1)^2*binomial(n,k) (0 <= k <= n).
  • A125093 (program): Triangle T(n,k) = n*A054525(n,k) read by rows.
  • A125095 (program): Expansion of phi(-x) * psi(x^4) in powers of x where psi(), phi() are Ramanujan theta functions.
  • A125096 (program): Expansion of -1 + (phi(q) * phi(q^2) + phi(-q^2) * phi(q^4)) / 2 in powers of q.
  • A125100 (program): Triangle read by rows: T(n,k) = Fibonacci(k+1)*binomial(n,k) + (k+1)*binomial(n,k+1) (0 <= k <= n).
  • A125102 (program): Triangle read by rows: T(n,k)=(k+1)binomial(n,k) + [3-(-1)^k]binomial(n,k+1)/2 (0<=k<=n).
  • A125103 (program): Triangle read by rows: T(n,k) = binomial(n,k) + 2^k*binomial(n,k+1) (0 <= k <= n).
  • A125107 (program): Subtract compositions (A011782) from Catalan numbers (A000108).
  • A125110 (program): Cubes which have a partition as the sum of 2 squares.
  • A125111 (program): Cubes which do not have a partition as the sum of 2 squares.
  • A125115 (program): Differences between consecutive abundant numbers.
  • A125116 (program): Number of 8 X 8 pandiagonal Franklin squares with magic sum 4n.
  • A125117 (program): First differences of A034887.
  • A125118 (program): Triangle read by rows: T(n,k) = value of the n-th repunit in base (k+1) representation, 1<=k<=n.
  • A125119 (program): Values of repunits with odd length L in base (L+3)/2 representation.
  • A125120 (program): Sum of values of repunits of length n in base b representation with 1<b<=n+1.
  • A125124 (program): Decimal expansion of the flattening (inverse) of the World Geodetic System 1984 ellipsoid, second upgrade.
  • A125125 (program): Decimal expansion of the geocentric gravitational constant (mass of Earth’s atmosphere included) of the World Geodetic System 1984 Ellipsoid, second upgrade.
  • A125128 (program): a(n) = 2^(n+1) - n - 2, or partial sums of main diagonal of array A125127 of k-step Lucas numbers.
  • A125130 (program): Successive sums of consecutive primes that form a triangular grid.
  • A125131 (program): Product 1-p, where p ranges over the prime factors of n with multiplicity.
  • A125137 (program): a(n) = p^p + 1, where p = prime(n).
  • A125139 (program): SENSigma: Multiplicative with a(p^e) = p*(p^e-1)/(p-1) - (-1)^e.
  • A125140 (program): SEPSigma(n) = (-1)^(Sum_i r_i)*Sum_{d|n} (-1)^(Sum_j Max(r_j))*d =Product_i (Sum_{1<=s_i<=r_i} p_i^s_i)+(-1)^r_i where n=Product_i p_i^r_i, d=Product_j p_j^r_j, p_j^max(r_j) is the largest power of p_j dividing n.
  • A125141 (program): a(1) = 2; for n>1, a(n)=SENSigma(a(n-1)), where SENSigma(m) = (-1)^((Sum_i r_i)+Omega(m))*Sum_{d|m} (-1)^((Sum_j Max(r_j))+Omega(d))*d = Product_i (Sum_{1<=s_i<=r_i} p_i^s_i)+(-1)^(r_i+1) if m=Product_i p_i^r_i, d=Product_j p_j^r_j, p_j^max(r_j) is the largest power of p_j dividing m.
  • A125144 (program): Increments in the number of decimal digits of 4^n.
  • A125145 (program): a(n) = 3a(n-1) + 3a(n-2). a(0) = 1, a(1) = 4.
  • A125164 (program): Positive integers n such that no prime exists of the form (k! + 3n - 1), (k! + 3n) or (k! + 3n + 1) for any k.
  • A125165 (program): Triangle read by rows: T(n,k) = C(n,k) + 3*C(n,k+1) + 2*C(n,k+2) (0<=k<=n).
  • A125166 (program): Triangle, companion to A125165, left border = n^3.
  • A125167 (program): Numbers n such that the n-th prime + n-th nonprime is itself prime.
  • A125168 (program): a(n) = gcd(n, A032741(n)) where A032741(n) is the number of proper divisors of n.
  • A125169 (program): a(n) = 16*n + 15.
  • A125170 (program): Binomial transform of an infinite lower triangular matrix with (1,1,2,4,8,…) in every column and the rest zeros. Let the left column = A007051, then for k > 1, T(n,k) = (n-1,k) + (n-1,k-1).
  • A125171 (program): Riordan array ((1-x)/(1-3*x+x^2),x/(1-x)) read by rows.
  • A125172 (program): Triangle T(n,k) with partial column sums of the even indexed Fibonacci numbers.
  • A125175 (program): Triangle T(n,k) = |A053123(n/2+k/2,k)| for even n+k, T(n,k)= A082985((n+k-1)/2,k) for odd n+k; read by rows, 0<=k<=n.
  • A125176 (program): Row sums of A125175.
  • A125177 (program): Triangle read by rows: T(n,0)=C(2n,n)/(n+1) for n>=0; T(n,n+1)=0; T(n,k)=T(n-1,k)+T(n-1,k-1) for 1<=k<=n.
  • A125179 (program): Triangle read by rows: T(n,1) = prime(n) (the n-th prime); T(n,k) = 0 for k > n; T(n,k) = T(n-1,k) + T(n-1,k-1) for 2 <= k <= n (1 <= k <= n).
  • A125180 (program): a(n) = 2*a(n-1) + prime(n) - prime(n-1), a(1)=2, where prime(n) denotes the n-th prime.
  • A125185 (program): Triangle read by rows: T(n,k) is the coefficient of t^k in the polynomial S(n,t)=[(1+t)(2+t)^n+(1-t)t^n]/2 (0<=k<=n).
  • A125186 (program): Number of digits 1 in all hyperbinary representations of n. A hyperbinary representation of a nonnegative integer n is a representation of n as a sum of powers of 2, each power being used at most twice.
  • A125187 (program): Number of Dumont permutations of the first kind of length 2n avoiding the patterns 1423 and 4132.
  • A125188 (program): Number of Dumont permutations of the first kind of length 2n avoiding the patterns 2413 and 4132. Also number of Dumont permutations of the first kind of length 2n avoiding the patterns 1423 and 3142.
  • A125190 (program): Number of ascents in all Schroeder paths of length 2n.
  • A125196 (program): Number of magic labelings of the Petersen graph with magic sum n.
  • A125198 (program): Number of magical labelings of the octahedral graph of magic sum n.
  • A125199 (program): Triangle read by rows: T(n,k) = 4*n*k - n - k, 1<=k<=n.
  • A125200 (program): n*(4*n^2 + n -1)/2.
  • A125201 (program): a(n) = 8*n^2 - 7*n + 1.
  • A125202 (program): a(n) = 4*n^2 - 6*n + 1.
  • A125218 (program): Numbers having at least two representations as 4*x*y-x-y with 1<=x<=y.
  • A125228 (program): Maximal number of squares of side 1 in a disk of radius n.
  • A125230 (program): Triangle T(n,k) (0<=k<=n) read by rows in which column k contains the binomial transform of the sequence of k 0’s, (k+1) 1’s, followed by 0’s.
  • A125231 (program): Triangle read by rows: T(n,k) = ceiling((k+1)/2)*binomial(n,k) (0 <= k <= n).
  • A125232 (program): Triangle T(n,k) read by rows: the (n-k)-th term of the k-fold iterated partial sum of the pentagonal numbers.
  • A125233 (program): Triangle T(n,k) read by rows, the (n-k)-th term of the k times repeated partial sum of the hexagonal numbers, 0 <= k < n, 0 < n.
  • A125234 (program): Triangle T(n,k) read by rows: the k-th column contains the k-fold iterated partial sum of A000566.
  • A125235 (program): Triangle with the partial column sums of the octagonal numbers.
  • A125238 (program): Differences between consecutive deficient numbers.
  • A125239 (program): Smallest prime divisor of 10*T(n)+1 = 5*n*(n+1)+1, where T(n) = 1 + 2 + … + n.
  • A125250 (program): Square array, read by antidiagonals, where A(1,1) = A(2,2) = 1, A(1,2) = A(2,1) = 0, A(n,k) = 0 if n < 1 or k < 1, otherwise A(n,k) = A(n-2,k-2) + A(n-1,k-2) + A(n-2,k-1) + A(n-1,k-1).
  • A125254 (program): Smallest prime divisor of 4n-1 that is of the form 4k-1.
  • A125255 (program): Smallest prime divisor of 4n-1.
  • A125256 (program): Smallest odd prime divisor of n^2 + 1.
  • A125257 (program): Smallest prime divisor of 4n^2+3 that is of the form 6k+1.
  • A125258 (program): Smallest prime divisor of n^4-n^2+1.
  • A125266 (program): Number of repetitions in A007918.
  • A125267 (program): Number of Motzkin paths with no peaks and with level steps at height 0 having three colors except that consecutive level steps at height 0 must have different colors.
  • A125273 (program): Eigensequence of triangle A085478: a(n) = Sum_{k=0..n-1} A085478(n-1,k)*a(k) for n > 0 with a(0) = 1.
  • A125274 (program): Eigensequence of triangle A078812: a(n) = Sum_{k=0..n-1} A078812(n-1,k)*a(k) for n > 0 with a(0)=1.
  • A125282 (program): G.f. satisfies: A(x) = Sum{n>=0} x^n * A(n*x).
  • A125287 (program): a(n) = mu(n) * A000217(n).
  • A125289 (program): Numbers with unique nonzero digit in decimal representation.
  • A125291 (program): Number of partitions of n into positive digit values of its ternary representation.
  • A125292 (program): Numbers having either no ones or no twos in their ternary representation.
  • A125293 (program): Numbers with at least one 1 and one 2 in ternary representation.
  • A125294 (program): Numerator of Sum_{k=1..n} k^2 / Product_{k=1..n} k^2.
  • A125299 (program): Numbers whose names in English start with a consonant.
  • A125301 (program): a(3n) = n, a(3n+1) = (n+2)*a(3n), a(3n+2) = (n+2)*a(3n+1).
  • A125305 (program): Number of 132-segmented permutations of length n.
  • A125343 (program): Number of base 6 circular n-digit numbers with adjacent digits differing by 4 or less.
  • A125370 (program): Number of base 7 circular n-digit numbers with adjacent digits differing by 5 or less.
  • A125396 (program): Number of base 8 circular n-digit numbers with adjacent digits differing by 6 or less.
  • A125421 (program): Number of base 9 circular n-digit numbers with adjacent digits differing by 7 or less.
  • A125445 (program): Number of base 10 circular n-digit numbers with adjacent digits differing by 8 or less.
  • A125468 (program): Number of base 11 circular n-digit numbers with adjacent digits differing by 9 or less.
  • A125493 (program): Composite deficient numbers.
  • A125494 (program): Composite evil numbers.
  • A125495 (program): Composite odious numbers.
  • A125497 (program): Evil cubes.
  • A125498 (program): Odious cubes.
  • A125499 (program): Deficient even numbers.
  • A125500 (program): Expansion of -LambertW(-x^2*exp(x))/x^2.
  • A125510 (program): Theta series of 4-dimensional lattice QQF.4.g.
  • A125514 (program): Theta series of 4-dimensional lattice QQF.4.i.
  • A125518 (program): a(n) = tau(n) * prime(n).
  • A125521 (program): a(n) is the minimal difference between two distinct n-digit numbers with property that when one of them is typed into a calculator and rotated 180 degrees, the other one is seen.
  • A125550 (program): a(n) = C(prime(n+2), prime(n)).
  • A125552 (program): Maximal value of m such that 3^m <= n! : a(n) = floor( log(n!) / log(3) ).
  • A125557 (program): Primes in the sequence a(n)=n^2+3/2-1/2*(-1)^n.
  • A125558 (program): Central column of triangle A090181.
  • A125559 (program): Numbers n such that 2n^3 + 7 is prime. For n>=8, bases in which 2007 is prime.
  • A125562 (program): a(n) = denominator of (2n + 1)!/3^n.
  • A125563 (program): Denominator of (4n+1)!/5^n.
  • A125575 (program): Initial digit of squares of primes.
  • A125577 (program): a(0) = 1; for n >= 1, a(n) = n^2 - a(n-1).
  • A125583 (program): Number of letters in the n-th prime number (in French).
  • A125585 (program): Array of constant-spaced integers read by antidiagonals.
  • A125586 (program): 2^(2n-1) - (n+2)*3^(n-2).
  • A125592 (program): Evil numbers (A001969) multiplied by 2.
  • A125598 (program): a(n) = ((n+1)^(n-1) - 1)/n.
  • A125599 (program): Quotient ((2n)^(2n-2)-1)/(2n+1)/(2n-1).
  • A125602 (program): Centered triangular numbers that are prime.
  • A125603 (program): Numbers n such that 3n(n-1)/2 + 1 is prime.
  • A125608 (program): Triangle read by rows: given the left border = the Lucas numbers, (1, 3, 4, 7, …), T(n,k) = (n-1,k) + (n-1,k-1).
  • A125615 (program): Sum of the quadratic nonresidues of prime(n).
  • A125616 (program): (Sum of the quadratic nonresidues of prime(n)) / prime(n).
  • A125619 (program): Minimal number of blocks in any uniform (n,3)-splitting system.
  • A125630 (program): a(n) is the number of integers k less than 10^n such that the decimal representation of k lacks the digit 1 and at least one of digits 2,3,4,5,6,7,8,9.
  • A125641 (program): Square of the (3,1)-entry of the 3 X 3 matrix M^n, where M = [1,0,0; 1,1,0, 1,i,1].
  • A125643 (program): Squares and cubes (with repetition).
  • A125650 (program): Numerator of n(n+3)/(4(n+1)(n+2)) = sum(k=1..n, 1/(k(k+1)(k+2)) ).
  • A125651 (program): Numbers k such that A125650(k) is a perfect square.
  • A125652 (program): Numbers m such that m^2=A125650(k) for some k (belonging A125651).
  • A125662 (program): A convolution triangle of numbers based on A001906 (even indexed Fibonacci numbers).
  • A125667 (program): Eta numbers (from the Japanese word for “pariah” or “outcast”). These are the positive odd integers which cannot be used to make a hypotenuse of a primitive Pythagorean triangle (PPT).
  • A125677 (program): a(0) = a(1) = 1; for n>1, a(n) = a(n-2) + a(n-1) (mod n).
  • A125678 (program): a(0) = 1; for n>0, a(n) = (a(n-1)^2 reduced mod n) + 1.
  • A125682 (program): a(n) = (6^n-1)*3/5.
  • A125683 (program): Numerator of Sum_{k=1..n} (-1)^(k+1) * 1/(k*(k+1)).
  • A125687 (program): The base 6 numbers 4 44 444 4444 44444 … converted to base 10.
  • A125690 (program): Riordan array (1/(1-x-2x^2), x(1-x)/(1-x-2x^2)).
  • A125691 (program): Expansion of 1/(1 - x - 3x^2 + x^3).
  • A125692 (program): Riordan array (1-x*c(-x^2),x(1-x*c(-x^2)) where c(x) is the g.f. of A000108.
  • A125693 (program): Riordan array ((1-x)/(1-3*x), x*(1-x)/(1-3*x)).
  • A125694 (program): Riordan array ((1+3x-sqrt(1+2x+9x^2))/(2x),(1+3x-sqrt(1+2x+9x^2))/2).
  • A125695 (program): Expansion of (sqrt(1+2x+9x^2)+x-1)/(2x).
  • A125711 (program): In the “3x+1” problem, let 1 denote a halving step and 0 denote an x->3x+1 step. Then a(n) is obtained by writing the sequence of steps needed to reach 1 from 2n and reading it as a decimal number.
  • A125720 (program): A variation on the Thue-Morse sequence.
  • A125721 (program): a(n)=2*n!/d(n!); d(m)=A000005(m) is the number of divisors of m.
  • A125723 (program): Greatest common divisor of n^6 and 6^n.
  • A125725 (program): Numbers whose base-7 representation is 222….2.
  • A125728 (program): a(n) = Sum_{k=1..n} (number of positive integers <= k which are coprime to both k and n).
  • A125729 (program): Numbers whose base 7 representation is 555….5.
  • A125736 (program): a(n)=IntegerLog(n-1)+IntegerLog(n+1), where IntegerLog(n)=A001414(n).
  • A125746 (program): a(n) = smallest divisor d of n such that n <= {sum of d and all smaller divisors of n}.
  • A125747 (program): a(n) is the smallest positive integer such that (Sum_{t(k)|n, 1 <= k <= a(n)} t(k)) >= n, where t(k) is the k-th positive divisor of n.
  • A125748 (program): a(n) is the smallest positive integer such that Sum_{1<=k<=a(n), gcd(k,n)=1} k is >= n.
  • A125749 (program): a(n) is the smallest positive integer such that (Sum_{1<=k<=a(n), gcd(t(k),n)=1} t(k)) is >= n, where t(k) is the k-th positive integer which is coprime to n.
  • A125758 (program): Numbers congruent to 4 or 7 (mod 9).
  • A125760 (program): a(n) = Product_{k=1..n} A002109(k).
  • A125764 (program): Array of partial sums of rows of array in A086271, read by antidiagonals.
  • A125791 (program): a(n) = 2^(n*(n-1)*(n-2)/6) for n>=1.
  • A125811 (program): Number of coefficients in the n-th q-Bell number as a polynomial in q.
  • A125816 (program): a(n) = ((1+sqrt(13))^n + (1-sqrt(13))^n)/2.
  • A125817 (program): a(n) = ((1 + 3*sqrt(2))^n - (1 - 3*sqrt(2))^n)/(2*sqrt(2)).
  • A125818 (program): a(n) = ((1 + 3*sqrt(2))^n + (1 - 3*sqrt(2))^n)/2.
  • A125819 (program): a(n) = ((1 + 7*sqrt(2))^n - (1 - 7*sqrt(2))^n)/(14*sqrt(2)).
  • A125820 (program): a(n) = ((1 + 7*sqrt(2))^n + (1 - 7*sqrt(2))^n)/2.
  • A125821 (program): Numbers n for which 8n+5 and 8n+7 are twin primes.
  • A125822 (program): Numbers k for which 8*k + 1 and 8*k + 3 are twin primes.
  • A125823 (program): Numbers whose base 7 representation is 4444….4.
  • A125824 (program): Denominator of n!/3^n.
  • A125829 (program): Sprague-Grundy values for octal game .115.
  • A125831 (program): a(n) = (5^n - 1)/2.
  • A125833 (program): Numbers whose base 5 representation is 333333…….3.
  • A125835 (program): Numbers whose base-8 or octal representation is 22222222…….2.
  • A125836 (program): Numbers whose base 8 or octal representation is 555555555……5.
  • A125837 (program): Numbers whose base 8 or octal representation is 6666666……6.
  • A125842 (program): a(1)=1. a(n) = the number of terms from among the first floor(n/2) terms of the sequence which are coprime to n.
  • A125843 (program): a(1)=1. a(n) = the sum of the terms from among the first floor(n/2) terms of the sequence which are coprime to n.
  • A125849 (program): a(n) = sum_{m=1..n-1} floor[m(n-2)/2]^2.
  • A125853 (program): Squared radii of circles centered at a grid point in a square lattice hitting exactly 4 points. Indices k such that A004018(k)=4.
  • A125857 (program): Numbers whose base-9 representation is 22222222…….2.
  • A125858 (program): a(n) is the number of nonnegative integers k less than 10^n such that the decimal representation of k lacks at least one of digits 1,2,3,4,5,6,7,8,9.
  • A125866 (program): Odd numbers k such that cos(2*Pi/k) is an algebraic number of a 3-smooth degree, but not 2-smooth.
  • A125868 (program): Odd numbers k such that cos(2*Pi/k) is an algebraic number of a 5-smooth degree, but not 3-smooth.
  • A125869 (program): Numbers n such that p=10n+1 is prime and cos(2pi/p) is an algebraic number of a 5-smooth degree, but not 3-smooth.
  • A125870 (program): Odd numbers k such that cos(2*Pi/k) is an algebraic number of a 7-smooth degree, but not 5-smooth.
  • A125871 (program): Numbers n such that p=14n+1 is prime and cos(2pi/p) is an algebraic number of a 7-smooth degree, but not 5-smooth.
  • A125872 (program): Odd numbers k such that cos(2*Pi/k) is an algebraic number of an 11-smooth degree, but not 7-smooth.
  • A125873 (program): Prime numbers n such that cos(2pi/n) is an algebraic number of an 11-smooth degree, but not 7-smooth.
  • A125874 (program): Numbers n such that p=22n+1 is prime and cos(2pi/p) is an algebraic number of an 11-smooth degree, but not 7-smooth.
  • A125875 (program): Odd numbers k such that cos(2*Pi/k) is an algebraic number of a 13-smooth degree, but not 11-smooth.
  • A125876 (program): Prime numbers n such that cos(2pi/n) is an algebraic number of a 13-smooth degree, but not 11-smooth.
  • A125877 (program): Numbers n such that p=26n+1 is prime and cos(2pi/p) is an algebraic number of a 13-smooth degree, but not 11-smooth.
  • A125881 (program): Numbers k for which k^3+k^2-1 is prime.
  • A125894 (program): a(n) = floor(((1+sqrt(2))/2)^n).
  • A125895 (program): a(n) = floor(((1+sqrt(3))/2)^n).
  • A125898 (program): Floor((quadronacci ratio)^n).
  • A125899 (program): Floor(((Pentanacci ratio)^n).
  • A125902 (program): a(n) = sum of the first n primes which are coprime to n.
  • A125903 (program): a(n) = product of the first n primes which are coprime to n.
  • A125905 (program): a(0) = 1, a(1) = -4, a(n) = -4*a(n-1) - a(n-2) for n > 1.
  • A125906 (program): Riordan array (1/(1 + 5*x + x^2), x/(1 + 5*x + x^2))^(-1); inverse of Riordan array A123967.
  • A125908 (program): a(n) is the number of nonnegative integers k less than 10^n such that the decimal representation of k lacks the digits 1 and 2 and at least one of digits 3,4,5,6,7,8,9.
  • A125911 (program): Product of the even divisors of n.
  • A125913 (program): Sprague-Grundy values for octal game .144.
  • A125914 (program): Sprague-Grundy values for octal game .145.
  • A125915 (program): Sprague-Grundy values for octal game .147.
  • A125916 (program): Sprague-Grundy values for octal game .15 (Guiles).
  • A125922 (program): Sprague-Grundy values for octal game .316.
  • A125924 (program): Sprague-Grundy values for octal game .34.
  • A125925 (program): Sprague-Grundy values for octal game .351.
  • A125961 (program): Decimal expansion of e * sqrt(Pi) * erf(1).
  • A125962 (program): Numbers whose base-9 representation is 555555555……5.
  • A125964 (program): Numbers k such that k^3 + k^2 + k - 1 is prime.
  • A125989 (program): Sum of heights of 10’s in binary expansion of n.
  • A125991 (program): A106486-encodings of combinatorial games with zero value.
  • A125992 (program): A106486-encodings of combinatorial games with value 1.
  • A125993 (program): A106486-encodings of combinatorial games with value -1.
  • A125994 (program): A106486-encodings of combinatorial games equivalent to game {0|0}.
  • A125997 (program): A106486-encodings of combinatorial games equivalent to game {0|1}.
  • A125998 (program): A106486-encodings of combinatorial games equivalent to game {1|1}.
  • A126001 (program): A106486-encodings of nonnegative combinatorial games, i.e., games whose value is >= 0.
  • A126006 (program): Involution of nonnegative integers: Swap the positions of digits q0 <-> q1, q2 <-> q3, q4 <-> q5, etc. in the base-4 expansion of n (where n = … + q4*256 + q3*64 + q2*16 + q1*4 + q0).
  • A126007 (program): Involution of nonnegative integers: Keep the least significant quaternary digit q0 of n fixed, but swap the positions of digits q1 <-> q2, q3 <-> q4, …, etc. in the base-4 expansion of n (where n = … + q4*256 + q3*64 + q2*16 + q1*4 + q0).
  • A126008 (program): Involution of nonnegative integers: composition of involutions A057300 and A126007.
  • A126019 (program): a(0)=1, a(1)=2; for n>1, a(n)=3*a(n-1)+4*a(n-2)+5.
  • A126020 (program): Number of convex permutominoes of size n.
  • A126023 (program): a(0)=0, a(1)=1; for n>1, a(n) = a(n-1)*(a(n-1)+a(n-2)).
  • A126026 (program): Conjectured upper bound on area of the convex hull of any edge-to-edge connected system of regular unit hexagons (n-polyhexes).
  • A126030 (program): Riordan array (1/(1+x^3),x/(1+x^3)).
  • A126042 (program): Expansion of f(x^3)/(1-x*f(x^3)), where f(x) is the g.f. of A001764, whose n-th term is binomial(3n,n)/(2n+1).
  • A126062 (program): Array read by antidiagonals: see A128195 for details.
  • A126063 (program): Triangle read by rows: see A128196 for definition.
  • A126064 (program): Triangle read by rows, obtained by multiplying columns of triangle in A094587 by 1,2,4,8,16,… respectively.
  • A126068 (program): Expansion of 1 - x - sqrt(1 - 2*x - 3*x^2) in powers of x.
  • A126073 (program): Sum of numbers <= n which are multiples of 3 or 5 but not 15.
  • A126075 (program): Triangle T(n,k), 0 <= k <= n, read by rows, defined by: T(0,0)=1, T(n,k)=0 if k < 0 or if k > n, T(n,0) = 2*T(n-1,0) + T(n-1,1), T(n,k) = T(n-1,k-1) + T(n-1,k+1) for k >= 1.
  • A126079 (program): G.f.: (1-2*x)*sqrt(1-4*x).
  • A126080 (program): a(n) = number of positive integers < n that are coprime to exactly one prime divisor of n.
  • A126081 (program): a(n) = number of k, 1 <= k <= n, such that k divides ceiling(n/k).
  • A126082 (program): Binomial transform of A001113.
  • A126083 (program): a(n) = numerator of H(n) taken mod n, where H(n) = Sum_{k=1..n} 1/k is the n-th harmonic number.
  • A126086 (program): Number of paths from (0,0,0) to (n,n,n) such that at each step (i) at least one coordinate increases, (ii) no coordinate decreases, (iii) no coordinate increases by more than 1 and (iv) all coordinates are integers.
  • A126087 (program): Expansion of c(2*x^2)/(1-x*c(2*x^2)), where c(x) = (1-sqrt(1-4*x))/(2*x) is the g.f. of the Catalan numbers (A000108).
  • A126089 (program): Expansion of e.g.f.: (1-2*x)*sqrt(1-4*x).
  • A126091 (program): a(1)=1;a(2)=4; for n>2, a(n)=a(n-2)+3 if n is already in the sequence, a(n)=a(n-2)+1 otherwise.
  • A126093 (program): Inverse binomial matrix applied to A110877.
  • A126109 (program): a(n) = (5*10^n + 1)/3.
  • A126114 (program): Ultimate fixed-point under the mapping n->f(n), where f(n)=n if n is square else f(n)=n-Floor(Sqrt(n)).
  • A126115 (program): E.g.f.: sqrt(1+2*x)/(1-2*x).
  • A126116 (program): a(n) = a(n-1) + a(n-3) + a(n-4), with a(0)=a(1)=a(2)=a(3)=1.
  • A126119 (program): Numerators of sequence of fractions with e.g.f. (1+x)/(1-x)^(3/2).
  • A126120 (program): Catalan numbers (A000108) interpolated with 0’s.
  • A126121 (program): Numerators of sequence of fractions with e.g.f. sqrt(1+x)/(1-x)^2.
  • A126124 (program): Triangle, matrix inverse of A124733, companion to A123965.
  • A126126 (program): Triangle read by rows: matrix inverse of A110877.
  • A126130 (program): a(n) = (n+1)^n - n!.
  • A126136 (program): Binomial transform of A107430.
  • A126147 (program): a(n) = floor((Product_{k=1..n-1} prime(k))/prime(n)).
  • A126167 (program): Number of primitive exponential amicable pairs (i,j) with i<j and i<=10^n.
  • A126168 (program): Sum of the proper infinitary divisors of n.
  • A126181 (program): Triangle read by rows, T(n,k) = C(n,k)*Catalan(n-k+1), n >= 0, 0 <= k <= n.
  • A126184 (program): Number of hex trees with n edges and having no nonroot nodes of outdegree 2.
  • A126185 (program): Number of nonroot nodes of outdegree 2 in all hex trees with n edges.
  • A126189 (program): Number of hex trees with n edges and no adjacent vertices of outdegree 2.
  • A126190 (program): Number of pairs of adjacent vertices of outdegree 2 in all hex trees with n edges.
  • A126192 (program): Product of the even divisors of 2n.
  • A126199 (program): a(n) = prime(n)*prime(n+1) + prime(n) + prime(n+1).
  • A126205 (program): Number of 3’s in decimal expansion of 3^n, with n>=0.
  • A126206 (program): Number of 4’s in the decimal expansion of 4^n.
  • A126207 (program): Number of 5’s in decimal expansion of 5^n.
  • A126208 (program): Number of 6’s in decimal expansion of 6^n.
  • A126209 (program): Number of 7’s in decimal expansion of 7^n.
  • A126210 (program): Number of 8’s in decimal expansion of 8^n.
  • A126211 (program): Number of 9’s in decimal expansion of 9^n.
  • A126216 (program): Triangle read by rows: T(n,k) is the number of Schroeder paths of semilength n containing exactly k peaks but no peaks at level one (n >= 1; 0 <= k <= n-1).
  • A126217 (program): Triangle read by rows: T(n,k) is the number of 321-avoiding permutations of {1,2,…,n} having longest increasing subsequence of length k (1<=k<=n).
  • A126220 (program): Number of binary trees (i.e., rooted trees where each vertex has either 0, 1, or 2 children; and, when only one child is present, it is either a right child or a left child) with n edges and no adjacent vertices of outdegree 2.
  • A126221 (program): a(n)=c(n)+c(n-1)+2*c(n-2)+4*c(n-3)+8*c(n-4)+…+2^(n-2)*c(1)+2^(n-1)*c(0), where c(k) are the Catalan numbers (A000108).
  • A126223 (program): Number of level steps in all 2-Motzkin paths (i.e., Motzkin paths with blue and red level steps) of length n, without red level steps on the x-axis.
  • A126224 (program): Determinant of the n X n matrix in which the entries are 1 through n^2, spiraling inward starting with 1 in the (1,1)-entry.
  • A126225 (program): Least number k > 0 such that the numerator of Sum_{i=1..k} 1/prime(i)^n is a prime.
  • A126232 (program): Number of functions f:{1,2,…,n}->{1,2,…,n} such that Im(f) contains 5 fixed elements.
  • A126234 (program): a(0)=0; a(n)=a(n-1)-n, if a(n-1)>2n; otherwise a(n)=a(n-1)+n.
  • A126235 (program): Minimum length of a codeword in Huffman encoding of n symbols, where the k-th symbol has frequency k.
  • A126236 (program): Maximum length of a codeword in Huffman encoding of n symbols, where the k-th symbol has frequency k.
  • A126237 (program): Length of row n in table A126014.
  • A126246 (program): a(n) is the number of Fibonacci numbers among (F(1),F(2),F(3),…,F(n)) which are coprime to F(n), where F(n) is the n-th Fibonacci number.
  • A126247 (program): a(n) is the number of triangular numbers, from among (T(1), T(2), T(3), …, T(n)), which are coprime to T(n), where T(n) = n(n+1)/2 is the n-th triangular number.
  • A126248 (program): p*(p+1)*(p+2) where (p,p+2) are twin primes.
  • A126249 (program): p*(p+1)*(p+2)/6 where (p,p+2) are twin primes.
  • A126251 (program): a(n)=(p+2)!/p! if p prime and p+2 prime.
  • A126258 (program): Triangle generated by Pascal’s rule with left diagonal = 1,0,2,0,3,0,4,… and right diagonal =[1,1,1,1,1,…].
  • A126264 (program): a(n) = 5*n^2 + 3*n.
  • A126269 (program): Numbers n such that hcl(n,n) < hcl(n,n-1) where hcl(n,i) is the Huffman code length; see comments.
  • A126271 (program): a(n) = order of Galois group of the polynomial P(x) + n if P(x) + n (after dividing by the gcd of its coefficients) is irreducible, otherwise a(n) = 0, where P(x) = 128*x^8 - 256*x^6 + 160*x^4 - 32*x^2 + 1.
  • A126272 (program): a(1)=27; if n = Product p_i^e_i, n>1, then a(n) = Product p_{i+2}^{e_i+2}.
  • A126274 (program): Partial sum of A005915.
  • A126275 (program): Moment of inertia of all magic squares of order n.
  • A126276 (program): Moment of inertia of all magic cubes of order n.
  • A126277 (program): Triangle generated from Eulerian numbers.
  • A126281 (program): a(n) is the least m to satisfy the requirements of A052130.
  • A126284 (program): a(n) = 5*2^n - 4*n - 5.
  • A126286 (program): a(1) = 2, a(n) = n * LeastPrimeFactor(n+1) / LeastPrimeFactor(n).
  • A126287 (program): a(1) = 1, a(2) = 1, a(n) = n * LeastPrimeFactor(n-1) / LeastPrimeFactor(n)
  • A126288 (program): a(1) = 2, a(n) = n * LargestPrimeFactor(n+1) / LargestPrimeFactor(n).
  • A126289 (program): a(1) = 1, a(2) = 1, a(n) = n * LargestPrimeFactor(n-1) / LargestPrimeFactor(n).
  • A126303 (program): a(n) = number of nodes with odd distance to the root in the n-th plane general tree encoded by A014486(n). Both internal and terminal nodes (leaves) are counted.
  • A126304 (program): a(n) = number of nodes with nonzero even distance to the root in the n-th plane general tree encoded by A014486(n).
  • A126305 (program): a(n) = number of nodes with even distance to the root in the n-th plane general tree encoded by A014486(n). The root node itself is also included.
  • A126306 (program): a(n) = number of double-rises (UU-subsequences) in the n-th Dyck path encoded by A014486(n).
  • A126307 (program): a(n) is the length of the leftmost ascent (i.e., height of the first peak) in the n-th Dyck path encoded by A014486(n).
  • A126308 (program): Delete ‘10’-substrings in the binary expansion of n.
  • A126324 (program): a(2n) = Cat(n), a(2n+1) = 3*Cat(n), where Cat(n) = binomial(2n,n)/(n+1) are the Catalan numbers (A000108).
  • A126325 (program): Triangle read by rows: T(n,k) = binomial(2*n+1, n-k) (1 <= k <= n).
  • A126328 (program): Rounded value of n!/(n(n+1)/2); A000142(n)/A000217(n).
  • A126329 (program): Primes of the form 6p+5 where p is a prime.
  • A126330 (program): Primes of the form 4p+3 where p is a prime.
  • A126331 (program): Triangle T(n,k), 0 <= k <= n, read by rows defined by: T(0,0)=1, T(n,k)=0 if k < 0 or if k > n, T(n,0) = 4*T(n-1,0) + T(n-1,1), T(n,k) = T(n-1,k-1) + 5*T(n-1,k) + T(n-1,k+1) for k >= 1.
  • A126332 (program): Numbers n such that 10n + 13 is prime.
  • A126335 (program): a(n) = n*(4*n^2+5*n-3)/2.
  • A126352 (program): Denominator of z-sequence for the Sheffer (Appell type) triangle A134832 (circular succession numbers).
  • A126354 (program): a(n) = 6*a(n-2) - a(n-4) for n > 4, with a(1)=1, a(2)=0, a(3)=3, a(4)=2.
  • A126356 (program): a(n) is the n-th integer from among the positive integers which are coprime to (n+1).
  • A126357 (program): a(n) is the (n+1)st integer from among the positive integers which are coprime to n.
  • A126358 (program): Number of base 4 n-digit numbers with adjacent digits differing by one or less.
  • A126360 (program): Number of base 6 n-digit numbers with adjacent digits differing by one or less.
  • A126362 (program): Number of base 8 n-digit numbers with adjacent digits differing by one or less.
  • A126363 (program): Number of base 9 n-digit numbers with adjacent digits differing by one or less.
  • A126364 (program): Number of base 10 n-digit numbers with adjacent digits differing by one or less.
  • A126387 (program): Read binary expansion of n from the left; keep track of the excess of 1’s over 0’s that have been seen so far; sequence gives maximum(excess of 1’s over 0’s).
  • A126388 (program): Denominators in a series for the “alternating Euler constant” log(4/Pi).
  • A126390 (program): a(n) = Sum_{i=0..n} 2^i*B(i)*binomial(n,i) where B(n) = Bell numbers A000110(n).
  • A126391 (program): a(1)=1; for n>1: a(n) = sum of all subsets of (a(1),..,a(n-1)).
  • A126392 (program): Number of base 5 n-digit numbers with adjacent digits differing by two or less.
  • A126393 (program): Number of base 6 n-digit numbers with adjacent digits differing by two or less.
  • A126394 (program): Number of base 7 n-digit numbers with adjacent digits differing by two or less.
  • A126395 (program): Number of base 8 n-digit numbers with adjacent digits differing by two or less.
  • A126420 (program): a(n) = n^3 - n - 1.
  • A126421 (program): Numbers n for which n^3-n-1 is prime.
  • A126422 (program): Primes of the form k^4-k-1.
  • A126423 (program): a(n) = n^4 - n - 1.
  • A126426 (program): a(n) = n^5 - n - 1.
  • A126431 (program): a(n) = n * 10^n.
  • A126443 (program): a(n) = Sum_{k=0..n-1} C(n-1,k)*a(k)*2^k for n>0, with a(0)=1.
  • A126446 (program): Column 0 of triangle A126445; a(n) = binomial( binomial(n+2,3), n).
  • A126447 (program): Column 1 of triangle A126445; a(n) = C( C(n+3,3) - 1, n).
  • A126448 (program): Column 2 of triangle A126445; a(n) = C( C(n+4,3) - 4, n).
  • A126449 (program): Row sums of triangle A126445; a(n) = Sum_{k=0..n} C( C(n+2,3) - C(k+2,3), n-k).
  • A126451 (program): Column 0 of triangle A126450; a(n) = C( C(n+2,3) + 1, n).
  • A126452 (program): Column 1 of triangle A126450; a(n) = C( C(n+3,3), n).
  • A126453 (program): Row sums of triangle A126450: a(n) = Sum_{k=0..n} C( C(n+2,3) - C(k+2,3) + 1, n-k).
  • A126455 (program): Column 0 of triangle A126454; a(n) = C( C(n+2,3) + 2, n).
  • A126456 (program): Column 1 of triangle A126454; a(n) = C( C(n+3,3) + 1, n).
  • A126458 (program): Column 0 of triangle A126457; a(n) = C( C(n+2,3) + 3, n).
  • A126459 (program): Column 1 of triangle A126457; a(n) = C( C(n+3,3) + 2, n).
  • A126473 (program): Number of strings over a 5 symbol alphabet with adjacent symbols differing by three or less.
  • A126474 (program): Number of arrays in [1..6]^n with adjacent elements differing by three or less.
  • A126475 (program): Number of base 7 n-digit numbers with adjacent digits differing by three or less.
  • A126476 (program): Number of base 8 n-digit numbers with adjacent digits differing by three or less.
  • A126477 (program): Number of base 9 n-digit numbers with adjacent digits differing by three or less.
  • A126501 (program): Number of n-tuples of numbers [0..5] (leading zeros allowed) in which adjacent digits differ by 4 or less.
  • A126502 (program): Number of base 7 n-digit numbers with adjacent digits differing by four or less.
  • A126503 (program): Number of base 8 n-digit numbers with adjacent digits differing by four or less.
  • A126504 (program): Number of base 9 n-digit numbers with adjacent digits differing by four or less.
  • A126528 (program): Number of base 7 n-digit numbers with adjacent digits differing by five or less.
  • A126529 (program): Number of base 8 n-digit numbers with adjacent digits differing by five or less.
  • A126530 (program): Number of base 9 n-digit numbers with adjacent digits differing by five or less.
  • A126531 (program): Number of base 10 n-digit numbers with adjacent digits differing by five or less.
  • A126560 (program): a(n) = gcd(4(n+1)(n+2), n(n+3)), periodic with 8-cycle 4,2,2,4,8,2,2,8.
  • A126561 (program): Decimal expansion of (Pi^2-9)/12.
  • A126562 (program): Number of intersections of at least four edges in a cube of n X n X n smaller cubes.
  • A126564 (program): a(n) = floor( sin(n)*cos(n) ).
  • A126565 (program): a(n) = ceiling(sin(n)*cos(n)).
  • A126566 (program): a(0)=1; a(1)=2; a(2)=5; a(3)=14; for n>3: a(n) = 8*a(n-1)-20*a(n-2)+16*a(n-3)-a(n-4).
  • A126567 (program): Sequence generated from the E6 Cartan matrix.
  • A126568 (program): Binomial transform of A026641.
  • A126587 (program): a(n) is the number of integer lattice points inside the right triangle with legs 3n and 4n (and hypotenuse 5n).
  • A126588 (program): a(n) = prime(13*n).
  • A126590 (program): Multiples of 3 or 5 but not both.
  • A126592 (program): Sum of numbers less than or equal to n which are multiples of 3 or 5.
  • A126594 (program): Floor of the average of the prime factors of n with multiplicity.
  • A126596 (program): a(n) = binomial(4*n,n)*(2*n+1)/(3*n+1).
  • A126605 (program): Final three digits of 2^n.
  • A126606 (program): Fixed point of transformation of the seed sequence {0,2}.
  • A126611 (program): Sum x+y of generator pairs (x, y) {x and y coprime and not both odd} of primitive Pythagorean triangles, sorted.
  • A126613 (program): a(1)=1. a(n) = a(n-1) + (number of terms, from among terms a(1) through a(n-1), which are powers of primes {including 1}).
  • A126614 (program): a(n) = (2^prime(n) + 1)/3.
  • A126615 (program): Denominators in a harmonic triangle.
  • A126616 (program): a(n) = n for n < 10, a(10*n) = a(n), and if the terms a(10), a(20), a(30), … are deleted, one gets back the original sequence.
  • A126617 (program): a(n) = Sum_{i=0..n} (-2)^(n-i)*B(i)*binomial(n,i) where B(n) = Bell numbers A000110(n).
  • A126627 (program): a(n) is the number of nonnegative integers k less than 10^n such that the decimal representation of k lacks digits 1,2,3 and at least one of digits 4,5,6,7,8,9.
  • A126634 (program): a(n) is the number of nonnegative integers k less than 10^n such that the decimal representation of k lacks the digits 1,2,3,4 and at least one of digits 5,6,7,8,9.
  • A126635 (program): a(n) is the number of nonnegative integers k less than 10^n such that the decimal representation of k lacks the digits 1,2,3, at least one of digits 4,5 and at least one of digits 6,7,8,9.
  • A126637 (program): Difference x-y of generator pairs (x,y) {x and y coprime and not both odd, x>y} of primitive Pythagorean triangles, sorted on values x+y (A126611), then on x-y.
  • A126639 (program): a(n) is the number of integers k less than 10^n such that the decimal representation of k lacks the digit 1,2,3, at least one of digits 4,5,6 and at least one of digits 7,8,9.
  • A126640 (program): a(n) is the number of integers k less than 10^n such that the decimal representation of k lacks the digit 1 and 2, at least one of digits 3,4, at least one of digits 5,6 and at least one of digits 7,8,9.
  • A126641 (program): a(n) is the number of integers k less than 10^n such that the decimal representation of k lacks the digit 1, at least one of digits 2,3, at least one of digits 4,5, at least one of digits 6,7 and at least one of digits 8,9.
  • A126642 (program): a(n) is the number of integers k less than 10^n such that the decimal representation of k lacks the digits 1,2,3,4 and 5 and at least one of digits 6,7,8,9.
  • A126643 (program): a(n) is the number of integers k less than 10^n such that the decimal representation of k lacks the digits 1,2,3,4, at least one of digits 5,6 and at least one of digits 7,8,9.
  • A126644 (program): a(n) = 3*3^n - 3*2^n + 1.
  • A126645 (program): a(n) is the number of integers k less than 10^n such that the decimal representation of k lacks the digits 1,2,3,4 and 5, at least one of digits 6,7 and at least one of digits 8,9.
  • A126646 (program): a(n) = 2^(n+1) - 1.
  • A126656 (program): a(1)=1; for n>1, a(n) = Sum_{k=1..n-1} a(k) * floor(n/k).
  • A126663 (program): Absolute difference between largest prime factors of two successive semiprimes.
  • A126664 (program): Continued fraction expansion of sqrt(3)/2.
  • A126665 (program): a(n) = -n^2 + 9n + 53.
  • A126673 (program): Third diagonal of A126671.
  • A126674 (program): a(n) = n!*Sum_{j=0..n-1} 2^j/(j+1).
  • A126675 (program): Product_{i=2..n} |Stirling_1(i,2)|.
  • A126676 (program): Product_{i=3..n} |Stirling_1(i,3)|.
  • A126677 (program): Product_{i=4..n} |Stirling_1(i,4)|.
  • A126678 (program): Product_{i=5..n} |Stirling_1(i,5)|.
  • A126679 (program): Product_{i=3..n} Stirling_2(i,3).
  • A126680 (program): Product_{i=4..n} Stirling_2(i,4).
  • A126681 (program): a(n) = Product_{i=5..n} Stirling_2(i,5).
  • A126684 (program): Union of A000695 and 2*A000695.
  • A126690 (program): Multiplicative function defined for prime powers by a(p^k) = p + p^2 + p^3 + … + p^(k-1) - 1 (k >= 1).
  • A126691 (program): Prime numbers p such that 100-p is also a prime.
  • A126692 (program): Prime numbers p such that 1000-p is also a prime. All terms are shown.
  • A126693 (program): Prime numbers p such that 10000-p is also a prime.
  • A126694 (program): Expansion of g.f.: 1/(1 - 7*x*c(x)), where c(x) is the g.f. for A000108.
  • A126696 (program): Tenth-squares: floor(n/10)*ceiling(n/10).
  • A126706 (program): Positive integers which are neither squarefree integers nor prime powers.
  • A126713 (program): The triangle K referred to in A038200, read along rows.
  • A126718 (program): a(n) is the number of nonnegative integers k less than 10^n such that the decimal representation of k lacks the digits 1,2,3, at least one of digits 4,5, at least one of digits 6,7 and at least one of digits 8,9.
  • A126719 (program): a(n) = -n^2 + 9n + 23.
  • A126720 (program): Primes p such that p - q = 24, where q is the previous prime before p; or prime numbers preceded by precisely 23 composite numbers.
  • A126721 (program): Primes p such that q-p = 40, where q is the next prime after p.
  • A126725 (program): a(1)=0, a(2)=1; for n>2, a(n) = C(n,2)*(1+a(n-2)).
  • A126726 (program): Number of squares (of nonnegative integers) that require n binary (base-2) digits.
  • A126728 (program): Number of graphs on n nodes with edge chromatic number 2.
  • A126759 (program): a(0) = 1; a(2n) = a(n); a(3n) = a(n); otherwise write n = 6i+j, where j = 1 or 5 and set a(n) = 2i+2 if j = 1, otherwise a(n) = 2i+3.
  • A126760 (program): a(0) = 0, a(2n) = a(n), a(3n) = a(n), a(6n+1) = 2n + 1, a(6n+5) = 2n + 2.
  • A126765 (program): a(n) = number of L-convex polyominoes inscribed in an (n+1) X (n+1) box.
  • A126772 (program): Padovan factorials: a(n) is the product of the first n terms of the Padovan sequence. Similar to the Fibonacci factorial.
  • A126773 (program): a(n) = largest divisor of n which is coprime to the largest proper divisor of n. (a(1)=1.).
  • A126775 (program): a(n) = phi(n)^2 * d(n) = A000010(n)^2 * A000005(n).
  • A126778 (program): Number of functions f:{1,2,…,n}->{1,2,…,n} such that Im(f) contain two fixed elements.
  • A126779 (program): Number of functions f:{1,2,…,n}->{1,2,…,n} such that Im(f) contains 3 fixed elements.
  • A126780 (program): Number of functions f:{1,2,…,n}->{1,2,…,n} such that Im(f) contains 4 fixed elements.
  • A126781 (program): Number of functions f:{1,2,…,n}->{1,2,…,n} such that Im(f) contains 6 fixed elements.
  • A126785 (program): Numbers k such that 10*k + 11 is prime.
  • A126791 (program): Binomial matrix applied to A111418.
  • A126792 (program): Removing the first, fourth, seventh, tenth … term of the sequence yields the original sequence, augmented by 1.
  • A126795 (program): a(n) = gcd(n, Product_{p|n} (p+1)), where the product is over the distinct primes p that divide n.
  • A126800 (program): Smallest divisor of n which is greater than largest divisor d of n such that each integer from 1 to d is also a divisor of n.
  • A126801 (program): a(n) = smallest integer which is coprime to n and is > A057237(n).
  • A126804 (program): a(n) = (2n)! / (n-1)!.
  • A126812 (program): Ramanujan numbers (A000594) read mod 4.
  • A126813 (program): Ramanujan numbers (A000594) read mod 8.
  • A126814 (program): Ramanujan numbers (A000594) read mod 16.
  • A126815 (program): Ramanujan numbers (A000594) read mod 32.
  • A126825 (program): Ramanujan numbers (A000594) read mod 3.
  • A126826 (program): Ramanujan numbers (A000594) read mod 9.
  • A126827 (program): Ramanujan numbers (A000594) read mod 27.
  • A126832 (program): Ramanujan numbers (A000594) read mod 5.
  • A126833 (program): Ramanujan numbers (A000594) read mod 25.
  • A126836 (program): Ramanujan numbers (A000594) read mod 7.
  • A126839 (program): Ramanujan numbers (A000594) read mod 11.
  • A126842 (program): Ramanujan numbers (A000594) read mod 13.
  • A126848 (program): Arises in lower bound of the spectral norm of n X n symmetric random matrices.
  • A126862 (program): Numbers n that have a component C(1,1) when expanded in the binomial basis of order t=3.
  • A126864 (program): a(n) = gcd(n, Product_{p|n} (p-1)), where the product is over the distinct primes, p, that divide n.
  • A126865 (program): a(n) = gcd(Product_{p|n} (p+1)^b(p,n), Product_{p|n} (p-1)^b(p,n)), where the products are over the distinct primes, p, that divide n and p^b(p,n) is the highest power of p dividing n.
  • A126866 (program): a(n) = 13*a(n-1) - a(n-2).
  • A126867 (program): Largest even semiprime <= n^2.
  • A126868 (program): a(n) = (n+1)!! mod n.
  • A126869 (program): a(n) = Sum_{k = 0..n} binomial(n,floor(k/2))*(-1)^(n-k).
  • A126883 (program): a(n) = (2^0)*(2^1)*(2^2)*(2^3)…(2^n)-1 = 2^T(n) - 1 where T(n) = A000217(n) is the n-th triangular number.
  • A126884 (program): a(n) = (2^0)*(2^1)*(2^2)*(2^3)…(2^n)+1 = 2^T_n+1 (cf. A000217).
  • A126885 (program): T(n,k) = n*T(n,k-1) + k, with T(n,1) = 1, square array read by ascending antidiagonals (n >= 0, k >= 1).
  • A126890 (program): Triangle read by rows: T(n,k) = n*(n+2*k+1)/2, 0 <= k <= n.
  • A126899 (program): Coordination sequence for 6-dimensional cyclotomic lattice Z[zeta_9].
  • A126900 (program): Coordination sequence for 6-dimensional cyclotomic lattice Z[zeta_18].
  • A126904 (program): Coordination sequence for 8-dimensional cyclotomic lattice Z[zeta_24].
  • A126926 (program): Coordination sequence for 12-dimensional cyclotomic lattice Z[zeta_36].
  • A126930 (program): Inverse binomial transform of A005043.
  • A126931 (program): a(n) = A127359(n+1)/2 - A127359(n).
  • A126932 (program): Binomial transform of A127358.
  • A126933 (program): Quotients arising from sequence A053312.
  • A126934 (program): Define an array by d(m, 0) = 1, d(m, 1) = m; d(m, k) = (m - k + 1) d(m+1, k-1) - (k-1) (m+1) d(m+2, k-2). Sequence gives d(0,2n).
  • A126935 (program): Define an array by d(m, 0) = 1, d(m, 1) = m; d(m, k) = (m - k + 1) d(m+1, k-1) - (k-1) (m+1) d(m+2, k-2). Sequence gives d(n,3).
  • A126939 (program): “Model 1” for number of free alkanes on n points.
  • A126940 (program): “Model 2” for number of free alkanes on n points.
  • A126941 (program): The sequence b[n] defined in A126939.
  • A126942 (program): The sequence c[n] defined in A126939.
  • A126943 (program): The sequence d[n] defined in A126939.
  • A126944 (program): The sequence a[n]+b[n]+c[n]+d[n] defined in A126939.
  • A126945 (program): The sequence a[n]+b[n]+c[n]+d[n] defined in A126940.
  • A126946 (program): The sequence b[n] defined in A126940.
  • A126947 (program): The sequence c[n] defined in A126940.
  • A126948 (program): The sequence d[n] defined in A126940.
  • A126950 (program): a(1) = 1; for n>1, a(n) = the smallest number p > a(n-1) such that (a(n-1)+p)/2 is a cube.
  • A126951 (program): List of pairs: k followed by k^3.
  • A126952 (program): a(0)=1, a(n+1) = 5*a(n)-4*A117641(n) for n>=0.
  • A126953 (program): Triangle T(n,k), 0 <= k <= n, read by rows given by: T(0,0)=1, T(n,k)=0 if k < 0 or if k > n, T(n,0) = 3*T(n-1,0) + T(n-1,1), T(n,k) = T(n-1,k-1) + T(n-1,k+1) for k >= 1.
  • A126954 (program): Triangle T(n,k), 0 <= k <= n, read by rows given by: T(0,0)=1, T(n,k)=0 if k < 0 or if k > n, T(n,0) = 3*T(n-1,0) + T(n-1,1), T(n,k) = T(n-1,k-1) + T(n-1,k) + T(n-1,k+1) for k >= 1.
  • A126958 (program): Define an array by d(m, 0) = 1, d(m, 1) = m; d(m, k) = (m - k + 1) d(m+1, k-1) - (k-1) (m+1) d(m+2, k-2). Sequence gives d(n,4).
  • A126960 (program): Primes p such that (3p)^2 + 2 is prime.
  • A126962 (program): Define an array by d(m, 0) = 1, d(m, 1) = m; d(m, k) = (m - k + 1) d(m+1, k-1) - (k-1) (m+1) d(m+2, k-2). Sequence gives d(1,n).
  • A126963 (program): Numerators of sequence defined by f(0)=1, f(1)=5/4; f(n) = ( (6*n-1)*f(n-1) - (2*n-1)*f(n-2) )/(4n).
  • A126964 (program): a(n) = 2*n*(6*n-1).
  • A126965 (program): a(n) = (2*n)!*(2*n-1)/(2^n*n!).
  • A126966 (program): Expansion of sqrt(1 - 4*x)/(1 - 2*x).
  • A126967 (program): Expansion of e.g.f.: sqrt(1+4*x)/(1+2*x).
  • A126972 (program): Number of distinct values taken by the entropy for permutations of [1..n], where the entropy of a permutation pi is Sum_{k=1..n} (pi(k)-k)^2.
  • A126978 (program): a(n) = 104*n + 9977.
  • A126979 (program): a(n) = 24*n + 233.
  • A126980 (program): a(n) = 14*n + 47.
  • A126981 (program): Largest perfect square less than 2*10^n.
  • A126982 (program): Expansion of 1/(1+3*x*c(x)), c(x) the g.f. of Catalan numbers A000108.
  • A126983 (program): Expansion of 1/(1+x*c(x)), c(x) the g.f. of Catalan numbers A000108.
  • A126984 (program): Expansion of 1/(1+2*x*c(x)), c(x) the g.f. of Catalan numbers A000108.
  • A126985 (program): Expansion of 1/(1+8*x*c(x)), c(x) the g.f. of Catalan numbers A000108.
  • A126986 (program): Expansion of 1/(1+4*x*c(x)), c(x) the g.f. of Catalan numbers A000108.
  • A126987 (program): Expansion of 1/(1+5*x*c(x)), c(x) the g.f. of Catalan numbers A000108.
  • A126988 (program): Triangle read by rows: T(n,k) = n/k if k is a divisor of n; T(n,k) = 0 if k is not a divisor of n (1 <= k <= n).
  • A126990 (program): Largest prime preceding geometric mean of prime(n) and prime(n+2).
  • A126993 (program): a(n) = binomial(prime(n+3), prime(n)).
  • A126995 (program): a(n) = binomial(prime(n+2), 3).
  • A126996 (program): a(n) = binomial(prime(3+n), prime(3)).
  • A126997 (program): a(n) = binomial(prime(4+n), prime(4)).
  • A126998 (program): a(n) = binomial(prime(n+5), prime(5)).
  • A127002 (program): Number of partitions of n that have the form a+a+b+c where a,b,c are distinct.
  • A127013 (program): Triangle read by rows: reversal of A126988.
  • A127014 (program): a(n) = smallest k such that A(k) == 0 mod 2^n, where A(0) = 1 and A(k) = k*A(k-1) + 1 = A000522(k).
  • A127015 (program): Digits of the 2-adic integer lim_{n->infty} A127014(n).
  • A127016 (program): Expansion of 1/(1+7*x*c(x)), c(x) the g.f. of Catalan numbers A000108.
  • A127017 (program): Expansion of 1/(1+6*x*c(x)), where c(x) = g.f. for Catalan numbers A000108.
  • A127032 (program): Maximal value of m such that 5^m <= n! : a(n) = floor( log(n!) / log(5) ).
  • A127033 (program): Maximal value of m such that 7^m <= n!: a(n) = floor( log(n!) / log(7) ).
  • A127034 (program): Maximal value of m such that 11^m <= n! : a(n) = floor( log(n!) / log(11) ).
  • A127035 (program): Maximal value of m such that 13^m <= n! : a(n) = floor( log(n!) / log(13) ).
  • A127036 (program): a(n) = maximal value of m such that 17^m divides n! (17^m <= n!).
  • A127037 (program): Maximal value of m such that 19^m <= n! : a(n) = floor( log(n!) / log(19) ).
  • A127038 (program): Maximal value of m such that 23^m <= n! : a(n) = floor( log(n!) / log(23) ).
  • A127039 (program): Maximal value of m such that 29^m <= n! : a(n) = floor( log(n!) / log(29) ).
  • A127040 (program): a(n) = binomial(floor((3n+4)/2)),floor(n/2)).
  • A127041 (program): Maximal value of m such that 31^m <= n! : a(n) = floor( log(n!) / log(31) ).
  • A127053 (program): Expansion of 1/(1+9*x*c(x)), where c(x) = g.f. for Catalan numbers A000108.
  • A127057 (program): Triangle T(n,k), partial row sums of the n-th row of A127013 read right to left.
  • A127059 (program): Column 2 of triangle A127058.
  • A127064 (program): a(0)=1. a(n) = a(prime(n)(mod n)) + 1, where prime(n) is the n-th prime.
  • A127065 (program): a(n) = n! - (n-2)^2.
  • A127067 (program): Define an array by d(m, 0) = 1, d(m, 1) = m; d(m, k) = (m - k + 1) d(m+1, k-1) - (k-1) (m+1) d(m+2, k-2). Sequence gives d(2,n).
  • A127068 (program): Let d(m, 0) = 1, d(m, 1) = m, and d(m, k) = (m - k + 1)*d(m+1, k-1) - (k-1)*(m+1) d(m+2, k-2). Sequence gives d(3,n).
  • A127069 (program): Number of lines in a Pauli graph of order n.
  • A127070 (program): Define an array by d(m, 0) = 1, d(m, 1) = m; d(m, k) = (m - k + 1) d(m+1, k-1) - (k-1) (m+1) d(m+2, k-2). Sequence gives d(4,n).
  • A127071 (program): Quotients (3^p - 2^p - 1)/p, where p = prime(n).
  • A127072 (program): Numbers k that divide 3^k - 2^k - 1.
  • A127075 (program): a(1)=1. a(n) = a(n-1) + (sum of the earlier terms {among terms a(1) through a(n-1)} which are coprime to n).
  • A127076 (program): a(0)=1. a(n) = a(n-1) + (sum of the earlier terms {among terms a(0) through a(n-1)} which are coprime to n).
  • A127080 (program): Infinite square array read by antidiagonals: Q(m, 0) = 1, Q(m, 1) = 1; Q(m, 2k) = (m - 2k + 1)*Q(m+1, 2k-1) - (2k-1)*Q(m+2,2k-2), m*Q(m, 2k+1) = (m - 2k)*Q(m+1, 2k) - 2k(m+1)*Q(m+2, 2k-1).
  • A127093 (program): Triangle read by rows: T(n,k)=k if k is a divisor of n; otherwise, T(n,k)=0 (1 <= k <= n).
  • A127094 (program): Triangle, reversal of A127093.
  • A127096 (program): Triangle T(n,m) = A000012*A127094 read by rows.
  • A127097 (program): Triangle T(n,m) = A127093 * A126988 read by rows.
  • A127098 (program): Triangle T(n,m) read by rows: product A127093 * A127094.
  • A127099 (program): Triangle T(n,m) = A126988 *A127093 read by rows.
  • A127109 (program): n! in base 5.
  • A127110 (program): n! in base 3.
  • A127111 (program): a(n) = (n+1)! - (n)!!.
  • A127112 (program): n! in base 4.
  • A127113 (program): n! in base 6.
  • A127114 (program): n! in base 7.
  • A127115 (program): n! in base 8.
  • A127116 (program): n! in base 9.
  • A127118 (program): a(n) = n-th prime * n-th nonprime.
  • A127137 (program): Define an array by Q(m, 0) = 1, Q(m, 1) = 1; Q(m, 2k) = (m - 2k + 1)*Q(m+1, 2k-1) - (2k-1)*Q(m+2, 2k-2), m*Q(m, 2k+1) = (m - 2k)*Q(m+1, 2k) - 2k(m+1)*Q(m+2, 2k-1). Sequence gives Q(0,n).
  • A127138 (program): Q(1,n), where Q(m,k) is defined in A127080 and A127137,
  • A127139 (program): Inverse triangle of A126988.
  • A127140 (program): Square of triangle A127139, row sums = A101035.
  • A127144 (program): Q(2,n), where Q(m,k) is defined in A127080 and A127137,
  • A127145 (program): Q(3,n), where Q(m,k) is defined in A127080 and A127137,
  • A127146 (program): Q(n,4), where Q(m,k) is defined in A127080 and A127137.
  • A127147 (program): Q(n,5), where Q(m,k) is defined in A127080 and A127137.
  • A127148 (program): Q(n,6), where Q(m,k) is defined in A127080 and A127137.
  • A127161 (program): Integers whose aliquot sequences terminate by encountering a prime number.
  • A127162 (program): Composite numbers whose aliquot sequences terminate by encountering a prime number.
  • A127170 (program): Triangle read by rows: T(n,k) is the number of divisors of n that are divisible by k, with 1 <= k <= n.
  • A127173 (program): T(n,k) = A007427(n/k) if k divides n, T(n,k) = 0 otherwise.
  • A127185 (program): Triangle of distances between n>=1 and n>=m>=1 measured by the number of non-common prime factors.
  • A127189 (program): E.g.f.: sqrt((1+4*x)/(1+2*x)).
  • A127190 (program): Expansion of e.g.f. sqrt((1+2*x)/(1+4*x)).
  • A127191 (program): Related to the function “shin” - see reference for precise definition.
  • A127193 (program): A 9th-order Fibonacci sequence.
  • A127195 (program): Number of subsets of {1,2,…,n} which contain no three consecutive odd numbers.
  • A127197 (program): Numerator of n-th Van der Waerden-Ulam binary measure of the primes.
  • A127207 (program): Half-indexed Lucas numbers a(n)=round(sqrt((1+sqrt(5))/2)^n) a(2n)=L(n)=A000032, so a(n)=L(n/2).
  • A127210 (program): a(n) = 3^n*Lucas(n), where Lucas = A000204.
  • A127211 (program): a(n) = 4^n*Lucas(n), where Lucas = A000204.
  • A127212 (program): a(n) = 5^n*Lucas(n), where Lucas = A000204.
  • A127213 (program): a(n) = 6^n*Lucas(n), where Lucas = A000204.
  • A127214 (program): a(n) = 2^n*tribonacci(n) or (2^n)*A001644(n+1).
  • A127215 (program): a(n) = 3^n*tribonacci(n) or (3^n)*A001644(n+1).
  • A127216 (program): a(n) = 2^n*tetranacci(n) or (2^n)*A001648(n).
  • A127217 (program): Half-indexed Fibonacci numbers a(n)=round(sqrt((1+sqrt(5))/2)^n/sqrt(5)) a(2n)=F(n)=A000045, so a(n)=F(n/2).
  • A127220 (program): a(n) = 3^n*tetranacci(n) or (2^n)*A001648(n).
  • A127221 (program): a(n) = 2^n*pentanacci(n) or (2^n)*A023424(n-1).
  • A127222 (program): a(n) = 3^n*pentanacci(n) or (3^n)*A023424(n-1).
  • A127226 (program): a(0)=2, a(1)=2, a(n) = 2*a(n-1) + 6*a(n-2).
  • A127227 (program): a(n)= numerator of ((n + 3)! - (n - 3)!)/(n!).
  • A127228 (program): a(n)= numerator of ((n + 4)! - (n - 4)!)/(n!).
  • A127229 (program): a(n)= numerator of ((n + 5)! - (n - 5)!)/(n!).
  • A127230 (program): a(n) = (2n)! - 1.
  • A127231 (program): a(n) = (2n)! + 1.
  • A127233 (program): a(n) = n!*(n*(n+1)/2)!.
  • A127234 (program): a(n) = n! (sum(1..n-1))!.
  • A127236 (program): A Thue-Morse binomial triangle.
  • A127237 (program): Row sums of Thue-Morse binomial triangle A127236.
  • A127238 (program): Diagonal sums of Thue-Morse binomial triangle A127236.
  • A127239 (program): Central coefficients of Thue-Morse binomial triangle A127236.
  • A127240 (program): Partial sums of central coefficients of Thue-Morse binomial triangle A127236.
  • A127241 (program): A Thue-Morse triangle.
  • A127243 (program): Triangle whose k-th column is generated by (1+A010060(1+k)x)*x^k.
  • A127245 (program): Row sums of a signed Thue-Morse related triangle.
  • A127246 (program): Row sums of a Thue-Morse related triangle.
  • A127247 (program): A Thue-Morse falling factorial triangle.
  • A127248 (program): Triangle whose k-th column is generated by (1-A010060(1+k)*x)*x^k.
  • A127249 (program): A product of Thue-Morse related triangles.
  • A127250 (program): Sequence consisting of 1,3 or 5 with 3’s occurring at the odious indices given by A091855 and 5’s occurring at twice these odious indices.
  • A127252 (program): Sequence composed of 1 and -1 with the -1’s occurring at odious indexed positions given by A091855.
  • A127253 (program): Product of number triangles A127243 and A127248.
  • A127254 (program): (0,1) sequence whose zero positions are indexed by twice the odious numbers given by A091855.
  • A127255 (program): Partial sums of A127252.
  • A127260 (program): Indices n of odd numbers of the form 8*n+1 that are not primes.
  • A127261 (program): a(0)=2, a(1)=2, a(n) = 2*a(n-1) + 10*a(n-2).
  • A127262 (program): a(0)=2, a(1)=2, a(n) = 2*a(n-1) + 12*a(n-2).
  • A127265 (program): a(n) = floor((n + 1/2)^(n + 1/2)).
  • A127266 (program): Expansion of 1/Pi in base 2.
  • A127267 (program): a(n) = floor(n/pi(n)), where pi(n)=A000720(n) is the number of primes <=n.
  • A127275 (program): Expansion of (sqrt(1-4x)-x)/(1-4x).
  • A127276 (program): Hankel transform of A127275.
  • A127278 (program): Number of fixed points in range [A014137(n-1)..A014138(n-1)] of permutation A126313/A126314.
  • A127282 (program): Number of fixed points in range [A014137(n-1)..A014138(n-1)] of permutation A126315/A126316.
  • A127284 (program): a(n) = number of valleys (DU-steps) in the Dyck path encoded by A014486(n).
  • A127304 (program): a(n) = floor(n^(n + 1/2)).
  • A127307 (program): Positions of Dyck words beginning as UUD (110) in A014486/A063171.
  • A127308 (program): Number of ways of writing the n-th prime p(n) as a sum of 24 squares.
  • A127316 (program): a(n) = 2*n^2 - 4*n + 73.
  • A127319 (program): a(n)={binomial[n,(sum of decimal digits of n)] mod n}, with n>=1.
  • A127320 (program): Start with i=1 and j=2. Concatenate i and j, get k = floor ij/j, concatenate j and k, etc.
  • A127321 (program): First 4-dimensional hyper-tetrahedral coordinate; repeat m C(m+3,3) times; 4-D analog of A056556.
  • A127322 (program): Second 4-dimensional hyper-tetrahedral coordinate; 4-D analog of A056557.
  • A127323 (program): Third 4-dimensional hyper-tetrahedral coordinate; 4-D analog of A056557.
  • A127324 (program): Fourth 4-dimensional hyper-tetrahedral coordinate; 4-D analog of A056558.
  • A127325 (program): Hyper-tetrahedron with T(W,X,Y,Z)=Y-Z.
  • A127327 (program): Hyper-tetrahedron with T(W,X,Y,Z)=W-X.
  • A127328 (program): Inverse binomial transform of A026641; binomial transform of A127361.
  • A127329 (program): Semiprimes equal to the sum of three primes in arithmetic progression.
  • A127330 (program): Begin with the empty sequence and a starting number s = 0. At step k (k >= 1) append the k consecutive numbers s to s+k-1 and change the starting number (for the next step) to 2s+2.
  • A127333 (program): Numbers that are the sum of 6 consecutive primes.
  • A127334 (program): Numbers that are the sum of 7 consecutive primes.
  • A127335 (program): Numbers that are the sum of 8 successive primes.
  • A127336 (program): Numbers that are the sum of 9 consecutive primes.
  • A127337 (program): Numbers that are the sum of 10 consecutive primes.
  • A127338 (program): Numbers that are the sum of 11 consecutive primes.
  • A127339 (program): Numbers that are the sum of 12 consecutive primes.
  • A127342 (program): Product of 10 consecutive primes.
  • A127343 (program): Product of 11 consecutive primes.
  • A127344 (program): Product of 12 consecutive primes.
  • A127345 (program): a(n) = pq + pr + qr with p = prime(n), q = prime(n+1), and r = prime(n+2).
  • A127349 (program): a(n) = Sum_{i=n..n+1} Sum_{j=i+1..n+2} Sum_{k=j+1..n+3} prime(i)*prime(j)*prime(k).
  • A127356 (program): a(n) is the smallest k > 0 such that k^2 + prime(n) is prime.
  • A127357 (program): Expansion of 1/(1 - 2*x + 9*x^2).
  • A127358 (program): a(n) = Sum_{k=0..n} binomial(n, floor(k/2))*2^(n-k).
  • A127359 (program): a(n) = Sum_{k=0..n} binomial(n, floor(k/2))*3^(n-k).
  • A127360 (program): a(n) = Sum_{k=0..n} binomial(n, floor(k/2))*4^(n-k).
  • A127361 (program): a(n) = Sum_{k=0..n} binomial(n, floor(k/2))*(-2)^(n-k).
  • A127362 (program): a(n)=sum(k=0..n, C(n,floor(k/2))*(-3)^(n-k)}.
  • A127363 (program): a(n) = Sum_{k=0..n} C(n,floor(k/2))*(-4)^(n-k).
  • A127365 (program): Signed repeated natural numbers.
  • A127366 (program): Let m = floor(sqrt(n)); if n and m have the same parity, a(n) = n + m, otherwise a(n) = n - m.
  • A127367 (program): Inverse permutation to A127366.
  • A127368 (program): Relative prime triangle, read by rows.
  • A127369 (program): (n^3+n)*4^n.
  • A127370 (program): a(1)=1. a(n) = number of positive integers <= n and coprime to (Sum_{k=1..n-1} a(k)).
  • A127391 (program): Series expansion of the elliptic function sqrt(k) = theta_2/theta_3 in powers of q^(1/4).
  • A127392 (program): Expansion of the elliptic function sqrt(k(q))/q^(1/4) in powers of q, where sqrt(k(q)) = theta_2(q)/theta_3(q).
  • A127393 (program): Expansion of k/q^(1/2) in powers of q, where k is the elliptic function defined by sqrt(k) = theta_2/theta_3.
  • A127394 (program): Number of irreducible representations of Sp(2n,R) with same infinitesimal character as the trivial representation.
  • A127407 (program): Negative value of coefficient of x^(n-2) in the characteristic polynomial of a certain n X n integer circulant matrix.
  • A127408 (program): Negative value of coefficient of x^(n-3) in the characteristic polynomial of a certain n X n integer circulant matrix.
  • A127410 (program): Negative value of coefficient of x^(n-5) in the characteristic polynomial of a certain n X n integer circulant matrix.
  • A127413 (program): a(n) = Sum_{1<=k<=n, gcd(k,n)=1} prime(k).
  • A127415 (program): a(n) = Sum_{1<=k<=n, gcd(k,n)=1}, A000217(k).
  • A127416 (program): a(n) = Sum_{1<=k<=n, gcd(k,n)=1} (Sum_{i=1..k} gcd(i, k)).
  • A127418 (program): a(1)=1; for n>1, a(n) = the number of earlier terms a(k), 1<k<=n-1, such that (a(k)+n) is coprime to k.
  • A127419 (program): Recurrence: a(n) = a(n-1) + floor( (sqrt(8 * a(n-1) - 7) - 1)/2 ) for n>=2 with a(0)=1, a(1)=2.
  • A127421 (program): Numbers whose decimal expansion is a concatenation of 2 consecutive increasing nonnegative numbers.
  • A127423 (program): a(1) = 1; for n > 1, a(n) = n concatenated with n - 1.
  • A127424 (program): Numbers whose decimal expansion is a concatenation of 3 consecutive decreasing numbers.
  • A127427 (program): a(n) = v_3( (6n)! ) - v_3( (3n)! ), where v_3(N) is the 3-adic valuation A007949(N).
  • A127428 (program): v_5( (10n)! ) - v_5( (5n)! ), where v_p(N) is the p-adic valuation defined in A112765.
  • A127429 (program): 2^(n*(n-1)/2) - n!.
  • A127435 (program): Primes p such that (p-1)^2 + 1 is prime.
  • A127436 (program): Primes associated with A127435.
  • A127439 (program): Triangle read by rows, in which row n consists of first n terms of A054541.
  • A127440 (program): First differences of A008683.
  • A127446 (program): Triangle T(n,k) = n*A051731(n,k) read by rows.
  • A127448 (program): Triangle T(n,k) read by rows: matrix product A054525 * A127648.
  • A127449 (program): Triangle T(n,k) = n if gcd(n,k)=1, =0 otherwise.
  • A127450 (program): Beatty sequence for 1/(e^Pi - Pi^e), complement of A127451.
  • A127451 (program): Beatty sequence for 1/(1 - e^Pi + Pi^e), complement of A127450.
  • A127462 (program): a(1)=1; for n>1, a(n) = number of earlier terms a(k), 1<=k<=n-1, such that (k+a(k)) is coprime to n.
  • A127463 (program): a(0)=1. a(n) = number of earlier terms a(k), 0<=k<=n-1, such that (k+a(k)) is coprime to n.
  • A127465 (program): Triangle read by rows: T(n,k) = k*phi(n/k) if k|n, T(n,k)=0 otherwise.
  • A127466 (program): Triangle read by rows: A054525 * A127481 as infinite lower triangular matrices.
  • A127467 (program): Mobius transform of A127466.
  • A127469 (program): n * A062949(n).
  • A127470 (program): Triangle equal to the matrix product A127466 * A051731.
  • A127472 (program): Triangle T(n,k) = Sum_{j=k..n, j|n, k|j} phi(j) read by rows, 1<=k<=n.
  • A127473 (program): a(n) = phi(n)^2.
  • A127474 (program): Triangle, square of A054522.
  • A127475 (program): Triangle T(n,k) read by rows: T(n,k) = mu(n)*phi(k) if k|n, else T(n,k)=0.
  • A127478 (program): Triangle T(n,k) read by rows: matrix product A054523 * A054522.
  • A127481 (program): Triangle T(n,k) read by rows: T(n,k) = sum_{l=k..n, l|n, k|l} l*phi(k).
  • A127482 (program): Product of the nonzero digital products of all the prime numbers prime(1) to prime(n).
  • A127483 (program): Numbers n such that A100705(n) = n^3 + (n+1)^2 is prime.
  • A127489 (program): a(n) is the coefficient of the linear term in the polynomial (x-prime(n))*(x-prime(n+1))*(x-prime(n+2))*(x-prime(n+3))*(x-prime(n+4)).
  • A127501 (program): Triangle read by rows :T(n,k)=Sum_{j, j>=0}A089942(n,j)*binomial(j,k).
  • A127504 (program): Triangle T(n,k) = phi(n) if k|n, =0 otherwise.
  • A127505 (program): Triangle T(n,k) = mobius(n/k)*phi(k) if k|n, otherwise T(n,k)=0; 1<=k<=n.
  • A127506 (program): Triangle read by rows: T(n,k) = A054521(n,k)*A000010(k), 1<=k<=n .
  • A127507 (program): Triangle read by rows: T(n,k) = mu(n) where 1<=k<=n and mu=A008683.
  • A127509 (program): Number of n-tuples where each entry is chosen from the subsets of {1,2,3} such that the intersection of all n entries contains exactly one element.
  • A127510 (program): Triangle T(n,k) = k*mobius(n).
  • A127511 (program): a(n) = mu(n) * 2^(n-1).
  • A127512 (program): Triangle read by rows: T(n,k)= mobius(n)*binomial(n-1,k-1).
  • A127513 (program): Partial sums of A127511.
  • A127514 (program): Binomial transform of an infinite lower triangular matrix with mu(n) in the diagonal.
  • A127526 (program): Sequence related to fifth roots of certain Fibonacci fractions.
  • A127527 (program): Triangle T(n,k)= tau(k)*phi(n/k) if k|n, else T(n,k)=0.
  • A127531 (program): Number of jumps in all binary trees with n edges.
  • A127533 (program): Sum of jump-lengths of all binary trees with n edges.
  • A127534 (program): Number of jumps in all even trees with 2n edges.
  • A127536 (program): Sum of jump-lengths of all even trees with 2n edges.
  • A127540 (program): Number of odd-length branches starting at the root in all ordered trees with n edges.
  • A127543 (program): Triangle T(n,k), 0<=k<=n, read by rows given by :[ -1,1,1,1,1,1,1,…] DELTA [1,0,0,0,0,0,0,0,…] where DELTA is the operator defined in A084938.
  • A127545 (program): Multiples of 7 such that n +/- 1 are twin primes.
  • A127546 (program): a(n) = F(n)^2 + F(n+1)^2 + F(n+2)^2, where F(n) denotes the n-th Fibonacci number.
  • A127547 (program): a(n) = 13n + 4.
  • A127548 (program): O.g.f.: Sum_{n>=0} n!*(x/(1+x)^2)^n.
  • A127553 (program): a(n) = Product_{k=1..n} lcm(k,n)/gcd(k,n).
  • A127554 (program): Sum of the digits of left factorial !n.
  • A127561 (program): Array T(n,k) = n^2+5*n*k+5*k^2 read downwards antidiagonals, n,k>=0.
  • A127568 (program): Triangle T(n,k) = Bell(k) = A000110(k), 0<=k<=n.
  • A127569 (program): Triangle read by rows: product of the Mobius matrix A054525 by the diagonal matrix diag(A000203(n)).
  • A127570 (program): Triangle T(n,k) = sigma(k) if k|n, otherwise T(n,k)=0; 1 <= k <= n.
  • A127571 (program): Triangle T(n,k) = phi(n/k)*sigma(k) if k divides n, else 0.
  • A127572 (program): Triangle, T(n,k) = sigma(k) * n/k if k|n, T(n,k) = 0 otherwise.
  • A127573 (program): Triangle T(n, k) = k*sigma(k) if k divides n, else 0.
  • A127575 (program): Numbers n such that 16n+15 is prime.
  • A127576 (program): Primes of the form 16n+15.
  • A127577 (program): Numbers n for which 32n+31 is prime.
  • A127578 (program): Primes congruent to 31 mod 32.
  • A127579 (program): Primes of the form 64n+63.
  • A127580 (program): Numbers n for which 64n+63 is prime.
  • A127581 (program): Smallest prime of the form k*2^n - 1, for k >= 2.
  • A127589 (program): Primes of the form 16k + 5.
  • A127590 (program): Numbers n such that 16n+5 is prime.
  • A127591 (program): Numbers k such that 64k+21 is prime.
  • A127592 (program): Primes of the form 64k+21.
  • A127593 (program): Primes of the form 256 k + 85.
  • A127594 (program): Numbers k such that 256 k + 85 is prime.
  • A127595 (program): a(n) = F(4n) - 2F(2n) where F(n) = Fibonacci numbers A000045.
  • A127601 (program): Integer part of 4th root of product of first n primes.
  • A127611 (program): a(n) = numerator of the continued fraction which has the positive divisors of n as its terms.
  • A127612 (program): a(n) = denominator of the continued fraction which has the positive divisors of n as its terms. The terms are written in order from 1 for the integer part, to n for the final term of the continued fraction.
  • A127613 (program): a(n) = denominator of the continued fraction which has the positive divisors of n as its terms. The terms are written in order from n for the integer part, to 1 for the final term of the continued fraction.
  • A127614 (program): a(n) = numerator of the continued fraction which has the positive integers which are <= n and are coprime to n as its terms.
  • A127615 (program): a(n) = denominator of the continued fraction which has the positive integers which are <= n and are coprime to n as its terms. The terms are written in order from 1 for the integer part, to n-1 for the final term of the continued fraction.
  • A127616 (program): a(n) = denominator of the continued fraction which has the positive integers which are <= n and are coprime to n as its terms. The terms are written in order from n-1 for the integer part, to 1 for the final term of the continued fraction.
  • A127617 (program): Number of walks from (0,0) to (n,n) in the region 0 <= x-y <= 3 with the steps (1,0), (0, 1), (2,0) and (0,2).
  • A127618 (program): Number of walks from (0,0) to (n,n) in the region 0 <= x-y <= 4 with the steps (1,0), (0, 1), (2,0) and (0,2).
  • A127625 (program): Triangle T(n,k) = binomial(n-1,k-1)*A001511(k), 1<=k<=n, read by rows.
  • A127626 (program): Triangle T(n,k) = A018804(k) if k|n, else T(n,k)=0.
  • A127627 (program): Triangle T(n,k) = A054525(n,k)*A018804(k), read by rows 1<=k<=n.
  • A127628 (program): G.f. 1/(1-6*x*c(x)) where c(x) is the g.f. of A000108.
  • A127630 (program): Expansion of (1+x-x^2-x^3)/(1+x^2)^2.
  • A127632 (program): Expansion of c(x*c(x)), where c(x) is the g.f. for A000108.
  • A127638 (program): A054525 * A127640, where A127640 = infinite lower triangular matrix with the sequence of primes in the main diagonal and the rest zeros.
  • A127639 (program): A051731 * A127640, where A127640 = infinite lower triangular matrix with the sequence of primes in the main diagonal and the rest zeros.
  • A127640 (program): Triangle read by rows in which row n contains n-1 0’s followed by prime(n).
  • A127641 (program): A127640 * A051731 as infinite lower triangular matrices.
  • A127647 (program): Triangle read by rows: row n consists of n-1 zeros followed by Fibonacci(n).
  • A127648 (program): Triangle read by rows: row n consists of n zeros followed by n+1.
  • A127649 (program): A127648 * A054523 as infinite lower triangular matrices.
  • A127650 (program): n^n - (2n-1)!!.
  • A127651 (program): Triangle T(n,k) = n*k if k|n, 0 otherwise; 1<=k<=n.
  • A127668 (program): Concatenated indices of primes in prime factorization of n.
  • A127669 (program): Number of numbers mapped to A127668(n) with the map described there.
  • A127670 (program): Discriminants of Chebyshev S-polynomials A049310.
  • A127672 (program): Monic integer version of Chebyshev T-polynomials (increasing powers).
  • A127673 (program): One half of even powers of 2*x in terms of Chebyshev’s T-polynomials.
  • A127676 (program): Numerators of partial sums of a series for Pi*sqrt(2)/4.
  • A127677 (program): Scaled coefficient table for Chebyshev polynomials 2*T(2*n, sqrt(x)/2) (increasing even scaled powers, without zero entries).
  • A127682 (program): Number of non-isomorphic (i.e., defined up to a rotation and a reflection) maximal independent sets of the n-cycle graph having at least one symmetry axis. Also: Number of cyclic and palindromic compositions of n in which each term is either 2 or 3.
  • A127687 (program): Number of unlabeled maximal independent sets in the n-cycle graph.
  • A127690 (program): a(1)=3; for n>1, a(n) is such that a(1)^2+…+a(n)^2 = (1+a(n))^2.
  • A127691 (program): a(n) = (2*n+1)^n-(2*n-1)^n-(2*n)^n.
  • A127692 (program): Expansion of psi(x^4) + x * psi(x^12) in powers of x where psi() is a Ramanujan theta function.
  • A127693 (program): Expansion of psi(x^2) + x * psi(x^10) in powers of x where psi() is a Ramanujan theta function.
  • A127694 (program): Absolute value of coefficient of x^3 in polynomial whose zeros are 5 consecutive integers starting with the n-th integer.
  • A127696 (program): a(n) = (2*n)^n+(2*n+1)^n-(2*n+2)^n.
  • A127698 (program): Sum of n-th triangular number and its reversal.
  • A127699 (program): Length of period of the sequence (1^1^1^…, 2^2^2^…, 3^3^3^…, 4^4^4^…, …) modulo n.
  • A127701 (program): Infinite lower triangular matrix with (1, 2, 3, …) in the main diagonal, (1, 1, 1, …) in the subdiagonal and the rest zeros.
  • A127705 (program): Row sums of A127704.
  • A127712 (program): Row sums of the inverse of the triangle A(n,k) = 1/F(n+1) if k <= n <= 2k, 0 otherwise.
  • A127713 (program): A bisection of the row sums of the inverse of the triangle A(n,k) = 1/F(n+1) if k <= n <= 2k, 0 otherwise.
  • A127717 (program): A002260 * A007318.
  • A127718 (program): A007318 * A002260 as infinite lower triangular matrices; A002260 = [1; 1,2; 1,2,3; …].
  • A127719 (program): Floor of square root of sum of squares of n consecutive primes.
  • A127720 (program): Floor of square root of sum of squares of n odd consecutive primes.
  • A127721 (program): Floor of square root of sum of squares of n consecutive numbers.
  • A127722 (program): Floor of square root of sum of squares of n consecutive odd numbers.
  • A127723 (program): Floor of square root of sum of squares of the first n consecutive even numbers.
  • A127733 (program): Square of A127648 = Triangle read by rows, n^2 preceded by (n-1) zeros.
  • A127736 (program): a(n) = n*(n^2 + 2*n - 1)/2.
  • A127737 (program): A002260 * A127701.
  • A127738 (program): Triangle read by rows: the matrix product A004736 * A127701 of two triangular matrices.
  • A127739 (program): Triangle read by rows, in which row n contains the triangular number T(n) = A000217(n) repeated n times; smallest triangular number greater than or equal to n.
  • A127740 (program): Natural number transform of Aitken’s triangle.
  • A127741 (program): a(n) = (n+1) * A005493(n).
  • A127745 (program): Counts Bell numbers (except for Catalans) associated with the partition number [n].
  • A127750 (program): Row sums of inverse of number triangle A(n,k) = 1/(2n+1) if k <= n <= 2k, 0 otherwise.
  • A127752 (program): Row sums of inverse of number triangle A(n,k) = 1/(3n+1) if k <= n <= 2k, 0 otherwise.
  • A127754 (program): Row sums of inverse of number triangle A(n,k) = 1/L(n+1) if k <= n <= 2k, 0 otherwise, where L(n) = A000032(n).
  • A127757 (program): Integer part of Gauss’ Arithmetic-Geometric Mean M(1,n).
  • A127768 (program): Row sums of the inverse of number triangle A(n,k) = 1/C(n) if k <= n <= 2k, 0 otherwise, where C(n) = A000108(n).
  • A127769 (program): a(n)=3*C(4n-2,2n)/(2n+1)-2*0^n.
  • A127770 (program): a(n) = A127768(2n+1). A bisection of the row sums of the inverse of number triangle A(n,k) = 1/C(n) if k <= n <= 2k, 0 otherwise, where C(n) = A000108(n).
  • A127772 (program): Row sums of inverse of number triangle A(n,k) = 1/Euler_phi(n+1) if k <= n <= 2k, 0 otherwise.
  • A127773 (program): Triangle read by rows: row n consists of n-1 zeros followed by n(n+1)/2.
  • A127774 (program): Triangle read by rows: row n consists of n-1 zeros followed by A000292(n).
  • A127775 (program): Triangle read by rows: row n consists of n-1 zeros followed by 2n-1.
  • A127776 (program): a(n) = ( (2^n / n!) * Product_{k=0..n-1} (4*k + 1) )^2.
  • A127777 (program): A127773 * A002260 as infinite lower triangular matrices.
  • A127778 (program): Triangle T(n,k) = A002411(k) read by rows.
  • A127779 (program): Triangle read by rows: A004736 * A127773.
  • A127780 (program): A127775 * A002260 as infinite lower triangular matrices.
  • A127787 (program): Numbers n such that F(n) divides F(F(n)), where F(n) is a Fibonacci number.
  • A127802 (program): a(0) = 1, a(n) = 3*A036987(n), n>1.
  • A127804 (program): a(2n)=4^n, a(4*n+3)-(2^(4*n+3)+2^(2*n+1))=a(n).
  • A127806 (program): Row sums of number triangle A127805.
  • A127829 (program): Number triangle mod(C(floor(k/2),n-k),2).
  • A127830 (program): a(n)=sum{k=0..n, mod(C(floor(k/2),n-k),2)}.
  • A127833 (program): T(3n,2n), where T is the array in A127832.
  • A127835 (program): (Order of Galois group of Chebyshev polynomial)/(order of polynomial); or A124827(n)/n.
  • A127838 (program): a(1) = 1, a(2) = a(3) = a(4) = 0; a(n) = a(n-4) + a(n-3) for n > 4.
  • A127839 (program): a(1)=1, a(2)=…=a(5)=0, a(n) = a(n-5) + a(n-4) for n > 5.
  • A127840 (program): a(1)=1, a(2)=…=a(6)=0, a(n) = a(n-6)+a(n-5) for n>6.
  • A127841 (program): a(1)=1, a(2)=…=a(7)=0, a(n) = a(n-7)+a(n-6) for n>7.
  • A127842 (program): a(1)=1, a(2)=…=a(8)=0, a(n) = a(n-8)+a(n-7) for n>8.
  • A127843 (program): a(1) = 1, a(2) = … = a(9) = 0, a(n) = a(n-9)+a(n-8) for n>9.
  • A127844 (program): a(1) = 1, a(2) = … = a(10) = 0, a(n) = a(n-10)+a(n-9) for n>10.
  • A127846 (program): Series reversion of x/(1+5x+4x^2).
  • A127847 (program): a(n)=4^C(n,2)*(4^n-1)/3.
  • A127848 (program): Series reversion of x/(1+6x+5x^2).
  • A127849 (program): a(n) = 5^C(n,2)*(5^n-1)/4.
  • A127850 (program): a(n)=(2^n-1)*2^(n(n-1)/2)/(2^(n-1)).
  • A127851 (program): a(n) has n 1’s followed by C(n-1,2) 0’s.
  • A127852 (program): Numbers n such that A118679(n) = 1.
  • A127853 (program): Numbers n such that A118680(n) = 1.
  • A127854 (program): Largest number k such that k^2 divides A007781(6n+1).
  • A127858 (program): Positive integers n such that r(n^2)=r(n)^2, where r is the cyclic replacement map of the digits d of n in base 12, that is, d->d+1 if d<11 and d->0 if d=11.
  • A127859 (program): a(n)=r(A127858(n)) where A127858 is the sequence of positive integers with the property that r(n^2)=r(n)^2 and where r if the cyclic replacement map of the digits d of n in base 12 defined by d->d+1 if d<11 and d->0 if d=11.
  • A127860 (program): a(n)=A127858(n)^2 where A127858 is the sequence of positive integers with the property that r(n^2)=r(n)^2 and where r if the cyclic replacement map of the digits d of n in base 12 defined by d->d+1 if d<11 and d->0 if d=11.
  • A127861 (program): a(n)=A127859(n)^2 where A127859(n)=r(A127858(n)) and A127858 is the sequence of positive integers with the property that r(n^2)=r(n)^2, where r if the cyclic replacement map of the digits d of n in base 12 defined by d->d+1 if d<11 and d->0 if d=11.
  • A127864 (program): Number of tilings of a 2xn board with 1x1 and L-shaped tiles (where the L-shaped tiles cover 3 squares).
  • A127865 (program): Number of square tiles in all tilings of a 2 X n board with 1 X 1 and L-shaped tiles (where the L-shaped tiles cover 3 squares).
  • A127866 (program): Number of L-shaped tiles in all tilings of a 2 X n board with 1 X 1 and L-shaped tiles (where the L-shaped tiles cover 3 squares).
  • A127867 (program): Number of tilings of a 3xn board with 1x1 and L-shaped tiles (where the L-shaped tiles cover 3 squares).
  • A127872 (program): Triangle formed by reading A039599 mod 2.
  • A127873 (program): a(n) = (n^3)/2 + (3*n^2)/2 + 3*n + 3.
  • A127874 (program): Prime numbers of the form (x^3)/2+(3x^2)/2+3x+3.
  • A127875 (program): Numbers x for which (x^3)/2+(3x^2)/2+3x+3 is prime.
  • A127876 (program): Integers of the form (x^3)/6 + (x^2)/2 + x + 1.
  • A127877 (program): Integers of the form (x^4)/24 + (x^3)/6 + (x^2)/2 + x + 1 with x > 0.
  • A127878 (program): a(n) = n^4 + 4*n^3 + 12*n^2 + 24*n + 24.
  • A127883 (program): a(n) = 60*(n^5/120 + n^4/24 + n^3/6 + n^2/2 + n + 1).
  • A127884 (program): a(n) = floor(Fibonacci(n)/n).
  • A127893 (program): Riordan array (1/(1-x)^3, x/(1-x)^3).
  • A127894 (program): Inverse of Riordan array (1/(1-x)^3, x/(1-x)^3).
  • A127895 (program): Riordan array (1/(1+x)^3, x/(1+x)^3).
  • A127896 (program): Expansion of 1/(1 + 2*x + 3*x^2 + x^3).
  • A127897 (program): Series reversion of x/(1 + 2*x + 3*x^2 + x^3).
  • A127898 (program): Inverse of Riordan array (1/(1+x)^3, x/(1+x)^3).
  • A127899 (program): Transform related to the harmonic series.
  • A127902 (program): Series reversion of x/(1 + x + x^4).
  • A127904 (program): Smallest m such that A008687(m) = n.
  • A127905 (program): Construct triangle in which n-th row is obtained by expanding (1+x+x^3)^n and take the next-to-central column.
  • A127906 (program): a(n) = (n in base 10) * (n in base 2).
  • A127917 (program): Product of three numbers: n-th prime, previous number, and following number.
  • A127918 (program): Half of product of three numbers: n-th prime, previous and following number.
  • A127919 (program): 1/3 of product of three numbers: the n-th prime, the previous number and the following number.
  • A127920 (program): 1/6 of product of three numbers: n-th prime, previous and following number.
  • A127921 (program): 1/12 of product of three numbers: n-th prime, previous and following number.
  • A127922 (program): 1/24 of product of three numbers: n-th prime, previous and following number.
  • A127927 (program): G.f. A(x) satisfies: [x^(2n)] A(x)/Catalan(x)^n = A001764(n) = C(3n,n)/(2n+1) and [x^(2n+1)] A(x)/Catalan(x)^n = A001764(n+1) for n>=0, where Catalan(x) is the g.f. of A000108.
  • A127932 (program): a(4*n) = 4*n+1, a(4*n+1) = a(4*n+2) = a(4*n+3) = 4*n+4.
  • A127934 (program): a(8n)=8n+1, a(8n+1)=a(8n+2)=a(8n+3)=8n+5, a(8n+4)=8n+6, a(8n+5)=a(8n+6)=a(8n+7)=8n+8.
  • A127943 (program): a(n) = 2^binomial(n+1,2)/A046161(n).
  • A127944 (program): Partial sums of A093049.
  • A127945 (program): Hankel transform of central coefficients of (1+k*x-2x^2)^n, k arbitrary integer.
  • A127946 (program): Hankel transform of central coefficients of (1+k*x-3x^2)^n, k arbitrary integer.
  • A127947 (program): Hankel transform of central coefficients of (1+k*x+5x^2)^n, k arbitrary integer.
  • A127948 (program): Triangle, A004736 * A127899.
  • A127949 (program): A000012 as an infinite lower triangular matrix with all 1’s; A127899 = a simple transform; then A000012 * A127899. Given A051340, change all 1’s to -1. Triangle read by rows, (n-1) -1’s followed by “n”.
  • A127951 (program): Triangle, binomial transform of A126615.
  • A127952 (program): Triangle read by rows, T(n,k) = (n+1)*binomial(n-1,k-1).
  • A127953 (program): Triangle, A097805 * A126615.
  • A127954 (program): Triangle, A097805 * A127648.
  • A127959 (program): Nonprime numbers of the form 1 + Sum_{k=1..m} 2^(2*k - 1).
  • A127960 (program): a(n) = n^2*3^n.
  • A127961 (program): A007583(n) written in binary.
  • A127967 (program): A right-skewed Pascal triangle, with interspersed 1’s on main diagonal.
  • A127968 (program): a(n) = F(n+1) + (1-(-1)^n)/2, where F() = Fibonacci numbers A000045.
  • A127970 (program): Number triangle A127967 modulo 2.
  • A127971 (program): a(n) = fusc(n+1) + (1-(-1)^n)/2, fusc = A002487.
  • A127973 (program): a(2n)=A060632(n); a(2n+1)=A048896(n)/2.
  • A127974 (program): Numerators in expansion of (1-x)^(-2/3).
  • A127975 (program): Repeat 3^n three times.
  • A127976 (program): a(n) = ((6*n + 10)/27)*2^(n-1) + ((-1)^(n-1))*(6*n + 5)/27.
  • A127978 (program): a(n) = ((15*n + 34)/54)*2^(n-1) - (-1)^(n-1)*(6*n + 5)/27.
  • A127979 (program): a(n) = (5*n/18 + 19/54)*2^n - (-1)^(n-1)*(3*n + 4)/27.
  • A127980 (program): a(n) = (n + 2/3)*2^(n-1) - 1/2 - (-1)^(n-1)*(1/6).
  • A127981 (program): a(n) = (n + 1/3)*2^(n-1) - 1/2 + (-1)^(n-1)*(1/6).
  • A127982 (program): Numbers of the form (n - 1/3)2^(n) - n/2 + 1/4 + (-1)^n/12.
  • A127983 (program): Numbers of the form (n - 2/3)*2^(n) - n/2 + 3/4 - (-1)^n/12.
  • A127984 (program): a(n) = (n/3 + 7/9)*2^(n - 1) + (-1)^n/9.
  • A127985 (program): a(n) = floor(2^n*(n/3 + 4/9)).
  • A127986 (program): a(n) = n! + 2^n - 1.
  • A127988 (program): Sequence determining the parity of A025748.
  • A127989 (program): a(n) = 2*n^3 - 2*n + 9.
  • A127990 (program): Largest prime factor of 2*n^3 - 2*n + 9.
  • A127991 (program): 2*n^3 - 2*n + 9 divided by 3*largest prime factor.
  • A127992 (program): Number of distinct prime factors of 2*n^3 - 2*n + 9.
  • A127993 (program): Minimum bowling score for a game with n strikes.
  • A127994 (program): Maximum bowling score for a game with exactly n strikes.
  • A128012 (program): a(n) = 3*A001399(n).
  • A128013 (program): a(n) = (n^3 +n)*5^n.
  • A128014 (program): Central binomial coefficients C(2n,n) repeated.
  • A128015 (program): Binomial coefficients C(2n+1,n) repeated.
  • A128016 (program): Expansion of (1+x+x^2+x^3)/(1-x^2+x^4).
  • A128017 (program): Expansion of (1+2x+x^2-x^3)/(1-x^2+x^4).
  • A128018 (program): Expansion of (1-4*x)/(1-2*x+4*x^2).
  • A128019 (program): Expansion of (1-3x)/(1+3x^2).
  • A128020 (program): a(n) = the multiple of n which is > (sum{k=1 to n-1} a(k)) and is <= (n + sum{k=1 to n-1} a(k)).
  • A128021 (program): a(n) = A128020(n)/n.
  • A128022 (program): a(1)=1, a(n) = the multiple of n which is >= (sum{k=1 to n-1} a(k)) and is < (n + sum{k=1 to n-1} a(k)).
  • A128023 (program): a(n) = A128022(n)/n.
  • A128034 (program): a(0)=a(1)=1. a(n) = the multiple of n which is > a(n-1)+a(n-2) and is <= a(n-1)+a(n-2)+n.
  • A128035 (program): a(0)=a(1)=1. a(n) = the multiple of n which is >= a(n-1)+a(n-2) and is < a(n-1)+a(n-2)+n.
  • A128040 (program): a(n) = product of the primes which are <= the n-th squarefree positive integer. a(n) also is the LCM of the first n squarefree positive integers.
  • A128043 (program): (n^3+n)*6^n.
  • A128044 (program): a(n) = numerator of b(n), where b(1) = 1, b(n) = Sum_{k=1..n-1} b(n-k) * H(k); H(k) = Sum_{j=1..k} 1/j, the k-th harmonic number.
  • A128045 (program): a(n) = denominator of b(n), where b(1) = 1, b(n) = Sum_{k=1..n-1} b(n-k) * H(k); H(k) = Sum_{j=1..k} 1/j, the k-th harmonic number.
  • A128046 (program): Triangle read by rows: inverse of the lower triangular matrix (1/1; 1/1, 1/3; 1/1, 1/3, 1/5; …).
  • A128048 (program): (n^3+n)*8^n.
  • A128051 (program): (n^3+n)*7^n.
  • A128052 (program): a(n) = (F(2*n-1) + F(2*n+1))*(5/6 - cos(2*Pi*n/3)/3), where F(n) = Fibonacci(n).
  • A128053 (program): a(n)=A128056(n)/A128055(n).
  • A128054 (program): Count, omitting numbers of the form 6k+4 and doubling multiples of 6.
  • A128055 (program): a(n)=2^A128054(n).
  • A128056 (program): Hankel transform of A128057.
  • A128057 (program): Expansion of (1+x)/sqrt(1+4x^2).
  • A128058 (program): Expansion of 1/((1-x)sqrt(1-2x+5x^2)).
  • A128059 (program): a(n) = numerator((2*n-1)^2/(2*(2*n)!)).
  • A128060 (program): a(n) = 2*n - numerator((2*n-1)^2/(2*(2*n)!)).
  • A128063 (program): Hankel transform of A115962.
  • A128064 (program): Triangle T with T(n,n)=n, T(n,n-1)=-(n-1) and otherwise T(n,k)=0; 0<k<=n.
  • A128065 (program): Binomial transform of A128064.
  • A128074 (program): a(n) = (n^3+n)*9^n.
  • A128076 (program): Triangle T(n,k) = 2*n-k, read by rows.
  • A128077 (program): A128064 * A002260.
  • A128078 (program): A002260 * A128064.
  • A128079 (program): a(n) = Sum_{k=0..n} A000984(k)*A001263(n+1,k+1), where A000984 is the central binomial coefficients and A001263 is the Narayana triangle.
  • A128088 (program): a(n) = Sum_{k=0..n} A000108(k)*A001263(n+1,k+1), where A000108 is the Catalan numbers and A001263 is the Narayana triangle.
  • A128089 (program): Denominators in inverse of triangle A128078 by rows, n * each term in n-th row of A126615.
  • A128090 (program): Denominators in inverse of A128077, numerators = 1.
  • A128091 (program): Row sums of unsigned A128090.
  • A128092 (program): a(n) = largest multiple of n which is <= 2^n.
  • A128093 (program): a(n) = smallest multiple of n which is >= 2^n.
  • A128098 (program): Number of steps that touch the x-axis in all Motzkin paths of length n.
  • A128099 (program): Triangle read by rows: T(n,k) is the number of ways to tile a 3 X n rectangle with k pieces of 2 X 2 tiles and 3n-4k pieces of 1 X 1 tiles (0 <= k <= floor(n/2)).
  • A128100 (program): Triangle read by rows: T(n,k) is the number of ways to tile a 2 X n rectangle with k pieces of 2 X 2 tiles and n-2k pieces of 1 X 2 tiles (0 <= k <= floor(n/2)).
  • A128103 (program): Number of permutations of [n] with an even number of rises.
  • A128104 (program): a(n) = largest multiple of n which is < exp(n).
  • A128105 (program): a(n) = smallest multiple of n which is > exp(n).
  • A128106 (program): Sizes of possible gaps around a Gaussian prime: 1 and the even numbers in A001481.
  • A128111 (program): Expansion of q^(-1) * (phi(q) / phi(q^9) - 1) / 2 in powers of q^3 where phi() is a Ramanujan theta function.
  • A128115 (program): Mobius inversion of A103221.
  • A128116 (program): A128064 * A122432 (unsigned).
  • A128128 (program): Expansion of chi(-q^3) / chi^3(-q) in powers of q where chi() is a Ramanujan theta function.
  • A128129 (program): Expansion of (chi(-q^3)/ chi^3(-q) -1)/3 in powers of q where chi() is a Ramanujan theta function.
  • A128130 (program): Expansion of (1-x)/(1+x^4); period 8: repeat [1,-1,0,0,-1,1,0,0].
  • A128131 (program): a(n) = 2^A000096(n)*A128130(n).
  • A128132 (program): A natural number transform, companion to A127701.
  • A128133 (program): Binomial transform of A128132.
  • A128134 (program): A128132 * A007318.
  • A128135 (program): Row sums of A128134.
  • A128136 (program): A128132 * A002260.
  • A128137 (program): A002260 * A128132.
  • A128138 (program): A000012 * A128132.
  • A128139 (program): Triangle read by rows: matrix product A004736 * A128132.
  • A128140 (program): A128132 * A004736.
  • A128141 (program): A122432 (unsigned) * A128132.
  • A128142 (program): A128132 * A122432 (unsigned).
  • A128151 (program): A002260 * A097806.
  • A128152 (program): Numerator of Sum_{k=0..n} 1/binomial(n,k)^4.
  • A128153 (program): The number of regular pentagons found by constructing n equally-spaced points on each side of the pentagon and drawing lines parallel to the pentagon sides, as well as lines connecting vertices.
  • A128162 (program): a(n) = 3^n modulo Fibonacci(n).
  • A128173 (program): Numbers in ternary reflected Gray code order.
  • A128174 (program): Transform, (1,0,1,…) in every column.
  • A128175 (program): Binomial transform of A128174.
  • A128176 (program): A128174 * A007318.
  • A128177 (program): A128174 * A004736 as infinite lower triangular matrices.
  • A128179 (program): A097807 * A002260.
  • A128180 (program): A002260 * A097807.
  • A128181 (program): A007318 * A128179 as infinite lower triangular matrices.
  • A128182 (program): Binomial transform of A128180.
  • A128183 (program): Row sums of A128182.
  • A128184 (program): A051731 * A097806.
  • A128185 (program): A097806 * A051731.
  • A128186 (program): A051731 * A128174.
  • A128187 (program): Matrix product A128174 * A051731 read by rows.
  • A128188 (program): Row sums of A128187.
  • A128195 (program): a(n) = (2*n + 1)*(a(n - 1) + 2^n) for n >= 1, a(0) = 1.
  • A128196 (program): a(n) = (2*n - 1)*a(n - 1) + 2^n for n >= 1, a(0) = 1.
  • A128198 (program): Array read by antidiagonals. A scheme of arrangements: ArrScheme(k,n) = VarScheme(k,n-1) + k^n; ArrScheme(k,0) = 1. VarScheme(k,n) = (n*k+1)*(VarScheme(k,n-1) + k^n); VarScheme(k,0) = 1.
  • A128201 (program): Union of positive squares and the odd numbers.
  • A128202 (program): Configuration of discs on pegs after n steps of the optimal solution to the Towers of Hanoi problem moving an odd number of discs from peg 0 to peg 2, or an even number from peg 0 to peg 1.
  • A128203 (program): Sum of the digits of n*(n+1).
  • A128205 (program): a(n) = 2^(n-1)*A047240(n).
  • A128206 (program): Inverse of number triangle A128207.
  • A128208 (program): Inverse of number triangle A128210.
  • A128209 (program): Jacobsthal numbers(A001045) + 1.
  • A128212 (program): a(n) = Sum_digits(p), where p is the product of the digits of n.
  • A128213 (program): Expansion of (1-x+2x^2-2x^3)/(1-x+x^2)^2.
  • A128214 (program): Expansion of (1+2x+3x^2)/(1+x+x^2)^2.
  • A128217 (program): Nonnegative integers n such that the square-root of n differs from its nearest integer by less than 1/4.
  • A128218 (program): First differences of A128217.
  • A128219 (program): A000012 * A127701. a(1) = 1, a(2) = 2, a(3) = 2; by rows, n-1 terms of 2, 3, 4, … followed by “n”.
  • A128220 (program): Triangle, A127701 * A000012.
  • A128221 (program): A128174 * A127701.
  • A128222 (program): A127701 * A128174.
  • A128223 (program): a(n) = if n mod 2 = 0 then n*(n+1)/2 otherwise (n+1)^2/2-1.
  • A128225 (program): A127899 (unsigned) * A004736.
  • A128226 (program): Triangle, A004736 * A127899 (unsigned).
  • A128227 (program): Right border (1,1,1,…) added to A002260.
  • A128228 (program): A128229 * A002260.
  • A128229 (program): A natural number transform, inverse of signed A094587.
  • A128230 (program): Expansion of exp(x)/(1 - x - x^2/2!), where a(n) = 1 + n*a(n-1) + C(n,2)*a(n-2).
  • A128231 (program): Expansion of exp(x)/(1 - x^3/3!), where a(n) = 1 + binomial(n,3)*a(n-3).
  • A128232 (program): Expansion of exp(x)/(1 - x^4/4!), where a(n) = 1 + C(n,4)*a(n-4).
  • A128233 (program): Average of p(n) and p(p(n)), where p(k) is the k-th prime.
  • A128244 (program): Let s be the sum of the digits of n; a(n) is the product of the digits of s.
  • A128248 (program): a(n) = Sum_{k=1..phi(n)} t(k,n)*(-1)^k, where t(k,n) is the k-th positive integer that is coprime to n and phi(n) = A000010(n).
  • A128251 (program): n^4 - 1 divided by its largest fourth power divisor.
  • A128256 (program): A004736(signed) * A007318.
  • A128259 (program): Inverse Moebius transform of A128229.
  • A128260 (program): A128229 * A051731.
  • A128261 (program): a(n) = tau(n) + (n-1)*tau(n-1).
  • A128262 (program): Inverse Moebius transform of A127899 (unsigned).
  • A128282 (program): Regular symmetric triangle, read by rows, whose left half consists of the positive integers.
  • A128288 (program): a(n) = A023163(n)/3 for n > 1.
  • A128307 (program): Triangle, (1, 0, 1, 2, 4, 8, …) in every column.
  • A128308 (program): Binomial transform of A128307.
  • A128309 (program): 2*A000069(n).
  • A128311 (program): Remainder upon division of 2^(n-1)-1 by n.
  • A128321 (program): Column 0 of triangle A128320.
  • A128322 (program): Column 1 of triangle A128320; a(n) = A128321(n) + 2n*A128321(n-1), where A128321 is column 0 of triangle A128320.
  • A128331 (program): a(1)=1. a(n) = number of positive numbers <= n that are coprime to a(n-1).
  • A128334 (program): Binomial transform of A000594.
  • A128377 (program): Inverse binomial transform of A000594 (assuming offset 0 in both sequences).
  • A128378 (program): Partial sums of A128379.
  • A128379 (program): A000012^23 * A000594.
  • A128381 (program): A007318^24 * A000594.
  • A128386 (program): Expansion of c(3*x^2)/(1-x*c(3*x^2)), c(x) the g.f. of A000108.
  • A128387 (program): Expansion of c(5x^2)/(1-x*c(5x^2)), where c(x) is the g.f. of A000108.
  • A128406 (program): a(n) = (n+1)*2^(n*(n+1)).
  • A128407 (program): Triangle read by rows: T(n,n) = mobius(n) on the diagonal, zero elsewhere.
  • A128410 (program): A128408 * A000012.
  • A128411 (program): Coefficient array for orthogonal polynomials defined by C(2n,n).
  • A128413 (program): Inverse of number triangle A128412.
  • A128414 (program): Riordan array ((1-2x)/(1+2x),x/(1+2x)^2).
  • A128415 (program): Expansion of (1-4x^2)/(1+3x+4x^2).
  • A128416 (program): Expansion of (1-4x^2)/(1+4x+3x^2).
  • A128417 (program): Number triangle T(n,k)=2^(n-k)*C(2n,n-k).
  • A128418 (program): a(n) = Sum_{k=0..n} 2^(n-k)*C(2n,n-k).
  • A128419 (program): Expansion of 8/(sqrt(1-8*x)*(sqrt(1-8*x)+4*x+7)).
  • A128422 (program): Projective plane crossing number of K_{4,n}.
  • A128424 (program): a(n) = floor(sqrt(a(n-1)^2 + a(n-2)^2 + a(n-1)*a(n-2))), a(1)=1, a(2)=3.
  • A128425 (program): Primes in A000933.
  • A128426 (program): Decimal expansion of the location of a maximum of a Fibonacci Hamiltonian function.
  • A128427 (program): Last point where sum of n consecutive n-th powers does not exceed the next n-th power.
  • A128428 (program): Number of distinct prime factors of n^2+1.
  • A128429 (program): A linear recurrence sequence: a(n) = a(n-1) + a(n-3) + a(n-5) + a(n-6).
  • A128430 (program): Triangle read by rows: A054524 * A000012.
  • A128431 (program): Triangle read by rows: A054521 * A128407.
  • A128432 (program): Triangle read by rows: A128407 * A054521.
  • A128437 (program): a(n) = floor((numerator of H(n))/n), where H(n) = Sum_{k=1..n} 1/k is the n-th harmonic number.
  • A128438 (program): a(n) = floor((denominator of H(n))/n), where H(n) = Sum_{k=1..n} 1/k, the n-th harmonic number.
  • A128439 (program): a(n) = floor(n*t^n), where t=golden ratio=(1+sqrt(5))/2.
  • A128441 (program): a(n)=Floor(n*2^(n/2)).
  • A128443 (program): a(n) = floor(n*3^(n/2)).
  • A128445 (program): Number of facets of the Alternating Sign Matrix polytope ASM(n).
  • A128464 (program): Numbers that are congruent to {11, 17, 29} mod 30.
  • A128467 (program): a(n) = 30*n + 11.
  • A128468 (program): a(n) = 30*n + 17.
  • A128469 (program): Numbers of the form 30k+29 or possible lower bounds of twin primes pairs ending in 9.
  • A128470 (program): a(n) = 30*n + 1.
  • A128471 (program): 30*n+7.
  • A128473 (program): Numbers of the form 30*k+23 or numbers that cannot be part of a twin prime pair.
  • A128474 (program): Largest x such that 2^x divides n(n-3)!.
  • A128488 (program): a(n) = sum of terms in n-th row of irregular table A128487.
  • A128492 (program): Denominator of Sum_{k=1..n} 1/(2*k-1)^2.
  • A128493 (program): Denominators of partial sums for a series for (Pi^4)/96.
  • A128494 (program): Coefficient table for sums of Chebyshev’s S-Polynomials.
  • A128495 (program): Coefficient table for sums of squares of Chebyshev’s S-Polynomials.
  • A128496 (program): Row sums of unsigned triangle |A128495|=|S(2;n,m)| (sums of squares of Chebyshev’s S-polynomials).
  • A128497 (program): Coefficient table for sums over product of adjacent Chebyshev S-polynomials.
  • A128498 (program): Fourth column (m=3) of triangle A128494.
  • A128499 (program): Fifth column (m=4) of triangle A128494.
  • A128501 (program): a(n) = lcm{1 <= k <= n, gcd(k, 3) = 1}.
  • A128502 (program): Convolution array for Chebyshev’s S(n,x)=U(n,x/2) polynomials.
  • A128503 (program): Array for second (k=2) convolution of Chebyshev’s S(n,x)=U(n,x/2) polynomials.
  • A128504 (program): Row sums of array A128503 (second convolution of Chebyshev’s S(n,x)=U(n,x/2) polynomials).
  • A128505 (program): Irregular triangular array a(n,m) for third (k=3) convolution of Chebyshev’s S(n,x) = U(n,x/2) polynomials, read by rows (n >=0, 0 <= m <= floor(n/2)).
  • A128506 (program): Numerators of partial sums for a series for 3*sqrt(2)*(Pi^3)/2^7.
  • A128507 (program): Denominators of partial sums for a series for 3*sqrt(2)*(Pi^3)/2^7.
  • A128508 (program): Number of partitions p of n such that max(p)-min(p)=3.
  • A128514 (program): Triangle, Pell sequence in every column.
  • A128529 (program): Survivor of the Josephus problem, counting direction reversed after each step.
  • A128533 (program): a(n) = F(n)*L(n+2) where F=Fibonacci and L=Lucas numbers.
  • A128534 (program): a(n) = Fibonacci(n)*Lucas(n-1).
  • A128535 (program): a(n) = F(n)*L(n-2) where F = Fibonacci and L = Lucas numbers.
  • A128537 (program): a(n) = denominator of r(n): r(n) is such that, for every positive integer n, the continued fraction (of rational terms) [r(1);r(2),…,r(n)] equals n(n+1)/2, the n-th triangular number.
  • A128540 (program): Triangle A127647 * A097806, read by rows.
  • A128541 (program): Triangle, A097806 * A127647, read by rows.
  • A128542 (program): a(n) = ((2n)^(2n) - 1)/((2n+1)*(2n-1)).
  • A128543 (program): a(n) = floor(2^(n-2)*3*n).
  • A128544 (program): A007318 * A128540.
  • A128549 (program): Difference between triangular number and next perfect square.
  • A128552 (program): Column 2 of triangle A128545; a(n) is the coefficient of q^(2n+4) in the central q-binomial coefficient [2n+4,n+2].
  • A128563 (program): Column 2 of triangle A128562.
  • A128566 (program): Number of permutations of {1..n} with n inversions.
  • A128580 (program): Expansion of phi(x^3) * psi(x^4) - x * phi(x) * psi(x^12) in powers of x where phi(), psi() are Ramanujan theta functions.
  • A128582 (program): Expansion of f(x^4, x^12) * f(x, x^5) in powers of x where f(, ) is Ramanujan’s general theta function.
  • A128583 (program): Expansion of chi(x) * psi(x^2) * phi(-x^6) in powers of x where phi(), psi(), chi() are Ramanujan theta functions.
  • A128587 (program): Row sums of A128586.
  • A128588 (program): A007318 * A128587.
  • A128589 (program): A051731 * A127647.
  • A128591 (program): Expansion of f(x, x^5) * f(x, x^3) in powers of x where f(, ) is Ramanujan’s general theta function.
  • A128599 (program): a(n) = the numerator of the continued fraction [[n/1];[n/2],[n/3],..,[n/n]] = the numerator of [[n/n];[n/(n-1)],[n/(n-2)],..,[n/1]], where [x] is floor(x).
  • A128600 (program): a(n) = the denominator of the continued fraction [[n/1];[n/2],[n/3],..,[n/n]], where [x] is floor(x).
  • A128601 (program): a(n) = the denominator of the continued fraction [1;floor(n/(n-1)),floor(n/(n-2)),…,floor(n/1)].
  • A128603 (program): Numbers dividing p^6 for p a prime.
  • A128614 (program): Number of labeled plane trees with n edges in which no vertex has outdegree one.
  • A128615 (program): Expansion of x/(1+x+x^2-x^3-x^4-x^5).
  • A128616 (program): Expansion of q * psi(q^3) * psi(q^5) in powers of q where psi() is a Ramanujan theta function.
  • A128617 (program): Expansion of q^2 * psi(q) * psi(q^15) in powers of q where psi() is a Ramanujan theta function.
  • A128619 (program): A127647 * A128174.
  • A128620 (program): Row sums of A128619.
  • A128621 (program): A127648 * A128174.
  • A128624 (program): Row sums of A128623.
  • A128625 (program): Expansion of (1+3x)/(1-5x).
  • A128628 (program): An irregular triangular array read by rows, with shape sequence A000041(n) related to sequence A060850.
  • A128632 (program): McKay-Thompson series of class 6E for the Monster group with a(0) = -5.
  • A128633 (program): McKay-Thompson series of class 6E for the Monster group with a(0) = 4.
  • A128634 (program): Number of parallel permutations of length n.
  • A128636 (program): Expansion of 3 * (b(q^2)^2 / b(q)) / (c(q)^2 / c(q^2)) in powers of q where b(), c() are cubic AGM theta functions.
  • A128637 (program): Expansion of 3 * (b(q)^2/b(q^2)) / (c(q)^2/c(q^2)) in powers of q where b(), c() are cubic AGM theta functions.
  • A128638 (program): Expansion of q * (psi(q^3)^3 / psi(q)) / (phi(-q)^3 / phi(-q^3)) in powers of q where phi(), psi() are Ramanujan theta functions.
  • A128639 (program): Expansion of (1/3) * (c(q)^2 / c(q^2)) / (b(q)^2 / b(q^2)) in powers of q where b(), c() are cubic AGM theta functions.
  • A128640 (program): Expansion of (1/3) * (c(q^2)^2 / c(q)) / (b(q^2)^2 / b(q)) in powers of q where b(), c() are cubic AGM theta functions.
  • A128641 (program): Expansion of (1/3) * (c(q)^2 / c(q^2)) / (b(q^2)^2 / b(q)) in powers of q where b(), c() are cubic AGM theta functions.
  • A128642 (program): Expansion of (b(q) / b(q^2))^3 in powers of q where b() is a cubic AGM theta function.
  • A128643 (program): Expansion of (b(q^2) / b(q))^3 in powers of q where b() is a cubic AGM function.
  • A128650 (program): Number of polygons on n vertices with exactly three faces.
  • A128656 (program): Number of polygons on n vertices with four faces such that the source of the polygon lies on exactly two faces.
  • A128691 (program): Numbers of the form 2^k*p, where 1 <= k <= 8 and p is a prime > 2.
  • A128692 (program): Expansion of (theta_4(q) / theta_3(q))^4 in powers of q.
  • A128693 (program): Numbers of the form 3^k*p, where 1 <= k <= 6 and p is a prime different from 3.
  • A128696 (program): Alternating sum of the seventh powers of the first n Fibonacci numbers.
  • A128697 (program): Sum of the eighth powers of the first n Fibonacci numbers.
  • A128698 (program): Alternating sum of the eighth powers of the first n Fibonacci numbers.
  • A128703 (program): Numbers of the form 5^k*p, where 1 <= k <= 5 and p is a prime different from 5.
  • A128710 (program): Triangle read by rows: T(n,k) = (k+2)*binomial(n,k) (0 <= k <= n).
  • A128711 (program): Expansion of phi(x) * psi(x^4) * phi(-x^4)^4 in powers of x where phi(), psi() are Ramanujan theta functions.
  • A128712 (program): Expansion of q^(-1/8)* eta(q)^5* eta(q^2)^3/ eta(q^4)^2 in powers of q.
  • A128713 (program): Expansion of q^(-3/8)* eta(q)^7* eta(q^4)^2/ eta(q^2)^3 in powers of q.
  • A128714 (program): Number of skew Dyck paths of semilength n ending with a left step.
  • A128715 (program): A131830 + A103451 - A000012 as infinite lower triangular matrices.
  • A128716 (program): Triangle where the n-th row, of n terms in order, contains consecutive multiples of n. The smallest term of row n is the smallest integer greater than or equal to the largest term of row (n-1), for n >= 2.
  • A128721 (program): Number of UUU’s in all skew Dyck paths of semilength n.
  • A128723 (program): Number of skew Dyck paths of semilength n having no peaks at level 1.
  • A128725 (program): Number of skew Dyck paths of semilength n having no LL’s.
  • A128726 (program): Number of LL’s in all skew Dyck paths of semilength n.
  • A128729 (program): Number of skew Dyck paths of semilength n with no UDL’s.
  • A128730 (program): Number of UDL’s in all skew Dyck paths of semilength n.
  • A128732 (program): Number DL’s in all skew Dyck paths of semilength n.
  • A128734 (program): Number of LD’s in all skew Dyck paths of semilength n.
  • A128736 (program): Number of skew Dyck paths of semilength n and having no LDU’s.
  • A128737 (program): Number of LDU’s in all skew Dyck paths of semilength n.
  • A128740 (program): Number of DD’s in all skew Dyck paths of semilength n.
  • A128743 (program): Number of UU’s (i.e., doublerises) in all skew Dyck paths of semilength n.
  • A128745 (program): Triangle read by rows: T(n,k) is the number of skew Dyck paths of semilength n and having height of the last peak equal to k (1 <= k <= n).
  • A128746 (program): Height of the last peak summed over all skew Dyck paths of semilength n.
  • A128750 (program): Number of skew Dyck paths of semilength n having no ascents of length 1.
  • A128752 (program): Number of ascents of length at least 2 in all skew Dyck paths of semilength n.
  • A128758 (program): Expansion of q^(-1/3) * (eta(q^3) / eta(q))^4 in powers of q.
  • A128765 (program): Expansion of psi(q) * psi(q^10) / ( psi(q^2) * psi(q^5)) in powers of q where psi() is a Ramanujan theta function.
  • A128766 (program): Number of inequivalent n-colorings of the vertices of the 3D cube under full orthogonal group of the cube (of order 48).
  • A128770 (program): Expansion of phi(-q^9) / phi(-q) in powers of q where phi() is a Ramanujan theta function.
  • A128781 (program): Triangle of numbers a(n,k), n>=3, ceiling((n-3)/2)<=k<=n-3: a(n,k)=Sum[ Binomial[x + y + z, x]*Binomial[y + z, y]*Binomial[n - 2 - x - 2*y - 2*z, 2*n - 2*y - 5 - 2*k]*(2^x)*((-1)^z), {z, 0, (2*k - n + 3)/2}, {y, 0, n - 3 - k}, {x, 0, 2*k - n + 3 - 2*z}].
  • A128782 (program): a(n) = n^2*4^n.
  • A128784 (program): n^2*5^n.
  • A128785 (program): a(n) = n^2*6^n.
  • A128786 (program): n^2*7^n.
  • A128787 (program): n^2*8^n.
  • A128788 (program): a(n) = n^2*9^n.
  • A128789 (program): n^3*2^n.
  • A128790 (program): n^3*4^n.
  • A128791 (program): n^3*5^n.
  • A128792 (program): n^3*6^n.
  • A128793 (program): n^3*7^n.
  • A128794 (program): n^3*8^n.
  • A128795 (program): n^3*9^n.
  • A128796 (program): a(n) = n*(n-1)*2^n.
  • A128797 (program): (n^2-n)*3^n.
  • A128798 (program): n*(n-1)*4^n.
  • A128799 (program): a(n) = n*(n-1)*5^n.
  • A128800 (program): n*(n-1)*6^n.
  • A128801 (program): a(n) = n*(n-1)*7^n.
  • A128802 (program): a(n) = n*(n-1)*8^n.
  • A128803 (program): n*(n-1)*9^n.
  • A128806 (program): a(n) = A001316(n) + A046092(n).
  • A128810 (program): Triangle formed by reading triangle A064189 mod 2 .
  • A128814 (program): a(0)=1, a(n)= Product(k*(k+1)/2+1, k=1..n).
  • A128815 (program): Numbers n such that n-th and (n+2)th triangular numbers sum up to a prime.
  • A128816 (program): Number of partitions of an n-element set avoiding the pattern 12|3.
  • A128819 (program): Dimensions in which the simplex has two intermediate skeletons with the same centroid.
  • A128821 (program): Triangle T(n,k), 1<=k<=n, read by rows defined by :T(n,k)=C(n,k)*C(n-1,k-1)+C(n,k-1)*C(n-1,k)where C(n,k)=A007318(n,k) .
  • A128822 (program): Number of solutions to x/3 + y/4 + z/6 < n with x,y,z>=1 .
  • A128830 (program): a(n) = the number of positive divisors of n which are coprime to d(n), where d(n) = the number of positive divisors of n.
  • A128831 (program): Number of n-tuples where each entry is chosen from the subsets of {1,2,3} such that the intersection of all n entries is empty.
  • A128832 (program): Number of n-tuples where each entry is chosen from the subsets of {1,2,3,4} such that the intersection of all n entries is empty.
  • A128833 (program): Number of n-tuples where each entry is chosen from the subsets of {1,2,3,4,5} such that the intersection of all n entries is empty.
  • A128834 (program): Periodic sequence 0,1,1,0,-1,-1,…
  • A128835 (program): Numbers n such that n^n == 2 (mod 7), or 7 divides n^n-2.
  • A128862 (program): Numbers simultaneously triangular and centered triangular.
  • A128863 (program): a(0)=1. For n >= 1, a(n) = number of positive divisors of (n+a(n-1)).
  • A128865 (program): Number of n-tuples where each entry is chosen from the subsets of {1,2,3,4} such that the intersection of all n entries contains exactly one element.
  • A128866 (program): Number of n-tuples where each entry is chosen from the subsets of {1,2,3,4,5} such that the intersection of all n entries contains exactly one element.
  • A128869 (program): a(n) = the largest number one can subtract from 10^n such that the square of the result is strictly greater than 10^(2*n-1).
  • A128880 (program): Triangular numbers congruent to 1 or 5 mod 6.
  • A128882 (program): a(n) = n!! - 1.
  • A128884 (program): Sum of all matrix elements of n X n Vandermonde matrix of numbers 1,2,…,n, i.e., the matrix A with A[i,j] = i^(j-1), 1 <= i <= n, 1 <= j <= n.
  • A128889 (program): a(n) = (2^(n^2) - 1)/(2^n - 1).
  • A128893 (program): (1/p)*(binomial(2*p,p)+2*(p-1)), where p = n-th prime.
  • A128896 (program): Triangular numbers that are products of three distinct primes.
  • A128897 (program): a(n) = ((2n)^(2n-1)+1)/(2n+1).
  • A128899 (program): Riordan array (1,(1-2x-sqrt(1-4x))/(2x)).
  • A128902 (program): Number of degree n polynomials over GF(2) (with nonzero constant term) at Hamming distance 2 from some irreducible polynomial.
  • A128905 (program): Numbers k such that the k-th triangular number has exactly four distinct prime factors.
  • A128908 (program): Riordan array (1, x/(1-x)^2).
  • A128913 (program): a(n) = n*pi(n).
  • A128917 (program): Pentagonal numbers (A000326) which are also centered pentagonal numbers (A005891).
  • A128918 (program): a(n) = n*(n+1)/2 if n is odd, otherwise (n-1)*n/2 + 1.
  • A128919 (program): Numbers simultaneously heptagonal and centered heptagonal.
  • A128922 (program): Numbers simultaneously 10-gonal and centered 10-gonal.
  • A128927 (program): Primes which are the sum of the first k nonprimes for some k >= 2.
  • A128929 (program): Diameter of a special type of regular graph of degree 4 whose order maintain an increase in form of an arithmetic progression.
  • A128930 (program): Prime(n) * pi(n).
  • A128936 (program): a(n) = binomial(n, sum_digits_n).
  • A128937 (program): Triangle formed by reading A039598 mod 2.
  • A128939 (program): Maximal product over partitions of n into parts of the form 3k+1.
  • A128941 (program): Cardinality of the free modular lattice generated by two elements and a chain of length n.
  • A128952 (program): a(n) is equal to the number of positive integers m less than or equal to 10^n such that m is not divisible by the prime 3 and is not divisible by at least one of the primes 2, 5 and 7.
  • A128954 (program): a(n) is equal to the number of positive integers m less than or equal to 10^n such that m is not divisible by the prime 2 and is not divisible by at least one of the primes 3, 5 and 7.
  • A128955 (program): Numbers n such that n+(n+1)^3 is prime.
  • A128958 (program): Numbers n such that n^2+(n+1)^3 is prime.
  • A128959 (program): a(n) is equal to the number of positive integers m less than or equal to 10^n such that m is not divisible by at least one of the primes 2,3 and is not divisible by at least one of the primes 5,7.
  • A128960 (program): a(n) = (n^3 - n)*2^n.
  • A128961 (program): a(n) = (n^3 - n)*3^n.
  • A128962 (program): a(n) = (n^3 - n)*4^n.
  • A128963 (program): a(n) = (n^3 - n)*5^n.
  • A128964 (program): a(n) = (n^3-n)*6^n.
  • A128965 (program): a(n) = (n^3 - n)*7^n.
  • A128966 (program): Triangle read by rows of coefficients of polynomials Pn defined by P[0]=0, P[1]=x+1; for n >= 2, P[n]=(x+1)*P[n-1]+x*P[n-2].
  • A128967 (program): a(n) = (n^3-n)*8^n.
  • A128968 (program): a(n) is the n-th prime of the form x^2+n.
  • A128969 (program): a(n) = (n^3 - n)*9^n.
  • A128971 (program): A130125 * A000012.
  • A128972 (program): n^3 - 1 divided by its largest cube divisor.
  • A128973 (program): Triangle formed by reading A038622 mod 2 .
  • A128974 (program): Numbers k such that 12k does not divide Fibonacci(12k).
  • A128975 (program): a(n) = the number of unordered triples of integers (a,b,c) with a+b+c=n, whose bitwise XOR is zero. Equivalently, the number of three-heap nim games with n stones which are in a losing position for the first player.
  • A128977 (program): a(0)=a(1)=1; a(n) = lcm(a(n-1) + a(n-2), n).
  • A128980 (program): A054525 * A129691(unsigned).
  • A128982 (program): If in a line of n persons every n-th person is eliminated until only one person is left, which position P should one assume in the original lineup to avoid being eliminated?
  • A128985 (program): a(n) = (n^3 - n^2)*2^n.
  • A128986 (program): a(n) = (n^3 - n^2)*3^n.
  • A128987 (program): a(n) = (n^3 - n^2)*4^n.
  • A128988 (program): a(n) = (n^3 - n^2)*5^n.
  • A128989 (program): a(n) = (n^3 - n^2)*6^n.
  • A128990 (program): a(n) = (n^3 - n^2)*7^n.
  • A128991 (program): a(n) = (n^3 - n^2)*8^n.
  • A128992 (program): a(n) = (n^3 - n^2)*9^n.
  • A128999 (program): Start with an integer (in this case 1). First, add 5 or 6 if the integer is odd or even, respectively. Then divide by 2. Notice any a(1)<=5 converges to 5 and any a(1)>=6 converges to 6.
  • A129000 (program): Start with an integer (in this case, 1). First, add 5 or 8 if the integer is odd or even, respectively. Then divide by 2.
  • A129002 (program): a(n) = (n^3 + n^2)*2^n.
  • A129003 (program): (n^3+n^2)*3^n.
  • A129004 (program): (n^3+n^2)*4^n.
  • A129005 (program): (n^3+n^2)*5^n.
  • A129006 (program): (n^3+n^2)*6^n.
  • A129007 (program): (n^3+n^2)*7^n.
  • A129008 (program): (n^3+n^2)*8^n.
  • A129009 (program): (n^3+n^2)*9^n.
  • A129011 (program): a(n) = floor(n^(4/3)).
  • A129026 (program): a(n) = (1/2)*(n^4 + 11*n^3 + 53*n^2 + 97*n + 54).
  • A129027 (program): Odd-indexed terms of A129026.
  • A129028 (program): A129027(n)/4.
  • A129029 (program): a(n) = 8*n^4+44*n^3+106*n^2+100*n+30.
  • A129068 (program): A128894[n,k] for k=1 : Coxeter numbers as defined by Bulgadaev for exceptional group sequence using critical exponent solution.
  • A129069 (program): Numbers n such that (n-3)/2 is prime.
  • A129070 (program): Numbers n such that (n-5)/4 is prime.
  • A129071 (program): Numbers n such that (n-7)/6 is prime.
  • A129072 (program): Numbers n such that (n-13)/12 is prime.
  • A129073 (program): Numbers n such that (n-8)/7 is prime.
  • A129074 (program): Numbers n such that (n-9)/8 is prime.
  • A129075 (program): Numbers n such that (n-4)/3 is prime.
  • A129076 (program): a(n) = sigma(sigma(sigma(sigma(n)))), where sigma(n) = sum of divisors of n.
  • A129080 (program): Expansion of g.f. x*(x^4 - 5*x^3 + 10*x^2 - 12*x + 4)/((1-x)^2*(1 - 3*x + 2*x^2 - x^3)).
  • A129090 (program): a(1)=1; a(n) = gcd(a(n-1), n) + lcm(a(n-1), n).
  • A129091 (program): a(0)=1; a(n) = gcd(a(n-1), n) + lcm(a(n-1), n).
  • A129095 (program): Semi-Pell numbers: a(n) = a(n/2) (n even), a(n) = 2*a(n-1) + a(n-2) (n odd >1), with a(1) = 1.
  • A129096 (program): A bisection of A129095: a(n) = A129095(2n-1) for n>=1.
  • A129109 (program): Sums of three consecutive hexagonal numbers.
  • A129110 (program): A transformation of the Catalan sequence.
  • A129111 (program): Sums of three consecutive heptagonal numbers.
  • A129113 (program): Expansion of x^3 / (1 - x - 5*x^2 - x^3 + x^4).
  • A129116 (program): Multifactorial array: A(k,n) = k-tuple factorial of n, for positive n, read by ascending antidiagonals.
  • A129119 (program): Numbers of the form 2*p (with p a prime number) such that p^2+4 is prime.
  • A129123 (program): Number of 4-tuples of standard tableau with height less than or equal to 2.
  • A129128 (program): List of nodes generating two branches in the tree defined in sequence A129129.
  • A129129 (program): An irregular triangular array of natural numbers read by rows, with shape sequence A000041(n) related to sequence A060850.
  • A129132 (program): Partial sums of A051903.
  • A129134 (program): Expansion of (1 - phi(-q) * phi(-q^2)) / 2 in powers of q where phi() is a Ramanujan theta function.
  • A129135 (program): Number of permutations of [n] with exactly 5 fixed points.
  • A129136 (program): Permutations with exactly 6 fixed points.
  • A129137 (program): Number of trees on [n], rooted at 1, in which 2 is a descendant of 3.
  • A129138 (program): a(n) = number of positive divisors of n that are <= phi(n), where phi(n) = A000010(n).
  • A129139 (program): a(n) = number of positive integers which are coprime to n and are <= d(n), where d(n) = A000005(n).
  • A129142 (program): Start with the empty sequence and append in step k the consecutive numbers 2^k-1 to 2^k+k-2.
  • A129143 (program): Start with the empty sequence and append in step k the consecutive numbers 2^(k-1) to 2^(k-1)+k-1.
  • A129144 (program): a(1)=a(2)=1; for n>2: a(n) = (s = sum of all previous terms) minus (maximal square less than s).
  • A129146 (program): a(n) = n-th odd prime minus n-th odd composite number.
  • A129147 (program): Expansion of c(x(1+2x)), c(x) the g.f. of A000108.
  • A129148 (program): Expansion of (1-x-sqrt(1-6*x-7*x^2))/(2*(1+2*x)).
  • A129149 (program): Permutations with exactly 7 fixed points.
  • A129152 (program): The n-th arithmetic derivative of 5^6.
  • A129153 (program): Rencontres numbers: permutations with exactly 8 fixed points.
  • A129160 (program): Sum of the semi-abscissae of the first returns to the axis over all skew Dyck paths of semilength n.
  • A129164 (program): Sum of pyramid weights in all skew Dyck paths of semilength n.
  • A129167 (program): Number of base pyramids in all skew Dyck paths of semilength n.
  • A129169 (program): Number of UU’s starting at level 0 in all skew Dyck paths of semilength n.
  • A129171 (program): Sum of the heights of the peaks in all skew Dyck paths of semilength n.
  • A129180 (program): Total area below all Schroeder paths of semilength n.
  • A129184 (program): Shift operator, right.
  • A129185 (program): Shift operator, left.
  • A129186 (program): Right shift operator generating 1’s in shifted spaces.
  • A129187 (program): Decimal expansion of arcsinh(1/3).
  • A129188 (program): n + n-th prime + n-th composite.
  • A129189 (program): n-th prime + n-th composite - n.
  • A129194 (program): a(n) = n^2*(3/4 - (-1)^n/4).
  • A129195 (program): a(n)=denominator(n!/4^n).
  • A129196 (program): a(n) = denominator(3*(3+(-1)^n)/(n+1)^3).
  • A129197 (program): a(n) = numerator( 3*(3+(-1)^n)/(n+1)^3 ).
  • A129200 (program): Decimal expansion of arcsinh(1/4).
  • A129202 (program): Denominator of 3*(3+(-1)^n) / (n+1)^2.
  • A129203 (program): a(n) = numerator(3/(n+1)^3)*(3/2 + (-1)^n/2).
  • A129204 (program): The denominator of 2/n^3.
  • A129217 (program): Permutations with exactly 9 fixed points.
  • A129218 (program): Permutations with exactly 10 fixed points.
  • A129229 (program): a(n) = floor(n*r)-a(n-1), where r is the golden mean, (1+sqrt(5))/2.
  • A129230 (program): a(n) = floor(n*r) + floor((n-2)*r) + floor((n-4)*r) + … + floor(k*r), where r = golden ratio = (1 + sqrt(5))/2 and k = n mod 2.
  • A129232 (program): a(n)=Floor(n*r)+Floor((n-2)*r)+Floor((n-4)*r)+…+Floor(k*r), where r = 2^(1/2) and k=0 if n is even, k=1 if n is odd.
  • A129234 (program): Triangle read by rows: T(n,k) = n/k + k - 1 if n mod k = 0; otherwise T(n,k)=0 (1 <= k <= n).
  • A129235 (program): a(n) = 2*sigma(n) - tau(n), where tau(n) is the number of divisors of n (A000005) and sigma(n) is the sum of divisors of n (A000203).
  • A129236 (program): A054525 * A129234.
  • A129237 (program): A051731 * A129234.
  • A129238 (program): Permutations with exactly 11 fixed points.
  • A129247 (program): Invert transform of the Bell numbers.
  • A129251 (program): Number of distinct prime factors p of n such that p^p is a divisor of n.
  • A129252 (program): Smallest prime factor p of n such that p^p is a divisor of n, a(n)=1 if no such factor exists.
  • A129253 (program): Number of numbers not greater than n having at least one divisor p^e with p<=e, p prime.
  • A129254 (program): Numbers n such that both n and n+1 have at least one divisor of the form p^e with p<=e, p prime.
  • A129255 (program): Permutations with exactly 12 fixed points.
  • A129265 (program): Triangle read by rows: T(n,k) is the number of power of two divisors of n that are less than or equal to n/k.
  • A129267 (program): Triangle with T(n,k) = T(n-1,k-1) + T(n-1,k) - T(n-2,k-1) - T(n-2,k) and T(0,0)=1 .
  • A129269 (program): Decimal expansion of arcsinh(1/5).
  • A129271 (program): Number of labeled n-node connected graphs with at most one cycle.
  • A129272 (program): a(n)=(1/2)*(2*b(n+1)-3*b(n)+(1-(-1)^b(n))/2) where b(n)=A073941(n).
  • A129279 (program): a(0)=1. a(n) = the sum of the earlier terms which are <= n.
  • A129280 (program): a(1)=1. a(n) = the sum of the earlier terms which are <= n.
  • A129283 (program): (Arithmetic derivative of n) + n.
  • A129292 (program): Number of divisors of n^4 - 1 that are not greater than n.
  • A129294 (program): Number of divisors of n^3 - 1 that are not greater than n.
  • A129295 (program): Numbers m such that m^3 - 1 has no divisors d with 1 < d < m - 1.
  • A129296 (program): Number of divisors of n^2 - 1 that are not greater than n.
  • A129297 (program): Nonnegative integers m such that m^2-1 has no divisors d with 1<d<m-1.
  • A129303 (program): Expansion of eta(q^2)^3 * eta(q^5)^2 * eta(q^10) / eta(q)^2 in powers of q.
  • A129307 (program): Intersection of A000217 and A005098.
  • A129308 (program): a(n) is the number of positive integers k such that k*(k+1) divides n.
  • A129309 (program): a(n) = number of primes which are < c(n) and are coprime to c(n), where c(n) is the n-th composite.
  • A129312 (program): A minimal 2 X 2 subdeterminant array.
  • A129323 (program): Second column of PE^2.
  • A129324 (program): Third column of PE^2.
  • A129325 (program): Fourth column of PE^2.
  • A129326 (program): a(n) = (2*n+1)*(n-1)!.
  • A129327 (program): Second column of PE^3.
  • A129328 (program): Third column of PE^3.
  • A129329 (program): Fourth column of PE^3.
  • A129331 (program): Second column of PE^4.
  • A129332 (program): Third column of PE^4.
  • A129333 (program): Fourth column of PE^4.
  • A129334 (program): Triangle T(n,k) read by rows: inverse of the matrix PE = exp(P)/exp(1) given in A011971.
  • A129337 (program): Maximal possible degree of a Chebyshev-type quadrature formula with n nodes, in the case of the constant weight function on [ -1,1].
  • A129339 (program): Main diagonal of triangular array T: T(j,1) = 1 for ((j-1) mod 6) < 3, else 0; T(j,k) = T(j-1,k-1) + T(j,k-1) for 2 <= k <= j.
  • A129342 (program): a(2n) = a(n) + 2^(2n), a(2n+1) = 2^(2n+1).
  • A129343 (program): a(2n) = a(n), a(2n+1) = 4n+1.
  • A129344 (program): a(n) is the number of powers of 2 that have n decimal digits.
  • A129345 (program): a(2n) = A001542(n+1), a(2n+1) = A038761(n+1); a Pellian-related sequence.
  • A129346 (program): a(2n) = A100525(n), a(2n+1) = A001653(n+1); a Pellian-related sequence.
  • A129348 (program): Number of (directed) Hamiltonian circuits in the cocktail party graph of order n.
  • A129353 (program): A051731 * A115361.
  • A129359 (program): Numbers k such that A129357(8*k) == 2 (mod 4).
  • A129360 (program): A054525 * A115361.
  • A129361 (program): a(n) = Sum_{k=floor((n+1)/2)..n} F(k+1), F(k) = A000045(k).
  • A129362 (program): a(n) = Sum_{k=floor((n+1)/2)..n} J(k+1), J(k) = A001045(k).
  • A129364 (program): a(n) = Product_{k = 1..n} A066841(k).
  • A129366 (program): a(n) = Sum_{k=0..floor(n/2)} C(n-k), where C(n) = A000108(n).
  • A129368 (program): a(n)=sum{k=floor((n+1)/2)..n, C(2k,k)}.
  • A129369 (program): Expansion of 1/sqrt(1-4x)-x/sqrt(1-4x^2).
  • A129370 (program): a(n)=n^2-(n-1)^2*(1-(-1)^n)/8.
  • A129371 (program): a(n) = Sum_{k=0..floor(n/2)} (n-k)^2.
  • A129372 (program): Triangle read by rows: T(n,k) = 1 if k divides n and n/k is odd, T(n,k) = 0 otherwise.
  • A129375 (program): E.g.f. satisfies: A(x) = exp(x) * A(x^2)*A(x^3)*A(x^4)*…*A(x^n)*…
  • A129379 (program): a(n) = sum of sums of all sets of three distinct preceding terms; a(n) = n for n<=3.
  • A129380 (program): Partial sums of A129379.
  • A129383 (program): Expansion of g(x)-xg(x^2), g(x) the g.f. of A001405.
  • A129384 (program): a(n)=sum{k=0..floor(n/2), C(n-k,floor((n-k)/2))}.
  • A129388 (program): Primes that are equal to the mean of 5 consecutive squares.
  • A129389 (program): Numbers n such that the mean of 5 consecutive squares starting with n^2 is prime.
  • A129390 (program): Expansion of phi(x) * phi(-x^5) / (chi(-x^2) * chi(-x^10)) in powers of x where phi(), chi() are Ramanujan theta functions.
  • A129391 (program): Expansion of phi(-x) * phi(x^5) / (chi(-x^2) * chi(-x^10)) in powers of x where phi(), chi() are Ramanujan theta functions.
  • A129393 (program): Row sums of A129392.
  • A129395 (program): Row sums of A129394.
  • A129397 (program): Row sums of A129396.
  • A129400 (program): Number of walks of length n on one 60-degree wedge of the equilateral triangular lattice. The walk can go along the walls of the wedge, but cannot cross the walls.
  • A129401 (program): a(n) is the result of replacing with its successor prime each prime in the factorization of the n-th composite number.
  • A129402 (program): Expansion of phi(x^3) * psi(x^4) + x * phi(x) * psi(x^12) in powers of x where phi(), psi() are Ramanujan theta functions.
  • A129403 (program): Minimal number of edges in e-free non-deterministic finite automata (NFA) for regular expression c_1?c_2?…c_n?.
  • A129404 (program): Decimal expansion of L(3, chi3), where L(s, chi3) is the Dirichlet L-function for the non-principal character modulo 3.
  • A129405 (program): Expansion of L(3, chi3) in base 2, where L(s, chi3) is the Dirichlet L-function for the non-principal character modulo 3.
  • A129412 (program): Numbers n such that mean of 7 consecutive squares starting with n^2 is prime.
  • A129428 (program): Centered 47-gonal numbers.
  • A129438 (program): Expansion of (phi(q) * phi(q^2) + phi(-q^2) * phi(q^4)) / 2 in powers of q where phi() is a Ramanujan theta function.
  • A129441 (program): G.f. x*(1-x^2-x^3)/ ((1+x+x^2) * (x^4-x^3-x^2-2*x+1) ).
  • A129442 (program): Expansion of c(x)*c(x*c(x)) where c(x) is the g.f. of A000108.
  • A129444 (program): Numbers k such that the centered triangular number A005448(k) = 3*k*(k-1)/2 + 1 is a perfect square.
  • A129445 (program): Numbers k > 0 such that k^2 is a centered triangular number.
  • A129447 (program): Expansion of psi(q) * psi(q^3) * phi(q^3) / phi(q) in powers of q where psi(), phi() are Ramanujan theta functions.
  • A129448 (program): Expansion of q * psi(-q) * chi(q^3)^2 * psi(-q^9) in powers of q where psi(), chi() are Ramanujan theta functions.
  • A129449 (program): Expansion of psi(-x) * psi(-x^3) in powers of x where psi() is a Ramanujan theta function.
  • A129451 (program): Expansion of f(-x, -x^3) f(-x, x^2) in powers of x where f(, ) is Ramanujan’s general theta function.
  • A129458 (program): Row sums of triangle A129065 (v=1 member of a family).
  • A129460 (program): Third column (m=2) of triangle A129065.
  • A129463 (program): Row sums of triangle A129462 (v=2 member of a certain family).
  • A129464 (program): Second column (m=1) of triangle A129462 (v=2 member of a certain family).
  • A129465 (program): Third column (m=2) sequence of triangle A129462 (v=2 member of a certain family).
  • A129468 (program): Unitary abundance of n.
  • A129476 (program): a(n) is the concatenation in increasing order of all single-digit divisors of n.
  • A129480 (program): Prime(17n).
  • A129484 (program): Primes of the form 17k + 1.
  • A129487 (program): Unitary deficient numbers.
  • A129488 (program): Smallest odd prime dividing binomial(2n,n).
  • A129501 (program): A103994 * A115361.
  • A129502 (program): For n=2^k, a(n) = binomial(k + 2, 2), else 0.
  • A129504 (program): Row sums of triangle A129503.
  • A129506 (program): Number of partitions of a {2n-1}-set into n nonempty subsets.
  • A129507 (program): G.f.: (1+x+x^2-sqrt(1+2x+3x^2-2x^3+x^4))*2.
  • A129509 (program): G.f.: (1+x+x^2-sqrt(1+2x+3x^2-2x^3+x^4))/2.
  • A129514 (program): a(n) = gcd(Sum_{k|n} k, Sum_{1<k<n, k does not divide n} k) = gcd(sigma(n), n(n+1)/2 - sigma(n)) = gcd(sigma(n), n(n+1)/2), where sigma(n) = A000203(n).
  • A129516 (program): Numbers k such that k divides (k-1)!! - 1.
  • A129517 (program): Odd primes p such that p divides (p-1)!!-1.
  • A129521 (program): Numbers of the form p*q, p and q prime with q=2*p-1.
  • A129523 (program): Numbers of the form 2^j +- 2^i for 0 <= i < j, in ascending order.
  • A129526 (program): Number of n-bead two-color bracelets with 00 prohibited.
  • A129527 (program): a(2n) = a(n) + 2n, a(2n+1) = 2n + 1.
  • A129530 (program): a(n) = (1/2)*n*(n-1)*3^(n-1).
  • A129532 (program): 3n(n-1)4^(n-2).
  • A129533 (program): Array read by antidiagonals: T(n,k) = binomial(n+1,2)*binomial(n+k,n+1) for 0 <= k <= n.
  • A129538 (program): a(n) = smallest positive integer such that lcm(a(1), a(2), …, a(n)) is a multiple of the n-th triangular number n(n+1)/2.
  • A129543 (program): Gray code ordering of the prime numbers.
  • A129545 (program): Triangular numbers T such that T+1 is a prime.
  • A129547 (program): a(n)= n! - (n-1)!! - a(n-1), with a(1)=1!-0!!=0.
  • A129548 (program): Measures of entanglement in 3-qbits.
  • A129555 (program): A054523 * A129372.
  • A129556 (program): Numbers k such that centered pentagonal number A005891(k) = (5k^2 + 5k + 2)/2 is a perfect square.
  • A129557 (program): Numbers k>0 such that k^2 is a centered pentagonal number (A005891).
  • A129558 (program): A054523 * A129360.
  • A129559 (program): A054523 * A115361.
  • A129561 (program): A054523 * A115369.
  • A129564 (program): A129360 * A000012.
  • A129565 (program): A115359 * A000012 as infinite lower triangular matrices.
  • A129566 (program): A007318 * A129565.
  • A129567 (program): a(n) = number of positive divisors of the denominator of the n-th harmonic number H(n) = Sum_{k=1..n} 1/k.
  • A129569 (program): A129360 * A128174.
  • A129572 (program): A129372 * A097806.
  • A129573 (program): A097806 * A129372.
  • A129574 (program): Number of odd divisors of n plus the number of odd divisors of n - 1.
  • A129576 (program): Expansion of phi(x) * chi(x) * psi(-x^3) in powers of x where phi(), chi(), psi() are Ramanujan theta functions.
  • A129588 (program): Expansion of q^-1 * theta_2(q)^4 in powers of q^2.
  • A129589 (program): a(n) = 2*A000129(n) + A000129(n-1) - n.
  • A129591 (program): For each permutation p of {1,2,…,n} define min(p) = min{ p(i) + i : i = 1..n }; a(n) is the sum of min(p) of all p.
  • A129594 (program): Involution of nonnegative integers induced by the conjugation of the partition encoded in the run lengths of binary expansion of n.
  • A129597 (program): Central diagonal of array A129595.
  • A129598 (program): a(n) = n * A111089(n).
  • A129602 (program): Replace in the binary expansion of n each run of k 0’s (or 1’s) with 2k-1 0’s (or 1’s), except in the most significant run, double the number of 0’s (or 1’s).
  • A129603 (program): Replace in the binary expansion of n each run of k 0’s (or 1’s) with 2k-1 0’s (or 1’s).
  • A129617 (program): a(1) = 0; a(2) = a(3) = 1; for n > 3: a(n) = 16*a(n-2)+14*a(n-3).
  • A129628 (program): Inverse Moebius transform of A001511.
  • A129629 (program): Nonzero bisection of Moebius transform of A082392.
  • A129630 (program): Numbers n such that sum of digits of n+1 is a prime.
  • A129631 (program): Numbers n such that sum of digits of binomial(n+1,n-1) is a prime.
  • A129636 (program): Triangle T(n,k): base-3 digit sum of the Pascal type triangle A102363(n,k).
  • A129637 (program): Number of n-step paths that can go {west, southeast, southwest, northwest} on a 240-degree wedge on the equilateral triangular lattice.
  • A129639 (program): Number of meaningful differential operations of the k-th order on the space R^12.
  • A129647 (program): Largest order of a permutation of n elements with exactly 2 cycles. Also the largest LCM of a 2-partition of n.
  • A129652 (program): Exponential Riordan array [e^(x/(1-x)),x].
  • A129654 (program): Number of different ways to represent n as general polygonal number P(m,r) = 1/2*r*((m-2)*r-(m-4)) = n>1, for m,r>1.
  • A129667 (program): Dirichlet inverse of the Abelian group count (A000688).
  • A129682 (program): Number of ways tiling a 2 X n rectangle with 2 X 1 (domino) and 3 X 1 (tromino) tiles.
  • A129683 (program): Expansion of (1/(1-2x))*exp(2x/(1-2x)).
  • A129684 (program): Exponential Riordan array [1/(1-x^2/2), x].
  • A129685 (program): Exponential Riordan array [1-x^2/2, x].
  • A129686 (program): Triangle read by rows: row n is 0^(n-3), 1, 0, 1.
  • A129687 (program): A129686 * A007318.
  • A129688 (program): A129686 * A128174.
  • A129689 (program): A007318 * A129688.
  • A129690 (program): A129688 * A007318.
  • A129691 (program): Inverse of A054523.
  • A129695 (program): Laguerre transform of the Jacobsthal numbers.
  • A129696 (program): Antidiagonal sums of triangular array T defined in A014430: T(j,k) = binomial(j+1, k)-1 for 1 <= k <= j.
  • A129701 (program): Difference between successive primes cubed: a(n) = prime(n+1)^3 - prime(n)^3.
  • A129703 (program): Number of different walks generated by n steps that can only go in {east, southeast, southwest} directions on the 300-degree wedge in a 60-degree equilateral triangular lattice.
  • A129704 (program): Expansion of 1/(x^5 - 2*x^4 + x^3 - 2*x^2 + x - 1).
  • A129705 (program): Triangle T(n,m) = A000071(n+2)-m*(m+1)/2 read by rows.
  • A129707 (program): Number of inversions in all Fibonacci binary words of length n.
  • A129710 (program): Triangle read by rows: T(n,k) is the number of Fibonacci binary words of length n and having k 01 subwords (0 <= k <= floor(n/2)). A Fibonacci binary word is a binary word having no 00 subword.
  • A129711 (program): Triangle read by rows: T(n,k) is the number of Fibonacci binary words of length n and starting with exactly k 01’s (0<=k<=floor(n/2)). A Fibonacci binary word is a binary word having no 00 subword.
  • A129713 (program): Triangle read by rows: T(n,k) is the number of Fibonacci binary words of length n and starting with exactly k 1’s (0<=k<=n). A Fibonacci binary word is a binary word having no 00 subword.
  • A129715 (program): Number of runs in all Fibonacci binary words of length n. A Fibonacci binary word is a binary word having no 00 subword. A run is a maximal sequence of consecutive identical letters.
  • A129720 (program): Number of 0’s in odd position in all Fibonacci binary words of length n. A Fibonacci binary word is a binary word having no 00 subword.
  • A129722 (program): Number of 0’s in even position in all Fibonacci binary words of length n. A Fibonacci binary word is a binary word having no 00 subword.
  • A129726 (program): a(n) = a(n-1) + prime(n) - prime(n-1) + 2.
  • A129728 (program): a(n) = 2*(n-1) + Fibonacci(n).
  • A129742 (program): Numbers of the form: a(n)=((Prime[n] - 1)! - (Prime[n] - 1))/(2*Prime[n]).
  • A129743 (program): a(n) = -(u^n-1)*(v^n-1) with u = 2+sqrt(3), v = 2-sqrt(3).
  • A129744 (program): a(n) = -(u^n-1)*(v^n-1) with u = 1+sqrt(2), v = 1-sqrt(2).
  • A129750 (program): Absolute difference of final digits of consecutive primes.
  • A129753 (program): Floor(prime(n)/nonprime(n)).
  • A129755 (program): Triangular numbers t such that t+10 is a prime.
  • A129756 (program): Repetitions of odd numbers four times.
  • A129757 (program): a(n) = ceiling((2^n + 1 - 2*floor(2^(n/2)))/2).
  • A129760 (program): Bitwise AND of binary representation of n-1 and n.
  • A129761 (program): First differences of Fibbinary numbers (A003714).
  • A129763 (program): a(n) = Sum_{k=1..n} binomial(n+k-1, n)^2 / n.
  • A129765 (program): Triangle, (1, 1, 2, 2, 2, …) in every column.
  • A129768 (program): Number of odd nonprime numbers less than the n-th prime.
  • A129770 (program): a(0) = 0, a(1) = 1; for n>0, a(2n) = 3a(2n-1), a(2n+1) = 3a(2n) - 2a(n-1).
  • A129771 (program): Evil odd numbers.
  • A129772 (program): a(0) = 1, a(1) = 2; for n > 0, a(2n) = 3a(2n-1), a(2n+1) = 3a(2n) - 2a(n-1).
  • A129775 (program): Number of maximally clustered permutations in S_n; the maximally clustered permutations are those that avoid 3421, 4312 and 4321.
  • A129779 (program): a(1) = 1, a(2) = -1, a(3) = 2; for n > 3, a(n) = -(2*n-5)*a(n-1).
  • A129780 (program): The prime(n)-th lower twin prime.
  • A129781 (program): The prime(n)-th upper twin prime.
  • A129787 (program): Ceiling(3^n/n).
  • A129788 (program): a(n) = ceiling(4^n/n).
  • A129789 (program): a(n) = ceiling(5^n/n).
  • A129790 (program): a(n) = ceiling(6^n/n).
  • A129791 (program): a(n) = ceiling(7^n/n).
  • A129792 (program): a(n) = ceiling(8^n/n).
  • A129793 (program): a(n) = ceiling(9^n/n).
  • A129794 (program): a(n) = floor(4^n/n).
  • A129795 (program): a(n) = floor(5^n/n).
  • A129796 (program): a(n) = floor(6^n/n).
  • A129797 (program): a(n) = floor(7^n/n).
  • A129798 (program): a(n) = floor(8^n/n).
  • A129799 (program): a(n) = floor(9^n/n).
  • A129801 (program): Triangle read by rows in which row m (m>=0) gives the numbers 2*m*n + 1 for n = 0, …, m.
  • A129803 (program): Triangular numbers that are the sum of three consecutive triangular numbers.
  • A129804 (program): a(0) = 1, a(1) = 2; for n>0, a(2n) = 3a(2n-1) - a(2n-2), a(2n+1) = 3a(2n) - a(2n-1) - a(n-1).
  • A129805 (program): Primes congruent to +-1 mod 18.
  • A129806 (program): Primes congruent to +-5 mod 18.
  • A129807 (program): Primes congruent to +-7 mod 18.
  • A129814 (program): a(n) = Bernoulli(n) * (n+1)!.
  • A129818 (program): Riordan array (1/(1+x), x/(1+x)^2), inverse array is A039599.
  • A129819 (program): Antidiagonal sums of triangular array T: T(j,k) = (k+1)/2 for odd k, T(j,k) = 0 for k = 0, T(j,k) = j+1-k/2 for even k > 0; 0 <= k <= j.
  • A129820 (program): List of pairs of consecutive nonprime odd numbers {m-1,m+1}.
  • A129824 (program): a(n) = Product_{k=0..n} (1 + binomial(n,k)).
  • A129827 (program): Numbers k such that Euler’s totient phi(k) divided by 2 is a perfect square.
  • A129831 (program): Alternating sum of double factorials: n!! - (n-1)!! + (n-2)!! - … 1!!.
  • A129833 (program): a(n) = Sum_{k = 0..n } binomial(n + 1, k + 1)*binomial(n, k)*k!.
  • A129839 (program): a(n) = Stirling_2(n,3)^2.
  • A129842 (program): Primes p such that (p^2 - 3p - 2)/2 is prime.
  • A129847 (program): b(n) = number of set partitions of {1, 2, …, n} whose blocks consist only of elements that differ by two or less (that is, have only the forms {i}, {i,i+1}, {i,i+2}, or {i,i+1,i+2}).
  • A129854 (program): Decimal Gray code ordering of the semiprimes.
  • A129855 (program): A symmetrical triangle of coefficients based on A000217: a(n) = Binomial[n + 2, 2]; t(n,m)=a(n - m + 1)*a(m + 1).
  • A129856 (program): Primes that are one less than the difference between consecutive primes.
  • A129863 (program): Sums of three consecutive pentagonal numbers.
  • A129867 (program): Row sums of triangular array T: T(j,k) = k*(j-k)! for k < j, T(j,k) = 1 for k = j; 1 <= k <= j.
  • A129868 (program): Binary palindromic numbers with only one 0 bit.
  • A129869 (program): Number of positive clusters of type D_n.
  • A129871 (program): A variant of Sylvester’s sequence: a(0)=1 and for n>0, a(n) = (a(0)*a(1)*…*a(n-1)) + 1.
  • A129873 (program): Sequence s_n arising in enumeration of arrays of directed blocks (see Quaintance reference for precise definition).
  • A129889 (program): Write down n, then n*(n+1).
  • A129890 (program): a(n) = (2*n+2)!! - (2*n+1)!!.
  • A129891 (program): Sum of coefficients of polynomials defined in comments lines.
  • A129893 (program): a(n) = s!/(s-n)! where s = (n*(n+1)/2)+1.
  • A129895 (program): a(1)=1. a(n) = a(n-1) + number of triangular numbers among the first (n-1) terms of the sequence.
  • A129896 (program): a(1)=1. a(n) = a(n-1) + number of Fibonacci numbers among the first (n-1) terms of the sequence.
  • A129902 (program): Smallest multiple of n having exactly twice as many divisors as n.
  • A129903 (program): Expansion of 1/(1+x^2-x^3+x^4).
  • A129904 (program): Find the first two terms in A003215, say A003215(i) and A003215(j), that are divisible by a number in A016921 not 1, say by k = A016921(m). Then i + j + 1 = k and k is added to the sequence.
  • A129905 (program): Expansion of g.f.: (1-x)*(1+2*x)/((1+x)*(1-3*x+x^2)).
  • A129906 (program): n!/(n^2) when an integer.
  • A129908 (program): Quotient of the decimal representation of concatenated twin primes divided by 3.
  • A129910 (program): Quotient of the decimal representation of concatenated twin primes in reverse divided by 3.
  • A129911 (program): Primes in A129910.
  • A129920 (program): Expansion of -1/(1 - x + 3*x^2 - 2*x^3 + x^4 - 2*x^5 + x^6).
  • A129921 (program): Number of generalized compositions of n: words b_1^{i_1}b_2^{i_2}…b_k^{i_k} such that b_j’s and j_i’s are positive integers and sum b_j*i_j = n.
  • A129923 (program): (n+5)! / 5.
  • A129926 (program): Semiprimes n such that 3*n - 2 is a prime.
  • A129927 (program): 3-almost prime octagonal numbers.
  • A129928 (program): Primes equal to 3*Sp - 2, where Sp is a semiprime.
  • A129929 (program): Binomial transform of the periodic sequence with periodic pattern 1,1,1,0,0.
  • A129933 (program): (n*(n+1)/2+1)!/n!.
  • A129934 (program): Numerators of partial sums of a series for the inverse of the arithmetic-geometric mean (agM) of sqrt(2)/2 and 1.
  • A129936 (program): a(n) = (n-2)*(n+3)*(n+2)/6.
  • A129937 (program): The central binomial numbers Binomial[n,Floor[n/2] minus the SO(n) dimension as an algebraic projective variety dimension.
  • A129949 (program): a(n) = n! - binomial(n,3).
  • A129952 (program): Binomial transform of A124625.
  • A129953 (program): First differences of A129952.
  • A129954 (program): Second differences of A129952.
  • A129955 (program): Third differences of A129952.
  • A129957 (program): a(n) = n^3 if n is odd, n^3 + 1 otherwise.
  • A129958 (program): First differences of A129957.
  • A129959 (program): A129957(n) - n*(n-1)/2.
  • A129960 (program): a(n) = floor(sqrt(2*n!)).
  • A129961 (program): Main diagonal of triangular array T: T(j,1) = 1 for ((j-1) mod 8) < 4, else 0; T(j,k) = T(j-1,k-1)+T(j,k-1) for 2 <= k <= j.
  • A129966 (program): Triangular numbers which are differences of squares.
  • A129967 (program): a(n) = A061909(n)^2.
  • A129968 (program): a(n) = sum of digits of A061909(n).
  • A129969 (program): a(n) = A061909(n) with digits reversed.
  • A129970 (program): a(n) = A129967(n) with digits reversed.
  • A129971 (program): a(n) = A129968(n)^2.
  • A129972 (program): a(n) = 2*floor(log_2(n)) + 1.
  • A129973 (program): a(n) = A000045(n)-A000931(n).
  • A129979 (program): Left border of triangle A131088.
  • A129980 (program): Sum of the digits of the sum of n!!, with n>=0.
  • A129981 (program): Sum of n!!, with n>=0.
  • A129982 (program): Fibonacci numbers sandwiched between 1’s.
  • A129983 (program): Binomial transform of A129982.
  • A129984 (program): First differences of A129983.
  • A129986 (program): Second differences of A129983.
  • A129987 (program): Third differences of A129983.
  • A129988 (program): Fourth differences of A129983.
  • A129994 (program): Triangle read by rows: 2*A007318 - I.
  • A129995 (program): a(n) = (n + 1)*(n^2 + 2)*(n^3 + 3)*(n^4 + 4)/4!.
  • A129996 (program): a(n) = (-1)^[(n+1)/2] A000108([n/2]+1).
  • A129997 (program): a(n) = 4*a(n-1) + (n-6)*a(n-2).
  • A130002 (program): Alternating sum along antidiagonals of the array of A129952 and its iterated differences.
  • A130006 (program): Prime numbers arising from A050704.
  • A130008 (program): Noncomposite numbers sandwiched between 1’s.
  • A130011 (program): A self-describing sequence. Pick any integer n in the sequence; this n says: “There are n terms in the sequence that are <= 3n”. This sequence is the slowest increasing one with this property.
  • A130019 (program): a(n+2) = 6*a(n+1) + (-11 + n)*a(n) + (6 - 2*n)*a(n-1) for n >= 1.
  • A130020 (program): Triangle T(n,k), 0<=k<=n, read by rows given by [1,0,0,0,0,0,0,…] DELTA [0,1,1,1,1,1,1,…] where DELTA is the operator defined in A084938 .
  • A130025 (program): a(1)=1; a(n) = a(n-1) + (number of terms, from among terms a(1) through a(n-1), which are squarefree).
  • A130026 (program): Triangle (n,k) by columns, arithmetic sequences interspersed with k zeros.
  • A130029 (program): a(n) = Sum_{d|n} phi(n/d) * prime(d).
  • A130031 (program): Row sums of triangle A129467.
  • A130032 (program): Row sums of unsigned triangle A129467.
  • A130034 (program): Denominators of partial sums of a series for the inverse of the arithmetic-geometric mean (agM) of 1 and sqrt(2)/2.
  • A130035 (program): Numerators of partial sums of a series for the inverse of the arithmetic-geometric mean (AGM) of sqrt(3)/2 and 1.
  • A130036 (program): Denominators of partial sums of a series for the inverse of the arithmetic-geometric mean (agM) of 1 and sqrt(3)/2.
  • A130037 (program): Numerators of partial sums of a series for the inverse of the arithmetic-geometric mean (agM) of 1/2 and 1.
  • A130038 (program): Even numbers n such that n-7 is prime, but neither n-3 nor n-5 is prime.
  • A130039 (program): Numerators of partial sums of a series for the inverse of the arithmetic-geometric mean (agM) of 2/sqrt(5) and 1.
  • A130040 (program): Denominators of partial sums of a series for the inverse of the arithmetic-geometric mean (agM) of 2/sqrt(5) and 1.
  • A130047 (program): Left half of Pascal’s triangle (A034868) modulo 2.
  • A130053 (program): G.f. A(x) = (1-x+x^2)/(1-x)^3 - x*[Sum_{n>=0} x^(n + 2^n)]/(1-x)^2 .
  • A130054 (program): Inverse Moebius transform of A023900.
  • A130063 (program): Primes p such that p divides 3^((p+1)/2) - 2^((p+1)/2) - 1.
  • A130064 (program): a(n) = (n / SmallestPrimeFactor(n)) * GreatestPrimeFactor(n).
  • A130065 (program): a(n) = (n / GreatestPrimeFactor(n)) * SmallestPrimeFactor(n).
  • A130068 (program): Maximal power of 2 dividing the binomial coefficient binomial(m, 2^k) where m >= 1 and 1 <= 2^k <= m.
  • A130070 (program): Moebius transform of A130069.
  • A130071 (program): Triangle, A007444(k) in each column interspersed with k zeros.
  • A130072 (program): a(n) = 5^n - 3^n - 2^n.
  • A130075 (program): a(n) = (5^p - 3^p - 2^p)/p, where p = prime(n).
  • A130082 (program): Smallest number whose eighth power has at least n digits.
  • A130087 (program): Denominator of product{k=1 to n} k^mu(k), where mu is the Moebius function A008683.
  • A130091 (program): Numbers having in their canonical prime factorization mutually distinct exponents.
  • A130092 (program): Numbers with at least two factors having in their canonical prime factorization equal exponents.
  • A130093 (program): A051731 * a lower triangular matrix with A036987 on the main diagonal and the rest zeros.
  • A130094 (program): A051731 * an infinite lower triangular matrix with A007427 in the main diagonal.
  • A130095 (program): Inverse Möbius transform of odd-indexed Fibonacci numbers.
  • A130102 (program): E.g.f.: (e^x - x)^2.
  • A130103 (program): Expansion of e.g.f. e^(2x)-(1+x)*e^x+x.
  • A130104 (program): Expansion of x(1-3x+5x^2-2x^3)/((1-x)^3*(1-2x)).
  • A130106 (program): A051731 * diagonalized matrix of A063659.
  • A130107 (program): Möbius transform of A063659.
  • A130114 (program): Inverse Moebius transform of A037019.
  • A130119 (program): a(n) = gcd(n^2 - 19, 45).
  • A130123 (program): Infinite lower triangular matrix with 2^k in the right diagonal and the rest zeros. Triangle, T(n,k), n zeros followed by the term 2^k. Triangle by columns, (2^k, 0, 0, 0, …).
  • A130124 (program): Triangle defined by A130123 * A002260, read by rows.
  • A130125 (program): Triangle defined by A128174 * A130123, read by rows.
  • A130127 (program): Triangle defined by A000012 * A130125, read by rows.
  • A130128 (program): Triangle read by rows: T(n,k) = (n - k + 1)*2^(k-1).
  • A130129 (program): a(n) = (3*n+1)*2^n.
  • A130130 (program): a(0)=0, a(1)=1, a(n)=2 for n >= 2.
  • A130137 (program): Number of Fibonacci binary words of length n having no 0110 subword. A Fibonacci binary word is a binary word having no 00 subword.
  • A130145 (program): Number of nonisomorphic orthogonal arrays OA(8*n+4,4,2,2).
  • A130146 (program): n appears k times, where k = last digit of n.
  • A130151 (program): Period 6: repeat [1, 1, 1, -1, -1, -1].
  • A130154 (program): Triangle read by rows: T(n, k) = 1 + 2*(n-k)*(k-1) (1 <= k <= n).
  • A130165 (program): a(1)=1; a(n)=prime(mod(a(n-1),10)).
  • A130174 (program): a(n) = n-1 + (total number of digits in a(1), …, a(n-1)).
  • A130175 (program): 2n+1 appears (last digit of 2n+1) times .
  • A130176 (program): Numbers n with property that the largest prime factor is a Sophie Germain prime.
  • A130183 (program): Row sums of triangle A130182.
  • A130185 (program): Third column (m=2) of triangle A130182.
  • A130187 (program): Numerators of rationals r(n) related to the z-sequence of the Sheffer matrix A060821 for Hermite polynomials.
  • A130188 (program): Denominators of rationals r(n) related to the z-sequence of the Sheffer matrix A060821 for Hermite polynomials.
  • A130190 (program): Denominators of z-sequence for the Sheffer matrix (triangle) A094816 (coefficients of Poisson-Charlier polynomials).
  • A130194 (program): Let M = lower triangular matrix with 1’s on and below the main diagonal, with columns multiplied by +1, +1, -1, -1, repeated; form M^2; read across rows of resulting triangle.
  • A130195 (program): Row sums of triangle A130194.
  • A130196 (program): Period 3: repeat [1, 2, 2].
  • A130198 (program): Single paradiddle. In percussion, the paradiddle is a four-note drum sticking pattern consisting of two alternating notes followed by two notes on the same hand.
  • A130199 (program): Evil oblong (promic) numbers.
  • A130200 (program): Evil triangular numbers.
  • A130201 (program): Odious oblong (promic) numbers.
  • A130202 (program): Odious triangular numbers.
  • A130205 (program): a(n) = n^2 - a(n-1) - a(n-2), with a(1) = 1 and a(2) = 2.
  • A130207 (program): Diagonalized matrix of A000010.
  • A130208 (program): Diagonalized matrix of A000203, Sigma(n).
  • A130209 (program): Diagonalized matrix of d(n), A000005.
  • A130210 (program): Triangle read by rows: matrix product A051731 * A130209.
  • A130212 (program): T(k, n) = sum_(1 <= j <= k) [j | k] j mu(k / j) floor(n / k), triangle read by rows.
  • A130213 (program): Order of modular group of degree 3^(n-1) + 1.
  • A130214 (program): Order of modular group of degree 5^(n-1)+1.
  • A130215 (program): Order of modular group of degree 7^(n-1)+1.
  • A130216 (program): a(0) = 3; a(n) = a(n-1) + (number of multiples of 3 so far in the sequence).
  • A130218 (program): Partial sums of A100119. Sum of first n of the n-th centered n-gonal numbers.
  • A130224 (program): a(1) = 1; a(n) = a(n-1) + (number of times the digit 1 has appeared in the sequence so far).
  • A130225 (program): a(1) = 2; a(n) = a(n-1) + (number of times the digit 2 has appeared in the sequence so far).
  • A130231 (program): a(1) = 3; a(n) = a(n-1) + (number of times the digit 3 has appeared in the sequence so far).
  • A130233 (program): a(n) is the maximal k such that Fibonacci(k) <= n (the “lower” Fibonacci Inverse).
  • A130234 (program): Minimal index k of a Fibonacci number such that Fibonacci(k) >= n (the ‘upper’ Fibonacci Inverse).
  • A130235 (program): Partial sums of the ‘lower’ Fibonacci Inverse A130233.
  • A130236 (program): Partial sums of the ‘upper’ Fibonacci Inverse A130234.
  • A130237 (program): The ‘lower’ Fibonacci Inverse A130233(n) multiplied by n.
  • A130238 (program): Partial sums of A130237.
  • A130239 (program): Maximal index k of the square of a Fibonacci number such that Fib(k)^2 <= n (the ‘lower’ squared Fibonacci Inverse).
  • A130240 (program): Partial sums of A130239.
  • A130241 (program): Maximal index k of a Lucas number such that Lucas(k) <= n (the ‘lower’ Lucas (A000032) Inverse).
  • A130242 (program): Minimal index k of a Lucas number such that Lucas(k)>=n (the ‘upper’ Lucas (A000032) Inverse).
  • A130243 (program): Partial sums of the ‘lower’ Lucas Inverse A130241.
  • A130244 (program): Partial sums of the ‘upper’ Lucas Inverse A130242.
  • A130245 (program): Number of Lucas numbers (A000032) <= n.
  • A130246 (program): Partial sums of A130245.
  • A130247 (program): Inverse Lucas (A000032) numbers: index k of a Lucas number such that Lucas(k)=n; max(k|Lucas(k) < n), if there is no such index.
  • A130248 (program): Partial sums of the Lucas Inverse A130247.
  • A130249 (program): Maximal index k of a Jacobsthal number such that A001045(k)<=n (the ‘lower’ Jacobsthal inverse).
  • A130250 (program): Minimal index k of a Jacobsthal number such that A001045(k) >= n (the ‘upper’ Jacobsthal inverse).
  • A130251 (program): Partial sums of A130249.
  • A130252 (program): Partial sums of A130250.
  • A130253 (program): Number of Jacobsthal numbers (A001045) <=n.
  • A130255 (program): Maximal index k of an odd Fibonacci number (A001519) such that A001519(k) = Fibonacci(2k-1) <= n (the ‘lower’ odd Fibonacci Inverse).
  • A130256 (program): Minimal index k of an odd Fibonacci number A001519 such that A001519(k) = Fibonacci(2*k-1) >= n (the ‘upper’ odd Fibonacci Inverse).
  • A130257 (program): Partial sums of the ‘lower’ odd Fibonacci Inverse A130255.
  • A130258 (program): Partial sums of the ‘upper’ odd Fibonacci Inverse A130256.
  • A130259 (program): Maximal index k of an even Fibonacci number (A001906) such that A001906(k) = Fib(2k) <= n (the ‘lower’ even Fibonacci Inverse).
  • A130260 (program): Minimal index k of an even Fibonacci number A001906 such that A001906(k) = Fib(2k) >= n (the ‘upper’ even Fibonacci Inverse).
  • A130261 (program): Partial sums of the ‘lower’ even Fibonacci Inverse A130259.
  • A130262 (program): Partial sums of the ‘upper’ even Fibonacci Inverse A130260.
  • A130265 (program): Triangle read by rows: matrix product A007318 * A051340.
  • A130266 (program): A051340 * A128174.
  • A130267 (program): A051731 * A051340.
  • A130269 (program): A002260 * A051340.
  • A130270 (program): Triangle read by rows, T(n) followed by 1, 2, 3, …, n-1.
  • A130271 (program): Triangle read by rows: A051340^2.
  • A130290 (program): Number of nonzero quadratic residues modulo the n-th prime.
  • A130291 (program): Number of quadratic residues (including 0) modulo the n-th prime.
  • A130292 (program): Numbers that are sums of fifth powers of two distinct primes.
  • A130293 (program): Number of necklaces of n beads with up to n colors, with cyclic permutation {1,..,n} of the colors taken to be equivalent.
  • A130296 (program): Triangle read by rows: T[i,1]=i, T[i,j]=1 for 1 < j <= i = 1,2,3,…
  • A130297 (program): A130296^2.
  • A130298 (program): A051340 * A130296.
  • A130299 (program): A130296 * A051340.
  • A130300 (program): A007318 * A130296.
  • A130302 (program): A000012 * A130296.
  • A130303 (program): A130296 * A000012.
  • A130304 (program): Triangle, (1,1,0,0,1,1,…) in every column.
  • A130305 (program): A007318 * A130304.
  • A130307 (program): A051731 * A130296.
  • A130312 (program): Each Fibonacci number F(n) appears F(n) times.
  • A130313 (program): A000012 * A054523.
  • A130321 (program): Triangle, (2^0, 2^1, 2^2, …) in every column.
  • A130322 (program): A130321^2.
  • A130323 (program): A007318^(-1) * A130322.
  • A130324 (program): A059268^2.
  • A130328 (program): Triangle of differences between powers of 2, read by rows.
  • A130329 (program): A059268 * A130321.
  • A130330 (program): Triangle read by rows, the matrix product A130321 * A000012, both taken as infinite lower triangular matrices.
  • A130331 (program): Number of divisors of A123240(n).
  • A130380 (program): Catalan numbers halved and rounded to the next integer.
  • A130404 (program): Partial sums of A093178.
  • A130406 (program): Column 1 of triangle A130405.
  • A130407 (program): A diagonal of triangle A130405.
  • A130416 (program): Numerator of partial sums for a series of (17/18)*Zeta(4) = (17/1680)*Pi^4.
  • A130417 (program): Denominator of partial sums for a series of (17/18)*Zeta(4)= (17/1680)*Pi^4.
  • A130423 (program): Main diagonal of array A[k,n] = n-th sum of 3 consecutive k-gonal numbers, k>2.
  • A130424 (program): Main diagonal of array A[k,n] = n-th sum of k consecutive k-gonal numbers, k>2.
  • A130425 (program): a(n) = numerator of Sum_{k=1..n} 1/k^(n+1-k).
  • A130426 (program): a(n) = denominator of Sum_{k=1..n} 1/k^(n+1-k).
  • A130446 (program): Integers in [1, 425] expressible as a difference of the terms of the unique optimal Golomb ruler of order 24. See A130444.
  • A130447 (program): Numbering the days of a 365-day year from 1 (Jan 01) to 365 (Dec 31), these are the days that start months.
  • A130449 (program): a(0) = 1; a(n) = 4^(n+1)*a(n-1)+1.
  • A130451 (program): Number of divisors of A123193(n).
  • A130453 (program): A097806 * A059268.
  • A130458 (program): Final term in the rows of triangle A130457: a(n) = A130457(n, 3n), for n>=0.
  • A130459 (program): A059268 * A097806.
  • A130460 (program): Infinite lower triangular matrix,(1,0,0,0,…) in the main diagonal and (1,2,3,…) in the subdiagonal.
  • A130461 (program): Triangle, antidiagonals of an array generated from A130460.
  • A130469 (program): Triangular array read by rows: T(j,k) = k*(j-k)! for k < j, T(j,k) = 1 for k = j; 1 <= k <= j.
  • A130470 (program): Antidiagonal sums of triangular array T: T(j,k) = k*(j-k)! for k < j, T(j,k) = 1 for k = j; 1 <= k <= j.
  • A130471 (program): First differences of antidiagonal sums of triangular array T: T(j,k) = k*(j-k)! for k < j, T(j,k) = 1 for k = j; 1 <= k <= j.
  • A130472 (program): A permutation of the integers: a(n) = (-1)^n * floor( (n+1)/2 ).
  • A130473 (program): Partial sums of A087172.
  • A130476 (program): Row sums of triangle A130461.
  • A130477 (program): T(n,k) is the number of permutations of [n] with maximum descent k, T(n,k) for n >= 0 and 0 <= k <= n, triangle read by rows.
  • A130478 (program): Triangle T(n,k) = n! / A130477(n,k).
  • A130480 (program): a(n) = lcm(b(0),b(1),b(2),…,b(n)), where b(m) = A130479(m).
  • A130481 (program): a(n) = Sum_{k=0..n} (k mod 3) (i.e., partial sums of A010872).
  • A130482 (program): a(n) = Sum_{k=0..n} (k mod 4) (Partial sums of A010873).
  • A130483 (program): a(n) = Sum_{k=0..n} (k mod 5) (Partial sums of A010874).
  • A130484 (program): a(n) = Sum_{k=0..n} (k mod 6) (Partial sums of A010875).
  • A130485 (program): a(n) = Sum_{k=0..n} (k mod 7) (Partial sums of A010876).
  • A130486 (program): a(n) = Sum_{k=0..n} (k mod 8) (Partial sums of A010877).
  • A130487 (program): a(n) = Sum_{k=0..n} (k mod 9) (Partial sums of A010878).
  • A130488 (program): a(n) = Sum_{k=0..n} (k mod 10) (Partial sums of A010879).
  • A130489 (program): a(n) = Sum_{k=0..n} (k mod 11) (Partial sums of A010880).
  • A130490 (program): a(n) = Sum_{k=0..n} (k mod 12) (Partial sums of A010881).
  • A130493 (program): Triangle read by rows in which row n contains n! repeated n times.
  • A130494 (program): Row sums of triangle A130478.
  • A130496 (program): Repetition of even numbers, with initial zeros, five times.
  • A130497 (program): Repetition of odd numbers five times.
  • A130505 (program): a(n) = 3*a(n-1) if n is odd, otherwise 6*a(n-1).
  • A130507 (program): First differences of A130845.
  • A130508 (program): a(1)=2. a(2)=3. a(3)=1. a(n+3) = 3 + a(n), for all positive integers n.
  • A130509 (program): a(1)=3. a(2)=1. a(3)=2. a(n+3) = 3 + a(n), for all positive integers n.
  • A130517 (program): Triangle read by rows: row n counts down from n in steps of 2, then counts up the remaining elements in the set {1,2,…n}, again in steps of 2.
  • A130518 (program): a(n) = Sum_{k=0..n} floor(k/3). (Partial sums of A002264.)
  • A130519 (program): a(n) = Sum_{k=0..n} floor(k/4). (Partial sums of A002265.)
  • A130520 (program): a(n) = Sum_{k=0..n} floor(k/5). (Partial sums of A002266.)
  • A130526 (program): A permutation of the integers induced by the lower and upper Wythoff sequences.
  • A130527 (program): A permutation of the integers induced by the Beatty sequence for sqrt(2).
  • A130532 (program): a(n) + a(n - 1) is alternatively a square or a cube.
  • A130540 (program): Triangle read by rows T(n,k) in which column k lists the terms of A000203 interspersed with (k-1) zeros, 1 <= k <= n.
  • A130541 (program): A002260 * A125093^(-1).
  • A130543 (program): Multiplicative persistence of n!.
  • A130545 (program): Numerators of 2*Sum_{k=1..n} 1/binomial(2*k,k), n >= 1.
  • A130546 (program): Denominators of 2*Sum_{k=1..n} 1/binomial(2*k,k), n >= 1.
  • A130547 (program): Numerators of 6*((Sum_{k=1..n} 1/binomial(2*k,k)) - 1/3), n >= 1.
  • A130548 (program): Denominators of 6*(sum(1/binomial(2*k,k),k=1..n)-1/3), n>=1.
  • A130549 (program): Numerators of partial sums for a series for 2*Zeta(2)/3 = (Pi^2)/9.
  • A130550 (program): Denominators of partial sums for a series for 2*Zeta(2)/3 = (Pi^2)/9.
  • A130551 (program): Numerators of partial sums for a series of (4/5)*Zeta(3).
  • A130552 (program): Denominators of partial sums for a series of (4/5)*Zeta(3).
  • A130553 (program): Numerators of partial sums for a series for 2*Pi*sqrt(3)/9.
  • A130554 (program): Denominators of partial sums for a series for 2*Pi*sqrt(3)/9.
  • A130556 (program): A model of the atomic nucleus (Shell model of nucleus). A triangle.
  • A130558 (program): Denominators of partial sums of a series for 6*(5-4*Zeta(3)).
  • A130560 (program): Numerators of Sheffer a-sequence for Jabotinsky type triangle S2(3):=A035342.
  • A130563 (program): Fourth column (m=3) of the Laguerre-Sonin a=1/2 coefficient triangle.
  • A130564 (program): Member k=5 of a family of generalized Catalan numbers.
  • A130565 (program): Member k=6 of a family of generalized Catalan numbers.
  • A130566 (program): Pyramidal 47-gonal numbers.
  • A130567 (program): Expansion of x*(2 - 7*x + 2*x^2)/((1-x)*(1-4*x)*(1-2*x)).
  • A130568 (program): Generalized Beatty sequence 1+2*floor(n*phi), which contains infinitely many primes.
  • A130569 (program): Numbers of the form k*2^m + 1 for k odd, m >=1, that are not Proth numbers (A080075) (2^m <= k).
  • A130570 (program): Primes of the form k*2^m + 1 for k odd, m >=1, that are not Proth primes (A080076) (2^m <= k).
  • A130578 (program): Number of different possible rows (or columns) in an n X n crossword puzzle.
  • A130584 (program): A007318 * A054522.
  • A130586 (program): Row sums of triangle A130585.
  • A130587 (program): Binomial transform of A130008.
  • A130589 (program): a(n) = F(F(n)-1), where F(n) = A000045(n) (the Fibonacci numbers).
  • A130593 (program): Evil semiprimes.
  • A130595 (program): Triangle read by rows: lower triangular matrix which is inverse to Pascal’s triangle (A007318) regarded as a lower triangular matrix.
  • A130596 (program): Partial sums of skinny numbers (A061909).
  • A130597 (program): Inverse binomial transform of decimal expansion of Pi.
  • A130599 (program): Transformation of sequence 3^k by sandwiching it between 1’s.
  • A130602 (program): A shell geometric model of the atomic nucleus.
  • A130603 (program): a(0)=0, a(n) = the n-th positive integer that is coprime to (a(n-1)+1).
  • A130606 (program): a(n) = prime(n+1)^n - prime(n)^n where prime(n) is the n-th prime number.
  • A130607 (program): Prime(n+1)^n + prime(n)^n.
  • A130612 (program): Sum of the first 10^n squares.
  • A130614 (program): a(n) = p^(p-2), where p = prime(n).
  • A130619 (program): Let M(n) = {{n, 0, 1}, {1, 0, 0}, {0, 1, 0}}, then a(n) is the upper-right term of M(n)*M(n-1)*…*M(1) (empty matrix product yields the identity).
  • A130624 (program): Binomial transform of A101000.
  • A130625 (program): First differences of A130624.
  • A130626 (program): Second differences of A130624.
  • A130630 (program): Periodic sequence with period 1 1 1 1 1 0 0 0 0.
  • A130632 (program): Number of natural numbers between d(n) and d(n+1), where d(n) denotes the number of divisors of n.
  • A130633 (program): Additive persistence of Fibonacci numbers.
  • A130634 (program): Additive persistence of double factorials.
  • A130636 (program): a(n) = n*a(n-3) + a(n-4) for n >= 4.
  • A130637 (program): a(n) = n*a(n-2) + a(n-5) for n >= 5 and with a(0)=0, a(1)=1, a(2)=0, a(3)=3, a(4)=0.
  • A130638 (program): a(n) = 1 iff d(n) = d(n+1), otherwise a(n)=0, where d(n) is the number of divisors of n, A000005.
  • A130641 (program): The first entry of the vector v[n]=M[n]v[n-1], where M[n] is a 7 X 7 matrix M[n] = [[n, 0, 0, 0, 0, 0, 1], [1, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1, 0]] and v[0] is the column vector [0, 0, 0, 0, 0, 0, 1].
  • A130651 (program): 1/16 the number of permutations of 0..n having exactly 3 maxima.
  • A130652 (program): a(n) = 11^n - 2.
  • A130654 (program): Exponent m such that 2^m = A092505(n) = A002430(n) / A046990(n).
  • A130655 (program): Catalan transform of Catalan numbers C(n+1).
  • A130656 (program): Interlacing n^3/2 and n^2(n + 1)/2.
  • A130657 (program): Periodic (7 terms) 1 1 1 1 0 0 0.
  • A130658 (program): Period 4: repeat [1, 1, 2, 2].
  • A130659 (program): Period 4: repeat [0, 1, 2, 4].
  • A130664 (program): a(1)=1. a(n) = a(n-1) + (number of terms from among a(1) through a(n-1) which are factorials).
  • A130665 (program): a(n) = Sum_{k=0..n} 3^wt(k), where wt() = A000120().
  • A130667 (program): a(1) = 1; a(n) = max{ 5*a(k) + a(n-k) | 1 <= k <= n/2 } for n > 1.
  • A130668 (program): Diagonal of A129819.
  • A130671 (program): Triangular sequence based on Pascal’s triangle: t(n,m) = 2*binomial(m, n) - (1 + n*(m - n)).
  • A130673 (program): Smallest m of r=1,2,3,… where the generalized Euler constants (of D. H. Lehmer) E(r,m) change their sign: E(r,m) > 0 and E(r+1,m) < 0.
  • A130674 (program): a(n) = d(n)!, where d denotes the number of divisors of n.
  • A130675 (program): Factorial of bigomega(n).
  • A130684 (program): Triangle read by rows: T(n,k) = number of squares (not necessarily orthogonal) all of whose vertices lie in an (n + 1) X (k + 1) square lattice.
  • A130685 (program): a(0)=0; a(n) = n-th integer from among those positive integers which are coprime to (a(n-1) + n).
  • A130686 (program): Absolute difference of final digits of two consecutive triangular numbers.
  • A130687 (program): Numbers n such that a_1! + a_2! + … + a_m! is a square number, where a_1a_2…a_m is the decimal expansion of n.
  • A130692 (program): a(n) is the smallest number m such that the sum of the digits of n+m is n.
  • A130706 (program): a(0) = 1, a(1) = 2, a(n) = 0 for n > 1.
  • A130707 (program): a(n+3) = 3*(a(n+2) - a(n+1)) + 2*a(n).
  • A130711 (program): Number of compositions of n such that the smallest part divides every part.
  • A130713 (program): a(0)=a(2)=1, a(1)=2, a(n)=0 for n > 2.
  • A130716 (program): a(0)=a(1)=a(2)=1, a(n)=0 for n>2.
  • A130717 (program): Second differences of A130845.
  • A130718 (program): 2*(prime(n)-2)!.
  • A130719 (program): a(n) = n-th digit after the decimal point of the decimal representation of the n-th harmonic number.
  • A130722 (program): The twice repeated nonnegative integers at even indices, the non-repeated nonnegative integers at odd indices.
  • A130723 (program): Least common multiple of 3 and n^2+n+1.
  • A130724 (program): a(n) = lcm(n,3) / gcd(n,3).
  • A130726 (program): Factorial of the largest prime less than or equal to n.
  • A130727 (program): List of triples 2n+1, 2n+3, 2n+2.
  • A130731 (program): Period 4: repeat [1, 2, 0, 0].
  • A130732 (program): Floor(Fibonacci(n)/Prime(n)).
  • A130734 (program): List of numbers of cents you can have in US coins without having change for a dollar.
  • A130744 (program): a(n) = n*(n+2)*n!.
  • A130746 (program): Triangle red by rows: T(n,m) = binomial(n+m,1+n), 1<=m<=n.
  • A130747 (program): A self-referential sequence related to Mancala solitaire (see comment).
  • A130748 (program): Place n points on each of the three sides of a triangle, 3n points in all; a(n) = number of nondegenerate triangles that can be constructed using these points (plus the 3 original vertices) as vertices.
  • A130750 (program): Binomial transform of A010882.
  • A130752 (program): Binomial transform of periodic sequence (2, 3, 1).
  • A130753 (program): A folded-back triangular sequence based on symmetry of CnH2*n+2 straight chain alkanes and the number of hydrogen atoms of a given symmetry type: Besides methane at 4 there are only three symmetry types: two CH3’s->6: a single CH2->2, two CH2’s->4.
  • A130755 (program): Binomial transform of periodic sequence (3, 1, 2).
  • A130758 (program): a(n) = n if n is not an odd prime number. Otherwise, a(n) = k, where k is the smallest integer such that n < 10^k.
  • A130759 (program): Partial sums of A130707.
  • A130762 (program): A fold back triangular sequence for A003991: symmetrical folding and addition of.
  • A130763 (program): Natural numbers such that d(n)!+ 1 is a square, where d(n) is the number of divisors of n, A000005.
  • A130764 (program): ASCII codes for upper case letters.
  • A130765 (program): ASCII codes for lower case letters.
  • A130766 (program): 3n+2 sandwiched by tripled 3n+1 .
  • A130770 (program): One third of the least common multiple of 3 and n^2+n+1.
  • A130772 (program): Periodic sequence with period 2 2 0 -2 -2 0.
  • A130773 (program): a(0)=0, a(1)=2, a(n)=2n+1 for n >= 2.
  • A130774 (program): Cumulative concatenation of A000204 Lucas numbers (beginning at 1).
  • A130775 (program): a(1) = 0; for n > 1: a(n) = 2*(prime(n)-1)!/(prime(n)+1).
  • A130777 (program): Coefficients of first difference of Chebyshev S polynomials.
  • A130778 (program): Period 6: repeat [1, -1, -3, -3, -1, 1].
  • A130779 (program): a(0)=a(1)=1, a(2)=2, a(n)=0 for n >= 3.
  • A130781 (program): Sequence is identical to its third differences: a(n+3) = 3*a(n+2) - 3*a(n+1) + 2*a(n), with a(0)=a(1)=1, a(2)=2.
  • A130782 (program): Period 5, repeat [1, 1, 2, 1, 1].
  • A130783 (program): Maximum value of the n-th difference of a permutation of 0..n.
  • A130784 (program): Period 3: repeat [1, 3, 2].
  • A130785 (program): Sequence identical to its third differences: a(n+3) = 3a(n+2)-3a(n+1)+2a(n), with a(0)=1, a(1)=4, a(2)=9.
  • A130788 (program): Solar planets’ average orbit velocity (inverse ratio relative to one of Mercury), multiplied by 3 and rounded to the nearest integer.
  • A130790 (program): Number of nodes in the Lucas-Pratt primality tree rooted at prime(n).
  • A130793 (program): Periodic sequence with period 3: 1, 3, 5.
  • A130794 (program): Periodic sequence with period 1,5,3.
  • A130796 (program): Primes p such that nextprime(p)-p is not power of 2.
  • A130797 (program): a(1)=1; for n >= 2, a(n) = floor(n!/(Sum_{k=1..n-1} a(k))).
  • A130800 (program): Numbers k such that both 2k+1 and 3k+1 are primes.
  • A130806 (program): Period 6: 1,4,3,-1,-4,-3.
  • A130809 (program): If X_1, …, X_n is a partition of a 2n-set X into 2-blocks then a(n) is equal to the number of 3-subsets of X containing none of X_i, (i=1,…,n).
  • A130810 (program): If X_1,…,X_n is a partition of a 2n-set X into 2-blocks then a(n) is equal to the number of 4-subsets of X containing none of X_i, (i=1,…,n).
  • A130811 (program): If X_1,…,X_n is a partition of a 2n-set X into 2-blocks then a(n) is equal to the number of 5-subsets of X containing none of X_i, (i=1,…n).
  • A130812 (program): If X_1,…,X_n is a partition of a 2n-set X into 2-blocks then a(n) is equal to the number of 6-subsets of X containing none of X_i, (i=1,…n).
  • A130813 (program): If X_1,…,X_n is a partition of a 2n-set X into 2-blocks then a(n) is equal to the number of 7-subsets of X containing none of X_i, (i=1,…n).
  • A130815 (program): Period 6: repeat [1, 5, 4, -1, -5, -4].
  • A130816 (program): a(1) = 2, a(2) = 2, a(3) = 1, a(n) = a(n-3) + floor(a(n-2)/2) for n >= 4.
  • A130818 (program): Decimal expansion of number whose Engel expansion is the sequence of squares, that is, 1, 4, 9, 16,…
  • A130819 (program): 2*k appears 2*k-1 times.
  • A130820 (program): Decimal expansion of number whose Engel expansion is given by the sequence: 1,1,2,2,3,3,4,4,…Ceiling[n/2],…
  • A130821 (program): 2n-1 appears 2n times.
  • A130822 (program): Two 1’s, one 2, four 3’s, three 4’s …
  • A130823 (program): Each odd number appears thrice.
  • A130824 (program): a(n) = 2*A004273(n).
  • A130829 (program): 2n+1 appears 2n times.
  • A130830 (program): Irregular triangle read by rows: row(1) = [1,2,3]; thereafter row(n+1) is the tensor square of row(n).
  • A130831 (program): Irregular triangle read by rows: row(1) = [1,2]; thereafter row(n+1) is the tensor square of row(n).
  • A130835 (program): Sum of all numbers having n or fewer digits and having the sum of their digits equal to n.
  • A130836 (program): Square array d(m,n) = multiplicative distance between m>=1 and n>=1, read by antidiagonals.
  • A130838 (program): Sorted list of strings that can be obtained by starting with 12 and repeatedly doubling any substring in place.
  • A130840 (program): a(n) = floor((1/16)*(16 + 2^n - 8*n + 8*n^2)).
  • A130844 (program): a(n) = 2*a(n-1) + a(n-2) - a(n-3) + a(n-4), with a(1) = 0, a(2) = 3, a(3) = 5 and a(4) = 17.
  • A130845 (program): a(4n) = a(4n+1) = a(4n+2) = A001477(n), a(4n+3) = A005408(n).
  • A130848 (program): Periodic sequence with period (2, 5, 3, -2, -5, -3).
  • A130849 (program): a(n) is half the sum of the terms in the n-th antidiagonal of the table A130836.
  • A130850 (program): Triangle read by rows, 0 <= k <= n, T(n,k) = Sum_{j=0..n} A(n,j)*binomial(n-j,k) where A(n,j) are the Eulerian numbers A173018.
  • A130851 (program): Catalan numbers A000108(n) modulo 9.
  • A130853 (program): Runs of 1’s of lengths 1, Fibonacci numbers F(1), F(2), F(3), … (A000045) separated by 0’s.
  • A130854 (program): Runs of 1’s of lengths 1 for decimal expansion of Pi (A000796), separated by 0’s.
  • A130855 (program): 2n appears 2n+1 times, 2n+1 appears 2n times.
  • A130856 (program): The digital root (A010888) of the Catalan numbers A000108.
  • A130857 (program): a(n) = (n-1)*n*(n+1)*(n+2)*(2n+11)/120.
  • A130859 (program): 1729-gonal numbers.
  • A130861 (program): a(n) = (n-1)*(2*n+5).
  • A130862 (program): a(n) = (n-1)*(n+2)*(2*n+11)/2.
  • A130863 (program): Ratio of quadruple Sum of k^2-1 to quadruple sum of k made into an integer sequence: (1/6)*(-1 + n)(2 + n)(3 + n)(7 + n).
  • A130869 (program): Partial sums of A130752.
  • A130873 (program): Sums of two distinct prime 4th powers.
  • A130874 (program): Anti-divisorial numbers: the product of all anti-divisors of all integers less than or equal to n.
  • A130875 (program): Absolute difference of final digits of two consecutive cubes.
  • A130876 (program): Centered 1729-gonal numbers.
  • A130877 (program): Numbers that are congruent to {0, 5} mod 9.
  • A130878 (program): Inverse Moebius transform of A100107.
  • A130879 (program): An antidiagonal triangular sequence based on sums of fractal self-similar level count totals of the sort: Sum_{n=0..m} k^(2^n).
  • A130880 (program): Decimal expansion of 2*sin(Pi/18).
  • A130881 (program): Numbers n such that n = Sum_digits[(n+k)*abs(n-k)] for some k>=0.
  • A130883 (program): a(n) = 2*n^2 - n + 1.
  • A130884 (program): 3n^3 + 2n^2 + n + 1.
  • A130885 (program): 3n^3 - 2n^2 + n - 1.
  • A130886 (program): 4n^4 + 3n^3 + 2n^2 + n + 1.
  • A130887 (program): Inverse Moebius transform of the Mersenne numbers: a(n) = Sum_{d|n} (2^d - 1).
  • A130888 (program): Triangle read by rows, A051731(n,k) dot (1, 3, 7, 15, …) with like numbers of terms.
  • A130891 (program): a(n) = n if n is not an odd prime number. Otherwise, a(n) = k*floor(n/10), where k is the smallest integer such that n < 10^k.
  • A130892 (program): a(n) = n if n is not an odd prime number. Otherwise, a(n) = k*ceiling(n/10), where k is the smallest integer such that n < 10^k.
  • A130893 (program): Lucas numbers (beginning with 1) mod 10.
  • A130894 (program): Numerator of Sum_{k=1..n} H(k)*H(n+1-k), where H(k) is the k-th harmonic number (Sum_{j=1..k} 1/j).
  • A130895 (program): Denominator of Sum_{k=1..n} H(k)*H(n+1-k), where H(k) is the k-th harmonic number (Sum_{j=1..k} 1/j).
  • A130896 (program): For D_n type groups as polyhedra that are pyramid-like: {F,V,E,dimension}->{2*n+1,2*n+1,2*n,(2*n+1)*((2*n+1)-1)/2} such that Euler’s equation is true: V=E-F+2.
  • A130904 (program): Numbers n such that the trajectory of the map n -> (n + lpf(n)) / 2 reaches 3, where lpf(n) is the least prime factor of n (A020639).
  • A130905 (program): E.g.f.: exp(x^2 / 2) / (1 - x).
  • A130906 (program): E.g.f.: exp(x^3/3!)/(1-x).
  • A130907 (program): E.g.f.: exp(x+x^2/2)/(1-x).
  • A130908 (program): E.g.f.: exp(x+x^2/2!+x^3/3!)/(1-x)
  • A130909 (program): Simple periodic sequence (n mod 16).
  • A130910 (program): Sum {0<=k<=n, k mod 16} (Partial sums of A130909).
  • A130911 (program): a(n) is the number of primes with odd binary weight among the first n primes minus the number with an even binary weight.
  • A130912 (program): Fermat quotients, mod p: ((2^(p-1) - 1)/p) mod p = A007663(n) mod p.
  • A130915 (program): Number of permutations in the symmetric group S_n in which cycle lengths are odd and greater than 1.
  • A130916 (program): a(n) = smallest integer >= n which has only prime factors 2, 3 and 5.
  • A130917 (program): a(n) is the sum of the digital roots of all of the previous terms.
  • A130918 (program): Simple self-inverse permutation of natural numbers: List each block of A000108(n) numbers from A014137(n-1) to A014138(n-1) in reverse order.
  • A130974 (program): Period 6: repeat [1, 1, 1, 3, 3, 3].
  • A130976 (program): G.f.: 8/(3 + 5*sqrt(1-16*x)).
  • A130977 (program): G.f.: 5/(2 + 3*sqrt(1-20*x)).
  • A130978 (program): G.f.: 12/(5 + 7*sqrt(1-24*x)).
  • A130979 (program): G.f.: 7/(3 + 4*sqrt(1-28*x)).
  • A130980 (program): G.f.: 16/(7 + 9*sqrt(1 - 32*x)).
  • A131015 (program): Period 12: repeat 1, 1, 3, 2, 2, 1, 4, 4, 2, 3, 3, 4.
  • A131016 (program): Smallest semiprime == 1 (mod n).
  • A131017 (program): Period 6: repeat [1, 1, 2, -1, 2, 1].
  • A131019 (program): Semiperimeters of quadrilaterals whose sides are 4 consecutive odd primes.
  • A131022 (program): Triangular array T read by rows: T(j,1) = 1 for ((j-1) mod 6) < 3, else 0; T(j,k) = T(j-1,k-1) + T(j,k-1) for 2 <= k <= j.
  • A131023 (program): First subdiagonal of triangular array T: T(j,1) = 1 for ((j-1) mod 6) < 3, else 0; T(j,k) = T(j-1,k-1) + T(j-1,k) for 2 <= k <= j.
  • A131024 (program): Row sums of triangular array T: T(j,1) = 1 for ((j-1) mod 6) < 3, else 0; T(j,k) = T(j-1,k-1) + T(j-1,k) for 2 <= k <= j.
  • A131026 (program): Periodic sequence (2, 2, 1, 0, 0, 1).
  • A131027 (program): Period 6: repeat [4, 3, 1, 0, 1, 3].
  • A131028 (program): Periodic sequence (7, 4, 1, 1, 4, 7).
  • A131029 (program): Periodic sequence (11, 5, 2, 5, 11, 14).
  • A131030 (program): Period 6: repeat [16, 7, 7, 16, 25, 25].
  • A131031 (program): Triangle read by rows: A097806 * A130321.
  • A131032 (program): A097806 * A130296.
  • A131033 (program): A130296 * A097806.
  • A131035 (program): A051340 * A129686.
  • A131036 (program): First differences of A131711.
  • A131037 (program): Sequence A001333 with last digits set to zero.
  • A131039 (program): Expansion of (1-x)*(2*x^2-4*x+1)/(1-2*x+5*x^2-4*x^3+x^4).
  • A131040 (program): a(n) = (1/2+1/2*i*sqrt(11))^n + (1/2-1/2*i*sqrt(11))^n, where i=sqrt(-1).
  • A131041 (program): a(n) = 2*a(n-1) - a(n-2) - a(n-4).
  • A131042 (program): Natural numbers A000027 with 6n+3 and 6n+4 terms swapped.
  • A131045 (program): Binomial transform of Euler’s totient function phi(n+1).
  • A131046 (program): A007318 * A000203.
  • A131047 (program): (1/2) * ((A007318 - A007318^(-1)).
  • A131048 (program): (1/3) * ((A007318^2 - A007318^(-1)).
  • A131049 (program): (1/4) * (A007318^3 - A007318^(-1)).
  • A131050 (program): (1/5) * ((A007318^4 - A007318^(-1)).
  • A131051 (program): Row sums of triangle A133805.
  • A131052 (program): A131047 * A000012.
  • A131053 (program): A000012 * A131047.
  • A131055 (program): 1 followed by repeats of 2*k.
  • A131056 (program): A007318 * A131055.
  • A131060 (program): 3*A007318 - 2*A000012 as infinite lower triangular matrices.
  • A131061 (program): Triangle read by rows: T(n,k) = 4*binomial(n,k) - 3 for 0 <= k <= n.
  • A131063 (program): Triangle read by rows: T(n,k) = 5*binomial(n,k) - 4 for 0 <= k <= n.
  • A131064 (program): Binomial transform of [1, 1, 5, 5, 5, …].
  • A131065 (program): Triangle read by rows: T(n,k) = 6*binomial(n,k) - 5 for 0 <= k <= n.
  • A131066 (program): Binomial transform of [1, 1, 6, 6, 6, …].
  • A131067 (program): Triangle read by rows: T(n,k) = 7*binomial(n,k) - 6 for 0 <= k <= n.
  • A131068 (program): Binomial transform of [1, 1, 7, 7, 7, …].
  • A131075 (program): First subdiagonal of triangular array T: T(j,1) = 1 for ((j-1) mod 8) < 4, else 0; T(j,k) = T(j-1,k-1) + T(j,k-1) for 2 <= k <= j.
  • A131076 (program): Row sums of triangular array T: T(j,1) = 1 for ((j-1) mod 8) < 4, else 0; T(j,k) = T(j-1,k-1) + T(j,k-1) for 2 <= k <= j.
  • A131078 (program): Periodic sequence (1, 1, 1, 1, 0, 0, 0, 0).
  • A131079 (program): Periodic sequence (2, 2, 2, 1, 0, 0, 0, 1).
  • A131080 (program): Periodic sequence (4, 4, 3, 1, 0, 0, 1, 3).
  • A131081 (program): Periodic sequence (8, 7, 4, 1, 0, 1, 4, 7).
  • A131082 (program): Periodic sequence (15, 11, 5, 1, 1, 5, 11, 15).
  • A131083 (program): Periodic sequence (26, 16, 6, 2, 6, 16, 26, 30).
  • A131084 (program): A129686 * A007318. Riordan triangle (1+x, x/(1-x)).
  • A131085 (program): Triangle T(n,k) (n>=0, 0<=k<=n-1) read by rows, A007318 * A129686.
  • A131086 (program): Triangle read by rows: T(n,k) = 2*binomial(n,k) - (-1)^(n-k) (0 <= k <= n).
  • A131087 (program): Triangle read by rows: T(n,k) = 2*binomial(n,k) - (1 + (-1)^(n-k))/2 (0 <= k <= n).
  • A131088 (program): 2*A051731 - A054525 as infinite lower triangular matrices.
  • A131089 (program): a(n) = Sum_{d|n} (2 - mu(d)).
  • A131090 (program): First differences of A131666.
  • A131091 (program): Partial sums of A131707.
  • A131092 (program): Coefficient of y^(n-2) in expansion of (y+n!)^n.
  • A131093 (program): a(1)=1, a(n) = a(n-1) + sum of odd numbers which are among the first (n-1) terms of the sequence.
  • A131094 (program): Triangle where n-th row contains the smallest n positive integers (listed in order) with exactly n nonleading 0’s in their binary representations.
  • A131095 (program): Triangle where n-th row contains the smallest n positive integers (listed in order) with exactly n nonleading 0’s in their binary representations and where the smallest term in the n-th row is > that the largest term in the (n-1)th row.
  • A131096 (program): 3-smooth numbers in ternary representation.
  • A131097 (program): Sum of digits of 3-smooth numbers in ternary representation.
  • A131098 (program): Partial sums of A151798.
  • A131099 (program): a(n) = n times number of divisors of n of form 3m+1 - n times number of divisors of form 3m+2.
  • A131101 (program): Numbers that when added it to their prime factors +1 the result is a prime number, member of A131102.
  • A131102 (program): Prime numbers arising from A131101.
  • A131107 (program): Rectangular array read by antidiagonals: k objects are each put into one of n boxes, independently with equal probability. a(n, k) is the expected number of boxes with exactly one object (n, k >= 1). Sequence gives the denominators.
  • A131108 (program): T(n,k) = 2*A007318(n,k) - A097806(n,k).
  • A131110 (program): A000012 * A133084.
  • A131111 (program): T(n, k) = 3*binomial(n,k) - 2*I(n,k), where I is the identity matrix; triangle T read by rows (n >= 0 and 0 <= k <= n).
  • A131112 (program): T(n,k) = 4*binomial(n,k) - 3*I(n,k), where I is the identity matrix; triangle T read by rows (n >= 0 and 0 <= k <= n).
  • A131113 (program): T(n,k) = 5*binomial(n,k) - 4*I(n,k), where I is the identity matrix; triangle T read by rows (n >= 0 and 0 <= k <= n).
  • A131114 (program): T(n,k) = 6*binomial(n,k) - 5*I(n,k), where I is the identity matrix; triangle T read by rows (n >= 0 and 0 <= k <= n).
  • A131115 (program): Triangle read by rows: T(n,k) = 7*binomial(n,k) for 1 <= k <= n with T(n,n) = 1 for n >= 0.
  • A131118 (program): a(4n) = -n^2, a(4n+1) = n^2, a(4n+2) = 1-n^2, a(4n+3) = n*(n+1).
  • A131119 (program): a(n) = (-1)^n * Sum_{i=1..floor(n/2)} i * floor(n/(n-i)).
  • A131120 (program): a(1)=1. a(n+1) = n!/lcm(a(1),a(2),…,a(n)).
  • A131121 (program): a(n) = A131120(n+1)/n.
  • A131124 (program): Expansion of q^(-1) * (phi(-q) / psi(q^4))^2 in powers of q where phi(), psi() are Ramanujan theta functions.
  • A131125 (program): McKay-Thompson series of class 8E for the Monster group with a(0) = 4.
  • A131126 (program): Expansion of (phi(q^2) / phi(-q))^2 in powers of q where phi() is a Ramanujan theta function.
  • A131127 (program): Table read by rows: 2*A007318(n,m) - (-1)^(n+m)*A097806(n,m).
  • A131128 (program): Binomial transform of [1, 1, 5, 1, 5, 1, 5, …].
  • A131129 (program): 3*A007318 - 2*A097806, where A007318 = Pascal’s triangle and A097806 = the pairwise operator.
  • A131130 (program): Binomial transform of [1,1,7,1,7,1,7,1,…].
  • A131131 (program): 4*A007318 - 3*A097806.
  • A131132 (program): a(n) = a(n-1) + a(n-2) + 1 if n is a multiple of 6, otherwise a(n) = a(n-1) + a(n-2).
  • A131133 (program): a(0)=1; for n > 0, a(n) = (1/n + 1/a(n-1))*lcm(n, a(n-1)).
  • A131134 (program): a(1)=1. a(n) = (1/n + 1/a(n-1)) * lcm(n,a(n-1)).
  • A131135 (program): Denominator of (ordinary) expansion of log((x/2-1)/(x-1)).
  • A131136 (program): Denominator of (exponential) expansion of log((x/2-1)/(x-1)).
  • A131137 (program): Denominator of (exponential) expansion of log((2*x/3-1)/(x-1)).
  • A131138 (program): a(n)=log_3(A131137(n)).
  • A131174 (program): a(2n) = 2*A000217(n), a(2n+1) = A000217(n).
  • A131176 (program): a(n) = (n^5-n-10)/10.
  • A131178 (program): Non-plane increasing unary binary (0-1-2) trees where the nodes of outdegree 1 come in 2 colors.
  • A131179 (program): a(n) = if n mod 2 == 0 then n*(n+1)/2, otherwise (n-1)*n/2 + 1.
  • A131181 (program): A 2-way classification of integers: complement of A026416.
  • A131182 (program): Table T(n,k) = n!*k^n, read by upwards antidiagonals.
  • A131185 (program): Period 6: repeat [0, 2, -1, 0, -1, 3].
  • A131186 (program): Period 12: repeat 0, 1, 2, 0, 2, 4, 0, 4, 3, 0, 3, 1.
  • A131187 (program): a(n) = the number of positive integers < n that are neither a divisor of n nor a divisor of (n+1).
  • A131189 (program): Numbers n>=0 such that d(n) = (n^1 + 1) (n^2 + 2) … (n^14 + 14) / 14!, e(n) = (n^1 + 1) (n^2 + 2) … (n^15 + 15) / 15!, and f(n) = (n^1 + 1) (n^2 + 2) … (n^16 + 16) / 16! take nonintegral values.
  • A131191 (program): Numbers n>=0 such that d(n) = (n^1 + 1) (n^2 + 2) … (n^22 + 22) / 22!, e(n) = (n^1 + 1) (n^2 + 2) … (n^23 + 23) / 23!, and f(n) = (n^1 + 1) (n^2 + 2) … (n^24 + 24) / 24! take nonintegral values.
  • A131193 (program): Period 6: repeat [0, 1, -3, 3, -1, 0].
  • A131198 (program): Triangle T(n,k), 0 <= k <= n, read by rows, given by [1,0,1,0,1,0,1,0,…] DELTA [0,1,0,1,0,1,0,1,…] where DELTA is the operator defined in A084938.
  • A131201 (program): Period 24: repeat [0,1,2,5,2,9,0,9,8,5,8,1,0,-1,-2,-5,-2,-9,0,-9,-8,-5,-8,-1].
  • A131203 (program): Number of cycles of length n under the mapping x -> x^2-2 modulo Fermat prime 2^(2^m)+1, where m is any fixed integer such that n divides 2^m-1.
  • A131204 (program): Primes p of the form 16n+1, that is, primes congruent to 1 mod 16.
  • A131205 (program): a(n) = a(n-1) + a(floor(n/2)) + a(ceiling(n/2)).
  • A131209 (program): Maximal distance between two signed permutations of n elements.
  • A131210 (program): Numbers n such that 24n - 1 is prime.
  • A131211 (program): a(n)=(n^5-n-30)/30.
  • A131215 (program): Numbers which are both 11-gonal and centered 11-gonal.
  • A131216 (program): Numbers X such that 99*X^2 - 2178 is a square.
  • A131217 (program): Triangular sequence of a Gray code type made from Pascal’s triangle modulo 2 as b(n,m)=Mod[binomial[n,m],2]:A047999: a(n,m)=Mod[b(n,m)+b(n,m+1),2].
  • A131219 (program): Algorithm for a triangular sequence of the product of a modulo 2 Pascal’s triangle with an Hadamard-Silvester Gray code binary triangular sequence.
  • A131227 (program): 2*A051340 - A128174.
  • A131229 (program): Numbers congruent to {1,7} mod 10.
  • A131230 (program): 2*A130296 - A128174.
  • A131231 (program): 3*A130296 - 2*A128174.
  • A131233 (program): a(n) = number of positive integers <= n which don’t have 2 or more distinct prime divisors in common with n.
  • A131234 (program): Starts with 1, then n appears Fibonacci(n-1) times.
  • A131238 (program): Triangle read by rows: T(n,k) = 2*binomial(n,k) - binomial(floor((n+k)/2), k) (0 <= k <= n).
  • A131239 (program): Triangle, T(n,k) = 3*A007318(n,k) - 2*A046854(n,k), read by rows.
  • A131240 (program): T(n,k) = 2*A046854(n,k) - I.
  • A131241 (program): 3*A046854 - 2*I.
  • A131242 (program): Partial sums of A059995: a(n) = sum_{k=0..n} floor(k/10).
  • A131244 (program): Row sums of triangle A131243.
  • A131246 (program): Row sums of triangle A131245.
  • A131247 (program): 2*A052509 - A000012.
  • A131248 (program): 2*A004070 - A000012.
  • A131250 (program): A007318 * A004070.
  • A131251 (program): A000012 * A052509.
  • A131253 (program): Row sums of triangle A131252.
  • A131254 (program): A004070 * A000012.
  • A131255 (program): A004070 * A000012(signed).
  • A131259 (program): a(2n)=A000217(n), a(2n+1)=-2*A000217(n).
  • A131268 (program): Triangle read by rows: T(n,k) = 2*binomial(n-floor((k+1)/2),floor(k/2)) - 1, 0<=k<=n.
  • A131269 (program): a(n) = 3*a(n-1) - 2*a(n-2) - a(n-3) + a(n-4) with n>3, a(0)=1, a(1)=2, a(2)=3, a(3)=6.
  • A131270 (program): Triangle T(n,k) = 2*A046854(n,k) - 1, read by rows.
  • A131271 (program): Ranks in natural order of 2^n increasing real numbers appearing in limit cycles of interval iterations, or Median Spiral Order.
  • A131281 (program): E.g.f.: 2*(x-1)*tan(x/2+Pi/4)-x^2+2.
  • A131282 (program): Period 6: repeat [1, 2, 3, 3, 4, 5].
  • A131289 (program): Period 12: repeat 1, 1, 3, -3, -3, 1, -1, -1, -3, 3, 3, -1.
  • A131290 (program): 1 followed by period 6: repeat [3, 2, 0, -1, 0, 2].
  • A131291 (program): Period 9: repeat [5, 4, 5, 3, 4, 3, 5, 4, 5].
  • A131292 (program): a(2n+1)=3a(2n)-3a(2n-1)+2a(2n-2), a(2n+2)=3a(2n+1)-3a(2n), a(0)=a(1)=a(2)=1.
  • A131293 (program): Concatenate a(n-2) and a(n-1) to get a(n); start with a(0)=0, a(1)=1, delete the leading zero. Also: concatenate Fibonacci(n) 1’s.
  • A131294 (program): a(n)=ds_3(a(n-1))+ds_3(a(n-2)), a(0)=0, a(1)=1; where ds_3=digital sum base 3.
  • A131295 (program): a(n)=ds_4(a(n-1))+ds_4(a(n-2)), a(0)=0, a(1)=1; where ds_4=digital sum base 4.
  • A131296 (program): a(n) = ds_5(a(n-1))+ds_5(a(n-2)), a(0)=0, a(1)=1; where ds_5=digital sum base 5.
  • A131297 (program): a(n) = ds_11(a(n-1))+ds_11(a(n-2)), a(0)=0, a(1)=1; where ds_11=digital sum base 11.
  • A131298 (program): A difference of Fibonacci and Padovan numbers.
  • A131299 (program): Triangle T(n,k) = 3*binomial(n-floor((k+1)/2), floor(k/2))-2 with k=0..n, read by rows.
  • A131300 (program): a(n) = 3*a(n-1) - 2*a(n-2) - a(n-3) + a(n-4) with n>3, a(0)=1, a(1)=2, a(2)=3, a(3)=7.
  • A131301 (program): Regular triangle read by rows: T(n,k) = 3*binomial(floor((n+k)/2),k)-2.
  • A131307 (program): (A127701 * A000012 + A000012(signed) * A127701) - A000012.
  • A131308 (program): Alternate A001477 and tripled 2*A000027.
  • A131309 (program): Rabbit-like sequence for phi^2.
  • A131322 (program): Row sums of triangle A131321.
  • A131323 (program): Odd numbers whose binary expansion ends in an even number of 1’s.
  • A131324 (program): 2*A049310 - A000012(signed).
  • A131325 (program): Triangle |3*|A049310(n,k)| - 2| read by rows, 0 <= k <= n.
  • A131326 (program): Row sums of A131325.
  • A131327 (program): Triangle |4*|A049310(n,k)| - 3| read by rows, 0<=k<=n.
  • A131328 (program): Row sums of triangle A131327.
  • A131333 (program): A131332 * A000012.
  • A131334 (program): A000012(signed) * A065941.
  • A131335 (program): A000012 * A131334.
  • A131337 (program): Row sums of triangle A131336.
  • A131350 (program): 2*A007318 - A049310 as infinite lower triangular matrices.
  • A131352 (program): Row sums of triangle A133935.
  • A131355 (program): Partial sums of A065423 plus one.
  • A131356 (program): Numbers k such that p1=10k+9 and p2=p1+2 are twin primes (and p1^2 == p2^2 == 1 (mod 10)).
  • A131358 (program): a(3*k) = 0, a(3*k+1) = k+1, a(3*k+2) = -k.
  • A131360 (program): a(4n) = a(4n+1) = 0, a(4n+2) = 2n, a(4n+3) = 2n+1.
  • A131369 (program): Period 10: repeat [5, 4, 5, 4, 3, 4, 5, 4, 5, 0].
  • A131370 (program): a(n) = 3a(n-1) - 3a(n-2) + 2a(n-3), a(0) = 3, a(1) = 2, a(2) = 0.
  • A131372 (program): Period 7: repeat [1, -1, 0, 1, 0, -1, 1].
  • A131375 (program): A007318 + A046854 - A049310.
  • A131377 (program): Starting with 1, the sequence a(n) changes from 1 to 0 or back when the next number n is a prime.
  • A131378 (program): Starting with 0, the sequence a(n) changes from 0 to 1 or back when the next number n is a prime.
  • A131379 (program): Period 4: repeat [1, 0, -1, 1].
  • A131380 (program): a(3n) = 2n, a(3n+1) = 2n+2, a(3n+2) = 2n+1.
  • A131381 (program): a(n) = binomial(2*n,n) mod (n+2), with n>=1.
  • A131383 (program): Total digital sum of n: sum of the digital sums of n for all the bases 1 to n (a ‘digital sumorial’).
  • A131385 (program): Product ceiling(n/1)*ceiling(n/2)*ceiling(n/3)*…*ceiling(n/n) (the ‘ceiling factorial’).
  • A131386 (program): a(n) = (-1)^n*n*(n-2).
  • A131398 (program): 3*A007318 - A097806 - A000012.
  • A131403 (program): Row sums of triangle A131402.
  • A131405 (program): Row sums of triangle A131404.
  • A131406 (program): 3*A128174 - 2*A000012(signed).
  • A131410 (program): A127647 * A000012.
  • A131411 (program): Triangle read by rows: T(n,k) = Fibonacci(n) + Fibonacci(k) - 1.
  • A131412 (program): a(n) = n*(Fibonacci(n) - 1) + Fibonacci(n + 2) - 1.
  • A131414 (program): A130302 + A130303 - A000012.
  • A131415 (program): (A007318 * A000012) + (A000012 * A007318) - A007318.
  • A131416 (program): (A000012 * A002260) + (A002260 * A000012) - A000012.
  • A131421 (program): Triangle read by rows (n>=1, 1<=k<=n): T(n,k) = 2*(n+k) - 3.
  • A131422 (program): (A000012 * A127773) + (A127773 * A000012) - A000012.
  • A131423 (program): a(n) = n*(n+2)*(2*n-1)/3. Also, row sums of triangle A131422.
  • A131424 (program): Triangle read by rows: T(n,k) = prime(n) + prime(k) - 3, 1 <= k <= n.
  • A131425 (program): Row sums of triangle A131424.
  • A131426 (program): a(n) = 2*prime(n) - 3.
  • A131427 (program): A000108(n) preceded by n zeros.
  • A131428 (program): a(n) = 2*C(n) - 1, where C(n) = A000108(n) are the Catalan numbers.
  • A131429 (program): Triangle read by rows: T(n,k) = C(n) + C(k) - 1 where C(n) = A000108(n) are the Catalan numbers, 0 <= k <= n.
  • A131430 (program): Row sums of triangle A131429.
  • A131431 (program): 3n + 1 preceded by n zeros.
  • A131433 (program): Number of prime knots on n crossings having Arf invariant 0.
  • A131434 (program): Number of prime knots on n crossings having Arf invariant 1.
  • A131435 (program): Recursive sequence generated from a Petersen graph.
  • A131436 (program): Triangle read by rows, (n-1) zeros followed by 2^n - 1.
  • A131437 (program): (A000012 * A131436) + (A131436 * A000012) - A000012.
  • A131438 (program): (2+n)*2^n-2-3*n.
  • A131439 (program): Inverse binomial transform of A131438 (assuming zero offset in both sequences)
  • A131441 (program): Row sums of triangle A130757 (coefficients of scaled Laguerre-Sonin polynomials n!(2^(n-m))*L(n,1/2,x)).
  • A131451 (program): Product of the nonzero digital products of all the numbers 1 to n (a ‘total digital-product factorial’ in base 10).
  • A131452 (program): a(3n)=4n, a(3n+1)=4n+2, a(3n+2)=4n+1.
  • A131464 (program): a(n) = 4*n^3 - 3*n^2 + 2*n - 1.
  • A131465 (program): a(n)=4n^4-3n^3+2n^2-n+1.
  • A131466 (program): a(n) = 5n^4 - 4n^3 + 3n^2 - 2n + 1.
  • A131470 (program): a(n)=smallest number that gives a product with the sum of digits of n written in base 2 greater than n.
  • A131471 (program): a(n)=n^5+n.
  • A131472 (program): a(n) = n^6 + n.
  • A131473 (program): a(n) = n^6 - n.
  • A131474 (program): a(n) = ceiling(n/2)*ceiling(n^2/2).
  • A131475 (program): a(n) = floor(n/2) * floor(n^2/2).
  • A131476 (program): a(n) = floor(n^3/3).
  • A131477 (program): a(n) = ceiling(n^3/3).
  • A131478 (program): a(n) = ceiling(n^4/4).
  • A131479 (program): a(n) = floor(n^4/4).
  • A131491 (program): 2*prime(n)!.
  • A131499 (program): Primes p such that nextprime(p)=p+4 and previousprime(p)<p-4.
  • A131500 (program): Radii of orbits of planets in solar system, in units of radius of orbit of Mercury, multiplied by 4.
  • A131501 (program): Xm/CV where Xm is a point of maximum error using an approximation method for x^(1/2) which I have found and CV is the population coefficient of variation from my list of error values.
  • A131503 (program): Nonnegative integers n for which cos(n) is positive.
  • A131505 (program): n, -1, n, 2n+2.
  • A131506 (program): 2n+1 appears 2n-1 times.
  • A131507 (program): 2n+1 appears n+1 times.
  • A131508 (program): 2*A000027 (natural numbers) sandwiched by tripled A001477 (nonnegative numbers).
  • A131509 (program): a(n) = (n + 1)*(n^2 + 2)*(n^3 + 3)/6.
  • A131515 (program): a(n+2) = 34*a(n+1) - a(n) + 2; a(1) = 1 and a(2) = 16.
  • A131516 (program): a(n)=1 if n is an odd prime number, otherwise, a(n)=n.
  • A131520 (program): Number of partitions of the graph G_n (defined below) into “strokes”.
  • A131521 (program): Expansion of 9/(4 + 5*sqrt(1-36*x)).
  • A131522 (program): Triangular sequence from coefficients of polynomials of a type gives by a geometric average of two consecutive dihedral group elliptical invariants: p(x,n)=(x^n - 1)*(x^(n + 1) - 1): associate with B_n as odd SO(2*n+1) group.
  • A131524 (program): Number of possible palindromic rows (or columns) in an n X n crossword puzzle.
  • A131530 (program): Numbers k such that k^2 - k - 1 and k^2 - k + 1 are twin primes.
  • A131531 (program): Period 6: repeat [0, 0, 1, 0, 0, -1].
  • A131532 (program): Period 6: repeat [0, 0, 0, 0, 1, 1].
  • A131533 (program): Period 6: repeat [0, 0, 0, 0, 1, -1].
  • A131534 (program): Period 3: repeat [1, 2, 1].
  • A131553 (program): a(n) = Product_{k=1..n, gcd(k,n)=1} (1+k).
  • A131554 (program): Period 5: repeat [1, 1, -1, 1, -1].
  • A131555 (program): Period 6: repeat [0, 0, 1, 1, 2, 2].
  • A131556 (program): Period 6: repeat [1, -2, 1, -1, 2, -1].
  • A131557 (program): Triangular numbers that are the sums of five consecutive triangular numbers.
  • A131561 (program): Period 3: repeat [1, 1, -1].
  • A131562 (program): a(n)= -3a(n-1) -3a(n-2)-2a(n-3), a(0)=1, a(1)=-2, a(2)=2.
  • A131568 (program): a(n) = sum of numbers which in base 2 contain exactly n digits 1 and not more than n digits 0.
  • A131569 (program): a(n) = (1/2)*(F(n+2)-1)*(F(n+2)-2) + F(n), where F() are the Fibonacci numbers.
  • A131572 (program): a(0)=0 and a(1)=1, continued such that absolute values of 2nd differences equal the original sequence.
  • A131575 (program): First differences of A131572.
  • A131576 (program): Number of ways to represent n as a sum of an even number of consecutive integers.
  • A131577 (program): Zero followed by powers of 2 (cf. A000079).
  • A131579 (program): Period 10: repeat 0, 3, 6, 9, 2, 5, 8, 1, 4, 7.
  • A131581 (program): The next prime greater than the square root of 10^n.
  • A131588 (program): Interlaces A007583 with A083420.
  • A131589 (program): Expansion of -(3+9*x+2*x^2)/((x+1)*(x^2+3*x+1)).
  • A131594 (program): Decimal expansion of sqrt(2)/3, the volume of a regular octahedron with edge length 1.
  • A131595 (program): Decimal expansion of 3*(sqrt(25 + 10*sqrt(5))), the surface area of a regular dodecahedron with edges of unit length.
  • A131597 (program): Bigomega of Pisano periods mod n, i.e., number of prime divisors with multiplicity of the period length of Fibonacci residues mod n.
  • A131598 (program): Period 3: repeat [2, 5, 8].
  • A131600 (program): Number of different configurations of an n-block of a shift space with k symbols where each symbol but the first must appear isolated and separated from others by a block of length at least m made of first symbols. Here k=19 and m=2.
  • A131601 (program): The number of different configurations of an n-block of a shift space with k symbols where each symbol but the first must appear isolated and separated from others by an block of length at least m made of first symbol. Here k=49 and m=2.
  • A131606 (program): Triangle read by rows: row n gives coefficients of the polynomial p(x, n) = Sum[Fibonacci[n]^i*x^(n - i), {i, 0, n}].
  • A131607 (program): Pell companion numbers A001333 without last digit.
  • A131609 (program): Mirror image of triangle in A131606.
  • A131612 (program): (Fibonacci(n)^(n+1)-1)/(Fibonacci(n)-1).
  • A131614 (program): Numbers k such that the decimal expansion of 3^k contains no 8.
  • A131615 (program): Numbers k such that the decimal expansion of 3^k contains no 7.
  • A131616 (program): Numbers k such that the decimal expansion of 3^k contains no 6.
  • A131617 (program): Numbers k such that the decimal expansion of 3^k contains no 5.
  • A131618 (program): Numbers k such that the decimal expansion of 3^k contains no 4.
  • A131625 (program): Numbers k such that decimal expansion of 3^k contains no 2.
  • A131629 (program): Numbers k such that the decimal expansion of 3^k contains no 3.
  • A131631 (program): Supersubfactorials: partial product of positive subfactorials (A000166).
  • A131634 (program): n-th even semiprime minus n-th odd semiprime.
  • A131635 (program): Triangle T(n,m)=m*n*binomial(m+n,m)^2/(2*(m+n)) read by rows.
  • A131640 (program): First differences are periodic: 50, 50, 75, 50, 50, 75, …
  • A131644 (program): a(n) = 2^(a(n-1)) mod n.
  • A131649 (program): Number of distinct improper 2-coloring of edges for odd-order cyclic graphs.
  • A131651 (program): Positive integers obtained as the difference of two triangular numbers in exactly 4 ways.
  • A131654 (program): Difference mod 10 of successive digits of Pi.
  • A131658 (program): For n >= 1, put A_n(z) = Sum_{j>=0} (n*j)!/(j!^n) * z^j and B_n(z) = Sum_{j>=0} (n*j)!/(j!^n) * z^j * (Sum__{k=j+1..j*n} (1/k)), and let u(n) be the largest integer for which exp(B_n(z)/(u(n)*A_n(z))) has integral coefficients. The sequence is u(n).
  • A131664 (program): A string of n 1’s repeated n times.
  • A131665 (program): Sequence is identical to its third differences in absolute value: a(0), a(1), a(2), a(2n+1)=3a(2n)-3a(2n-1)+2a(2n-2), a(2n+2)=3a(2n+1)-3a(2n), with a(0)=a(1)=0, a(2)=1.
  • A131666 (program): First differences of (A113405 prefixed with a 0).
  • A131667 (program): List of triples 2n, 1-2n, 0, n >= 1.
  • A131668 (program): Smallest number whose sum of digits is 2n+1.
  • A131669 (program): Odd digits followed by positive even digits.
  • A131670 (program): Period 5: repeat [1, 0, -1, 0, 1].
  • A131673 (program): Size of the largest BDD of symmetric Boolean functions of n variables when the sink nodes are counted.
  • A131674 (program): Size of the largest BDD of symmetric Boolean functions of n variables when the sink nodes are not counted.
  • A131675 (program): a(n) = (Product_{i=1..5} n^i+i)/5!.
  • A131676 (program): a(n) = (Product_{i=1..6} n^i+i) / 6!.
  • A131677 (program): a(n) = (Product_{i=1..7} n^i+i) / 7!.
  • A131678 (program): a(n) = (Product_{i=1..8} n^i+i) / 8!.
  • A131679 (program): a(n) = (Product_{i=1..9} n^i+i) / 9!.
  • A131680 (program): a(n) = (Product_{i=1..10} n^i+i)/10!.
  • A131682 (program): a(n) = (n^1 + 1!)*(n^2 + 2!)*(n^3 + 3!)/3!.
  • A131686 (program): Sum of squares of five consecutive primes.
  • A131689 (program): Triangle of numbers T(n,k) = k!*Stirling2(n,k) = A000142(k)*A048993(n,k) read by rows, T(n, k) for 0 <= k <= n.
  • A131695 (program): a(n) = 0 iff 2*prime(n+1) = prime(n) + prime(n+2), otherwise a(n) = 1.
  • A131698 (program): Cumulative concatenation of A000032 Lucas numbers (beginning at 2).
  • A131706 (program): Squares of the form 4*A014574(n-1) + 1.
  • A131707 (program): Period 12: repeat 1, 1, 3, 7, 7, 1, 9, 9, 7, 3, 3, 9 .
  • A131708 (program): A024494 prefixed by a 0.
  • A131709 (program): Number of partitions into “bus routes” of an n X 1 grid.
  • A131710 (program): Overlay of Pell numbers: a(n)=A000129(n)+A000129(n-6).
  • A131711 (program): Period 12: repeat 0, 1, 2, 5, 2, 9, 0, 9, 8, 5, 8, 1.
  • A131712 (program): Period 4: repeat [1, 3, 7, 9].
  • A131713 (program): Period 3: repeat [1, -2, 1].
  • A131714 (program): Period 6: repeat [1, -2, 2, -1, 2, -2].
  • A131715 (program): Period 12: repeat 0,2,4,0,-6,8,0,-2,-4,0,6,-8.
  • A131716 (program): Period 6: repeat [0, 1, 2, 5, 8, 9].
  • A131717 (program): Natural numbers A000027 with 6n+4 and 6n+5 terms swapped.
  • A131718 (program): Period 6: repeat [1, 1, 2, 1, 2, 1].
  • A131719 (program): Period 6: repeat [0, 1, 1, 1, 1, 0].
  • A131720 (program): Period 6: repeat [0, 1, -1, 1, -1, 0].
  • A131721 (program): Overlay of Pell companion numbers: a(n)=A001333(n)+A001333(n-6).
  • A131722 (program): Period 6: repeat [0, 10, 10, 10, 10, 10].
  • A131723 (program): a(2*n) = 1-n^2, a(2*n+1) = n*(n+1).
  • A131724 (program): Period 6: repeat [1, 9, 7, 13, 11, 9].
  • A131725 (program): Partial sums of A131711.
  • A131726 (program): Pell numbers A000129 with 0 instead of last digit.
  • A131727 (program): Pell numbers A000129 without last digit.
  • A131728 (program): a(4n) = n, a(4n+1) = 2n+1, a(4n+2) = n+1, a(4n+3) = 0.
  • A131729 (program): Period 4: repeat [0, 1, -1, 1].
  • A131730 (program): a(4n) = n, a(4n+1) = -n-1, a(4n+2) = n+1, a(4n+3) = -n.
  • A131731 (program): Period 4: repeat [2, -3, 4, -3].
  • A131732 (program): a(4*k) = 2*k+1, a(4*k+1) = -4*k-3, a(4*k+2) = 2*k+2, a(4*k+3) = 0.
  • A131733 (program): Primes (A000040) - odds (A005408).
  • A131734 (program): Hexaperiodic [0, 1, 0, 1, 0, -1].
  • A131735 (program): Period 6: repeat [0, 0, 1, 1, 1, 1].
  • A131736 (program): Period 6: repeat [0, 0, 1, -1, -1, 1].
  • A131737 (program): Essentially even numbers followed by duplicated odd numbers.
  • A131738 (program): a(0) = 0. a(n) = (n+1)*(-1)^n, n>0 .
  • A131739 (program): a(4n) = a(4n+1) = n, a(4n+2) = 3n+2, a(4n+3) = 3n+3.
  • A131740 (program): a(n) = sum of n successive primes after the n-th prime.
  • A131742 (program): a(4n) = a(4n+1) = 0, a(4n+2) = 3n+1, a(4n+3) = 3n+2.
  • A131743 (program): Period 4: repeat [0, 1, 0, 2].
  • A131750 (program): Numbers that are both centered triangular and centered square.
  • A131751 (program): Numbers that are both centered triangular and centered pentagonal.
  • A131755 (program): a(n) = floor of the average of distances between consecutive positive divisors of n. Also, a(n) = floor((n-1)/(d(n)-1)), where d(n) = A000005(n).
  • A131756 (program): Period 3: repeat [2, -1, 3].
  • A131757 (program): Period 10: repeat 3, 3, 3, -7, 3, 3, -7, 3, 3, -7.
  • A131762 (program): Number of 1s in the 1’s complement of the 32-bit binary representation of n.
  • A131763 (program): Series reversion of x*(1-4x)/(1-x) is x*A(x) where A(x) is the generating function.
  • A131764 (program): Inverse Euler transform of central binomial coefficients A000984.
  • A131765 (program): Series reversion of x*(1-5x)/(1-x) .
  • A131767 (program): 2*A007318 - A065941.
  • A131768 (program): 2*(A007318 * A097807) - A000012.
  • A131769 (program): Number of connected components in the double Bruhat cells for simple Lie groups of type B_n (or C_n).
  • A131779 (program): Triangle read by rows: T(n,k) = 2*A065941(n-1,k-1) - (-1)^(n+k).
  • A131780 (program): Row sums of triangle A131779.
  • A131781 (program): 2*A046854 - A000012 (signed by columns + - + -, …).
  • A131783 (program): A000012 * (A004736 + A002260 - I).
  • A131789 (program): The length of the n-th run of identical consecutive values in the sequence A000005, where A000005(k) is the number of divisors of k.
  • A131793 (program): 3 odds, 3 evens.
  • A131798 (program): a(n) = the maximum value from among (d(n+1),d(n+2),d(n+3),…,d(2n)), where d(m) is the number of positive divisors of m.
  • A131800 (program): Period 4: repeat [1, 2, 5, 6].
  • A131804 (program): Antidiagonal sums of triangular array T: T(j,k) = -(k+1)/2 for odd k, T(j,k) = 0 for k = 0, T(j,k) = j+1-k/2 for even k > 0; 0 <= k <= j.
  • A131805 (program): Row sums of triangular array T: T(j,k) = -(k+1)/2 for odd k, T(j,k) = 0 for k = 0, T(j,k) = j+1-k/2 for even k > 0; 0 <= k <= j.
  • A131806 (program): Period 4: repeat [0, 2, 4, 6].
  • A131807 (program): Partial sums of A131377.
  • A131808 (program): Partial sums of A131378.
  • A131810 (program): Additive persistence of Catalan numbers.
  • A131815 (program): The 2n-th derivative of exp(1 - 1/(1 - x^2)) evaluated at 0.
  • A131816 (program): Triangle read by rows: A130321 + A059268 - A000012 as infinite lower triangular matrices, where A130321 = (1; 2,1; 4,2,1; …), A059268 = (1; 1,2; 1,2,4; …) and A000012 = (1; 1,1; 1,1,1; …).
  • A131817 (program): a(n) = A051340(n) + A130321(n) - A000012(n).
  • A131818 (program): A130296 + A002260 - A000012. Triangle read by rows: row n consists of n, 2, 3, 4, …, n.
  • A131819 (program): A131818 * A000012 as infinite lower triangular matrices. Triangle read by rows, partial sums starting from the right of A131818.
  • A131820 (program): Row sums of triangle A131819.
  • A131821 (program): Triangle read by rows: row n consists of n followed by (n-2) ones then n.
  • A131822 (program): Increment each prime factor for each term of the least prime signature sequence derived from A080577.
  • A131830 (program): Triangle read by rows: T(n,0) = T(n,n) = n + 1 for n >= 0, and T(n,k) = binomial(n,k) for 1 <= k <= n - 1, n >= 2.
  • A131832 (program): 2*(A131830) - A000012.
  • A131833 (program): a(n) = 2^(n+1) - 1 + 3*n.
  • A131835 (program): Numbers starting with 1.
  • A131843 (program): Triangle read by rows: 2*A131821 - A000012.
  • A131844 (program): 3*A131821 - 2*A000012.
  • A131846 (program): Expansion of series reversion of x*(1-6*x)/(1-x).
  • A131848 (program): Least nonnegative number which when added to the n-th semiprime gives a multiple of n.
  • A131849 (program): Cardinality of largest subset of {1,…,n} such that the difference between any two elements of the subset is never one less than a prime.
  • A131851 (program): Real part of the function z(n)=Sum(d(k)*i^k: d as in n=Sum(d(k)*2^k), i=sqrt(-1)).
  • A131852 (program): Imaginary part of the function z defined in A131851.
  • A131853 (program): Numbers m such that z(m)=(0,0) with z as defined in A131851.
  • A131854 (program): Numbers m such that A131851(m) = 0.
  • A131855 (program): Numbers m such that A131852(m) = 0.
  • A131856 (program): Numbers m such that z(m)=(0,1) with z as defined in A131851.
  • A131857 (program): Numbers m such that A131852(m) = 1.
  • A131858 (program): Numbers m such that z(m)=(1,0) with z as defined in A131851.
  • A131859 (program): Numbers m such that A131851(m) = 1.
  • A131860 (program): Numbers m such that z(m)=(1,1) with z as defined in A131851.
  • A131861 (program): Numbers m such that A131851(m) > 0.
  • A131862 (program): Numbers m such that A131852(m) > 0.
  • A131863 (program): Numbers m such that A131851(m) < 0.
  • A131864 (program): Numbers m such that A131852(m) < 0.
  • A131865 (program): Partial sums of powers of 16.
  • A131866 (program): Distance of n-th semiprime to nearest square.
  • A131869 (program): Expansion of series reversion of x*(1-8*x)/(1-x).
  • A131870 (program): Period 8: repeat [1, 2, 3, 4, 6, 7, 8, 9].
  • A131873 (program): Triangle, A131844 * A000012 as infinite lower triangular matrices.
  • A131874 (program): a(n) = (7*n^2 + 15*n + 2) / 2.
  • A131875 (program): Triangle, A000012 * A131844 as infinite lower triangular matrices.
  • A131876 (program): 2*A131873 - A000012.
  • A131877 (program): a(n) = 14*n + 1.
  • A131880 (program): a(n) = the n-th positive integer which is coprime to (2^n -1). a(n) = the n-th term of row n in triangle A131879.
  • A131885 (program): a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) for n >= 4 starting with a(0) = 1, a(1) = 2, a(2) = 4, and a(3) = 6.
  • A131887 (program): Number of Khalimsky-continuous functions with a three-point codomain.
  • A131889 (program): a(n) is the number of shapes of balanced trees with constant branching factor 3 and n nodes. The node is balanced if the size, measured in nodes, of each pair of its children differ by at most one node.
  • A131894 (program): A131843 * A000012.
  • A131895 (program): a(n) = (n + 2)*(5*n + 1)/2.
  • A131896 (program): A000012 * A131843.
  • A131897 (program): A130321 + A131821 - A000012.
  • A131898 (program): a(n) = 2^(n+1) + 2*n - 1.
  • A131899 (program): A002260 + A131821 - A000012.
  • A131900 (program): A131821 + A128174 - A000012.
  • A131901 (program): 2*A002024 - A131821.
  • A131911 (program): 2*A131821 - A128174.
  • A131912 (program): Row sums of triangle A131911.
  • A131913 (program): Product of the square matrix in A065941 and the column vector (1, 2, 3, …)’.
  • A131914 (program): 3*A002024 - 2*A051340.
  • A131919 (program): A002024 + A131821 - A000012.
  • A131920 (program): Decimal expansion of 2/log(2).
  • A131922 (program): 2*A002024 - A130296.
  • A131923 (program): Triangle read by rows: T(n,k) = binomial(n,k) + n.
  • A131924 (program): Row sums of triangle A131923.
  • A131925 (program): 2*A002024 - A000012(signed).
  • A131926 (program): Expansion of series reversion of x(1-7x)/(1-x).
  • A131927 (program): Expansion of series reversion of x * (1 - 9*x) / (1 - x).
  • A131933 (program): a(n) = A056866(n)/4.
  • A131935 (program): a(n) is the number of Khalimsky-continuous functions with four-point codomain and an n-point range.
  • A131937 (program): a(1)=1; a(2)=4. a(n) = a(n-1) + (n-th positive integer which does not occur in sequence A131938).
  • A131938 (program): a(1)=2; a(2)=5. a(n) = a(n-1) + (n-th positive integer which does not occur in sequence A131937).
  • A131940 (program): Least common multiple of {1, 7, 13, 19, 25, …, (6n+1)} (A016921).
  • A131941 (program): Partial sums of ceiling(n^2/2) (A000982).
  • A131943 (program): Expansion of b(q) * b(q^2) in powers of q where b() is a cubic AGM theta function.
  • A131944 (program): Expansion of (1 - b(q)*b(q^2)) / 3 where b() is a cubic AGM function. Expansion of (1 - eta(q)^3 * eta(q^2)^3 / (eta(q^3) * eta(q^6))) / 3 in powers of q.
  • A131946 (program): Expansion of (phi(-q) * phi(-q^3))^2 in powers of q where phi() is a Ramanujan theta function.
  • A131947 (program): Expansion of (1 - (phi(-q) * phi(-q^3))^2)/4 in powers of q where phi() is a Ramanujan theta function.
  • A131948 (program): Triangle T(n,k) = 2*A002024(n+1,k+1) + A007318(n,k) - 2, read by rows.
  • A131949 (program): Row sums of triangle A131948.
  • A131950 (program): A002024 + A131821 + A007318 - 2*A000012 as infinite lower triangular matrices.
  • A131951 (program): a(n) = 2^n + n*(n+3).
  • A131953 (program): A130321 + A059268 - A000012(signed).
  • A131961 (program): Expansion of f(x, x^2) * f(x^2, x^2) in powers of x where f(, ) is Ramanujan’s general theta function.
  • A131962 (program): Expansion of psi(x) * phi(-x^12) / chi(-x^4) in powers of x where phi(), psi(), chi() are Ramanujan theta functions.
  • A131963 (program): Expansion of f(x, x^2) * f(x^4, x^12) in powers of x where f(, ) is Ramanujan’s general theta function.
  • A131964 (program): Expansion of f(x^2, x^10) / f(x, x^3) in powers of x where f(, ) is Ramanujan’s general theta function.
  • A131965 (program): a(n) = 1 + Sum_{i=2..n-1} n*a(i).
  • A131969 (program): First differences of A020806.
  • A131970 (program): 1 followed by 2n 2’s.
  • A131971 (program): a(0) = a(1) = a(2) = 1; a(n) = (a(n-1) + a(n-2) + a(n-3)) mod n.
  • A131973 (program): Period 8: repeat 121, 242, 363, 484, 605, 726, 847, 968.
  • A131974 (program): Period 8: repeat [1, 2, 3, 4, -5, -4, -3, -2].
  • A131977 (program): Analog of A131976 for the icosahedron.
  • A131980 (program): A coefficient tree from the list partition transform relating A000129, A000142, A000165, A110327, and A110330.
  • A131986 (program): Expansion of (eta(q) / eta(q^9))^3 in powers of q.
  • A131987 (program): Representation of a dense para-sequence.
  • A131989 (program): Start with the symbol **|* and for each iteration replace * with **|*. This sequence is the number of *’s between each dash.
  • A131991 (program): a(n) = 1 + prime(n) + prime(n)^2 + prime(n)^3.
  • A131992 (program): a(n) = 1 + prime(n) + prime(n)^2 + prime(n)^3 + prime(n)^4.
  • A131993 (program): 1 + prime(n) + prime(n)^2 + prime(n)^3 + prime(n)^4 + prime(n)^5.
  • A131996 (program): Number of partitions of n into distinct powers of 2 or of 3.
  • A131999 (program): Expansion of eta(q)^2 * eta(q^2) * eta(q^4)^3 / eta(q^8)^2 in powers of q.
  • A132000 (program): Expansion of (1/3) * b(q) * b(q^2) * c(q)^2 / c(q^2) in powers of q where b(), c() are cubic AGM functions.
  • A132001 (program): Expansion of 1 - (1/3) * b(q) * b(q^2) * c(q)^2 / c(q^2) in powers of q where b(), c() are cubic AGM functions.
  • A132002 (program): Expansion of phi(q^3) / phi(q) in powers of q where phi() is a Ramanujan theta function.
  • A132003 (program): Expansion of (phi(q^3) / phi(q)) * phi(-q^2) * phi(-q^6) in powers of q where phi() is a Ramanujan theta function.
  • A132004 (program): Expansion of (1 - phi(q^3) / phi(q) * phi(-q^2) * phi(-q^6)) / 2 in powers of q where phi() is a Ramanujan theta function.
  • A132009 (program): a(1) = 1; for n>=2, a(n) = n-th positive integer which is coprime to the largest prime divisor of n.
  • A132013 (program): T(n,j) for an iterated mixed order Laguerre transform. Coefficients of the normalized generalized Laguerre polynomials (-1)^n*n!*L(n,1-n,x).
  • A132014 (program): T(n,j) for double application of an iterated mixed order Laguerre transform: Coefficients of Laguerre polynomial (-1)^n*n!*L(n,2-n,x).
  • A132027 (program): a(n) = Product_{k=0..floor(log_3(n))} floor(n/3^k), n>=1.
  • A132028 (program): Product{0<=k<=floor(log_4(n)), floor(n/4^k)}, n>=1.
  • A132029 (program): Product{0<=k<=floor(log_5(n)), floor(n/5^k)}, n>=1.
  • A132030 (program): a(n) = Product_{k=0..floor(log_6(n))} floor(n/6^k), n>=1.
  • A132031 (program): Product{0<=k<=floor(log_7(n)), floor(n/7^k)}, n>=1.
  • A132032 (program): Product{0<=k<=floor(log_8(n)), floor(n/8^k)}, n>=1.
  • A132033 (program): Product{0<=k<=floor(log_9(n)), floor(n/9^k)}, n>=1.
  • A132044 (program): Triangle T(n,k) = binomial(n, k) - 1 with T(n,0) = T(n,n) = 1, read by rows.
  • A132045 (program): Row sums of triangle A132044.
  • A132046 (program): Triangle read by rows: T(n,0) = T(n,n) = 1, and T(n,k) = 2*binomial(n,k) for 1 <= k <= n - 1.
  • A132047 (program): 3*A007318 - 2*A103451 as infinite lower triangular matrices.
  • A132048 (program): 3*A007318 - A103451 - A000012.
  • A132050 (program): Denominator of 2*n*A000111(n-1)/A000111(n): approximations of Pi using Euler (up/down) numbers.
  • A132058 (program): Row sums of triangle A132057 (s2(8)).
  • A132059 (program): Alternating row sums of triangle A132057 (s2(8)).
  • A132062 (program): Sheffer triangle (1,1-sqrt(1-2*x)). Extended Bessel triangle A001497.
  • A132064 (program): Numbers multiplied by 4 and written backwards.
  • A132066 (program): Irregular array: the sum of the first m terms of row n is the m-th positive divisor of n.
  • A132068 (program): Irregular array: row n has A000010(n) terms: the sum of the first m terms of row n is the m-th positive integer which is coprime to n.
  • A132071 (program): A007318 + A002024 - A103451 as infinite lower triangular matrices.
  • A132072 (program): Row sums of triangle A132071.
  • A132073 (program): A007318 + A131821 - A103451 as infinite lower triangular matrices.
  • A132074 (program): Row sums of triangle A132073.
  • A132076 (program): a(1)=1, a(2)=2. a(n), for every positive integer n, is such that Product_{k=1..n} (Sum_{j=1..k} a(j)) = Sum_{k=1..n} Product_{j=1..k} a(j).
  • A132078 (program): Multiply previous term by 6 and reverse.
  • A132079 (program): a(n) = (5^n + 3)/2
  • A132081 (program): Triangle (read by rows) with row sums = Motzkin sums (also called Riordan numbers) (A005043): T(n,s) = (1/n)*C(n,s)*(C(n-s,s+1) - C(n-s-2,s-1)).
  • A132083 (program): a(n) = n-th positive integer which is coprime to (2^n +1). Also, a(n) = final term of row n in triangle A132082.
  • A132084 (program): A051717(2n).
  • A132086 (program): Record values in A132085.
  • A132090 (program): a(n) = pi(pi(n)), where pi = A000720.
  • A132095 (program): Denominators of Blandin-Diaz compositional Bernoulli numbers (B^cos)_2,n.
  • A132101 (program): a(n) = (A001147(n) + A047974(n))/2.
  • A132106 (program): a(n) = 1 + floor(sqrt(n)) + Sum_{i=1..n} floor(n/i).
  • A132107 (program): Expansion of (f(x) / f(x^3))^6 in powers of x where f() is a Ramanujan theta function.
  • A132108 (program): Triangle T(n,k) = binomial(n,k)+n-k read by rows.
  • A132109 (program): a(n) = (2^(n+1) + n^2 + n)/2.
  • A132110 (program): A007318 + A059268 - A000012 as infinite lower triangular matrices.
  • A132111 (program): Triangle read by rows: T(n,k) = n^2 + k*n + k^2, 0 <= k <= n.
  • A132112 (program): a(n) = n*(n+1)*(11*n+1)/6.
  • A132113 (program): Multiply previous term by 8 and reverse.
  • A132114 (program): Multiply previous term by 7 and reverse.
  • A132117 (program): Binomial transform of [1, 7, 17, 17, 6, 0, 0, 0, …].
  • A132118 (program): Triangle read by rows: T(n,k) = n*(n-1)/2 + 2*k - 1.
  • A132119 (program): A002260 + A000027 - A000012 as infinite lower triangular matrices.
  • A132121 (program): Triangle read by rows: T(n,k)=n*(n+1)*((3*k+2)*n+1)/6, 0<=k<=n.
  • A132122 (program): a(n) = n * (n+1)^2 * (3*n^2 + 4*n + 2) / 12.
  • A132123 (program): a(n) = n * (2*n + 1) * (6*n^2 + 4*n + 1) / 3.
  • A132124 (program): a(n) = n*(n+1)*(8*n + 1)/6.
  • A132125 (program): Number of distinct Fibonacci divisors of the factorial of n.
  • A132127 (program): a(n) = (n^3 + 3*n - 2)/2.
  • A132128 (program): A051340 + A000027 - A000012.
  • A132136 (program): Expansion of -lambda(t + 1) in powers of the nome q = exp(Pi i t).
  • A132137 (program): a(1)=1, a(n)=maximal digit of sum a(1)+…+a(n-1).
  • A132140 (program): Numbers containing no zeros in ternary representation and with an initial 1.
  • A132141 (program): Numbers whose ternary representation begins with 1.
  • A132148 (program): Triangular array T(n,k) = C(n,k)*Lucas(n-k), 0 <= k <= n.
  • A132151 (program): Period 8: repeat [0, 1, 0, 0, 0, 0, -1, 0].
  • A132158 (program): a(3n+k) = 3a(3n+k-1)-3a(3n+k-2)+2a(3n+k-3) for k = 0,1; a(3n+2) = 3a(3n-1)-3a(3n-2), with a(0) = 0,a(1) = 1,a(2) = 3.
  • A132159 (program): Lower triangular matrix T(n,j) for double application of an iterated mixed order Laguerre transform inverse to A132014. Coefficients of Laguerre polynomials (-1)^n * n! * L(n,-2-n,x).
  • A132162 (program): a(2n+1) = 3*a(2*n) - 4*n with a(0) = 1, a(1) = 3.
  • A132167 (program): Row sums of triangle A132166 (s1(7)).
  • A132168 (program): Alternating row sums of triangle A132166 (s1(7)).
  • A132169 (program): Irregular triangle read by rows. A141616(n)/4.
  • A132171 (program): 3^n repeated 3^n times.
  • A132173 (program): Maternal generation number of A063882(n).
  • A132174 (program): Index of starting position of n-th generation of terms in A063882.
  • A132175 (program): Index of end of n-th generation of terms in A063882.
  • A132176 (program): Value of A063882 at start of n-th generation of terms.
  • A132177 (program): Value of A063882 at end of n-th generation of terms.
  • A132179 (program): Expansion of f(-x^2)^2 * f(x, x^2) / f(-x^3)^3 in powers of x where f(,) is a Ramanujan theta function.
  • A132180 (program): Expansion of f(q, q^2) * f(-q^3) / f(-q^2)^2 in powers of q where f(, ), f() are Ramanujan theta functions.
  • A132182 (program): a(n) = floor(n^(n -1/2)).
  • A132188 (program): Number of 3-term geometric progressions with no term exceeding n.
  • A132189 (program): Number of non-constant 3-term geometric progressions with no term exceeding n.
  • A132190 (program): Numbers n such that 7*n^2 + 1 is prime.
  • A132194 (program): a(n) = 1 if n-th prime is 0 or 2 mod 3, otherwise 0.
  • A132196 (program): a(2n+1) = 2a(2n)-n for the odd indices. Smallest strictly positive integer not yet in the list for the even indices, a(2n).
  • A132197 (program): 2^n-1 written 2^n-1 times.
  • A132199 (program): Rowland’s prime-generating sequence: first differences of A106108.
  • A132200 (program): Numbers in (4,4)-Pascal triangle .
  • A132207 (program): Triangle read by rows: row n lists first 2*4^n terms of an array read by rows, in which row k gives 2*4^n + 3*k - 1; 5*4^n + 3*k - 1, with k>=0 in each array.
  • A132208 (program): a(n) = 15n(n+1) + 11.
  • A132209 (program): a(0) = 0 and a(n) = 2*n^2 + 2*n - 1, for n>=1.
  • A132214 (program): Numbers that are sums of seventh powers of two distinct primes.
  • A132215 (program): Numbers that are sums of eighth powers of two distinct primes.
  • A132217 (program): Expansion of psi(x^6) / psi(-x) in powers of x where psi() is a Ramanujan theta function.
  • A132222 (program): Beatty sequence 1+2*floor(n*Pi/2), which contains infinitely many primes.
  • A132223 (program): A dense infinitive sequence.
  • A132226 (program): Placement sequence for the dense normalized fractal sequence A132224.
  • A132227 (program): a(n) = 3*prime(n) - 5.
  • A132230 (program): Primes congruent to 1 (mod 30).
  • A132231 (program): Primes congruent to 7 (mod 30).
  • A132232 (program): Primes congruent to 11 (mod 30).
  • A132233 (program): Primes congruent to 13 (mod 30).
  • A132234 (program): Primes congruent to 19 (mod 30).
  • A132235 (program): Primes congruent to 23 (mod 30).
  • A132236 (program): Primes congruent to 29 (mod 30).
  • A132237 (program): Primes congruent to {7, 23} mod 30.
  • A132238 (program): Primes congruent to {11, 13} mod 30.
  • A132239 (program): Primes congruent to {17, 19} mod 30.
  • A132240 (program): Primes congruent to {1, 29} mod 30.
  • A132241 (program): Twin primes congruent to {11, 13} mod 30.
  • A132242 (program): Twin primes congruent to {17, 19} mod 30.
  • A132243 (program): Twin primes congruent to {1, 29} mod 30.
  • A132247 (program): Twin primes congruent to {1, 11, 13, 17, 19, 29} mod 30.
  • A132248 (program): Isolated primes congruent to 1 (mod 30).
  • A132249 (program): Isolated primes congruent to 11 (mod 30).
  • A132250 (program): Isolated primes congruent to 13 (mod 30).
  • A132251 (program): Isolated primes congruent to 17 (mod 30).
  • A132252 (program): Isolated primes congruent to 19 (mod 30).
  • A132253 (program): Isolated primes congruent to 29 (mod 30).
  • A132262 (program): First term in a sum partition of the even-indexed Fibonacci numbers.
  • A132264 (program): Product{0<=k<=floor(log_12(n)), floor(n/12^k)}, n>=1.
  • A132269 (program): a(n) = Product_{k>=0} (1 + floor(n/2^k)).
  • A132270 (program): a(n) = floor((n^7-1)/(7*n^6)), which is the same as integers repeated 7 times.
  • A132271 (program): Product{k>=0, 1+floor(n/10^k)}.
  • A132272 (program): Product{k>0, 1+floor(n/10^k)}.
  • A132278 (program): Number of distinct terms in rows 1 through n of the triangle of the Narayana numbers (A001263).
  • A132280 (program): Triangle read by rows: T(n,k) is the number of paths in the first quadrant from (0,0) to (n,0), consisting of steps U=(1,1), D=(1,-1), h=(1,0) and H=(2,0), having k H steps (0<=k<=floor(n/2)).
  • A132285 (program): Mirror odd numbers.
  • A132286 (program): Mirror odd numbers A132285(n) divided by 11.
  • A132287 (program): Primes in A132286.
  • A132288 (program): Mirror odd numbers with only two prime divisor.
  • A132292 (program): Integers repeated 8 times: a(n) = floor((n-1)/8).
  • A132294 (program): The first three terms are 1. After that, a(n)=(a(n-1))^2-a(n-2)-a(n-3).
  • A132295 (program): Sum of the nonsquare numbers not larger than n.
  • A132296 (program): Sum of the noncube numbers less than or equal to n.
  • A132297 (program): Number of distinct Markov type classes of order 2 possible in binary strings of length n.
  • A132301 (program): Expansion of f(-x, -x^5) * f(-x)^2 / f(-x^6)^3 in powers of x where f(, ) and f() are Ramanujan theta functions.
  • A132302 (program): Expansion of f(-x, -x^5) * f(-x^6) / f(-x)^2 in powers of x where f(, ) and f() are Ramanujan theta functions.
  • A132306 (program): a(n) = Sum_{k=0..2n-1} C(2n-1,k)*trinomial(n,k) for n>0 with a(0)=1.
  • A132307 (program): 2*A007318^(2) - A000012.
  • A132308 (program): a(n) = 2*3^n - n - 1.
  • A132309 (program): A007318^(-1) * A132307.
  • A132310 (program): a(n) = 3^n*Sum_{ k=0..n } binomial(2*k,k)/3^k.
  • A132314 (program): a(n) = n*2^floor((n+1)/2).
  • A132315 (program): Sum of the non-fourth powers less than or equal to n.
  • A132327 (program): Product{k>=0, 1+floor(n/3^k)}.
  • A132328 (program): a(n) = Product_{k>0} (1+floor(n/3^k)).
  • A132338 (program): Decimal expansion of 1 - 1/phi.
  • A132340 (program): a(n+1) = if {a(k):1<=k<=n} is a permutation of [1:n] then 2*a(n) else a(n)-1.
  • A132341 (program): Main diagonal of A132339.
  • A132342 (program): a(n) = (a(n-1)*a(n-4)) - (a(n-2)*a(n-3)), with a(1)=a(2)=a(3)=a(4)=1.
  • A132344 (program): a(n) = n*2^(floor(n/2)).
  • A132345 (program): Number of increasing three-term geometric sequences from the integers {1,2,…,n}.
  • A132349 (program): If n is a k-th power with k >= 2 then a(n) = k, otherwise a(n) = 0.
  • A132350 (program): If n > 1 is a k-th power with k >= 2 then a(n) = 0, otherwise a(n) = 1.
  • A132351 (program): Partial sums of A132350.
  • A132352 (program): Partial sums of A132351.
  • A132353 (program): a(n) = 3*a(n-1) - a(n-3) + 3*a(n-4), starting with 1, 2, 6, 20.
  • A132354 (program): Integers m such that 7*m + 1 is a square.
  • A132355 (program): Numbers of the form 9*h^2 + 2*h, for h an integer.
  • A132356 (program): a(2*k) = k*(10*k+2), a(2*k+1) = 10*k^2 + 18*k + 8, with k >= 0.
  • A132357 (program): a(n) = 3*a(n-1) - a(n-3) + 3*a(n-4).
  • A132364 (program): Expansion of 1/(1-x^2*c(x)), c(x) the g.f. of A000108.
  • A132366 (program): Partial sum of centered tetrahedral numbers A005894.
  • A132367 (program): Period 6: repeat [1, 1, 2, -1, -1, -2].
  • A132368 (program): a(0), …, a(7) are 0,1,2,3,6,4,5,7; for n >= 8, a(n) = a(n-8) + 8.
  • A132369 (program): PrimePi(n)!.
  • A132370 (program): Array read by antidiagonals: T(m,n) = number of spotlight tilings of a width 1 m X n frame.
  • A132371 (program): a(n) = n! - Sum_{j=1..n-1} j!.
  • A132372 (program): T(n, k) counts Schroeder n-paths whose ascent starting at the initial vertex has length k. Triangle T(n,k), read by rows.
  • A132373 (program): Expansion of c(6*x^2)/(1-x*c(6*x^2)), where c(x) is the g.f. of A000108.
  • A132374 (program): Expansion of c(7*x^2)/(1 - x*c(7*x^2)), where c(x) is the g.f. of A000108.
  • A132375 (program): Expansion of c(8*x^2)/(1 - x*c(8*x^2)), where c(x) is the g.f. of A000108.
  • A132377 (program): a(n) = PrimePi(n)^n.
  • A132380 (program): Period 8: repeat [0, 0, 1, 1, 0, 0, -1, -1].
  • A132382 (program): Lower triangular array T(n,k) generator for group of arrays related to A001147 and A102625.
  • A132383 (program): 4^n written 4^n times.
  • A132384 (program): a(n) = Sum_{ k <= n, k is not an i-th power with i >= 2} k.
  • A132387 (program): a(n) = n with each digit d of n replaced by d mod 4.
  • A132390 (program): Number of binary pattern classes in the (2,n)-rectangular grid; two patterns are in same class if one of them can be obtained by reflection or rotation of the other one.
  • A132395 (program): a(n) = (11^(n+2) + 12^(2*n+1))/133.
  • A132397 (program): Second trisection of A024494.
  • A132398 (program): Numbers n such that 11*n^2 + 1 is prime.
  • A132400 (program): Period 4: repeat [1, 5, 3, 1].
  • A132401 (program): Period 8: repeat 0, 0, 1, 1, 2, -1, -1, -2.
  • A132402 (program): Binomial transform of A004524 starting at 1.
  • A132405 (program): Floor(exp(n)/n^2).
  • A132406 (program): Floor(exp(n)/n^3).
  • A132407 (program): a(n) = ceiling(exp(n)/n).
  • A132408 (program): Ceiling(exp(n)/n^2).
  • A132409 (program): Ceiling(exp(n)/n^3).
  • A132411 (program): a(0) = 0, a(1) = 1 and a(n) = n^2 - 1 with n >= 2.
  • A132412 (program): Floor(n^2*exp(n)).
  • A132413 (program): Ceiling(n^2*exp(n)).
  • A132417 (program): a(16j+i) := 8(16j+i) + e_i, for j >= 0, 0 <= i <= 15, where e_0, …, e_15 are 2, -2, -6, -10, -14, -18, -22, -26, -30, -34, -38, -42, -46, -50, -54, 6.
  • A132419 (program): Period 6: repeat [1, 1, -2, -1, -1, 2].
  • A132428 (program): Central terms of triangle A132427.
  • A132429 (program): Period 4: repeat [3, 1, -1, -3].
  • A132433 (program): a(1) = 2; for n>=2, a(n) = 8*a(n-1) + 1.
  • A132434 (program): a(n) = A132433(n) - 33.
  • A132436 (program): A binomial recursion : a(n)=p(n) (see comment).
  • A132437 (program): A binomial recursion : a(n)=q(n) (see comment).
  • A132440 (program): Infinitesimal Pascal matrix: generator (lower triangular matrix representation) of the Pascal matrix, the classical operator xDx, iterated Laguerre transforms, associated matrices of the list partition transform and general Euler transformation for sequences.
  • A132442 (program): Triangle, n-th row = first n terms of n-th row of an array formed by A051731 * A127093(transform).
  • A132458 (program): Let df(n,k) = Product_{i=0..k-1} (n-i) be the descending factorial and let P(m,n) = df(n-1,m-1)^2*(2*n-m)/((m-1)!*m!). Sequence gives P(4,n).
  • A132459 (program): Sums of squared coefficients in the negative powers of the Catalan function: a(n) = Sum_{k=1..n+1} [x^(n-k+1)] 1/C(x^2)^k, where C(x) is the g.f. of A000108.
  • A132460 (program): Irregular triangle read by rows of the initial floor(n/2) + 1 coefficients of 1/C(x)^n, where C(x) is the g.f. of the Catalan sequence (A000108).
  • A132461 (program): Row squared sums of triangle of Lucas polynomials (A034807) for n>0: Sum_{k=0..floor(n/2)} A034807(n,k)^2, with a(0)=1.
  • A132464 (program): Let df(n,k) = Product_{i=0..k-1} (n-i) be the descending factorial and let P(m,n) = df(n-1,m-1)^2*(2*n-m)/((m-1)!*m!). Sequence gives P(6,n).
  • A132465 (program): Let df(n,k) = Product_{i=0..k-1} (n-i) be the descending factorial and let P(m,n) = df(n-1,m-1)^2*(2*n-m)/((m-1)!*m!). Sequence gives P(7,n).
  • A132466 (program): Let df(n,k) = Product_{i=0..k-1} (n-i) be the descending factorial and let P(m,n) = df(n-1,m-1)^2*(2*n-m)/((m-1)!*m!). Sequence gives P(8,n).
  • A132468 (program): Longest gap between numbers relatively prime to n.
  • A132469 (program): a(n) = (2^(5n)-1)/31.
  • A132476 (program): A007318^(-1) * [3*A007318^2 - 2*A000012].
  • A132477 (program): Row sums of triangle A132476.
  • A132478 (program): A007318^(-1) * [4*A007318^(2) - 3*A000012].
  • A132479 (program): Row sums of triangle A132478.
  • A132583 (program): a(n) = n 2’s sandwiched between two 1’s.
  • A132584 (program): a(0)=0, a(1)=4; for n > 1, a(n) = 18*a(n-1) - a(n-2) + 8.
  • A132588 (program): Let b(k) be the k-th term of the flattened irregular array where the m-th row contains the positive divisors of m (b(k) = A027750(k)). Then a(n) = gcd(b(n), n).
  • A132589 (program): a(n) = gcd(A038566(n), n).
  • A132592 (program): X-values of solutions to the equation X*(X + 1) - 8*Y^2 = 0.
  • A132593 (program): Nonnegative integer solutions X to the equation: X(X + 1) - 10*Y^2 = 0.
  • A132594 (program): Values X satisfying the equation: X(X + 1) - 7*Y^2 = 0.
  • A132596 (program): X-values of solutions to the equation X*(X + 1) - 6*Y^2 = 0.
  • A132607 (program): X-values of solutions to the equation X*(X + 1) - 11*Y^2 = 0.
  • A132609 (program): Antidiagonal sum of table A072590(n,k) = n^(k-1)*k^(n-1) for n>=1.
  • A132632 (program): Minimal m > 0 such that Fibonacci(m) == 0 (mod n^2).
  • A132634 (program): a(n) = Fibonacci(n) mod n^2.
  • A132635 (program): Number of primes, 0’s, and 1’s in [0, n^2).
  • A132636 (program): a(n) = Fibonacci(n) mod n^3.
  • A132637 (program): Composite number C(n) raised to power C(n).
  • A132641 (program): Number of partitions of n, p(n), raised to power p(n).
  • A132644 (program): X-values of solutions to the equation X*(X + 1) - 13*Y^2 = 0.
  • A132650 (program): Number of divisors of n, d(n) raised to power d(n).
  • A132651 (program): Sum of proper divisors of n, s(n) raised to power s(n), for n > 1.
  • A132652 (program): Sum of divisors of n, sigma(n) raised to power sigma(n).
  • A132664 (program): a(1)=1, a(2)=2, a(n) = a(n-1) + n if the minimal positive integer not yet in the sequence is greater than a(n-1), else a(n) = a(n-1) - 1.
  • A132665 (program): a(1)=1, a(2)=3, a(n) = a(n-1) + n if the minimal positive integer not yet in the sequencer is greater than a(n-1), else a(n) = a(n-1)-1.
  • A132666 (program): a(1)=1, a(n) = 2*a(n-1) if the minimal positive integer not yet in the sequence is greater than a(n-1), else a(n) = a(n-1)-1.
  • A132667 (program): a(1)=1, a(n) = 3*a(n-1) if the minimal positive integer not yet in the sequence is greater than a(n-1), else a(n) = a(n-1) - 1.
  • A132668 (program): a(1)=1, a(n) = 4*a(n-1) if the minimal positive integer not yet in the sequence is greater than a(n-1), else a(n) = a(n-1) - 1.
  • A132669 (program): a(1)=1, a(n) = 5*a(n-1) if the minimal positive integer not yet in the sequence is greater than a(n-1), else a(n) = a(n-1) - 1.
  • A132670 (program): a(1)=1, a(n) = 6*a(n-1) if the minimal positive integer not yet in the sequence is greater than a(n-1), else a(n) = a(n-1) - 1.
  • A132671 (program): a(1)=1, a(n) = 7*a(n-1) if the minimal positive integer not yet in the sequence is greater than a(n-1), else a(n) = a(n-1) - 1.
  • A132672 (program): a(1)=1, a(n) = 8*a(n-1) if the minimal positive integer not yet in the sequence is greater than a(n-1), else a(n) = a(n-1) - 1.
  • A132673 (program): a(1)=1, a(n) = 9*a(n-1) if the minimal positive integer number not yet in the sequence is greater than a(n-1), else a(n) = a(n-1) - 1.
  • A132674 (program): a(1)=1, a(n) = 10*a(n-1) if the minimal positive integer not yet in the sequence is greater than a(n-1), else a(n) = a(n-1) - 1.
  • A132677 (program): Period 3: repeat [1, 2, -3].
  • A132679 (program): Starting with a(1)=1 and a(2)=2: if m is a term then also 4*m and 4*m+3.
  • A132680 (program): Number of ones in binary representation of odious numbers.
  • A132681 (program): Infinitesimal generator matrix for a diagonally-shifted Pascal matrix, binomial(n+m,k+m), for m=1, related to Laguerre(n,x,m).
  • A132683 (program): a(n) = binomial(2^n + n, n).
  • A132684 (program): a(n) = binomial(2^n + n + 1, n).
  • A132685 (program): a(n) = binomial(2^n + 2*n, n).
  • A132686 (program): a(n) = binomial(2^n + 2*n + 1, n).
  • A132687 (program): a(n) = binomial(2^n + 3*n - 1, n).
  • A132688 (program): a(n) = binomial(2^n + 3*n, n).
  • A132689 (program): a(n) = binomial(2^n + 3*n + 1, n).
  • A132696 (program): Decimal expansion of 6/Pi.
  • A132697 (program): Decimal expansion of 7/Pi.
  • A132698 (program): Decimal expansion of 8/Pi.
  • A132699 (program): Decimal expansion of 9/Pi.
  • A132700 (program): Decimal expansion of Pi/31.
  • A132701 (program): Decimal expansion of 11/Pi.
  • A132702 (program): Decimal expansion of 12/Pi.
  • A132703 (program): Decimal expansion of 13/Pi.
  • A132704 (program): Decimal expansion of 14/Pi.
  • A132706 (program): Decimal expansion of 16/Pi.
  • A132707 (program): Decimal expansion of 17/Pi.
  • A132708 (program): Period 6: repeat [4, 2, 1, -4, -2, -1].
  • A132709 (program): Decimal expansion of 19/Pi.
  • A132710 (program): Infinitesimal generator for a diagonally-shifted Lah matrix, unsigned A105278, related to n! Laguerre(n,-x,1).
  • A132711 (program): Decimal expansion of 21/Pi.
  • A132712 (program): Decimal expansion of 22/Pi.
  • A132713 (program): Decimal expansion of 23/Pi.
  • A132714 (program): Decimal expansion of 24/Pi.
  • A132715 (program): Decimal expansion of 25/Pi.
  • A132716 (program): Decimal expansion of 26/Pi.
  • A132717 (program): Decimal expansion of 27/Pi.
  • A132718 (program): Decimal expansion of 28/Pi.
  • A132720 (program): Sequence is identical to its second differences in absolute values.
  • A132723 (program): Binomial transform of A132429.
  • A132727 (program): a(n) = 3 * 2^(n-1) * a(n-1) with a(0) = 1.
  • A132728 (program): Triangle T(n, k) = 4 - 3*(-1)^k, read by rows.
  • A132729 (program): Triangle T(n, k) = 2*binomial(n, k) - 3 with T(n, 0) = T(n, n) = 1, read by rows.
  • A132730 (program): Row sums of triangle A132729.
  • A132731 (program): Triangle T(n,k) = 2 * binomial(n,k) - 2 with T(n,0) = T(n,n) = 1, read by rows.
  • A132732 (program): Row sums of triangle A132731.
  • A132733 (program): Triangle T(n, k) = 4*binomial(n, k) - 5 with T(n, 0) = T(n, n) = 1, read by rows.
  • A132734 (program): Row sums of triangle A132733.
  • A132735 (program): Triangle T(n,k) = binomial(n,k) + 1 with T(n,0) = T(n,n) = 1, read by rows.
  • A132736 (program): Row sums of triangle A132735.
  • A132737 (program): Triangle T(n,k) = 2*binomial(n,k) + 1, read by rows.
  • A132738 (program): Row sums of triangle A132737.
  • A132739 (program): Largest divisor of n not divisible by 5.
  • A132740 (program): Largest divisor of n coprime to 10.
  • A132741 (program): Largest divisor of n having the form 2^i*5^j.
  • A132742 (program): Triangle T(n,m) = 1 + ((2*n*3^m) mod 12), read by rows.
  • A132744 (program): Decimal expansion of Pi/28.
  • A132745 (program): Row sums of (A008550 formatted as a triangular array).
  • A132747 (program): a(n) = number of non-isolated divisors of n.
  • A132749 (program): Triangle T(n,k) = binomial(n, k) with T(n, 0) = 2, read by rows.
  • A132750 (program): A132749 * [1, 2, 3, …] = A007318 * A065190.
  • A132751 (program): Triangle T(n, k) = 2/Beta(n-k+1, k) - 1, read by rows.
  • A132752 (program): Triangle T(n, k) = 2*A132749(n, k) - 1, read by rows.
  • A132753 (program): a(n) = 2^(n+1) - n + 1.
  • A132754 (program): a(n) = n*(n + 23)/2.
  • A132755 (program): a(n) = n*(n + 25)/2.
  • A132756 (program): a(n) = n*(n + 27)/2.
  • A132757 (program): a(n) = n*(n+29)/2.
  • A132758 (program): a(n) = n*(n + 31)/2.
  • A132759 (program): a(n) = n*(n+13).
  • A132760 (program): a(n) = n*(n+15).
  • A132761 (program): a(n) = n*(n+17).
  • A132762 (program): a(n) = n*(n + 19).
  • A132763 (program): a(n) = n*(n+21).
  • A132764 (program): a(n) = n*(n+22).
  • A132765 (program): a(n) = n*(n + 23).
  • A132766 (program): a(n) = n*(n+24).
  • A132767 (program): a(n) = n*(n + 25).
  • A132768 (program): a(n) = n*(n + 26).
  • A132769 (program): a(n) = n*(n + 27).
  • A132770 (program): a(n) = n*(n + 28).
  • A132771 (program): a(n) = n*(n + 29).
  • A132772 (program): a(n) = n*(n + 30).
  • A132773 (program): a(n) = n*(n + 31).
  • A132774 (program): A natural number operator.
  • A132775 (program): A007818 * A132774.
  • A132776 (program): A128064 (unsigned) * A007318.
  • A132777 (program): Nonsquare numbers which are the sum of 2 distinct squares.
  • A132780 (program): a(0)=1. a(n+1)=2*a(n)-A130151(n).
  • A132787 (program): Triangle read by rows: T(n,k) = 2*A001263(n,k) - 1.
  • A132788 (program): a(n) = 2*binomial(2*n,n)/(n+1) - n.
  • A132789 (program): Triangle read by rows: T(n,k) = A007318(n-1, k-1) + A001263(n, k) - 1.
  • A132790 (program): Row sums of triangle A132789.
  • A132791 (program): Numbers k such that the sum of the digits of 4^k is prime.
  • A132792 (program): The infinitesimal Lah matrix: generator of unsigned A111596.
  • A132796 (program): Second diagonal of Gely numbers.
  • A132798 (program): Period 6: repeat [0, 2, 1, 0, -2, -1].
  • A132804 (program): A trisection of A024495.
  • A132805 (program): A trisection of A024495.
  • A132807 (program): A000108(n) + A000079(n) - 1.
  • A132812 (program): Triangle read by rows, n>=1, 1<=k<=n, T(n,k) = k*binomial(n,k)^2/(n-k+1).
  • A132813 (program): Triangle read by rows: A001263 * A127648 as infinite lower triangular matrices.
  • A132814 (program): A007318^(-1) * A132813.
  • A132818 (program): The matrix product A127773 * A001263 of infinite lower triangular matrices.
  • A132819 (program): A001263 * A127773.
  • A132820 (program): Row sums of triangle A132819.
  • A132823 (program): A007318 + 2*A103451 - 2*A000012.
  • A132824 (program): Row sums of triangle A132823.
  • A132825 (program): Triangle read by rows: zeros except for right border which are the partition numbers A000041.
  • A132850 (program): a(0)=1; a(n) = the smallest prime dividing (n+a(n-1)), for n>=1.
  • A132851 (program): a(0)=1. a(n) = the largest squarefree integer which divides (n+a(n-1)), for n>=1.
  • A132857 (program): a(0)=1. a(n) = phi(n+a(n-1)), for n>=1, where phi(m) is the number of positive integers which are <= m and are coprime to m.
  • A132863 (program): Expansion of 1/(1-3x*c(4x)), where c(x) is the g.f. of A000108.
  • A132864 (program): Expansion of 1/(1-4x*c(5x)), where c(x) is the g.f. of A000108.
  • A132865 (program): Expansion of 1/(1-5x*c(6x)), where c(x) is the g.f. of A000108.
  • A132866 (program): Expansion of 1/(1-6x*c(7x)), where c(x) is the g.f. of A000108.
  • A132868 (program): a(n) = 3*a(n-1) - a(n-3) + 3*a(n-4), n > 3.
  • A132881 (program): a(n) is the number of isolated divisors of n.
  • A132885 (program): Triangle read by rows: T(n,k) is the number of paths in the right half-plane from (0,0) to (n,0), consisting of steps U=(1,1), D=(1,-1), h=(1,0) and H=(2,0), having k H=(2,0) steps (0 <= k <= floor(n/2)).
  • A132894 (program): Number of (1,0) steps in all paths of length n with steps U=(1,1), D=(1,-1) and H=(1,0), starting at (0,0), staying weakly above the x-axis (i.e., in all length-n left factors of Motzkin paths).
  • A132895 (program): Even numbers for which all divisors, with the exception of 1 and 2, are isolated. A positive divisor, k, of n is isolated if neither (k-1) nor (k+1) divides n.
  • A132896 (program): Triangle read by rows: T(n,k)=number of prime divisors of C(n,k), counted with multiplicity (0<=k<=n).
  • A132897 (program): Expansion of 1/(1-9x*c(10x)), where c(x) is the g.f. of A000108.
  • A132898 (program): Triangle read by rows: T(n,k) = (-1)^(n-1)*n + (-1)^(k-1)*k - 1, 1 <= k <= n.
  • A132899 (program): Row sums of triangle A132898.
  • A132900 (program): Colored Motzkin paths where each of the steps has three possible colors.
  • A132903 (program): Numbers formed by concatenating 3 consecutive prime numbers.
  • A132904 (program): Numbers formed by concatenating 4 consecutive prime numbers.
  • A132905 (program): Numbers formed by concatenating 5 consecutive prime numbers.
  • A132906 (program): Numbers formed by concatenating 6 consecutive prime numbers.
  • A132907 (program): Numbers formed by concatenating 7 consecutive prime numbers.
  • A132908 (program): Numbers formed by concatenating 8 consecutive prime numbers.
  • A132909 (program): Numbers formed by concatenating 9 consecutive prime numbers.
  • A132911 (program): a(n)=(n+1)(2n)!/2^n.
  • A132912 (program): a(n)=C(n+2,2)(2n)!/2^n.
  • A132913 (program): a(n) = ceiling(sqrt(n) + n^(1/3)).
  • A132914 (program): a(n) = floor(sqrt(n) + n^(1/3)).
  • A132918 (program): Identity matrix with interpolated zeros.
  • A132919 (program): Triangle read by rows: T(n,k) = Fibonacci(n) + k - 1.
  • A132920 (program): a(n) = n*Fibonacci(n) + binomial(n, 2).
  • A132921 (program): Triangle read by rows: T(n,k) = n + Fibonacci(k) - 1, 1 <= k <= n.
  • A132922 (program): Row sums of triangle A132921.
  • A132923 (program): Triangle by columns, F(n) followed by (F(n)+1), (F(n)+2), (F(n)+3), …
  • A132924 (program): Triangle read by columns, 2^(n-1) followed by (2^(n-1) + 1), (2^(n-1) + 2), (2^(n-1) + 3), …
  • A132925 (program): a(n) = 2^n - 1 + n*(n-1)/2.
  • A132927 (program): Concatenation of first n elements of the divisor function d(n), where d(n) is the number of divisors of n.
  • A132943 (program): Concatenation of first n imperfect numbers.
  • A132944 (program): a(n)=Floor[n^(1/3)+n^(1/4)].
  • A132945 (program): Generalization of an a(n)=3*2^n*a(n-1) as 3=(m+1) and 2=m To give general term: t(n,m)=a(n)=(m+1)^n*m^(n*(n-1)/2).
  • A132950 (program): Generalization of an a(n)=3*2^n*a(n-1) as 3=(m+1) and 2=m To give general term: t(n,m)=a(n)=(m+1)^n*m^(n*(n-1)/2) ( here n taken first).
  • A132951 (program): Period 6: repeat [1, 3, 1, -1, -3, -1].
  • A132954 (program): Period 6: repeat [1, 2, 4, -1, -2, -4].
  • A132958 (program): a(n) = n!*Sum_{d|n} (-1)^(d+1)/d!.
  • A132964 (program): Convolution triangle of A006190.
  • A132965 (program): Expansion of f(-q^8) * chi(q)^2 in powers of q where f(), chi() are Ramanujan theta functions.
  • A132969 (program): Expansion of phi(q) * chi(q) in powers of q where phi(), chi() are Ramanujan theta functions.
  • A132970 (program): Expansion of phi(-x) * chi(-x) in powers of x where phi(), chi() are Ramanujan theta functions.
  • A132971 (program): a(2*n) = a(n), a(4*n+1) = -a(n), a(4*n+3) = 0, with a(0) = 1.
  • A132972 (program): Expansion of chi(q)^3 / chi(q^3) in powers of q where chi() is a Ramanujan theta function.
  • A132973 (program): Expansion of psi(-q)^3 / psi(-q^3) in powers of q where psi() is a Ramanujan theta function.
  • A132974 (program): Expansion of psi(-q^3) / psi(-q)^3 in powers of q where psi() is a Ramanujan theta function.
  • A132975 (program): Expansion of q * psi(-q^9) / psi(-q) in powers of q where psi() is a Ramanujan theta function.
  • A132977 (program): Expansion of q^(-1/3) * (eta(q^6)^4 / (eta(q) * eta(q^3) * eta(q^4) * eta(q^12)))^2 in powers of q.
  • A132979 (program): Expansion of psi(q^3) / psi(q)^3 in powers of q where psi() is a Ramanujan theta function.
  • A132981 (program): Equal sides of isosceles Heronian triangles, ordered.
  • A132983 (program): a(n) = ceiling(n^(1/3) + n^(1/4)).
  • A132993 (program): Triangle t(n,m) = P(n-m+1) * P(m+1) read by rows, 0<=m<=n, where P=A000041 are the partition numbers.
  • A132995 (program): a(n) = gcd(sum{k=1…n} p(k), product{j=1…n} p(j)), where p(k) is the k-th prime.
  • A132996 (program): a(n) = gcd(Sum_{k=1..n} c(k), Product_{j=1..n} c(j)), where c(k) is the k-th composite.
  • A132998 (program): a(n) = n^4 - n^3 - n^2.
  • A132999 (program): Imperfect numbers: Not equal to sum of proper divisors.
  • A133009 (program): One defining property of the sequences {A, B} = {A000069, A001969} is that they are the unique pair of sets complementary with respect to the nonnegative integers such that q(n) = |{x : x, y in A, x < y, x + y = n}| = |{x : x, y in B, x < y, x + y = n}| for all n >= 0. The present sequence gives the values of q(n).
  • A133012 (program): Even imperfect numbers.
  • A133016 (program): Even imperfect numbers, divided by 2.
  • A133018 (program): Partition number of n, raised to power n.
  • A133019 (program): Product of n-th prime and n-th prime written backwards.
  • A133020 (program): Divisors of 10000.
  • A133022 (program): Product of n-th Fibonacci number and n-th Fibonacci number written backwards.
  • A133024 (program): Divisors of 8128, the 4th perfect number.
  • A133025 (program): Divisors of 33550336, the 5th perfect number.
  • A133027 (program): Divisors of 1701.
  • A133030 (program): Divisors of 5130.
  • A133032 (program): a(n) = n^p(n), where p(n) is the partition number of n.
  • A133034 (program): First differences of Padovan sequence A000931.
  • A133037 (program): Squares of members of the Padovan sequence A000931.
  • A133038 (program): Cubes of A000931.
  • A133039 (program): a(n) = P(n)^3 - P(n)^2 where P(n) = A000931(n).
  • A133040 (program): Divisors of 1900.
  • A133041 (program): Sum of n and partition number of n.
  • A133042 (program): Cubes of partition numbers.
  • A133043 (program): Number of segments needed to draw the spiral of equilateral triangles with side lengths which follow the Padovan sequence.
  • A133044 (program): Area of the spiral of equilateral triangles with side lengths which follow the Padovan sequence, divided by the area of the initial triangle.
  • A133053 (program): Squares of Motzkin numbers.
  • A133054 (program): Cubes of Motzkin numbers.
  • A133061 (program): 5*p^5 - 3*p^3 - 2*p^2, where p = prime(n).
  • A133062 (program): a(n) = 5*p^5 - 3*p^3 + 2*p^2 with p = prime(n).
  • A133063 (program): 5*p^5 + 3*p^3 - 2*p^2, where p = prime(n).
  • A133064 (program): a(n) = 5*p^5 + 3*p^3 + 2*p^2, where p = prime(n).
  • A133068 (program): Number of surjections from an n-element set to an eight-element set.
  • A133070 (program): a(n) = n^5 - n^3 - n^2.
  • A133071 (program): a(n) = n^5 - n^3 + n^2.
  • A133072 (program): a(n) = n^5 + n^3 - n^2.
  • A133073 (program): a(n) = n^5 + n^3 + n^2.
  • A133075 (program): Divisors of 2000.
  • A133079 (program): Expansion of f(x)^3 - 3 * x * f(x^9)^3 in powers of x^3 where f() is a Ramanujan theta function.
  • A133080 (program): Interpolation operator: Triangle with an even number of zeros in each line followed by 1 or 2 ones.
  • A133081 (program): An interpolation operator, companion to A133080.
  • A133082 (program): Triangle read by rows: T(k,m) = dimension of shape space for k labeled points in R^m (1 <= k <= m-1, m >= 2).
  • A133083 (program): A000012 * A133080.
  • A133084 (program): A007318 * A133080.
  • A133085 (program): A133084 * A000012.
  • A133086 (program): Row sums of triangle A133085.
  • A133087 (program): A133080 * A007318.
  • A133088 (program): A007318^(-1) * A133080.
  • A133089 (program): Expansion of f(x)^3 in powers of x where f() is a Ramanujan theta function.
  • A133090 (program): A133081 * [1,2,3,…].
  • A133091 (program): A133080 * A002260.
  • A133092 (program): Row sums of triangle A133091.
  • A133093 (program): A007318 * A097806 * A133080.
  • A133094 (program): A007318 * A133080 * A097806, as infinite lower triangular matrices.
  • A133095 (program): Row sums of triangle A133094.
  • A133100 (program): Expansion of f(x, x^4) in powers of x where f(, ) is Ramanujan’s general theta function.
  • A133101 (program): Expansion of f(x^2, x^3) in powers of x where f(, ) is Ramanujan’s general theta function.
  • A133106 (program): Number of Ferrers diagrams with a single Ferrers puncture with the same orientation inscribed strictly inside with half-perimeter = n.
  • A133109 (program): Triangle read by rows, A042965 on the diagonal, 0 elsewhere.
  • A133111 (program): a(n) = 1/(1!*2!*3!*4!)*sum {1 <= x_1, x_2, x_3, x_4 <= n} |det V(x_1,x_2,x_3,x_4)|, where V(x_1,x_2,x_3,x_4} is the Vandermonde matrix of order 4.
  • A133113 (program): A128174 * A007318 * A133080.
  • A133114 (program): A000012 * A007318 * A133080.
  • A133116 (program): 2*A133114 - A000012.
  • A133122 (program): Odd numbers which cannot be written as the sum of an odd prime and 2^i with i > 0.
  • A133124 (program): A007318 * [1, 2, 2, 3, 2, 3, 2, 3, 2, …].
  • A133125 (program): A133080 * A000244.
  • A133128 (program): Triangle of first differences of A120070 with a leftmost column of A002522.
  • A133129 (program): Number of black/white colorings of a 3 X n rectangle which have no monochromatic 2 by 2 subsquares.
  • A133131 (program): a(4n) = 3n+1, a(4n+1) = -3n, a(4n+2) = -3n-3, a(4n+3) = 3n+2.
  • A133132 (program): Number of surjections from an n-element set to a ten-element set.
  • A133133 (program): a(n) is the largest prime factor of the sum of the largest prime factors of numbers from 2 to n.
  • A133137 (program): a(1) = 1, a(2) = 2, a(n) = smallest number not the sum of 4th powers of 2 distinct earlier terms.
  • A133138 (program): Triangle T(n,k) of the coefficients of the polynomials Q(n,x)=(1+x)[(1+x)^(n-1)+x^(n-1)], Q(0,x)=2.
  • A133140 (program): a(0) = 2, a(n) = 2^n + 2 for n>=1.
  • A133141 (program): Numbers which are both centered pentagonal (A005891) and centered hexagonal numbers (A003215).
  • A133142 (program): Numbers which are both centered square and decagonal numbers.
  • A133143 (program): Maximal number of mutually nonattacking Super Queens on an n X n board. (A Super Queen is a queen with both queen and knight powers.)
  • A133145 (program): Period 4: repeat [1, 2, 4, 8].
  • A133146 (program): Antidiagonal sums of the triangle A133128.
  • A133147 (program): a(n) = a(n-1) + Sum_{k=0..floor(log_2(n-1))} a(2^k), a(1) = 1.
  • A133155 (program): Numbers formed by setting bits representing odd primes, where bit_no = (prime - 1)/2. Setting bit number b is the same as OR-ing with 2^b (i.e., bit numbers start at zero).
  • A133156 (program): Irregular triangle read by rows: coefficients of U(n,x), Chebyshev polynomials of the second kind with exponents in decreasing order.
  • A133157 (program): Numbers k such that k^2 + k - 41 is prime.
  • A133158 (program): Binomial transform of A126568, second binomial transform of A026641.
  • A133160 (program): Numbers k such that k^3 + k + 91 is prime.
  • A133161 (program): Indices of the triangular numbers which are also centered triangular number.
  • A133162 (program): Trajectory of 1 under the morphism 1 -> {1,1,2,1}, 2 -> {2}.
  • A133179 (program): A modular binomial sum transform of 2^n .
  • A133180 (program): sum[k^6]/sum[k^2], {k, 1, A047380(n)}].
  • A133186 (program): Period 4: repeat [1, 2, 1, -4].
  • A133190 (program): a(n) = 2*a(n-1) - a(n-2) + 2*a(n-3).
  • A133195 (program): Smallest number whose sum of digits is 3n.
  • A133196 (program): n+2 repeated n times.
  • A133200 (program): A001263 * A136521 as infinite lower triangular matrices, where A001263 = the Narayana triangle and A136521 = an infinite lower triangular matrix with (1, 2, 2, 2, …) in the main diagonal and the rest zeros.
  • A133201 (program): a(n) = A133195(n)/3.
  • A133203 (program): a(n) = a(n-1) + 8*n + 4, n > 2.
  • A133205 (program): Fully multiplicative with a(p) = p*(p+1)/2 for prime p.
  • A133209 (program): a(n) = 4a(n-1) - 6a(n-2) + 4a(n-3), n > 3; a(0) = 3, a(1) = 2, a(2) = a(3) = 0.
  • A133212 (program): a(n) = 4a(n-1) - 6a(n-2) + 4a(n-3), n > 3; a(0) = 1, a(1) = 4, a(2) = 12, a(3) = 32.
  • A133214 (program): Delannoy paths counted by number of weak peaks.
  • A133216 (program): Integers that are simultaneously triangular (A000217) and decagonal (A001107).
  • A133217 (program): Indices of decagonal numbers (A001107) that are also triangular (A000217).
  • A133218 (program): Indices of triangular numbers (A000217) that are also decagonal (A001107).
  • A133221 (program): A001147 with each term repeated.
  • A133223 (program): Sum of digits of primes (A007605), sorted and with duplicates removed.
  • A133224 (program): Let P(A) be the power set of an n-element set A and let B be the Cartesian product of P(A) with itself. Remove (y,x) from B when (x,y) is in B and x <> y and let R35 denote the reduced set B. Then a(n) = the sum of the sizes of the union of x and y for every (x,y) in R35.
  • A133246 (program): Odd numbers n with property that no odd Fibonacci number is divisible by n.
  • A133252 (program): Partial sums of A006000.
  • A133254 (program): Sums of a triangular number A000217 > 0 and a square A000290 > 0.
  • A133256 (program): a(4*n+1) = 4*n+1, a(4*n+2) = 4*n+2, a(4*n+3) = 4*n+4, a(4*n+4) = 4*n+3.
  • A133257 (program): The number of edges on a piece of paper that has been folded n times (see comments for more precise definition).
  • A133259 (program): a(6n) = 6n+1, a(6n+1) = 6n+2, a(6n+2) = 6n+3, a(6n+3) = 6n+6, a(6n+4) = 6n+5, a(6n+5) = 6n+4.
  • A133263 (program): Binomial transform of (1, 2, 0, 1, -1, 1, -1, 1, …).
  • A133264 (program): Smallest number whose sum of digits is 3n+1.
  • A133265 (program): Diagonal of the A135356 triangle.
  • A133269 (program): Fractal sequence consisting of quadruples, each of which contains the tones comprising a major 7th chord (i.e., root, major third, fifth, and major 7th), with the tones in an octave assigned to the numbers 1..12, and with the n-th quadruple using a(n) as its root.
  • A133271 (program): Indices of 7-gonal numbers which are also centered 7-gonal numbers.
  • A133272 (program): Indices of centered heptagonal numbers (A069099) which are also heptagonal numbers (A000566).
  • A133273 (program): Indices of centered decagonal numbers which are also decagonal numbers.
  • A133274 (program): Numbers which are both 12-gonal and centered 12-gonal numbers.
  • A133275 (program): Numbers X such that 30*X^2-45 is a square.
  • A133278 (program): Triangle read by rows, with n-th row the smallest non-constant n-term arithmetic progression of primes beginning with prime(n).
  • A133280 (program): Triangle formed by: 1 even, 2 odd, 3 even, 4 odd, … starting with zero.
  • A133283 (program): Numbers n such that 30*n^2 + 6 is a square.
  • A133284 (program): Indices of the 12-gonal numbers which are also centered 12-gonal number or numbers X such that 30*X^2-24*X+3 is a square.
  • A133285 (program): Indices of the centered 12-gonal numbers which are also 12-gonal number, or numbers X such that 120*X^2-120*X+36 is a square.
  • A133286 (program): a(n) is the difference by which n^n overestimates the value of (1/2) Sum_{k>=0} k^n/2^k.
  • A133290 (program): Prime powers of the form (6n+1)^k.
  • A133292 (program): Period 9: repeat [1, 1, 2, 4, 7, 2, 7, 4, 2].
  • A133293 (program): First differences of A133292.
  • A133294 (program): a(n) = 2*a(n-1) + 10*a(n-2), a(0)=1, a(1)=1.
  • A133296 (program): Smallest number whose sum of digits is 2n.
  • A133297 (program): a(n) = n!*Sum_{k=1..n} (-1)^(k+1)*n^(n-k-1)/(n-k)!.
  • A133298 (program): a(n) = 1 + Sum_{i=1..n} Sum_{j=1..n} Sum_{k=1..n} i^(j+k).
  • A133301 (program): a(n) is the n-th pentagonal number which is the sum of two consecutive pentagonal numbers.
  • A133305 (program): a(n) = (1/n)*Sum_{i=0..n-1} C(n,i)*C(n,i+1)*4^i*5^(n-i), a(0) = 1.
  • A133306 (program): a(n) = (1/n)*Sum_{i=0..n-1} C(n,i)*C(n,i+1)*5^i*6^(n-i), a(0)=1.
  • A133307 (program): a(n) = (1/n)*Sum_{i=0..n-1} C(n,i)*C(n,i+1)*6^i*7^(n-i), a(0)=1.
  • A133308 (program): a(n) = (1/n)*Sum_{i=0..n-1} C(n,i)*C(n,i+1)*7^i*8^(n-i), a(0)=1.
  • A133309 (program): a(n) = (1/n)*Sum_{i=0..n-1} C(n,i)*C(n,i+1)*8^i*9^(n-i), a(0)=1.
  • A133310 (program): a(3n) = 2n+1, a(3n+1) = 2n+2, a(3n+2) = 2n+1.
  • A133311 (program): The nonnegative integers reordered in groups of 5 even numbers followed by 5 odd numbers.
  • A133317 (program): Dimensions of certain Lie algebra (see reference for precise definition).
  • A133322 (program): Centered square numbers that are prime powers of the form (4n+1)^k.
  • A133323 (program): Hex (or centered hexagonal) numbers that are prime powers of the form (6n+1)^k.
  • A133324 (program): 7-gonal numbers which are sum of 2 consecutive 7-gonal numbers.
  • A133325 (program): Numbers such that 2*X^2-82 is a square.
  • A133326 (program): Numbers n such that 2*n^2 + 41 is a square.
  • A133327 (program): Indices of the 7-gonal numbers that are the sum of 2 consecutive 7-gonal numbers.
  • A133328 (program): Values of n such that the sum of the 7-gonal number (5*n^2 - 3*n)/2 and the following 7-gonal number is a 7-gonal number.
  • A133331 (program): a(2n+1) = 3a(2n)-3a(2n-1)+2a(2n-2), a(2n+2) = 3a(2n+1)-3a(2n), a(0) = 0, a(1) = 1, a(2) = 3.
  • A133335 (program): a(3*n) = 3*a(3*n-1)-3*a(3*n-2)+2*a(3*n-3), a(3*n+1) = 3*a(3*n)-3*a(3*n-1)+2*a(3*n-2), a(3*n+2) = 3*a(3*n+1)-3*a(3*n) with a(0)=1, a(1)=2, a(2)=3.
  • A133336 (program): Triangle T(n,k), 0 <= k <= n, read by rows, given by [1,1,1,1,1,1,1,…] DELTA [0,1,0,1,0,1,0,1,0,…] where DELTA is the operator defined in A084938.
  • A133337 (program): a(3n) = 0, a(3n+1) = a(3n+2) = 5^n.
  • A133341 (program): A007318 * A134312.
  • A133342 (program): Concatenation of binary expansion of n-th row of Pascal’s triangle.
  • A133343 (program): a(n) = 2*a(n-1) + 13*a(n-2), for n>1, a(0)=1, a(1)=1.
  • A133345 (program): a(n) = 2*a(n-1) + 14*a(n-2) for n>1, a(0)=1, a(1)=1.
  • A133348 (program): Dimensions of certain Lie algebra (see reference for precise definition).
  • A133349 (program): Dimensions of certain Lie algebra (see reference for precise definition).
  • A133350 (program): Dimensions of certain Lie algebra (see reference for precise definition).
  • A133351 (program): Dimensions of certain Lie algebra (see reference for precise definition).
  • A133355 (program): Dimensions of certain Lie algebra (see reference for precise definition).
  • A133356 (program): a(n) = 2*a(n-1) + 16*a(n-2) for n>1, a(0)=1, a(1)=1.
  • A133360 (program): Number of surjections from an n-element set to a nine-element set.
  • A133361 (program): Multiply by 9 and reverse.
  • A133362 (program): Decimal expansion of 1/(2 log 2).
  • A133363 (program): Numbers n such that 1+Sum[3k, k=1,2,…,n] is prime.
  • A133368 (program): Period 5: 1, 1, 3, 7, 3.
  • A133369 (program): a(n+1) = (3*a(n) + 2*a(n-1)) mod 37; a(0) = 0, a(1) = 1.
  • A133371 (program): Triangle read by rows: T(i,j) is the number of i-permutations of 14 objects a,b,c,d,e,f,g,h,i,j,k,l,m,n, with repetition allowed, containing j a’s.
  • A133375 (program): Catalan numbers with digits sorted in increasing order and zeros suppressed.
  • A133383 (program): 10 followed by 2n 9’s.
  • A133384 (program): Numbers with n 0’s between 1 and 2.
  • A133386 (program): Number of forests of labeled rooted trees with n nodes, containing exactly 2 trees of height one, all others having height zero.
  • A133387 (program): Greatest prime p such that 6*n-p is prime.
  • A133390 (program): Period 18: repeat 1, 4, 7, 2, 2, 5, 4, 1, 1, 8, 5, 2, 7, 7, 4, 5, 8, 8.
  • A133394 (program): a(n)=a(n-2)+a(n-5).
  • A133395 (program): Terms in A061725 that are of form 3*prime.
  • A133398 (program): Numbers that are not Mersenne primes.
  • A133399 (program): Triangle T(n,k)=number of forests of labeled rooted trees with n nodes, containing exactly k trees of height one, all others having height zero (n>=0, 0<=k<=floor(n/2)).
  • A133400 (program): a(0)=a(1)=a(2) = 1, thereafter a(n) = a(n-1)*a(n-2)*a(n-3) + 1.
  • A133401 (program): Diagonal of polygorial array T(n,k) = n-th polygorial for k = n, for n > 2.
  • A133405 (program): a(n) = 3*a(n-1) - a(n-3) + 3*a(n-4).
  • A133407 (program): a(n) = a(n-1) + 5*a(n-2) for n >= 2, a(0)=1, a(1)=2.
  • A133408 (program): Numbers n such that n is a substring of both its square and its cube in base 2 (written in base 10).
  • A133409 (program): Zero followed by partial sums of A133405.
  • A133410 (program): Least prime p such that p-6*n is prime.
  • A133417 (program): a(n) = sqrt(2*(P(n)^4 + 16*P(n+1)^4 + P(n+2)^4)), where P() = Pell numbers A000129.
  • A133431 (program): Old-fashioned version of A002504 (the initial 1 should be omitted since 1 is no longer regarded as a prime, although it was in 1912).
  • A133436 (program): Generated by a kind of sieve (see Comments lines).
  • A133440 (program): a(1)=1; a(n) = Sum_{1<=k<=n, gcd(k,n)=1} floor(sqrt(k)).
  • A133443 (program): a(n) = Sum_{k=0..n} C(n,floor(k/2))*(-1)^k*3^(n-k).
  • A133444 (program): a(n)=sum{k=0..n, C(n,floor(k/2))*(-1)^k*4^(n-k)}.
  • A133445 (program): Write numbers in ternary under each other (right justified), read diagonals in SW-NE direction, sum digits.
  • A133448 (program): a(n) = 3*a(n-1) - a(n-3) + 3*a(n-4).
  • A133450 (program): Difference between 4*n^2 and the average of the two prime numbers which bracket this number.
  • A133453 (program): a(n) = 3*a(n-1) - a(n-3) + 3*a(n-4).
  • A133455 (program): a(n) = 3*a(n-1) - 3*a(n-2) + 2*a(n-3).
  • A133456 (program): Period 18: repeat 3, 3, -5, 0, 3, -1, -3, 0, 7 followed by their negatives.
  • A133460 (program): 3^n*2^(n^2).
  • A133461 (program): 4^n*3^(n^2).
  • A133462 (program): a(n+1)-10a(n)=3(-3, -2, -1, 0, 1, 2, 3, 4, 5 …).
  • A133463 (program): Partial sums of the sequence that starts with 2 and is followed by A111575.
  • A133464 (program): a(3n)=4^n, a(3n+1)=2*4^n, a(3n+2)=3*4^n.
  • A133466 (program): Positive integers k for which there is exactly one integer i in {1,2,3,…,k-1} such that i*k is a square.
  • A133467 (program): a(n) = a(n-1) + 6*a(n-2) for n >= 2, a(0)=1, a(1)=2.
  • A133469 (program): a(n) = a(n-1) + 7*a(n-2) for n >= 2, a(0)=1, a(1)=2.
  • A133471 (program): a(n) = (n^2)*a(n-1) + a(n-2).
  • A133472 (program): 6 followed by numbers with n-1 0’s between 1 and 5.
  • A133473 (program): 2 followed by numbers with n-1 3’s before 5.
  • A133474 (program): Inverse binomial transform of (A113405 preceded by 0).
  • A133476 (program): a(n) = Sum_{k>=0} binomial(n,5*k+1).
  • A133477 (program): Sum of cubefree divisors of n excluding 1.
  • A133479 (program): a(n) = a(n-1) + 8*a(n-2) for n >= 2, a(0)=1, a(1)=2.
  • A133480 (program): Left 3-step factorial (n,-3)!: a(n) = (-1)^n * A008544(n).
  • A133482 (program): a(p_1^e_1*p_2^e_2*…..*p_m^e_m) = (p_1^p_1)^e_1*(p_2^p^2)^e_2*…..*(p_m^p_m)^e_m where p_1^e_1*p_2^e_2*…..*p_m^e_m is the prime decomposition of n.
  • A133486 (program): a(n) = Sum_{ k = 0 to n-1} ( subtract k modulo 9 from 9, multiply this by k-th power of 10 ).
  • A133488 (program): a(1) = 1. a(n) = a(n-1) + a(m), where m is the largest term of the sequence {a(k)} which is less than n.
  • A133493 (program): Base 8 version of A102363.
  • A133494 (program): Diagonal of the array of iterated differences of A047848.
  • A133496 (program): a(n) = (29*n)^2.
  • A133499 (program): a(n) = n^7 - n.
  • A133508 (program): Record numbers of steps associated with the terms of A133503.
  • A133510 (program): Number of primitive H-invariant prime ideals in O_q(M_{2,n}) generic quantum matrices.
  • A133511 (program): a(n) = 3 A113405(n)- A113405(n+1).
  • A133512 (program): Accept F(1), reject F(1), accept F(2), reject F(2), accept F(3), …,.
  • A133513 (program): Period 6: repeat [0, 1, -3, 0, -1, 3].
  • A133517 (program): Smallest k such that p(n)^3 - k is prime where p(n) is the n-th prime.
  • A133518 (program): Smallest k such that p(n)^3 + k is prime where p(n) is the n-th prime.
  • A133519 (program): Smallest k such that p(n)^4 - k is prime where p(n) is the n-th prime.
  • A133520 (program): Smallest k such that p(n)^4 + k is prime where p(n) is the n-th prime.
  • A133522 (program): Smallest k such that p(n)^5 + k is prime where p(n) is the n-th prime.
  • A133524 (program): Sum of squares of four consecutive primes.
  • A133525 (program): Sum of third powers of four consecutive primes.
  • A133526 (program): Sum of fourth powers of four consecutive primes.
  • A133527 (program): Sum of fifth powers of four consecutive primes.
  • A133528 (program): Sum of sixth powers of four consecutive primes.
  • A133529 (program): Sum of squares of three consecutive primes.
  • A133530 (program): Sum of third powers of three consecutive primes.
  • A133531 (program): Sum of fourth powers of three consecutive primes.
  • A133532 (program): Sum of fifth powers of three consecutive primes.
  • A133533 (program): Sum of sixth powers of three consecutive primes.
  • A133534 (program): Sum of third powers of two consecutive primes.
  • A133535 (program): Sum of fourth powers of two consecutive primes.
  • A133536 (program): Sum of fifth powers of two consecutive primes.
  • A133537 (program): Sum of sixth powers of two consecutive primes.
  • A133538 (program): Sum of seventh powers of two consecutive primes.
  • A133539 (program): Sum of third powers of five consecutive primes.
  • A133540 (program): Sum of fourth powers of five consecutive primes.
  • A133541 (program): Sum of fifth powers of five consecutive primes.
  • A133542 (program): Sum of sixth powers of five consecutive primes.
  • A133543 (program): Sum of seventh powers of five consecutive primes.
  • A133545 (program): (A000012 * A007318 - A007318 * A000012) - A000012.
  • A133546 (program): Binomial transform of [1,3,5,6,7,8,9,10,11,…] (i.e., positive integers except 2 and 4).
  • A133547 (program): a(n) = sum of squares of first n odd primes.
  • A133548 (program): a(n) = sum of cubes of first n odd primes.
  • A133549 (program): Sum of the fourth powers of the first n odd primes.
  • A133550 (program): Sum of fifth powers of n odd primes.
  • A133555 (program): Order of A113709(n) among composite positive integers.
  • A133558 (program): a(n) = a(n-1) + 9*a(n-2) for n >= 2, a(0)=1, a(1)=2.
  • A133562 (program): Numbers which are the sum of the squares of seven consecutive primes.
  • A133566 (program): Triangle read by rows: (1,1,1,…) on the main diagonal and (0,1,0,1,…) on the subdiagonal.
  • A133567 (program): A007318 * A133566.
  • A133569 (program): A133566 * A007318 as infinite lower triangular matrices.
  • A133572 (program): Row sums of triangle A133571.
  • A133577 (program): a(n) = a(n-1) + 10*a(n-2) for n >= 2, a(0)=1, a(1)=2.
  • A133578 (program): Let p = prime(n); then a(n) = (sum of prime factors of p+1) + (sum of prime factors of p-1). a(1) = 4 by convention.
  • A133579 (program): a(0)=a(1)=1; for n > 1, a(n) = 3*a(n-1) if a(n-1) and n are coprime, otherwise a(n) = a(n-1)/gcd(a(n-1), n).
  • A133582 (program): a(n) is found from a(n-1) by dividing by D-1 and multiplying by D, where D is the smallest number that is not a divisor of a(n-1).
  • A133585 (program): Expansion of x - x^2*(2*x+1)*(x^2-2) / ( (x^2-x-1)*(x^2+x-1) ).
  • A133586 (program): Expansion of x*(1+2*x)/( (x^2-x-1)*(x^2+x-1) ).
  • A133592 (program): a(n)=2*a(n-1)+6*a(n-2) for n>=3, a(0)=1, a(1)=2, a(2)=8 .
  • A133594 (program): a(n)=3*a(n-1)+12*a(n-2) for n>=3, a(0)=1, a(1)=3, a(2)=18 .
  • A133599 (program): A097806 * A133080 * A007318.
  • A133600 (program): Row sums of triangle A133599.
  • A133601 (program): A007318 * (A097806 + A133080 - I), I = Identity matrix.
  • A133602 (program): The matrix-vector product A133080 * A000108.
  • A133603 (program): The matrix-vector product A133566 * A000108.
  • A133607 (program): Triangle read by rows: T(n, k) = qStirling2(n, k, q) for q = -1, with 0 <= k <= n.
  • A133610 (program): Partial sums of pyramidal sequence A053616.
  • A133620 (program): Binomial(n+p,n) mod n where p=10.
  • A133621 (program): Numbers k such that binomial(k+p,k) mod k = 1, where p=10.
  • A133622 (program): a(n) = 1 if n is odd, a(n) = n/2+1 if n is even.
  • A133623 (program): Binomial(n+p, n) mod n where p=3.
  • A133624 (program): Binomial(n+p, n) mod n, where p=4.
  • A133625 (program): Binomial(n+p, n) mod n where p=5.
  • A133628 (program): a(1)=1, a(n) = a(n-1) + (p-1)*p^(n/2-1) if n is even, else a(n) = a(n-1) + p^((n-1)/2), where p=4.
  • A133629 (program): a(1)=1, a(n) = a(n-1) + (p-1)*p^(n/2-1) if n is even, otherwise a(n) = a(n-1) + p^((n-1)/2), where p=5.
  • A133631 (program): a(n) = a(n-1) - 4*a(n-2), a(0)=1, a(1)=2.
  • A133632 (program): a(1)=1, a(n) = (p-1)*a(n-1), if n is even, otherwise a(n) = p*a(n-2), where p = 5.
  • A133637 (program): Expansion of q^(-1) * psi(-q) / psi(-q^3)^3 in powers of q where psi() is a Ramanujan theta function.
  • A133638 (program): a(n) = 2prime(n) + prime(n-1) - 3*n.
  • A133639 (program): Mobius transform of b(n) where b(8n + 1) = A080995(n).
  • A133640 (program): List of pairs n,4n, where n is the least unused number so far.
  • A133641 (program): a(n) = 2*L(n) + L(n-1) - n, L(n) = n-th Lucas number A000204(n).
  • A133642 (program): a(n) = 4*a(n-1)+20*a(n-2) for n>=3, a(0)=1, a(1)=4, a(2)=32.
  • A133645 (program): Integers arising in A133677.
  • A133646 (program): a(n)=5*a(n-1)+30*a(n-2) for n>=3, a(0)=1, a(1)=5, a(2)=50 .
  • A133647 (program): A133566 * A000244.
  • A133648 (program): a(n) = 2*3^n + 3^(n-1) - (n+1).
  • A133649 (program): A007318^(-1) * A133648.
  • A133653 (program): A007318^(-1) * A003261.
  • A133654 (program): a(n) = 2*A000129(n) - 1.
  • A133655 (program): a(n) = 2*A016777(n) + A016777(n-1) - (n+1).
  • A133657 (program): Expansion of q * (phi(q) * psi(q^4))^2 in powers of q where phi(), psi() are Ramanujan theta functions.
  • A133665 (program): a(n) = a(n-1) - 9*a(n-2), a(0) = 1, a(1) = 3.
  • A133666 (program): a(n) = a(n-1) - 16*a(n-2), a(0)=1, a(1)=4.
  • A133667 (program): a(n) = a(n-1) - 25*a(n-2), a(0)=1, a(1)=5.
  • A133668 (program): a(n) = a(n-1) - 36*a(n-2), a(0)=1, a(1)=6.
  • A133669 (program): a(n) = a(n-1) - 49*a(n-2), a(0)=1, a(1)=7.
  • A133670 (program): Partial sums of A000016.
  • A133671 (program): a(n) = a(n-1) - 64*a(n-2), a(0)=1, a(1)=8.
  • A133672 (program): a(n) = a(n-1) - 81*a(n-2), a(0)=1, a(1)=9.
  • A133673 (program): a(n) = n*L(n) + (n-1)*L(n-1) where L(n) is the Lucas number.
  • A133674 (program): a(n) = |A061395(n+1) - A061395(n)|.
  • A133677 (program): Integers k such that prime(k)*(2*prime(k)-1)/3 is an integer.
  • A133678 (program): a(n)=6*a(n-1)+42*a(n-2) for n>=3, a(0)=1, a(1)=6, a(2)=72 .
  • A133679 (program): a(n) = 7*a(n-1) + 56*a(n-2) for n>=3, a(0)=1, a(1)=7, a(2)=98.
  • A133680 (program): a(n)=8*a(n-1)+72*a(n-2) for n>=3, a(0)=1, a(1)=8, a(2)=128 .
  • A133681 (program): a(n)=9*a(n-1)+90*a(n-2) for n>=3, a(0)=1, a(1)=9, a(2)=162 .
  • A133682 (program): Number of regular complex polytopes in n-dimensional unitary complex space.
  • A133683 (program): Linear recurrence a(n) = a(n-3) + 2a(n-5), starting from all-one initial conditions.
  • A133684 (program): a(2n) = A001045(n); a(1)=1; a(2n+1) = 2*A001045(n-1) for n >= 1.
  • A133686 (program): Number of labeled n-node graphs with at most one cycle in each connected component.
  • A133689 (program): a(n) = smallest integer that is > n and is a multiple of every proper divisor of n.
  • A133690 (program): Expansion of (phi(-q) * phi(q^2))^2 in powers of q where phi() is a Ramanujan theta function.
  • A133691 (program): Expansion of (1 - (phi(-q) * phi(q^2))^2) / 4 in powers of q where phi() is a Ramanujan theta function.
  • A133692 (program): Expansion of phi(-q) * phi(q^2) in powers of q where phi() is a Ramanujan theta function.
  • A133693 (program): Expansion of (1 - phi(-q) * phi(q^2)) / 2 in powers of q where phi() is a Ramanujan theta function.
  • A133694 (program): a(n) = (3*n^2 + 3*n - 4)/2.
  • A133695 (program): a(n) = 2*A008683 - 1.
  • A133698 (program): Triangle, diagonal = A001227 with the rest zeros.
  • A133699 (program): A051731 * A133698.
  • A133700 (program): A051731 * A001227; a(n) = Sum_{d|n} A001227(d).
  • A133701 (program): A133698 * A051731.
  • A133702 (program): A051731 * A023136.
  • A133704 (program): A051731 * a diagonalized matrix of A133696.
  • A133708 (program): First differences of A047835.
  • A133710 (program): Column l=3 of irregular triangle in A133709.
  • A133718 (program): Column 3 of array in A133713.
  • A133725 (program): a(n) = Sum_{d|n} mu(n/d)*d*(3*d - 1)/2.
  • A133727 (program): A051731 * A007438 as a diagonalized matrix.
  • A133728 (program): A128174 * A127775.
  • A133729 (program): A007318 * A133728.
  • A133730 (program): Alternating sign sequence A033999 interleaved with Jacobsthal sequence A001045.
  • A133734 (program): A000012 * A002865 as a diagonalized matrix.
  • A133735 (program): A000012 * A133734.
  • A133747 (program): Decimal expansion of the nonzero invariant of the Weierstrass elliptic function with half-periods 1/2 and i/2.
  • A133748 (program): Decimal expansion of the first root of the Weierstrass elliptic function P(1/2 | 1/2, i/2).
  • A133749 (program): Decimal expansion of -2*cos((2*Pi)/9) + 2*sqrt(3)*sin((2*Pi)/9).
  • A133751 (program): a(n) = 2*(2+n)! + 2^n.
  • A133752 (program): a(n) = 256^n.
  • A133754 (program): a(n) = n^5 - n^3.
  • A133755 (program): Number of positive integers less than n/3 that are coprime to n.
  • A133759 (program): Numbers that are the sum of a nonzero pentagonal number and a nonzero square in at least one way.
  • A133760 (program): Sum of the number of divisors of the numbers between prime(n) and prime(n+1).
  • A133765 (program): Primes that contain the digit 4 or the digit 9.
  • A133766 (program): a(n) = (4*n+1)*(4*n+3)*(4*n+5).
  • A133767 (program): a(n) = (4*n+3)*(4*n+5)*(4*n+7).
  • A133783 (program): Primes containing only digits from set (1,2,3,4,5,6).
  • A133789 (program): Let P(A) denote the power set of an n-element set A. Then a(n) = the number of pairs of elements {x,y} of P(A) for which either 0) x and y are disjoint and for which x is not a subset of y and y is not a subset of x, 1) x and y are disjoint and for which either x is a subset of y or y is a subset of x, or 2) x and y intersect but for which x is not a subset of y and y is not a subset of x.
  • A133790 (program): A014963*A100994.
  • A133795 (program): a(n) = n-th semiprime + n-th non-semiprime.
  • A133796 (program): a(n) = n-th prime + n-th semiprime.
  • A133798 (program): a(n) = A002467(n) - 1.
  • A133799 (program): a(2) = 1, a(3)=3; for n >= 4, a(n) = (n-2)!*Stirling_2(n,n-1)/2 = n!/4.
  • A133800 (program): Triangle read by rows in which row n gives number of ways to partition n labeled elements into k pie slices allowing the pie to be turned over (n >= 1, 1 <= k <= n).
  • A133803 (program): Floor log A055213(n).
  • A133806 (program): Alternate terms of A131708 and A000079.
  • A133807 (program): A007318 * (A097806 + A133566 - I), where I is the identity matrix.
  • A133818 (program): a(n) = (8*n+3)*(8*n+5)*(8*n+7)*(8*n+9).
  • A133819 (program): Triangle whose rows are sequences of increasing squares: 1; 1,4; 1,4,9; … .
  • A133820 (program): Triangle whose rows are sequences of increasing cubes: 1; 1,8; 1,8,27; … .
  • A133821 (program): Triangle whose rows are sequences of increasing fourth powers: 1; 1,16; 1,16,81; … .
  • A133823 (program): Triangle whose rows are sequences of increasing and decreasing cubes:1; 1,8,1; 1,8,27,8,1; … .
  • A133824 (program): Triangle whose rows are sequences of increasing and decreasing fourth powers: 1; 1,16,1; 1,16,81,16,1; … .
  • A133825 (program): Triangle whose rows are sequences of increasing and decreasing triangular numbers: 1; 1,3,1; 1,3,6,3,1; … .
  • A133826 (program): Triangle whose rows are sequences of increasing and decreasing tetrahedral numbers: 1; 1,4,1; 1,4,10,4,1; … .
  • A133827 (program): Number of solutions to x + 7 * y = 2 * n in triangular numbers.
  • A133829 (program): a(n) = the largest “non-isolated divisor” of 2n. A positive divisor k of n is non-isolated if k-1 or k+1 also divides n.
  • A133837 (program): Semiprimes from partition of sequence of positive integers.
  • A133846 (program): a(n)*a(n-7) = a(n-1)a(n-6)+a(n-3)+a(n-4) with initial terms a(1)=…=a(7)=1.
  • A133851 (program): Sloping binary representation of powers of 4 (A000302), slope = -1 .
  • A133853 (program): a(n) = (64^n - 1)/63.
  • A133869 (program): Numbers k such that 32*k + 1 is prime.
  • A133870 (program): Primes of the form 32*n + 1.
  • A133872 (program): Period 4: repeat [1, 1, 0, 0].
  • A133873 (program): n modulo 3 repeated 3 times.
  • A133874 (program): n modulo 4 repeated 4 times.
  • A133875 (program): n modulo 5 repeated 5 times.
  • A133876 (program): n modulo 6 repeated 6 times.
  • A133877 (program): n modulo 7 repeated 7 times.
  • A133878 (program): n modulo 8 repeated 8 times.
  • A133879 (program): n modulo 9 repeated 9 times.
  • A133880 (program): n modulo p repeated p times (where p=10).
  • A133881 (program): Even numbers k such that binomial(k+p,k) mod k = 1, where p=10.
  • A133882 (program): a(n) = binomial(n+2,n) mod 2^2.
  • A133883 (program): a(n) = binomial(n+3,n) mod 3^2.
  • A133884 (program): a(n) = binomial(n+4,n) mod 4.
  • A133885 (program): Binomial(n+5,n) mod 5^2.
  • A133886 (program): a(n) = binomial(n+6,n) mod 6.
  • A133887 (program): Binomial(n+7,n) mod 7^2.
  • A133888 (program): Binomial(n+8,n) mod 8.
  • A133889 (program): a(n) = binomial(n+9,n) mod 9.
  • A133890 (program): Binomial(n+10,n) mod 10.
  • A133891 (program): a(n) = binomial(n+p,n) mod p, where p=12.
  • A133893 (program): Numbers m such that binomial(m+3,m) mod 3 = 0.
  • A133894 (program): Numbers m such that binomial(m+4,m) mod 4 = 0.
  • A133895 (program): Numbers m such that binomial(m+5,m) mod 5 = 0.
  • A133896 (program): Numbers m such that binomial(m+6,m) mod 6 = 0.
  • A133897 (program): Numbers m such that binomial(m+7,m) mod 7 = 0.
  • A133898 (program): Numbers m such that binomial(m+8,m) mod 8 = 0.
  • A133899 (program): Numbers m such that binomial(m+9,m) mod 9 = 0.
  • A133914 (program): Row sums of triangle A133913.
  • A133915 (program): a(n) = Sum_{i=0..n} C(2n-i,n+i)*2^i.
  • A133925 (program): Number of compositions of n into parts of size 2 and 3 with no three consecutive 2s and no two consecutive 3s.
  • A133926 (program): Number of equivalence classes of compositions of n into parts of size 2 and 3 under the following equivalence relation: We make a “move” by changing three consecutive 2s into two consecutive 3s or vice versa. Two compositions are equivalent if we can reach one from the other by a series of moves.
  • A133931 (program): Expansion of x*(2-4*x^2-x^3)/((1-x)^2*(1-x-x^2)).
  • A133933 (program): a(n) = (1 + n * (n - 2) + (n - 1)!) mod (4*n).
  • A133934 (program): A007318 * (a diagonalized version of A124625).
  • A133935 (program): A007318 * A093178 as a diagonalized matrix.
  • A133936 (program): Number of times prime powers occur in the columns of tables A133232 and A133233.
  • A133937 (program): A100994-n/A014963.
  • A133942 (program): a(n) = (-1)^n * n!.
  • A133953 (program): A second integer solution:d=2;h=1; A 4 X 4 vector Markov of a game matrix MA and an anti- game matrix MB such that game_valueMa+game_ValueMB =0 and the score is the sum of the vector out put of the Markov: MA={{0,1},{1,d}}; MB={{1/h,0},(2 - d + 1/h + h),h}}; Characteristic Polynomial is: -1 + 4 x^2 - 4 x^3 + x^4.
  • A133985 (program): Expansion of f(-x, x^2) in powers of x where f(, ) is Ramanujan’s general theta function.
  • A133988 (program): Expansion of phi(x) / chi(x^3) in powers of x where phi(), chi() are Ramanujan theta functions.
  • A133989 (program): Define fu(1,1) = 0. Then a(n) = fu(1,n) = smallest number t such that an n X 1 strip of n squares can be cut into n squares using p_1, p_2, …, p_t cuts where p_t is a prime number or p_t = 1.
  • A133990 (program): a(n) = Sum_{k=0..n} (-1)^(n-k) * binomial(n,k) * binomial(2^k + n - 1,n).
  • A133991 (program): a(n) = Sum_{k=0..n} binomial(n,k)*binomial(2^k+n-1,n).
  • A133992 (program): a(n) = tau( prime(n)*prime(prime(n)) - 1 ).
  • A133993 (program): a(n) = a(n-1) + 3*a(n-2) - a(n-3) - 2*a(n-4), n > 3.
  • A134002 (program): Positive integers n such that n(n+5)=a(a+5)+b(b+5) is solvable in positive integers.
  • A134003 (program): Positive integers n for which n^2+(n+5)^2 is prime.
  • A134006 (program): a(n) = 1^n + 3^n + 5^n + 7^n.
  • A134007 (program): a(n) = 1^n + 3^n + 5^n + 7^n + 9^n.
  • A134008 (program): a(n) = 1^n + 3^n + 5^n + 7^n + 9^n + 11^n.
  • A134010 (program): n^(initial digit of n).
  • A134011 (program): Period 9: repeat [1, 2, 3, 4, 5, 4, 3, 2, 1].
  • A134012 (program): Period 5: repeat 1, 6, 11, 6, 1.
  • A134013 (program): Expansion of q * phi(q) * psi(q^8) in powers of q where phi(), psi() are Ramanujan theta functions.
  • A134014 (program): Expansion of phi(-q) * phi(q^4) in powers of q where phi() is a Ramanujan theta function.
  • A134015 (program): Expansion of (1 - phi(-q) * phi(q^4)) / 2 in powers of q where phi() is a Ramanujan theta function.
  • A134016 (program): Inverse score permutation of an Fibonacci -anti-Fibonacci zero sum game of 2 X 2 matrices.
  • A134017 (program): Period 9: repeat 1, 2, 4, 3, 5, 3, 4, 2, 1.
  • A134018 (program): Let P(A) be the power set of an n-element set A. Then a(n) = the number of pairs of elements {x,y} of P(A) for which either 0) x and y are disjoint and for which either x is a subset of y or y is a subset of x, or 1) x and y are intersecting but for which x is not a subset of y and y is not a subset of x.
  • A134019 (program): Let P(A) be the power set of an n-element set A. Then a(n) = the number of pairs of elements {x,y} of P(A) for which either 0) x and y are intersecting but for which x is not a subset of y and y is not a subset of x, or 1) x = y.
  • A134020 (program): Numbers that are one less than a square and have exactly 4 divisors.
  • A134021 (program): Length of n in balanced ternary representation.
  • A134022 (program): Number of negative trits in balanced ternary representation of n.
  • A134023 (program): Number of zeros in balanced ternary representation of n.
  • A134024 (program): Number of positive trits in balanced ternary representation of n.
  • A134025 (program): Numbers for which the balanced ternary representation is the same length as the ternary representation.
  • A134026 (program): Numbers that are in balanced ternary representation longer than in ternary representation.
  • A134027 (program): Nonnegative numbers that are palindromes in balanced ternary representation.
  • A134028 (program): Reversal of n in balanced ternary representation.
  • A134029 (program): Period 9: repeat 3, 2, 4, 1, 5, 1, 4, 2, 3.
  • A134030 (program): Areas of regular n-sided polygons with length of each side equal to 1 (rounded).
  • A134045 (program): Let P(A) be the power set of an n-element set A. Then a(n) = the number of pairs of elements {x,y} of P(A) for which either 0) x and y are disjoint and for which either x is a subset of y or y is a subset of x, or 1) x and y are intersecting but for which x is not a subset of y and y is not a subset of x, or 2) x = y.
  • A134057 (program): a(n) = binomial(2^n-1,2).
  • A134058 (program): Triangle T(n, k) = 2*binomial(n, k) with T(0, 0) = 1, read by rows.
  • A134059 (program): Triangle T(n, k) = 3*binomial(n,k) with T(0, 0) = 1, read by rows.
  • A134060 (program): Triangle T(n,k) = A124927(n,k) + A134058(n,k) - A007318(n,k), read by rows.
  • A134061 (program): Triangle, A124928 + A134059 - A007318.
  • A134062 (program): Row sums of triangle A134061.
  • A134063 (program): a(n) = (1/2)*(3^n - 2^(n+1) + 3).
  • A134064 (program): Let P(A) be the power set of an n-element set A. Then a(n) = the number of pairs of elements {x,y} of P(A) for which either 0) x and y are intersecting but for which x is not a subset of y and y is not a subset of x, or 1) x and y are intersecting and for which either x is a proper subset of y or y is a proper subset of x, or 2) x = y.
  • A134067 (program): Row sums of triangle A134066.
  • A134068 (program): a(n) = 2*a(n-2) + 4*a(n-3), with initial terms 0, 3, 3.
  • A134077 (program): Expansion of psi(x) * phi(-x)^3 / chi(-x^3)^3 in powers of x where phi(), psi(), chi() are Ramanujan theta functions.
  • A134079 (program): Expansion of q^(-2/3) * c(-q)^2 / 9 in powers of q where c(q) is a cubic AGM theta function.
  • A134080 (program): Expansion of (f(-q^5)^5 / f(-q) + f(q^5)^5 / f(q)) / 2 in powers of q^2 where f() is a Ramanujan theta function.
  • A134081 (program): Triangle T(n, k) = binomial(n, k)*((2*k+1)*(n-k) +k+1)/(k+1), read by rows.
  • A134082 (program): Triangle read by rows, (n-1) zeros followed by (2n, 1).
  • A134083 (program): A007318 * A134082.
  • A134095 (program): E.g.f.: A(x) = 1/(1 - LambertW(-x)^2).
  • A134099 (program): Odd nonprimes that are preceded by but not followed by primes.
  • A134100 (program): Primes p > 3 such that neither p-2 nor p-4 are prime.
  • A134101 (program): Odd nonprimes such that the prior odd number is not a prime but the next odd number is a prime.
  • A134115 (program): Powers of 9 written backwards and sorted.
  • A134116 (program): Primes p such that q-p = 34, where q is the next prime after p.
  • A134119 (program): a(n) = floor(n^2/10) - floor((n-1)^2/10).
  • A134120 (program): Primes p such that q-p = 42, where q is the next prime after p.
  • A134121 (program): Primes p such that q-p = 44, where q is the next prime after p.
  • A134124 (program): Primes p such that q-p = 50, where q is the next prime after p.
  • A134136 (program): a(n) = 2*a(n-2) + 4*a(n-3), with initial terms 0, 1, 1.
  • A134137 (program): Alternating row sums of triangle A049352 (S1p(4)).
  • A134138 (program): Alternating row sums of triangle A046089 (S1p(3)).
  • A134142 (program): List of quadruples: 2*(-4)^n, -3*(-4)^n, 2*(-4^n), 2*(-4)^n, n >= 0.
  • A134153 (program): a(n) = 15n^2 + 9n + 1.
  • A134154 (program): a(n) = 15n^2 - 9n + 1.
  • A134155 (program): a(n) = 1 + 21 n + 168 n^2 + 588 n^3 + 1029 n^4.
  • A134156 (program): a(n) = 2*tau(n) - n, where tau(n) is the number of divisors of n (A000005).
  • A134158 (program): a(n) = 1 + 27n + 252n^2 + 882n^3 + 1029n^4.
  • A134159 (program): a(n) = 13 + 165*n + 756*n^2 + 1470*n^3 + 1029*n^4.
  • A134160 (program): a(n) = 163 + 1053*n + 2520*n^2 + 2646*n^3 + 1029*n^4.
  • A134161 (program): a(n) = 373 + 1947n + 3780n^2 + 3234n^3 + 1029n^4.
  • A134163 (program): 1 + 12*n + 81*n^3 + n*(105*n + 81*n^3)/2.
  • A134165 (program): Let P(A) be the power set of an n-element set A. Then a(n) = the number of pairs of elements {x,y} of P(A) for which either 0) x and y are disjoint and for which either x is a subset of y or y is a subset of x, or 1) x and y are disjoint and for which x is not a subset of y and y is not a subset of x, or 2) x and y are intersecting but for which x is not a subset of y and y is not a subset of x, or 3) x = y.
  • A134168 (program): Let P(A) be the power set of an n-element set A. Then a(n) = the number of pairs of elements {x,y} of P(A) for which either 0) x and y are disjoint and for which either x is a subset of y or y is a subset of x, or 1) x and y are intersecting but for which x is not a subset of y and y is not a subset of x, or 2) x and y are intersecting and for which either x is a proper subset of y or y is a proper subset of x, or 3) x = y.
  • A134169 (program): a(n) = 2^(n-1)*(2^n - 1) + 1.
  • A134171 (program): a(n) = (9/2)*(n-1)*(n-2)*(n-3).
  • A134172 (program): Expansion of x^2*(1+x)*(1-x+x^2) / ((1-x)^2*(1+x^2)^2).
  • A134173 (program): a(n) = Sum_{k=0..n} binomial(n,k)*binomial(2^k,n).
  • A134174 (program): a(n) = Sum_{k=0..n} (-1)^(n-k) * binomial(n,k) * binomial(2^k,n).
  • A134175 (program): a(n) = (32/2)*(n-1)*(n-2)*(n-3)*(n-4).
  • A134176 (program): a(n) = (3/8)*(n-1)*(n-2)*(27*n^2-137*n+180).
  • A134177 (program): Expansion of phi(-x^3) * psi(x^4) + x * phi(-x) * psi(x^12) in powers of x where phi(), psi() are Ramanujan theta functions.
  • A134181 (program): Difference between cumulative prime and odd sums.
  • A134183 (program): A Hankel transform of a Catalan product.
  • A134184 (program): A transform of the central binomial coefficients A001405.
  • A134186 (program): A 3 person 9 X 9 Markov approach to a zero sum game where: Sum[game_value(MAi),{i,1,3}]=0 and two of the games are minimal Pisot vector Markovs and the third is a negative Fibonacci: Characteristic Polynomial: -1 + 3 x^2 + 3 x^3 - 4 x^4 - 5 x^5 + x^6 + 4 x^7 - x^9; MA1={{0,1,0},{,0,0,1},{1,1,0}};Det=1 ;gv=-1/4; MA2={{0,1,1},{1,0,0},{0,1,0}};Det=1;gv=-1/4 MA2={{0,0,1},{0,1,0},{1,0,-1}};Det=-1;gv=1/2.
  • A134193 (program): a(1) = 1; for n>1, a(n) = the smallest positive integer not occurring among the exponents in the prime-factorization of n.
  • A134195 (program): Antidiagonal sums of square array A126885.
  • A134199 (program): A002260 + A134082 - I as infinite lower triangular matrices; I = Identity matrix.
  • A134201 (program): Number of rigid hypergroups of order n.
  • A134202 (program): Number of rigid Hv-groups of order n.
  • A134224 (program): A004736 + A134082 - I as infinite lower triangular matrices; I = Identity matrix.
  • A134225 (program): A007436 + A134082 - A000012 as infinite lower triangular matrices; where A000012 = (1; 1,1; 1,1,1; …).
  • A134226 (program): Triangle T(n, k) = 3*n - 4 if k = n-1 otherwise k, read by rows.
  • A134227 (program): Row sums of triangle A134226.
  • A134230 (program): a(n) = (10^n+1)^2-1.
  • A134231 (program): Triangle T(n, k) = n -k +1 with T(n, n-1) = 2*n-1 and T(n, n) = 1, read by rows.
  • A134234 (program): Triangle read by rows, n-th row = n terms of 2n, 2n+2, 2n+4, …, 1; with a(1) = 1.
  • A134235 (program): Triangle read by rows: a(1) = 1; then n-th row = n terms of (n+2), (n+4), (n+6), …, n.
  • A134237 (program): Triangle read by rows, a(1) = 1, n-th row n terms of: (2n-1, 2n, 2n+1, …, followed by n).
  • A134238 (program): Row sums of triangle A134237.
  • A134239 (program): A127899(unsigned) * A007318.
  • A134241 (program): a(n) = 8*(n-1)*(n-2)*(n-3)*(6*n^2-37*n+60).
  • A134247 (program): A007318 * triangle by rows, n-th row = (n-1) zeros followed by T(n), 1.
  • A134249 (program): Triangle read by rows, taken from the lower triangular matrix (M * A000012 + A000012 * M) - A000012; where M = lower triangular matrix with (1,1,1,…) in the main diagonal and the triangular numbers in the subdiagonal and A000012 = (1; 1,1; 1,1,1; …).
  • A134250 (program): Expansion of x*(4+9*x-7*x^2) / ((1-x)*(1+3*x-x^2)).
  • A134267 (program): a(n) = |A090964(n+1) - A090964(n)|.
  • A134269 (program): Number of solutions to the equation p^k - p^(k-1) = n, where k is a positive integer and p is prime.
  • A134270 (program): a(n)=2a(n-1)+a(n-2)-4a(n-4).
  • A134271 (program): a(n) = a(n-2) + 2*a(n-3), n > 3; with a(0)=0, a(1)=1, a(2)=2, a(3)=0.
  • A134286 (program): Characteristic sequence for sequence A026905.
  • A134287 (program): Fifth column of triangle A103371 (without leading zeros).
  • A134288 (program): a(n) = binomial(n+7,7)*binomial(n+7,6)/(n+7).
  • A134289 (program): Eighth column (and diagonal) of Narayana triangle A001263.
  • A134290 (program): Ninth column (and diagonal) of Narayana triangle A001263.
  • A134291 (program): Tenth column (and diagonal) of Narayana triangle A001263.
  • A134295 (program): a(n) = Sum_{k=1..n} ((n-k)!*(k-1)! - (-1)^k).
  • A134297 (program): a(n) = 107*n.
  • A134298 (program): a(n) = (107*n)^5.
  • A134301 (program): Periodic sequence (0, 2, 6, 2, 0).
  • A134309 (program): Triangle read by rows, where row n consists of n zeros followed by 2^(n-1).
  • A134310 (program): (A000012 * A134309 + A134309 * A000012) - A000012, where the sequences are interpreted as lower triangular matrices.
  • A134311 (program): Row sums of triangle A134310.
  • A134312 (program): A097806 * A134309.
  • A134314 (program): First differences of A134429.
  • A134315 (program): A134309 * A097806.
  • A134316 (program): a(n) = index of first derangement of 1..n (n>=2).
  • A134317 (program): A128174 * A134309.
  • A134318 (program): A007318 * A134317.
  • A134319 (program): A007318 * a triangle by rows: for n > 0, n zeros followed by 2^n - 1.
  • A134323 (program): a(n) = Legendre(-3, prime(n)).
  • A134327 (program): a(n) = (n^5-n-5)/5.
  • A134334 (program): Numbers which are not divisible by the number of their prime factors (counted with multiplicity).
  • A134340 (program): Expansion of psi(x)^3 * f(-x^3)^3 / chi(-x)^2 in powers of x where psi(), chi(), f() are Ramanujan theta functions.
  • A134341 (program): Numbers whose fifth powers have a partition as a sum of fifth powers of four positive integers.
  • A134342 (program): Accepted inputs by a certain adaptive automaton (number 4258072) with two adaptive functions and unary numbers as input.
  • A134343 (program): Expansion of psi(-x)^2 in powers of x where psi() is a Ramanujan theta function.
  • A134345 (program): Number of partitions of n into odd squarefree parts.
  • A134346 (program): Triangle read by rows: T(n,k) = (2^(n+1)-1)*binomial(n,k).
  • A134347 (program): A007318^(-1) * A134346.
  • A134348 (program): A007318^(-1) * A134347.
  • A134350 (program): Row sums of triangle A134349.
  • A134351 (program): Binomial transform of [1, 5, -1, 5, -1, 5, …]. Inverse binomial transform of A134350.
  • A134352 (program): A130123 * A128174.
  • A134353 (program): Row sums of triangle A134352.
  • A134358 (program): Coefficient of y^(n-3) in expansion of (y+n!)^n.
  • A134361 (program): a(n) = smallest integer >= n which has only prime factors 2 and 3.
  • A134362 (program): a(n) is the number of functions f:X->X, where |X| = n, such that for every x in X, f(f(x)) != x (i.e., the square of the function has no fixed points; note this implies that the function has no fixed points).
  • A134366 (program): a(n) = (n!)^(n-1).
  • A134367 (program): a(n) = (n!)^(n-2).
  • A134372 (program): a(n) = ((2n)!)^2.
  • A134374 (program): a(n) = ((2n+1)!)^2.
  • A134375 (program): a(n) = (n!)^4.
  • A134376 (program): Numbers whose sum of prime factors (counted with multiplicity) is not prime.
  • A134377 (program): Binomial transform of A045621.
  • A134378 (program): A084938 * [1,2,3,…], where A084938 = the Delta operator.
  • A134381 (program): Row sums of triangle A134380.
  • A134389 (program): A transform of floor((n+2)/2) with Hankel transform floor((n+2)/2)*(cos(Pi*n/2) + sin(Pi*n/2)).
  • A134391 (program): The sequence A_0, A_1, A_2, A_3, …, where the A_k are defined in A064990.
  • A134392 (program): A077028 * A000012, that is Rascal’s triangle (as matrix) multiplied by a lower triangular matrix of ones (main diagonal of ones included).
  • A134393 (program): Row sums of triangle A134392.
  • A134394 (program): Triangle T(n,k) = Sum_{j=k..n} A077028(j,k), read by rows.
  • A134395 (program): A007318 * A077028.
  • A134396 (program): A007318 * A000125.
  • A134398 (program): Triangle read by rows: T(n, k) = (k-1)*(n-k) + binomial(n-1,k-1).
  • A134399 (program): Matrix product of Binomial triangle A007318 and triangle with (1, 1, 2, 3, 4, 5, …) in the main diagonal and the rest zeros.
  • A134400 (program): M * A007318, where M = triangle with (1, 1, 2, 3, …) in the main diagonal and the rest zeros.
  • A134401 (program): Row sums of triangle A134400.
  • A134402 (program): Triangle read by rows, for n > 0, n zeros followed by n.
  • A134403 (program): Triangle read by rows: row n consists of (n, n, (n+1), (n+2), (n+3), …).
  • A134404 (program): Triangle read by rows in which row n contains Fib(0), …, Fib(n-1), Fib(n), Fib(n-1), …, Fib(0).
  • A134405 (program): -1 before list of quadruples -2n-1, 2n+2, -2n, 2n+1.
  • A134406 (program): Composite numbers of the form k^2 + 1.
  • A134407 (program): Numbers n such that n^2 + 1 is composite.
  • A134410 (program): Second-order Lucas numbers; a(n) = (2n+3)*Lucas(n) - n*Lucas(n-1).
  • A134414 (program): Expansion of eta(q)^2 / (eta(q^2) * eta(q^4)^6) in powers of q.
  • A134416 (program): Expansion of eta(q^4)^2 / (eta(q^2) * eta(q)^6) in powers of q.
  • A134417 (program): A007318 * Triangle with A133632 as the diagonal and the rest zeros.
  • A134418 (program): Row sums of triangle A134417.
  • A134420 (program): Composite squarefree numbers of the form k^2 + 1.
  • A134421 (program): Partial sums of A134021.
  • A134422 (program): Square numbers which are sums of 2 distinct nonzero squares.
  • A134425 (program): Number of paths of length n in the first quadrant, starting at the origin and consisting of 2 kinds of upsteps U=(1,1) (U1 and U2), 3 kinds of flatsteps F=(1,0) (F1, F2 and F3) and 1 kind of downsteps D=(1,-1).
  • A134426 (program): Triangle read by rows: T(n,k) is the number of paths of length n in the first quadrant, starting at the origin, ending at height k and consisting of 2 kind of upsteps U=(1,1) (U1 and U2), 3 kind of flatsteps F=(1,0) (F1, F2 and F3) and 1 kind of downsteps D=(1,-1).
  • A134427 (program): Numbers k such that k^2 + 1 is a composite squarefree number.
  • A134429 (program): a(n) = (-1)^(1 + n) * 2 * ( -1/2 -n + (-1)^((1 + n)*(2 + n)/2)).
  • A134430 (program): Period 4: repeat [1, -2, -2, 1].
  • A134432 (program): Sum of entries in all the arrangements of the set {1,2,…,n} (to n=0 there corresponds the empty set).
  • A134433 (program): Triangle read by rows: T(n,k) is the number of permutations of {1,2,…,n} in which the last entry of the first increasing run is equal to k (1 <= k <= n).
  • A134437 (program): Number of cells in the 2nd rows of all deco polyominoes of height n. A deco polyomino is a directed column-convex polyomino in which the height, measured along the diagonal, is attained only in the last column.
  • A134438 (program): Number of tilings of a 3 X n rectangle with n trominoes.
  • A134441 (program): Last two digits of primes of form 4n+1 (A002144), excluding 5. Leading 0’s omitted.
  • A134442 (program): Last two digits of primes of form 4n+3 (A002145). Leading 0’s omitted.
  • A134443 (program): A007318^2 * A007248.
  • A134444 (program): (A000012 * A128174 + A128174 * A000012) - A000012.
  • A134446 (program): A128174 * A002260.
  • A134447 (program): A002260 * A128174.
  • A134449 (program): Sum of even products minus sum of odd products of different pairs of numbers from 1 to n.
  • A134451 (program): Ternary digital root of n.
  • A134455 (program): a(0) = a(1) = 1, a(2) = 2; a(n) = 2*a(n-2) + a(n-1)*a(n-3).
  • A134460 (program): First differences of A067186.
  • A134461 (program): Expansion of (phi(x) * psi(-x))^4 in powers of x where phi(), psi() are Ramanujan theta functions.
  • A134464 (program): (A127648 * A000012 + A000012 * A127773) - A000012.
  • A134465 (program): Row sums of triangle A134464.
  • A134467 (program): a(n) = n(n+1) - A000120(n), where A000120(n) = number of 1’s in binary expansion of n.
  • A134478 (program): Triangle read by rows, T(0,0) = 1; n-th row = (n+1) terms of n, n+1, n+2, …
  • A134479 (program): Row sums of triangle A134478.
  • A134480 (program): A134478 * A000012.
  • A134481 (program): Row sums of triangle A134480.
  • A134482 (program): Triangle read by rows: row n consists of n followed by the numbers n through 2n-2.
  • A134483 (program): Triangle read by rows: T(n,k) = 2n + k - 2; 1 <= k <= n.
  • A134484 (program): Triangle, read by rows, where T(n,k) = 2^[n*(n-1) - k*(k-1)] * binomial(n,k) for n>=k>=0.
  • A134485 (program): Row sums of triangle A134484(n,k) = 2^[n(n-1) - k(k-1)] * C(n,k).
  • A134486 (program): a(0)=1; for n>=1, a(n) = the largest prime dividing n*a(n-1) + 1.
  • A134488 (program): a(0)=1. a(n) = n + d(a(n-1)), where d(m) is the number of positive divisors of m.
  • A134489 (program): a(n) = Fibonacci(5*n + 2).
  • A134490 (program): a(n) = Fibonacci(5n + 3).
  • A134491 (program): Fibonacci(5n+4).
  • A134492 (program): a(n) = Fibonacci(6*n).
  • A134493 (program): a(n) = Fibonacci(6*n+1).
  • A134494 (program): a(n) = Fibonacci(6n+2).
  • A134495 (program): a(n) = Fibonacci(6n + 3).
  • A134496 (program): Numbers that are not lunar pseudoprimes.
  • A134497 (program): a(n) = Fibonacci(6n+5).
  • A134498 (program): a(n) = Fibonacci(7n).
  • A134499 (program): a(n) = Fibonacci(7*n+1).
  • A134500 (program): a(n) = Fibonacci(7n + 2).
  • A134501 (program): a(n) = Fibonacci(7n + 3).
  • A134502 (program): a(n) = Fibonacci(7n + 4).
  • A134503 (program): a(n) = Fibonacci(7n + 5).
  • A134504 (program): a(n) = Fibonacci(7n + 6).
  • A134506 (program): Number of 2 X 2 singular integer matrices with elements from {1,…,n}.
  • A134507 (program): Number of rectangles in a pyramid built with squares. The squares counted in A092498 are excluded.
  • A134508 (program): Row sums of triangle A134507.
  • A134510 (program): A112552 * A128174.
  • A134512 (program): Row sums of triangle A134511.
  • A134513 (program): A049310 * A097806.
  • A134515 (program): Third column (k=2) of triangle A134832 (circular succession numbers).
  • A134516 (program): Numbers that are divisible by 2*(sum of their digits).
  • A134517 (program): Primes of form 24n-1.
  • A134519 (program): Numbers remaining when the natural numbers (A000027) are arranged into a triangle and only the beginning and end terms of each row are retained.
  • A134520 (program): A007318 + A128174 - A000012 as infinite lower triangular matrices.
  • A134521 (program): Triangle read by rows: T(n,k) = binomial(n,k) + (n + k) mod 2.
  • A134522 (program): a(n) = 2^n + ceiling(n/2).
  • A134532 (program): Numbers n such that the sum of the digits of 5^n is prime.
  • A134533 (program): Numbers n such that the sum of the digits of 7^n is prime.
  • A134534 (program): Numbers n such that the sum of the digits of 11^n is prime.
  • A134535 (program): Numbers n such that the sum of the digits of 13^n is prime.
  • A134538 (program): a(n) = 5*n^2 - 1.
  • A134540 (program): A054525 * A000012.
  • A134541 (program): Triangle read by rows: A000012 * A054525 regarded as infinite lower triangular matrices.
  • A134544 (program): A051731 * A002260.
  • A134545 (program): A051731 * A004736.
  • A134546 (program): Lower triangular matrix multiplication: A004736 * A051731.
  • A134547 (program): a(n)=5n^2+20n+4.
  • A134548 (program): a(1)=1, a(n) = 2 + maximal digit of Sum_{j=1..n-1} a(j).
  • A134558 (program): Array read by antidiagonals, a(n,k) = gamma(n+1,k)*e^k, where gamma(n,k) is the upper incomplete gamma function and e is the exponential constant 2.71828…
  • A134559 (program): A127093 * A000012.
  • A134560 (program): A051731 * A127775.
  • A134565 (program): Expansion of reversion of (x - 2*x^2) / (1 - x)^3.
  • A134566 (program): a(n) = least m such that {-m*tau} > {n*tau}, where { } denotes fractional part and tau = (1 + sqrt(5))/2.
  • A134567 (program): a(n) = least m such that {-m*tau} < {n*tau}, where { } denotes fractional part and tau = (1 + sqrt(5))/2.
  • A134571 (program): Array T(n,k) by antidiagonals; T(n,k) = position in row n of k-th occurrence of the Fibonacci number F(2n) in A134567.
  • A134574 (program): Array, a(n,k) = total size of all n-length words on a k-letter alphabet, read by antidiagonals.
  • A134575 (program): A051731 * A127733.
  • A134576 (program): A127733 * A051731.
  • A134577 (program): A127170 * A127648.
  • A134579 (program): Column products of tables A133232 and A133233.
  • A134581 (program): a(n) = 4*a(n-1) - 7*a(n-2) + 6*a(n-3) - 3*a(n-4), starting with 0, 1, 2, 3.
  • A134582 (program): a(n) = (2*n)^2 - 4.
  • A134583 (program): Signature sequence of the Hausdorff dimension of the Cantor set log(2)/log(3).
  • A134591 (program): a(n) is n reflected in n-th prime: distance between a(n) and prime(n) equals distance between prime(n) and n.
  • A134593 (program): a(n) = 5*n^2 + 10*n + 1. Coefficients of the rational part of (1 + sqrt(n))^5.
  • A134594 (program): a(n) = n^2 + 10*n + 5: coefficients of the irrational part of (1 + sqrt(n))^5.
  • A134612 (program): Nonprime numbers such that the root mean cube of their prime factors is a prime (where the root mean cube of c and d is ((c^3+d^3)/2)^(1/3)).
  • A134616 (program): Numbers such that the sum of squares of their prime factors (taken with multiplicity) is a prime.
  • A134630 (program): 5*n^5 - 3*n^3 - 2*n^2. Coefficients and exponents are the prime numbers in decreasing order.
  • A134631 (program): a(n) = 5*n^5 - 3*n^3 + 2*n^2. Coefficients and exponents are the prime numbers in decreasing order.
  • A134632 (program): 5*n^5 + 3*n^3 - 2*n^2. Coefficients and exponents are the prime numbers in decreasing order.
  • A134633 (program): 5*n^5 + 3*n^3 + 2*n^2. Coefficients and exponents are the prime numbers in decreasing order.
  • A134635 (program): Row sums of triangle A134634.
  • A134636 (program): Triangle formed by Pascal’s rule given borders = 2n+1.
  • A134637 (program): Triangle, T(n,k) = T(n-1,k) + T(n-1,k-1), 1<k<n with borders given by the Tetrahedral numbers.
  • A134638 (program): Row sums of triangle A134637.
  • A134654 (program): a(n) = 2a(n-2)+4a(n-3), n > 3.
  • A134658 (program): Triangle read by rows, giving coefficients of extended Jacobsthal recurrence.
  • A134659 (program): Total number of odd coefficients in (1+x+x^2)^k for k=0,…,n.
  • A134660 (program): Number of odd coefficients in (1 + x + x^2 + x^3)^n.
  • A134667 (program): Period 6: repeat [0, 1, 0, 0, 0, -1].
  • A134668 (program): Period 6: repeat [1, -1, 0, 0, -1, 1].
  • A134675 (program): Row sums of triangle A134674.
  • A134681 (program): Number of digits of all the divisors of n.
  • A134683 (program): Expansion of 1+x*(2+3*x)/(1-4*x^2).
  • A134684 (program): n^(n+9).
  • A134693 (program): a(n)=A133806(n)+A133806(n+6).
  • A134717 (program): Odd Motzkin numbers.
  • A134718 (program): Even Motzkin numbers.
  • A134719 (program): Odd Padovan numbers.
  • A134720 (program): Even Padovan numbers.
  • A134734 (program): First differences of A084662.
  • A134735 (program): Primes followed by the difference from the next prime.
  • A134736 (program): a(1) = 5; for n >1, a(n) = a(n-1) + gcd(n, a(n-1)).
  • A134738 (program): Cubes which are not the sum of three squares.
  • A134739 (program): Cubes of (positive numbers that are not the sum of three nonzero squares), that is, the terms of A004214, cubed.
  • A134743 (program): First differences of A134736.
  • A134744 (program): First differences of A084663.
  • A134746 (program): Expansion of 1+k in powers of q^(1/2) where q is Jacobi’s nome and k is the elliptic modulus.
  • A134751 (program): Hankel transform of expansion of (1/(1-x^2))c(x/(1-x^2)), where c(x) is the g.f. of A000108.
  • A134752 (program): a(n) = 3^(2*n-1) + 2.
  • A134756 (program): Coefficients of a q-series of Zagier related to the Dedekind eta function.
  • A134757 (program): A007318 * A100071.
  • A134758 (program): a(n) = A000984(n) + n.
  • A134759 (program): a(n) = 2*A000984(n) - (n+1)
  • A134760 (program): a(n) = 2*A000984(n) - 1.
  • A134761 (program): A007318^(-2) * A134760.
  • A134762 (program): a(n) = 3*A000984(n) - 2.
  • A134763 (program): A000718^(-2) * A134762.
  • A134770 (program): a(n) = 4*A000984(n) - 3.
  • A134771 (program): A007318^(-2) * A134770.
  • A134773 (program): Primitive elements of A180054.
  • A134774 (program): G.f.: A(x) = Product_{n>=1} G(x^n,n)^n where G(x,n) = 1 + x*G(x,n)^n.
  • A134786 (program): McKay-Thompson series of class 4A for the Monster group with a(0) = 4.
  • A134795 (program): Concatenation of first n positive oblong numbers.
  • A134797 (program): Odd isolated primes.
  • A134804 (program): Remainder of triangular number A000217(n) modulo 9.
  • A134805 (program): Denominator of Sum_{i=1..n} 1/(i^2*binomial(2*i,i)).
  • A134812 (program): a(n) = 2a(n-2) + 4a(n-3), n >= 3.
  • A134813 (program): a(n) = b(n+1)-2b(n) where b() is A134812.
  • A134816 (program): Padovan’s spiral numbers.
  • A134824 (program): Generated by reverse of Schroeder II o.g.f.
  • A134825 (program): Floor of the even-indexed Bernoulli numbers B_{2n} = A000367(n)/A002445(n).
  • A134828 (program): Numerator of moments of Chebyshev U- (or S-) polynomials.
  • A134829 (program): Denominator of moments of Chebyshev U- (or S-) polynomials.
  • A134830 (program): Triangle of rank k of permutations of {1,2,…,n}.
  • A134831 (program): Alternating row sums of triangle A134830.
  • A134832 (program): Triangle of succession numbers for circular permutations.
  • A134833 (program): Alternating row sums of triangle A134832.
  • A134836 (program): Antidiagonals of the array: A007318 * A002260(transposed).
  • A134853 (program): Generalized mountain numbers.
  • A134859 (program): Wythoff AAA numbers.
  • A134860 (program): Wythoff AAB numbers; also, Fib101 numbers: those n for which the Zeckendorf expansion A014417(n) ends with 1,0,1.
  • A134861 (program): Wythoff BAA numbers.
  • A134862 (program): Wythoff ABB numbers.
  • A134863 (program): Wythoff BAB numbers.
  • A134864 (program): Wythoff BBB numbers.
  • A134867 (program): A010766 * A000012.
  • A134868 (program): A103451 * A002260.
  • A134869 (program): Row sums of triangle A134868.
  • A134870 (program): A051731 + A000012 - A103451.
  • A134871 (program): a(1) = 1, a(n) = tau(n) + n - 2 for n > 1.
  • A134875 (program): a(n)=the smallest sum of two nontrivial divisors of n, if any, whose product equals n; otherwise, a(n)=n.
  • A134889 (program): a(n)=the largest sum of two nontrivial divisors of n, if any, whose product equals n; otherwise, a(n)=n.
  • A134914 (program): Ceiling(n^(1/3)).
  • A134917 (program): a(n) = ceiling(n^(4/3)).
  • A134918 (program): Ceiling(n^(5/3)).
  • A134919 (program): Floor(n^(5/3)).
  • A134920 (program): Expansion of (1-x+sqrt(1-2x+5x^2))/(2(1-x)^2).
  • A134921 (program): a(n) = A132398(n)/6.
  • A134924 (program): Nearest-neighbors of isolated primes.
  • A134926 (program): Nearest-neighbors of odd isolated primes, divided by 2.
  • A134927 (program): a(0)=a(1)=1; a(n) = 3*(a(n-1) + a(n-2)).
  • A134928 (program): Triple composites.
  • A134931 (program): a(n) = (5*3^n-3)/2.
  • A134932 (program): a(n)=A134928(n)/2.
  • A134934 (program): a(n) = (14*n+1)^2.
  • A134937 (program): Squares that are the sum of a nonzero pentagonal number and a nonzero square in at least one way.
  • A134938 (program): Pentagonal numbers that are the sum of a nonzero pentagonal number and a nonzero square in at least one way.
  • A134939 (program): Numerator of the expected number of random moves in Tower of Hanoi problem with n disks starting on peg 1 and ending on peg 3.
  • A134940 (program): Define f(n) by e(n+1) = e(n) + 3^{n+1} - 1 + 2*f(n), where the rational numbers e(n) are defined in A134939; then a(n) is the numerator of f(n).
  • A134943 (program): Decimal expansion of (golden ratio divided by 3 = phi/3 = (1 + sqrt(5))/6).
  • A134944 (program): Decimal expansion of (1 + sqrt(5))/8, the golden ratio divided by 4.
  • A134945 (program): Decimal expansion of 1 + sqrt(5).
  • A134946 (program): Decimal expansion of (golden ratio divided by 6 = phi/6 = (1 + sqrt(5))/12).
  • A134953 (program): Length of the longest prime implicant of the Y function of order n.
  • A134958 (program): Number of hypertrees with n labeled vertices: analog of A030019 when edges of size 1 are allowed (with no two equal edges).
  • A134960 (program): a(n) = n*453060.
  • A134965 (program): a(1)=3, a(n) = a(n-1) + 7 + 2*mod(n-1, 2) for n>=2.
  • A134967 (program): List of quadruples: [-2n-1, 2n+2, -2n-1, 2n+2].
  • A134972 (program): Decimal expansion of 2 divided by golden ratio = 2/phi = 4/(1 + sqrt(5)) = 2*(-1 + phi).
  • A134973 (program): Decimal expansion of 3/phi = 6/(1 + sqrt(5)).
  • A134974 (program): Decimal expansion of 4*(-1 + phi) = 4*A094214, where the golden ratio phi = A001622.
  • A134976 (program): Decimal expansion of (6 divided by golden ratio = 6/phi = 12/(1 + sqrt(5))).
  • A134977 (program): Period 6: repeat [1, 4, 2, 3, 0, 2].
  • A134980 (program): a(n) = Sum_{k=0..n} binomial(n,k)*n^(n-k)*A000110(k).
  • A134981 (program): a(n) = A000110(n)*A000166(n).
  • A134986 (program): a(n) = smallest integer m not equal to n such that n = (floor(n^2/m) + m)/2.
  • A134987 (program): Third extended Jacobsthal recurrence: a(n)=4a(n-1)-6(n-2)+4a(n-3)-a(n-4)+2a(n-5).
  • A134990 (program): Interleave two arithmetic progressions 8,10,12,14,… and 15,13,11,9,… of differences +2 and -2 respectively.
  • A134999 (program): Triangle-shaped numbers.
  • A135002 (program): Decimal expansion of 2/e.
  • A135003 (program): Decimal expansion of 3/e.
  • A135004 (program): Decimal expansion of 4/e.
  • A135005 (program): Decimal expansion of 5/e.
  • A135006 (program): Decimal expansion of 6/e.
  • A135007 (program): Decimal expansion of 7/e.
  • A135008 (program): Decimal expansion of 8/e.
  • A135009 (program): Decimal expansion of 9/e.
  • A135011 (program): Decimal expansion of 11/e.
  • A135012 (program): Decimal expansion of 12/e.
  • A135013 (program): Partial sums of A000265.
  • A135019 (program): a(n) = -a(n-1) + 2a(n-2) - a(n-3), with a(0) = 0, a(1) = 1, a(2) = -3.
  • A135022 (program): Define a sequence of binary words by w(1)=10 and w(n+1)=w(n)w(n)Reverse[w(n)]. Sequence gives the limiting word w(infinity).
  • A135023 (program): (NextPrime[6*n] - PreviousPrime[6*n])/2.
  • A135028 (program): Decimal expansion of 28/e.
  • A135030 (program): Generalized Fibonacci numbers: a(n) = 6*a(n-1) + 2*a(n-2).
  • A135032 (program): a(n) = 6*a(n-1) + 4*a(n-2).
  • A135033 (program): Period 5: repeat [2, 4, 6, 8, 0].
  • A135034 (program): Positive integers n repeated 2n-1 times, with a leading a(0) = 0. Also: ceiling of square root of n.
  • A135035 (program): Binomial transform of abs(A134967).
  • A135036 (program): Sums of the products of n consecutive pairs of numbers.
  • A135037 (program): Sums of the products of n consecutive triples of numbers.
  • A135038 (program): Sums of the products of n consecutive quadruples of numbers.
  • A135039 (program): Ceiling(Pi*n^2).
  • A135042 (program): Binomial transform of [1, 1, 2, 0, -2, 4, -6, 8, -10, 12, …].
  • A135050 (program): Numbers k such that sum of digits of k^3 is 8. Multiples of 10 are omitted.
  • A135051 (program): Pyramid game person numbers that have integer solutions.
  • A135052 (program): Expansion of g.f.: (1-2*x-sqrt(1-4*x+8*x^3-4*x^4))/(2*x^2*(1-x)).
  • A135055 (program): Pentanacci numbers: a(n) = a(n-1) + a(n-2) + a(n-3) + a(n-4) + a(n-5) for n>4 and with a(0)=-2, a(1)=-1, a(2)=0, a(3)=1, a(4)=2.
  • A135056 (program): Pentanacci numbers: a(n) = a(n-1) + a(n-2) + a(n-3) + a(n-4) + a(n-5) if n>=5, and a(n) = n otherwise.
  • A135061 (program): a(n) = minimum (floor(n^3/m) + m) for any integer m >= 1.
  • A135064 (program): Numbers n such that the quintic polynomial x^5 - 10*n*x^2 - 24*n has Galois group A_5 over rationals.
  • A135065 (program): A127733 * A007318 as infinite lower triangular matrices.
  • A135072 (program): Minimal values of m associated with A135061.
  • A135074 (program): A binomial recursion: a(n) is the coefficient of x in z(n), where z(1) = x and z(n) = 1 + Sum_{k=1..n-1} (binomial(n,k) + 1)*z(k) for n > 1.
  • A135075 (program): A binomial recursion : a(n) = q(n) (see formula).
  • A135076 (program): Primes appearing in A001370.
  • A135079 (program): E.g.f. A(x) = Sum_{n>=0} exp(3^n*x)*x^n/n!.
  • A135086 (program): Triangle, antidiagonals of an array formed by A000012 * A130321(transform).
  • A135087 (program): Triangle T(n, k) = 2*A134058(n, k) - 1, read by rows.
  • A135089 (program): Triangle T(n,k) = 5*binomial(n,k) with T(0,0) = 1, read by rows.
  • A135091 (program): A007318 * triangle M, where M = A002426 * 0^(n-k), 0<=k<=n.
  • A135092 (program): Binomial transform of [1, 6, 1, 6, 1, 6, …].
  • A135094 (program): a(n) = 2*a(n-1) + 2*a(n-2) - 4*a(n-3) with n>2, a(0)=0, a(1)=1, a(2)=3.
  • A135095 (program): a(1)=1, a(n) = a(n-1) + n^5 if n odd, a(n) = a(n-1) + n^2 if n is even.
  • A135098 (program): First differences of A135094.
  • A135099 (program): a(1)=1, a(n) = a(n-1) + n^5 if n odd, a(n) = a(n-1) + n^3 if n is even.
  • A135124 (program): Numbers such that the digital sums in base 2, base 4 and base 8 are all equal.
  • A135130 (program): Let n = Product_{p} p ^ e_p be the prime factorization of n and let M = max{e_p + 1 }. Then n is in the sequence iff for all primes q in the range 3 <= q <= M we have e_q >= Sum_{r} floor( log_q (e_r + 1) ).
  • A135133 (program): a(n) = floor(S2(n)/3) mod 2, where S2(n) denotes the binary weight of n.
  • A135135 (program): Numbers n such that A111426(n) is even.
  • A135136 (program): a(n) = floor(S2(n)/2) mod 2, where S2(n) is the binary weight of n.
  • A135138 (program): a(n) = 5*a(n-2) + 2*a(n-3).
  • A135139 (program): a(n) = 5*a(n-2) + 2*a(n-3).
  • A135144 (program): Values of A060308 where A020482(m) != A060308(m-1).
  • A135147 (program): A binomial recursion : a(n) = p(n) (see formula).
  • A135148 (program): A binomial recursion : a(n) = q(n) (see formula).
  • A135149 (program): A binomial recursion : a(n) = p(n) (see formula).
  • A135150 (program): A binomial recursion : a(n) = q(n) (see formula).
  • A135151 (program): A002260 + A128174 - I, I = Identity matrix.
  • A135152 (program): A004736 + A128174 - I, I = Identity matrix.
  • A135153 (program): Repeat Pell numbers A000129.
  • A135158 (program): a(n) = 5^n - 3^n - 2^n.
  • A135159 (program): a(n) = 5^n - 3^n + 2^n.
  • A135160 (program): a(n) = 5^n + 3^n - 2^n.
  • A135161 (program): a(n) = 7^n - 5^n - 3^n - 2^n. Constants are the prime numbers in decreasing order.
  • A135162 (program): a(n) = 7^n - 5^n - 3^n + 2^n. Constants are the prime numbers in decreasing order.
  • A135163 (program): a(n) = 7^n - 5^n + 3^n - 2^n.
  • A135164 (program): a(n) = 7^n - 5^n + 3^n + 2^n.
  • A135165 (program): a(n) = 7^n + 5^n - 3^n - 2^n.
  • A135166 (program): a(n) = 7^n + 5^n - 3^n + 2^n.
  • A135167 (program): a(n) = 7^n + 5^n + 3^n - 2^n. Constants are the prime numbers in decreasing order.
  • A135168 (program): a(n) = 7^n + 5^n + 3^n + 2^n.
  • A135169 (program): Period 4: repeat [1, 5, 9, 5].
  • A135171 (program): 3^p - 2^p, where p = prime(n).
  • A135172 (program): a(n) = 3^prime(n) + 2^prime(n).
  • A135173 (program): 5^p - 3^p - 2^p, where p = prime(n).
  • A135174 (program): a(n) = 5^prime(n) - 3^prime(n) + 2^prime(n).
  • A135175 (program): 5^p + 3^p - 2^p, where p = prime(n).
  • A135176 (program): 5^p + 3^p + 2^p, where p = prime(n).
  • A135177 (program): a(n) = p^2*(p-1), where p = prime(n).
  • A135178 (program): a(n) = p^3 + p^2 where p = prime(n).
  • A135179 (program): p^5 - p^3 - p^2. Exponents are the prime numbers in decreasing order and p is the n-th prime.
  • A135180 (program): a(n) = p^5 - p^3 + p^2, where p = prime(n).
  • A135181 (program): p^5 + p^3 - p^2. Exponents are the prime numbers in decreasing order and p is the n-th prime.
  • A135182 (program): p^5 + p^3 + p^2. Exponents are prime numbers and p = prime(n).
  • A135210 (program): Numbers n such that Sum_digits(n) + Sum_digits(n+1) = Sum_digits(2*n+1).
  • A135211 (program): Expansion of psi(-x) / psi(-x^3) in powers of x where psi() is a Ramanujan theta function.
  • A135214 (program): a(1)=1, a(n) = a(n-1) + n^5 if n odd, a(n) = a(n-1) + n^4 if n is even.
  • A135215 (program): Maximal number of zero digits in square of number with n digits and without zero digits.
  • A135218 (program): A007318^(-5) * A001286, 5th inverse binomial transform of the Lah numbers.
  • A135221 (program): Triangle A007318 + A000012(signed) - I, I = Identity matrix, read by rows.
  • A135222 (program): Triangle A049310 + A000012 - I, read by rows.
  • A135223 (program): Triangle A000012 * A127648 * A103451, read by rows.
  • A135224 (program): Triangle A103451 * A007318 * A000012, read by rows. T(n, k) for 0 <= k <= n.
  • A135225 (program): Pascal’s triangle A007318 augmented with a leftmost border column of 1’s.
  • A135226 (program): Triangle A135225 + A007318 - A103451, read by rows.
  • A135227 (program): Triangle A000012 * A135225, read by rows.
  • A135229 (program): Triangle A000012(signed) * A103451 * A007318, read by rows.
  • A135230 (program): Triangle A103451 * A000012(signed) * A007318, read by rows.
  • A135231 (program): Row sums of triangle A135230.
  • A135232 (program): Sum of the products of the first n prime pairs.
  • A135246 (program): Shifted Pell recurrence: a(n) = 2*a(n-2) + a(n-4).
  • A135247 (program): a(n) = 3*a(n-1) + 2*a(n-2) - 6*a(n-3).
  • A135248 (program): a(n) = 4*a(n-1) - 4*a(n-2) + 2*a(n-4), with a(0)=a(1)=a(2)=0, and a(3)=1.
  • A135254 (program): Binomial transform of A131666.
  • A135258 (program): Inverse binomial transform of A131666 after removing A131666(0) = 0.
  • A135259 (program): a(n) = 3*A131666(n) - A131666(n+1).
  • A135260 (program): Fibonacci Connell sequence: 1 odd, 1 even, 2 odd, 3 even, 5 odd, 8 even, ….
  • A135261 (program): a(n) = 3*A131090(n) - A131090(n+1).
  • A135262 (program): a(3n)=10^n. a(3n+1)=4*10^n. a(3n+2)=7*10^n.
  • A135263 (program): a(n) = 2*A132357(n).
  • A135264 (program): a(n) = 3*A132357(n).
  • A135265 (program): Period 6: repeat [1, 1, 1, 2, 2, 2].
  • A135266 (program): Partial sums of A132357.
  • A135267 (program): Difference between partial sum of the first n primes and the first n even numbers greater than 0.
  • A135268 (program): a(0) = 1; a(n) = a(n-1) + n - gcd(n,a(n-1)).
  • A135273 (program): Row 9 of A038207.
  • A135274 (program): a(n) = prime(2*n) - prime(2*n-1) + prime(2*n+1).
  • A135275 (program): a(n) = prime(2n-1) + prime(2n) - prime(2n+1).
  • A135276 (program): a(0)=0, a(1)=1; for n>1, a(n) = a(n-1) + n^0 if n odd, a(n) = a(n-1) + n^1 if n is even.
  • A135277 (program): a(n) = prime(2n-1) + prime(2n) + prime(2n+1).
  • A135278 (program): Triangle read by rows, giving the numbers T(n,m) = binomial(n+1, m+1); or, Pascal’s triangle A007318 with its left-hand edge removed.
  • A135282 (program): Largest k such that 2^k appears in the trajectory of the Collatz 3x+1 sequence started at n.
  • A135283 (program): Sum of staircase twin primes according to the rule: top + bottom + next top.
  • A135284 (program): Sum of staircase twin primes according to the rule: top + bottom - next top.
  • A135285 (program): Sum of staircase twin primes according to the rule: top * bottom - next top.
  • A135286 (program): Sum of staircase twin primes according to the rule: top * bottom + next top.
  • A135287 (program): a(0)=1; for n > 0, a(n) = a(n-1)+n if a(n-1) is odd, else a(n) = a(n-1)/2.
  • A135289 (program): Row 10 of A038207.
  • A135290 (program): Row 11 of A038207.
  • A135291 (program): Product of the nonzero exponents in the prime factorization of n!.
  • A135293 (program): Differences between successive numbers whose sum of digits in base 3 is 2.
  • A135295 (program): a(n) = n^(number of decimal digits of n).
  • A135299 (program): Pascal’s triangle, but the last element of the row is the sum of the all the previous terms.
  • A135300 (program): Positive X-values of solutions to the equation 1!*X^4 - 2!*(X + 1)^3 + 3!*(X + 2)^2 - (4^2)*(X + 3) + 5^2 = Y^3.
  • A135301 (program): a(1)=1, a(n)=a(n-1)+n^0 if n odd, a(n)=a(n-1)+ n^2 if n is even.
  • A135307 (program): Number of Dyck paths of semilength n that do not contain the string UDDU.
  • A135317 (program): Sequence yielding an ordering of N*N derived from a family of recurrences. For any integer k define h(k,1)=1 and for n>1 define h(k,n)=h(k,n-1)+2*((-h(k,n-1)mod n)where “r mod s” denotes least nonnegative residue of r modulo s [informally, h(k,n) is got by “reflecting” h(k,n-1)in the least multiple of n that is >=h(k,n-1)]. Then for fixed k>=0 there are integers a(k), b(k), n(k) such that for all n>n(k) we have h(k,2*n+1)-h(k,2*n)=2*a(k)and h(k,2*n+2)-h(k,2*n+1)=2*b(k). For all k we have a(2*k+1)=a(2*k) and b(2*k+1)=1+b(2*k). Moreover b(2*k) is even for all k. The function k->(a(2*k),b(2*k)/2) is a bijection from the nonnegative integers N to N*N. It is “monotone” in the sense that k<=k’ whenever a(2*k)<=a(2*k’) and b(2*k)<=b(2*k’). The sequence given above is a(2*k).
  • A135318 (program): The Kentucky-2 sequence: a(n) = a(n-2) + 2*a(n-4), with a[0..3] = [1, 1, 1, 2].
  • A135319 (program): a(n) is the first digit after the decimal point in the decimal expansion of log_10(n), i.e., of the Briggsian logarithm of n.
  • A135322 (program): a(n) = gcd(n!, binomial(2n,n)).
  • A135323 (program): a(1)=1, a(n) = Sum_{p=prime, p|n} a(n/p)*p.
  • A135324 (program): a(n) = Sum_{k=1..phi(n)} k*t(k), where t(k) is the k-th positive integer which is coprime to n and phi(n) is the number of positive integers which are <= n and are coprime to n.
  • A135332 (program): a(1)=1; for n>1, a(n) = a(n-1) + n^0 if n odd, a(n) = a(n-1) + n^3 if n is even.
  • A135334 (program): Number of Dyck paths of semilength n having no UDDU’s starting at level 1.
  • A135335 (program): Number of Dyck paths of semilength n having no DDUU’s starting at level 2.
  • A135336 (program): Number of Dyck paths of semilength n with no UUDU’s starting at level 0.
  • A135337 (program): Number of Dyck paths of semilength n with no DUUU’s starting at level 1.
  • A135339 (program): Number of Dyck paths of semilength n having no DUDU’s starting at level 1.
  • A135342 (program): Number of distinct means of nonempty subsets of {1,…,n}.
  • A135343 (program): a(n) = 3*a(n-1) + 4*a(n-2) - a(n-3) + 3*a(n-4) + 4*a(n-5).
  • A135344 (program): a(n) = 3*a(n-1) - a(n-3) + 3*a(n-4).
  • A135345 (program): a(n) = 3*a(n-1) + 4*a(n-2) - a(n-3) + 3*a(n-4) + 4*a(n-5).
  • A135348 (program): Total sum of squares of number of distinct parts in all partitions of n.
  • A135350 (program): a(n) = 2*a(n-1) - a(n-3) + 2*a(n-4).
  • A135351 (program): a(n) = (2^n + 3 - 7*(-1)^n + 3*0^n)/6; or a(0) = 0 and for n > 0, a(n) = A005578(n-1) - (-1)^n.
  • A135352 (program): a(1) = 1, followed by period 5: repeat [1,2,2,1,3].
  • A135353 (program): a(n) = 3*a(n-1) - 3*a(n-2) + 2*a(n-3).
  • A135356 (program): Triangle T(p,s) read by rows: coefficients in the recurrence of sequences which equal their p-th differences.
  • A135358 (program): Numbers n such that 7^n and 7^(n+1) have the same number of decimal digits.
  • A135359 (program): a(n) is the smallest nonnegative number k such that n divides 2^k-k.
  • A135360 (program): a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) for n > 4, with first terms 1, 2, 4, 7.
  • A135364 (program): First column of a triangle - see Comments lines.
  • A135365 (program): a(n) = 3*a(n-1) - a(n-3) + 3*a(n-4) for n>3.
  • A135366 (program): a(n) is the smallest nonnegative k such that n divides 2^k + k.
  • A135368 (program): a(n) = (nextprime(12*n) - previousprime(12*n))/2.
  • A135370 (program): a(1)=1; then if n even a(n) = n + a(n-1), if n odd a(n) = 2*n + a(n-1).
  • A135374 (program): Mersenne numbers with digits sorted in increasing order and zeros suppressed.
  • A135376 (program): a(n) is the smallest prime that does not divide n(n+1)/2.
  • A135387 (program): Triangle read by rows, with (2, 1, 0, 0, 0, …) in every column.
  • A135389 (program): Number of walks of length 2*n+2 from origin to (1,1) in a square lattice.
  • A135390 (program): Number of walks from origin to (1,0,0) in a cubic lattice.
  • A135392 (program): A triangular sequence from a general proportionality to modular function polynomial triangular function.
  • A135394 (program): Number of walks of length 2n+2 from origin to (1,1,0) on a cubic lattice.
  • A135395 (program): Number of walks of length 2n+3 from origin to (1,1,1) on a cubic lattice.
  • A135397 (program): a(n) = 2^n * 3^(n^2).
  • A135399 (program): a(n) = (-1)^n + (-2)^n + 3^n (-1, -2 and 3 are the roots of the equation x^3 = 7*x + 6).
  • A135400 (program): a(n) = (4*n^4 - 4*n^3 - n^2 + 3*n)/2.
  • A135401 (program): a(n) = number of permutations (p(1),p(2),p(3),…,p(n)) of (1,2,3,…n) each of which is its own inverse and is such that p(k) = n + 1 - p(n+1-k) for all k in the range 1 <= k <= n.
  • A135403 (program): a(n) = 1 + 111110*n.
  • A135404 (program): Gessel sequence: the number of paths of length 2m in the plane, starting and ending at (0,1), with unit steps in the four directions (north, east, south, west) and staying in the region y > 0, x > -y.
  • A135405 (program): Sequence where the sum of each pair of consecutive elements is a square.
  • A135406 (program): Sum of squares of gaps between consecutive semiprimes.
  • A135407 (program): Partial products of A000032 (Lucas numbers beginning at 2).
  • A135412 (program): Integers that equal three times the Heronian mean of two positive integers.
  • A135413 (program): Number of at most 4-way branching ordered (i.e., plane) trees.
  • A135414 (program): a(1)=a(2)=1 and for n>=3, a(n)=n-a(a(n-2)).
  • A135416 (program): a(n) = A036987(n)*(n+1)/2.
  • A135417 (program): Number of mountain numbers (see A134941) with n digits.
  • A135423 (program): a(n) = (5*9^n + 1)/2.
  • A135424 (program): a(n) = n!^number of decimal digits of n!.
  • A135431 (program): a(n) = a(n-1) + a(n-2) + a(n-3) - a(n-4) with a(0)=0, a(1)=1, a(2)=2 and a(3)=3.
  • A135432 (program): a(n) = a(n-1) + a(n-2) + a(n-3) + a(n-4) - a(n-5) with a(0)=0, a(1)=1, a(2)=2, a(3)=3 and a(4)=4.
  • A135438 (program): Denominators (numerators are all 1) of the series: 1/1^2, (1/1^2)*(1/(1^2+2^2)), (1/1^2)*(1/(1^2+2^2))*(1/(1^2+2^2+3^2)), …
  • A135440 (program): a(n) = a(n-1) + 2a(n-2).
  • A135446 (program): a(n) = 3*a(n-1) - 3*a(n-2) + 2*a(n-3).
  • A135447 (program): Period 10: repeat [1, 2, 4, 8, 5, -1, -2, -4, -8, -5].
  • A135448 (program): Period 5: repeat [1, 5, 3, 4, -2].
  • A135449 (program): Period 5: repeat [1, 9, -7, 3, 5].
  • A135450 (program): a(n) = 3*a(n-1) + 4*a(n-2) - a(n-3) + 3*a(n-4) + 4*a(n-5).
  • A135453 (program): a(n) = 12*n^2.
  • A135456 (program): Number of surjections from an n-element set onto a seven-element set.
  • A135457 (program): a(n) = (2n-1)!! * Sum_{k=0..n-2}(-1)^k/(2k+1).
  • A135461 (program): a(n) = 1 if n is the norm of an Eisenstein prime (see A055664) otherwise 0.
  • A135462 (program): a(n) = number of Eisenstein primes (see A055664) of norm <= n.
  • A135466 (program): a(n) = (2*n-8)^2 * 2^(n-3).
  • A135472 (program): Shortest and lexicographically earliest string of decimal digits with property that when made into cycle every pair of digits from 0,0 to 9,9 can be seen exactly once.
  • A135481 (program): a(n) = 2^A007814(n+1) - 1.
  • A135482 (program): a(n) = (1/4)*Sum_{j=1..n} 2^prime(j).
  • A135483 (program): a(n) = Sum_{j=1..n} prime(j)*2^(j-2).
  • A135484 (program): a(n) = Sum_{i=1..n} i^prime(i), where prime(i) denotes i-th prime number.
  • A135485 (program): a(n) = Sum_{i=1..n) prime(i)^(i-1), where prime(i) denotes i-th prime number.
  • A135487 (program): a(n) = (n^2+5*n+5)*(2*n+2)!/(n+4)!.
  • A135489 (program): Number of tieless basketball games from the years 1896-1967 with n scoring events.
  • A135491 (program): Number of ways to toss a coin n times and not get a run of four.
  • A135492 (program): Number of ways to toss a coin n times and not get a run of five.
  • A135493 (program): Number of ways to toss a coin n times and not get a run of six.
  • A135497 (program): a(n) = n^5 - n^2.
  • A135499 (program): Numbers for which Sum_digits(odd positions) = Sum_digits(even positions).
  • A135500 (program): Generating function for Viswanath’s constant, using the golden string.
  • A135503 (program): a(n) = n*(n^2 - 1)/2.
  • A135504 (program): a(1)=1; for n>1, a(n) = a(n-1) + lcm(a(n-1),n).
  • A135505 (program): a(0) = 1; a(n) = [product_(i = 1..n) prime(i)^i] - 1, where prime(i) is i-th prime.
  • A135506 (program): a(n) = x(n+1)/x(n) - 1 where x(1)=1 and x(k) = x(k-1) + lcm(x(k-1),k).
  • A135507 (program): a(1)=1; for n>1, a(n)=2*a(n-1)+lcm(a(n-1),n).
  • A135508 (program): a(n) = x(n+1)/x(n) - 2 where x(1)=1 and x(n) = 2*x(n-1) + lcm(x(n-1),n).
  • A135509 (program): Nonnegative integers c such that there are nonnegative integers a and b that satisfy a^(1/2) + b^(1/2) = c^(1/2) and a^2 + b = c.
  • A135511 (program): Number of Pierce-Engel hybrid expansions of 3/b, b>=3.
  • A135512 (program): Number A(Bn,K) of all D-invariant ideals of the algebra NBn(K) of classical type over a field K if 2K=0.
  • A135513 (program): Number of Pierce-Engel hybrid expansions of 4/b, b>=4.
  • A135516 (program): a(0)=1; a(n) = (Product_{i=1..n} prime(i)^2) - 1, where prime(i) is the i-th prime.
  • A135517 (program): a(n) = 2^(A091090(n)-1).
  • A135518 (program): Generalized repunits in base 15.
  • A135519 (program): Generalized repunits in base 14.
  • A135520 (program): a(n) = 4*a(n-2).
  • A135521 (program): a(n) = 2^(A091090(n)) - 1.
  • A135522 (program): a(n) = 2*a(n-1) + 3*a(n-2), with a(0) = 2 and a(1) = 3.
  • A135523 (program): a(n) = A007814(n) + A209229(n).
  • A135524 (program): Row sums of A137152.
  • A135525 (program): Row sums of terms > 1 in A137152.
  • A135528 (program): 1, then repeat 1,0.
  • A135529 (program): Guy Steele’s sequence GS(4,5) (see A135416).
  • A135530 (program): a(n) = a(n-1) + 2*a(n-2) - 2*a(n-3), with a(0)=2, a(1)=1.
  • A135532 (program): a(n) = 2*a(n-1) + a(n-2), with a(0)= -1, a(1)= 3.
  • A135533 (program): Guy Steele’s sequence GS(4,6) (see A135416).
  • A135534 (program): a(1) = 1; for n>=1, a(2n) = A135561(n), a(2n+1) = 0.
  • A135536 (program): a(n) = 8*a(n-2), with a(0) = 7, a(1) = 14.
  • A135537 (program): Period 4: repeat [7, 5, 2, 4].
  • A135539 (program): Triangle read by rows: T(n,k) = number of divisors of n that are >= k.
  • A135540 (program): a(n) = 2^(A000523(n) - A000120(n) + 2) - 1.
  • A135541 (program): a(n) = 2*a(n-1) - a(n-2) + 2*a(n-3), with a(0) = 2, a(1) = 2.
  • A135542 (program): Guy Steele’s sequence GS(6,4) (see A135416).
  • A135552 (program): Riordan array (1/((1-2x)(1-x)^2), -x/(1-x)^2).
  • A135553 (program): Divisors of 11025.
  • A135555 (program): Prime sums of digits of n^4 associated with A135554.
  • A135556 (program): Squares of numbers not divisible by 3: a(n) = A001651(n)^2.
  • A135560 (program): a(n) = A007814(n) + A036987(n-1) + 1.
  • A135561 (program): a(n) = 2^A135560(n) - 1.
  • A135568 (program): a(n) = floor( Product_{i=1..n} prime(i)/i ).
  • A135569 (program): a(n) = S2(n)*2^n; where S2(n) is digit sum of n, n in binary notation.
  • A135570 (program): a(n) = 1 + Sum_{i=1..n} S2(i)*2^i, where S2(n) is digit sum of n, n in binary notation.
  • A135571 (program): Positive integers that are the difference of two positive triangular numbers in an odd number of ways.
  • A135572 (program): Numbers k such that the largest prime-power dividing k is a square.
  • A135573 (program): Array T(n,m) of super ballot numbers read along ascending antidiagonals.
  • A135574 (program): A024495 but with terms swapped in pairs.
  • A135575 (program): a(n) = A135574(n+1) - 2*A135574(n).
  • A135576 (program): Numbers whose binary expansion has only the digit “1” as first, central and final digit.
  • A135577 (program): Numbers that have only the digit “1” as first, central and final digit. For numbers with 5 or more digits the rest of digits are “0”.
  • A135582 (program): Expansion of 1/((1-x^2*c(x))(1-x-2x^2)) where c(x) is the g.f. of A000108.
  • A135583 (program): a(n) = 4*a(n-1) - 4 for n>0, a(0)=3.
  • A135585 (program): a(n) = Sum_{i=1..n} (floor(S2(i)/3) mod 2), where S2(i) = A000120(i).
  • A135586 (program): a(1)=0; for n >= 1, a(2n)=a(n)+2^A000120(n)-1, a(2n+1)=2a(2n).
  • A135587 (program): a(n) = A135586(2n).
  • A135593 (program): Number of n X n symmetric (0,1)-matrices with exactly n+1 entries equal to 1 and no zero rows or columns.
  • A135597 (program): Square array read by antidiagonals: row m (m >= 1) satisfies b(0) = b(1) = 1; b(n) = m*b(n-1) + b(n-2):
  • A135600 (program): Angled numbers with an internal digit as the vertex.
  • A135601 (program): Acute-angled numbers with an internal digit as the vertex.
  • A135609 (program): a(n) = (n!)^2 - n^n.
  • A135610 (program): Triangle read by rows: the k-th entry of row n is the number of particular connectivity requirements that a k-linked graph with n >= 2k vertices has to satisfy T(n,k) = (1/2) * n!/(k!*(n-2*k)!) where k runs from 1 to floor(n/2).
  • A135611 (program): Decimal expansion of sqrt(2) + sqrt(3).
  • A135616 (program): Number of permutations p of {1,2,…,n} such that p(x) is a polynomial in x, modulo n, of degree at most 2, for x=1,2,3,…,n.
  • A135618 (program): Even Motzkin numbers divided by 2.
  • A135619 (program): Even Padovan numbers divided by 2.
  • A135620 (program): a(n) = 2^(prime(n) - 2).
  • A135628 (program): Multiples of 28.
  • A135630 (program): 2^(prime(n) - 2) - 1.
  • A135631 (program): Multiples of 31.
  • A135634 (program): Palindromes formed from the reflected decimal expansion of e.
  • A135636 (program): Values of x in positive solutions (x,y,z) to the Diophantine 43x+7y+17z=400.
  • A135639 (program): a(n) = 839*n.
  • A135640 (program): Powers of 839.
  • A135646 (program): a(m, n) is the number of coprime pairs (i, j) with 1 <= i <= m, 1 <= j <= n; table of a(m, n) read by antidiagonals.
  • A135653 (program): Divisors of 496 (the 3rd perfect number), written in base 2.
  • A135654 (program): Divisors of 8128 (the 4th perfect number), written in base 2.
  • A135655 (program): Divisors of 33550336 (the 5th perfect number), written in base 2.
  • A135657 (program): Nonprimes of the form 24n+7.
  • A135659 (program): a(n) = 24*n + 7.
  • A135668 (program): a(n) = ceiling(n + sqrt(n)).
  • A135671 (program): a(n) = ceiling(n - n^(2/3)).
  • A135672 (program): a(n) = floor(n - n^(2/3)).
  • A135673 (program): Ceiling(n + n^(2/3)).
  • A135674 (program): Floor(n+n^(2/3)).
  • A135675 (program): a(n) = ceiling(n^(4/3) - n).
  • A135676 (program): a(n) = floor(n^(4/3) - n).
  • A135677 (program): a(n) = ceiling(n^(4/3)+n).
  • A135678 (program): Floor(n^(4/3)+n).
  • A135679 (program): a(n) = n if n = 1 or if n is prime. Otherwise, a(n) = 2 if n is even and a(n) = 3 if n is odd.
  • A135680 (program): a(n) = n if n = 1 or if n is prime. Otherwise, n = 4 if n is even and n = 5 if n is odd.
  • A135681 (program): a(n)=n if n=1 or if n=prime. Otherwise, n=4 if n is even and n=1 if n is odd.
  • A135682 (program): a(n)=n if n=1 or if n=prime. Otherwise, n=4 if n is even and n=7 if n is odd.
  • A135683 (program): Duplicate of A005451.
  • A135684 (program): a(n)=11 if n is a prime number. Otherwise, a(n)=n.
  • A135686 (program): a(n) = a(n-1) + A000045(n)*a(n-2), a(1) = 1, a(2) = 1.
  • A135690 (program): a(n) = a(n-2) - (a(n-1) - a(n-2)) if (n mod 2) = 0, otherwise a(n) = a(n-1) - (a(n-3) - a(n-4)), with a(0) = 0, a(1) = 1, a(2) = -1, a(3) = 2.
  • A135694 (program): Period 6: repeat [1, -1, -1, -1, 0, 2].
  • A135695 (program): Period 6: repeat [-1, -1, -2, -2, 3, 3].
  • A135696 (program): Palindromes with odd number of digits formed from the reflected decimal expansion of e.
  • A135697 (program): Palindromes formed from the reflected decimal expansion of Pi.
  • A135698 (program): Palindromes with odd number of digits formed from the reflected decimal expansion of Pi.
  • A135699 (program): Palindromes with odd number of digits formed from the reflected decimal expansion of golden ratio phi.
  • A135700 (program): Palindromes formed from the reflected decimal expansion of golden ratio phi.
  • A135703 (program): a(n) = n*(7*n-2).
  • A135704 (program): a(n) = 7*n^2 + 4*n + 1.
  • A135705 (program): a(n) = 10*binomial(n,2) + 9*n.
  • A135706 (program): a(n) = n*(5*n-3).
  • A135708 (program): Minimal total number of edges in a polyhex consisting of n hexagonal cells.
  • A135711 (program): Minimal perimeter of a polyhex with n cells.
  • A135712 (program): a(n) = (4*n^3 + 11*n^2 + 9*n + 2)/2.
  • A135713 (program): a(n) = n*(n+1)*(4*n+1)/2.
  • A135718 (program): a(n) = smallest divisor of n^2 that is not a divisor of n.
  • A135725 (program): Let d(i) be the i-th digit of the decimal expansion of e = 2.718281828459045235360287471352662…, so that d(0) = 2, d(1) = 7, d(2) = 1, etc. Then a(0) = 2, a(n) = d(d(n)) for n>0.
  • A135727 (program): Maximal value in orbit of n under the map A001281(x)=3x-1 if x odd, x/2 if x even.
  • A135731 (program): a(1) = 3; thereafter a(n+1) = a(n) + nextprime(a(n)) - prevprime(a(n)).
  • A135732 (program): Distances to next prime associated with A135731.
  • A135734 (program): a(n) = prime(n)*prime(n+1)*prime(n+2) - prime(n+3)^2.
  • A135736 (program): Nearest integer to n*Sum_{k=1..n} 1/k = rounded expected coupon collection numbers.
  • A135742 (program): E.g.f.: A(x) = Sum_{n>=0} exp( n*(n-1)/2 * x ) * x^n / n!.
  • A135743 (program): E.g.f.: A(x) = Sum_{n>=0} exp(n*(n+1)/2*x)*x^n/n!.
  • A135744 (program): E.g.f.: A(x) = Sum_{n>=0} exp( n*(n+1)*x ) * x^n/n!.
  • A135745 (program): E.g.f.: A(x) = Sum_{n>=0} exp((n-1)*x)^n * x^n/n!.
  • A135746 (program): E.g.f.: A(x) = Sum_{n>=0} exp(n^2*x) * x^n/n!.
  • A135747 (program): E.g.f.: A(x) = Sum_{n>=0} exp( (n^2-1)*x ) * x^n/n!.
  • A135748 (program): a(n) = Sum_{k=0..n} binomial(n,k)*2^(k^2).
  • A135749 (program): a(n) = Sum_{k=0..n} binomial(n,k)*(n-k)^k*k^k.
  • A135753 (program): E.g.f.: A(x) = Sum_{n>=0} exp((3^n-1)/2*x)*x^n/n!.
  • A135754 (program): E.g.f.: A(x) = Sum_{n>=0} exp((4^n-1)/3*x)*x^n/n!.
  • A135755 (program): a(n) = Sum_{k=0..n} C(n,k)*3^[k*(k-1)/2].
  • A135756 (program): a(n) = Sum_{k=0..n} C(n,k) * 2^(k*(k-1)).
  • A135757 (program): Central binomial coefficients at triangular positions: a(n) = A000984(n(n+1)/2).
  • A135758 (program): Catalan numbers at triangular positions: a(n) = A000108(n(n+1)/2).
  • A135764 (program): Distribute the natural numbers in columns based on the occurrence of “2” in each prime factorization; square array A(row,col) = 2^(row-1) * ((2*col)-1), read by descending antidiagonals.
  • A135765 (program): Distribute the odd numbers in columns based on the occurrence of “3” in each prime factorization; square array A(row, col) = 3^(row-1) * A007310(col), read by antidiagonals A(1,1), A(1,2), A(2,1), A(1,3), A(2,2), A(3,1), …
  • A135772 (program): Numbers having equal number of divisors and binary digits.
  • A135784 (program): a(n) = A000404(n)^2.
  • A135786 (program): a(n) = A000404(n)^4.
  • A135787 (program): a(n) = A000404(n)^5.
  • A135788 (program): a(n) = A000404(n)^6.
  • A135799 (program): Second column (k=1) of triangle A134832 (circular succession numbers).
  • A135801 (program): Fourth column (k=3) of triangle A134832 (circular succession numbers).
  • A135802 (program): Fifth column (k=4) of triangle A134832 (circular succession numbers).
  • A135803 (program): Sixth column (k=5) of triangle A134832 (circular succession numbers).
  • A135804 (program): Seventh column (k=6) of triangle A134832 (circular succession numbers).
  • A135805 (program): Eighth column (k=7) of triangle A134832 (circular succession numbers).
  • A135806 (program): Ninth column (k=8) of triangle A134832 (circular succession numbers).
  • A135807 (program): Tenth column (k=9) of triangle A134832 (circular succession numbers).
  • A135808 (program): Numerator of z-sequence for the Sheffer (Appell type) triangle A134832 (circular succession numbers).
  • A135809 (program): Number of coincidence-free length n lists of 3-tuples with all numbers 1,…,n in tuple position k, for k=1,2,3.
  • A135810 (program): Number of coincidence-free length n lists of 4-tuples with all numbers 1,…,n in tuple position k, for k=1..4.
  • A135811 (program): Number of coincidence-free length n lists of 5-tuples with all numbers 1,…,n in tuple position k, for k=1..5.
  • A135812 (program): Number of coincidence-free length n lists of 6-tuples with all numbers 1,…,n in tuple position k, for k=1..6.
  • A135813 (program): Number of coincidence-free length n lists of 7-tuples with all numbers 1,…,n in tuple position k, for k=1..7.
  • A135817 (program): Length of Wythoff representation of n.
  • A135818 (program): Number of 1’s (or A’s) in the Wythoff representation of n.
  • A135828 (program): Expansion of psi(x^2)^8 * (psi(x)^8 + psi(-x)^8) / 2 in powers of x^2 where psi() is a Ramanujan theta function.
  • A135829 (program): a(n) = F(n)*a(n-1) + a(n-2) with a(0) = 0, a(1) = 1.
  • A135836 (program): Column three of the triangular matrix listed by rows in A135835.
  • A135837 (program): A007318 * a triangle with (1, 2, 2, 4, 4, 8, 8, …) in the main diagonal and the rest zeros.
  • A135838 (program): Triangle read by rows: T(n,k) = 2^floor(n/2)*binomial(n-1,k-1).
  • A135839 (program): Triangle read by rows: starting with A138174, replace left border with (1, 1, 1, …).
  • A135840 (program): A135839 * A000012 as infinite lower triangular matrices.
  • A135841 (program): A000012 * A135839 as infinite lower triangular matrices.
  • A135849 (program): a(n) is the ratio of the sum of the bends (curvatures) of the circles in the n-th generation of an Apollonian packing to the sum of the bends in the initial four-circle configuration.
  • A135851 (program): a(n) = n-1, if n <= 2, otherwise A107458(n-1) + A107458(n-2).
  • A135852 (program): A007318 * A103516 as a lower triangular matrix.
  • A135853 (program): A103516 * A007318 as an infinite lower triangular matrix.
  • A135854 (program): a(n) = (n+1)*(2^n+1) for n > 0 with a(0)=1.
  • A135855 (program): A007318 * a tridiagonal matrix with (1, 4, 1, 0, 0, 0, …) in every column.
  • A135856 (program): A007318 * a bidiagonal matrix with all 1’s in the main diagonal and all 4’s in the subdiagonal.
  • A135857 (program): Partial sums triangle based on A016777. Riordan convolution triangle ((1 + 2*x)/(1-x)^2, x/(1-x)).
  • A135858 (program): A128229^2 * A000012.
  • A135859 (program): Row sums of triangle A135858.
  • A135860 (program): a(n) = binomial(n*(n+1), n).
  • A135861 (program): a(n) = binomial(n*(n+1),n)/(n+1).
  • A135862 (program): a(n) = binomial(n*(n+1),n)/(n^2+1).
  • A135863 (program): G.f. A(x) = 1 + 4x*A(x)^(1/2); A(x) = 1 + 8x^2 + 4x*sqrt(1 + 4x^2).
  • A135864 (program): G.f. A(x) satisfies: A(x) = 1 + 9x*A(x)^(1/3).
  • A135872 (program): Multiply the positive integers which are coprime to n in order (starting at 1). a(n) is the smallest such partial product that is >= n.
  • A135873 (program): Multiply the positive integers which are coprime to n in order (starting at 1). a(n) is the largest such partial product that is <= n.
  • A135874 (program): Multiply the positive divisors of n in order (starting at 1). a(n) is the smallest such partial product that is >= n.
  • A135875 (program): Multiply the positive divisors n in order (starting at 1). a(n) is the largest such partial product that is <= n.
  • A135901 (program): Number of terms in row n of irregular triangle A135879 for n>=0.
  • A135908 (program): Clique number of commuting graph of symmetric group S_n.
  • A135909 (program): Clique number of commuting graph of alternating group A_n.
  • A135913 (program): 2+4*2^n-3^n.
  • A135914 (program): a(n) = 4*3^n - 2*2^n - 1.
  • A135916 (program): (n^4 - 10*n^2 + 15*n - 6)/2.
  • A135918 (program): Genus of stage-n Menger sponge.
  • A135920 (program): O.g.f.: A(x) = Sum_{n>=0} x^n / Product_{k=0..n} (1 - k^2*x).
  • A135922 (program): Inverse binomial transform of A006116, which is the sum of Gaussian binomial coefficients [n,k] for q=2.
  • A135929 (program): Triangle read by rows: row n gives coefficients of polynomial P_n(x)= U_n(X,1) + 3 * U_{n-2}(X,1) where U is the Chebyshev polynomial of the second kind, in order of decreasing exponents.
  • A135932 (program): Primes whose integer square root remainder is also prime.
  • A135941 (program): a(n) = floor(n/S2(n)), where S2(n) is the binary weight of n.
  • A135947 (program): a(n)=(floor(3*S2(n)/2)) mod 2, where S2(n) is the binary weight of n.
  • A135949 (program): a(n)=5a(n-2)+2a(n-3).
  • A135961 (program): G.f.: A(x) = Sum_{n>=0} x^n/(1 - Fibonacci(n)*x).
  • A135962 (program): a(n) = binomial(floor(n*(sqrt(5)+1)/2), n) for n>=0.
  • A135963 (program): a(n) = binomial(floor(n*(sqrt(5)+3)/2), n) for n>=0.
  • A135964 (program): a(n) = binomial(floor(n*sqrt(2)),n) for n>=0.
  • A135965 (program): a(n) = binomial(floor(n*(1+sqrt(2))),n) for n>=0.
  • A135966 (program): Triangle, read by rows, where T(n,k) = fibonacci(k(n-k) + 1) for n>=k>=0.
  • A135967 (program): Row sums of triangle A135966.
  • A135971 (program): Ceiling(4*Pi*n^2).
  • A135973 (program): Ceiling(4/3*Pi*n^3).
  • A135974 (program): a(n) = the smallest integer m > n such that d(m) > d(n), where d(n) = number of divisors of n.
  • A135984 (program): a(n) = 24(prime(n))+7.
  • A135985 (program): Prime numbers of the form 24*p + 7 where p is prime.
  • A135989 (program): a(n) = 6*n + 3 + 90*floor((6*n+3)/10).
  • A135990 (program): Expansion of x^3*(x-1)*(x+1) / (x^5-2*x^4+x^2-1).
  • A135991 (program): Expansion of x^3*(x-1)^2*(x+1) / (x^6-3*x^5+3*x^4-x+1)
  • A135992 (program): Positive Fibonacci numbers swapped in pairs.
  • A135993 (program): a(0) = 0; a(n) = (floor(n/S2(n))) mod 2 for n >= 1, where S2(n) is the binary weight of n.
  • A135994 (program): First differences of A135992.
  • A135996 (program): Difference between 2^n and the largest factorial <= 2^n.
  • A135997 (program): Table of triples T(k,m) = k (m=1), 2-k (m=2) and 1-k (m=3).
  • A136000 (program): A010814(n) - 1.
  • A136002 (program): Numbers that are not the sum, minus 1, of a Pythagorean triple.
  • A136004 (program): a(n) = A005811(n) + 4.
  • A136006 (program): a(n) = n^6 - n^3.
  • A136008 (program): a(n) = n^6 - n^2.
  • A136010 (program): a(0)=20, a(1)=9; for n >= 0, a(n+2) = 7*a(n+1) + 9*a(n).
  • A136013 (program): a(n) = floor(n/2) + 2*a(floor(n/2)), a(0) = 0.
  • A136016 (program): a(n) = 9*n^2-1.
  • A136017 (program): a(n) = 36n^2 - 1.
  • A136035 (program): Remainder when dividing 2^q - 1 by q + 1 where q is the n-th prime.
  • A136037 (program): Numbers with at least three adjacent equal digits in binary representation.
  • A136038 (program): a(n) = n^6 - n^4.
  • A136043 (program): Period-lengths of the base-2 MR-expansions of the reciprocals of the positive integers.
  • A136045 (program): Bisection of A138546.
  • A136046 (program): Bisection of A138543.
  • A136047 (program): a(1)=1, a(n)=a(n-1)+n if n even, a(n)=a(n-1)+ n^2 if n is odd.
  • A136049 (program): a(n)=number of primes p such that (p,p+2) is a pair of twin primes with n^2 + n < p < n^2+3*n+2.
  • A136050 (program): Sum of digits of product of twin primes A037074.
  • A136051 (program): Primes p such that 5*p-4 is also prime.
  • A136052 (program): Daughter primes of order 3.
  • A136053 (program): Daughter primes of order 4.
  • A136054 (program): Daughter primes of order 5.
  • A136055 (program): Daughter primes of order 6.
  • A136056 (program): Daughter primes of order 7.
  • A136057 (program): Daughter primes of order 8.
  • A136058 (program): Daughter primes of order 9.
  • A136059 (program): Daughter primes of order 10.
  • A136060 (program): Daughter primes of order 11.
  • A136061 (program): Primes p such that (p+4)/5 is also prime.
  • A136062 (program): Mother primes of order 3.
  • A136063 (program): Mother primes of order 4.
  • A136064 (program): Mother primes of order 5.
  • A136065 (program): Mother primes of order 6.
  • A136066 (program): Mother primes of order 7.
  • A136067 (program): Mother primes of order 8.
  • A136068 (program): Mother primes of order 9.
  • A136069 (program): Mother primes of order 10.
  • A136070 (program): Mother primes of order 11.
  • A136071 (program): Father primes of order 2.
  • A136072 (program): Father primes of order 3.
  • A136073 (program): Father primes of order 4.
  • A136074 (program): Father primes of order 5.
  • A136075 (program): Father primes of order 6.
  • A136076 (program): Father primes of order 7.
  • A136077 (program): Father primes of order 8.
  • A136078 (program): Father primes of order 9.
  • A136079 (program): Father primes of order 10.
  • A136080 (program): Father primes of order 11.
  • A136082 (program): Son primes of order 5.
  • A136083 (program): Son primes of order 6.
  • A136084 (program): Son primes of order 7.
  • A136085 (program): Son primes of order 8.
  • A136086 (program): Son primes of order 9.
  • A136087 (program): Son primes of order 10.
  • A136088 (program): Son primes of order 11.
  • A136089 (program): Son primes of order 12.
  • A136090 (program): Son primes of order 13.
  • A136091 (program): Son primes of order 14.
  • A136097 (program): a(n) = A135951(n) /[(2^(n+1)-1) * 2^(n*(n-1)/2)].
  • A136104 (program): A007318 * A002110; a(n) = Sum_{k=0..n} binomial(n,k)*A002110(k).
  • A136105 (program): Partial sums of A051941.
  • A136107 (program): Number of representations of n as the difference of two positive triangular numbers.
  • A136119 (program): Limiting sequence when we start with the positive integers (A000027) and delete in step n >= 1 the term at position n + a(n).
  • A136120 (program): Limiting sequence when we start with the positive integers (A000027) and at step n >= 1 delete the a(n) terms at positions n+a(n) to n-1+2*a(n).
  • A136125 (program): Triangle read by rows: T(n,k) is the number of permutations of {1,2,…,n} in which the size of the last cycle is k (the cycles are ordered by increasing smallest elements; 1 <= k <=n).
  • A136128 (program): Number of components in all permutations of [1,2,…,n].
  • A136135 (program): Sum of squares until integer log : sopfr(n). Or also, s(s+1)(2s+1)/6 where s=sopfr(n).
  • A136137 (program): a(n+1)=sopfr(3a(n)+1), with sopfr=A001414. Finishes with 17 (fixed point).
  • A136138 (program): a(n+1)=sopfr(4a(n)+1), with sopfr=A001414. Finishes with the cycle (34, 137, 67, 269, 362, 36).
  • A136139 (program): a(n+1)=sopfr(5a(n)+1), with sopfr=A001414. Finishes with a cycle with length 16.
  • A136151 (program): Composites n with exactly two distinct prime divisors and of the form n=1+(any prime).
  • A136152 (program): Composites one larger than a prime and with exactly three distinct prime factors.
  • A136154 (program): Composites one larger than a prime, with exactly five distinct prime factors.
  • A136157 (program): Triangle by columns, (3, 1, 0, 0, 0, …) in every column.
  • A136158 (program): Sequence whose rows are generated by A136157^n * [1, 1, 0, 0, 0, …].
  • A136159 (program): A Chebyshev polynomial triangle of the first kind defined by T(n+1,x) = 3x*T(n,x) - T(n-1,x).
  • A136160 (program): Triangle T(n,k) = k*A053120(n,k).
  • A136161 (program): a(n) = 2*a(n-3)-a(n-6), starting a(0..5) = 0, 5, 2, 1, 3, 1.
  • A136169 (program): a(n) = 2*a(n-1) - [(n+1)/3] for n>0 with a(0) = 1.
  • A136178 (program): Irregular array read by rows: row n contains the GCDs of each pair of consecutive positive divisors of n.
  • A136179 (program): a(n) = Product_{k=1..d(n)-1) gcd(b(k), b(k+1)), where b(k) is the k-th positive divisor of n and d(n) is the number of positive divisors of n.
  • A136180 (program): a(n) = Sum_{k=1..d(n)-1) gcd(b(k), b(k+1)), where b(k) is the k-th positive divisor of n and d(n) is the number of positive divisors of n.
  • A136185 (program): Number of metacyclic groups of order p^n, prime p >= 3.
  • A136188 (program): Digital roots of the Fermat numbers in A000215(n).
  • A136201 (program): a(n) = 2*a(n-1) + 4*a(n-2) - 6*a(n-3) - 3*a(n-4).
  • A136203 (program): Derived Shabat linear tree transform of A053120: Triangle of coefficients of transformed Chebyshev’s T(n, x) polynomials (powers of x in increasing order) T(x,n)->c*T(c*x+d)+d: c=-1;d=1; as substitution: 1-x->y( here alternative starting polynomial of Q(y,1]=1-y.
  • A136210 (program): Numerators in continued fraction [0; 1, 3, 1, 3, 1, 3, …].
  • A136211 (program): Denominators in continued fraction [0; 1, 3, 1, 3, 1, 3, …].
  • A136214 (program): Triangle U, read by rows, where U(n,k) = Product_{j=k..n-1} (3*j+1) for n > k with U(n,n) = 1.
  • A136215 (program): Triangle T, read by rows, where T(n,k) = A007559(n-k)*C(n,k) where A007559 equals the triple factorials in column 0.
  • A136216 (program): Triangle T, read by rows, where T(n,k) = A008544(n-k)*C(n,k) where A008544 equals the triple factorials in column 0.
  • A136219 (program): Number of terms in rows of irregular triangle A136218.
  • A136240 (program): Numbers n among A006093 such that n^2 + n + 1 is prime.
  • A136241 (program): Numbers n among A006093 such that n^2 + n - 1 is prime.
  • A136242 (program): Numbers n among A008864 such that n^2 - n + 1 is prime.
  • A136245 (program): a(n) = (1/n!)*Sum_{k=0..n} Stirling1(n,k)*A062208(k).
  • A136251 (program): a(n) = n-th prime reduced modulo the sum of its digits.
  • A136252 (program): a(n) = a(n-1) + 2*a(n-2) - 2*a(n-3).
  • A136254 (program): Generator for the finite sequence A053016.
  • A136255 (program): Triangle T(n,k) read by rows: T(n,k) = (k+1) * A137276(n,k+1).
  • A136258 (program): a(n) = 2*a(n-1) - 2*a(n-2), with a(0)=1, a(1)=5.
  • A136261 (program): Triangle T(n,k) = k*A122188(n,k), read by rows.
  • A136264 (program): Expansion of (1+x)^2*(x^2-6*x+1)/(x-1)^4.
  • A136268 (program): Cyclic p-roots of prime lengths p(n).
  • A136270 (program): a(n) = 20*a(n-1) - 3*a(n-2).
  • A136272 (program): Waterbird take-off sequence. Complement of A166021.
  • A136277 (program): From the binary representation of n: binomial(number of ones, number of blocks of contiguous ones).
  • A136281 (program): Number of graphs on n labeled nodes with degree at most 2.
  • A136289 (program): Start with three pennies touching each other on a tabletop. In each generation, add pennies subject to the rule that a penny can be placed only when (at least) two pennies are already in position to determine its position; sequence gives number of pennies added at generation n.
  • A136290 (program): a(0)=1, a(1)=3, a(2)=9, a(3)=12, a(4)=15; thereafter a(n) = a(n-1) + a(n-3) - a(n-4).
  • A136293 (program): Linear bound on the genera of Heegaard splittings of closed, orientable 3-manifolds that admit a generalized triangulation with n generalized tetrahedra.
  • A136297 (program): a(n) = 3*a(n-1) - 3*a(n-2) + 3*a(n-3), with a(0)=1, a(1)=3, a(2)=1.
  • A136298 (program): a(n) = 3*a(n-1) - 4*a(n-3), with a(0)=1, a(1)=2, a(2)=4, a(3)=9.
  • A136299 (program): a(n) = 3*a(n-1) - 4*a(n-3), with a(0)=1, a(1)=2, a(2)=4, a(3)=7.
  • A136302 (program): Transform of A000027 by the T_{1,1} transformation (see link).
  • A136303 (program): Expansion of g.f. (1 +x^2)/((1-x)^2*(1 -3*x +2*x^2 -x^3)).
  • A136305 (program): Expansion of g.f. (3 -x +2*x^2)/(1 -3*x +2*x^2 -x^3).
  • A136307 (program): a(n)=n*(10^K) + a(n-1); a(0)=1; K=floor(log_10 a(n-1))+1.
  • A136310 (program): a(n)=a(n-1)*(2^K)+ n*(n+1)/2 ; a(0)=1; K=floor(log_2 n*(n+1)/2).
  • A136313 (program): a(1) = 1; for n>1, a(n) = a(n-1) + 8 mod 22.
  • A136315 (program): Period 10: repeat 1, 2, 3, 6, 5, 0, 7, 4, 9, 8 .
  • A136316 (program): 13 + 12*n - n^2.
  • A136319 (program): Decimal expansion of [phi, phi, …] = (phi + sqrt(phi^2 + 4))/2.
  • A136320 (program): Terms of A047241 swapped in pairs.
  • A136321 (program): Triangular sequence of coefficients of a polynomial recursion for C_n and B_n Cartan matrices: p(x, n) = (-2 + x)*p(x, n - 1) - p(x, n - 2) p(x,n)=x2-4*x+4-m:m=5;(related sequence: A_n:m=1,G_n,m=3,B_n,C_n,m=2) This triangular sequence is an extension to the Cartan pattern of matrices.
  • A136322 (program): a(n) is the ceiling of 2^n * (sqrt(2)-1), i.e., a(n)-1 is the number whose binary representation gives the first n bits of sqrt(2)-1.
  • A136324 (program): Interleaving of A002450(n), A002450(n) + 1.
  • A136325 (program): a(n) = 8*a(n-1)-a(n-2) with a(0)=0 and a(1)=3.
  • A136326 (program): a(n) = a(n-1) + 4a(n-2) - 4a(n-3).
  • A136327 (program): Numbers k such that binomial(2k-1, k-1) == 1 (mod k).
  • A136329 (program): Triangular sequence of coefficients of a polynomial recursion for C_n and B_n Cartan matrices: p(x, n) = (-2 + x)*p(x, n - 1) - p(x, n - 2) p(x,n)=x2-4*x+4-m:m=4;(related sequence: A_n:m=1,G_n,m=3,B_n,C_n,m=2) This triangular sequence is an extension to the Cartan pattern of matrices.
  • A136331 (program): The discriminant of the characteristic polynomial of the O+ and O- submatrix for spin 3 of the nuclear electric quadrupole Hamiltonian is a perfect square for these values.
  • A136333 (program): Numbers containing only digits coprime to 10 in their decimal representation.
  • A136334 (program): Triangular sequence from both a cubic expansion polynomial and a three deep polynomial recursion: Expansion polynomial: f(x,t)=1/(1 - 2*x*t + t^3); Recursion polynomials: p(x, n) = 2*x*p(x, n - 1) - p(x, n - 3);.
  • A136336 (program): a(n) = a(n-1) + 4*a(n-2) - 4*a(n-3) for n>3.
  • A136362 (program): Numbers n such that P+n is not irreducible, where P = x^8 - 8*x^6 + 20*x^4 - 16*x^2 + 2.
  • A136376 (program): a(n) = n*F(n) + (n-1)*F(n-1).
  • A136391 (program): a(n) = n*F(n) - (n-1)*F(n-1), where the F(j)’s are the Fibonacci numbers (F(0)=0, F(1)=1).
  • A136392 (program): a(n) = 6*n^2 - 10*n + 5.
  • A136393 (program): a(n) = C(3^n,n).
  • A136395 (program): Binomial transform of [1, 3, 4, 3, 2, 0, 0, 0, …].
  • A136396 (program): a(n) = 1 + n*(n+1)*(n^2-n+12)/12.
  • A136399 (program): Numbers having in their decimal representation at least one digit greater than 1.
  • A136400 (program): Replace all digits greater than 1 with 1 (in decimal representation).
  • A136401 (program): a(n) = 3*a(n-1) - 4*a(n-2) + 6*a(n-3) - 4*a(n-4).
  • A136403 (program): Absolute values of negative fundamental discriminants (A003657) that are not 3 mod 4 (A002145).
  • A136408 (program): a(n) = 3*a(n-1) - 4*a(n-2) + 6*a(n-3) - 4*a(n-4).
  • A136409 (program): a(n) = floor(n*log_3(2)).
  • A136410 (program): Numbers n having a proper divisor d > 2 such that d-1 divides n-1.
  • A136412 (program): a(n) = (5*4^n+1)/3.
  • A136417 (program): Number of squares <= 2^n.
  • A136419 (program): a(n) = binomial((n+2)*(n+1),(n+1)*n).
  • A136421 (program): a(n) = floor((x^n - (1-x)^n)/sqrt(2)+ 1/2) where x = (sqrt(2)+1)/2.
  • A136422 (program): Floor((x^n - (1-x)^n)/sqrt(3)+.5) where x = (sqrt(3)+1)/2.
  • A136423 (program): Floor((x^n - (1-x)^n)/2 +.5) where x = (sqrt(4)+1)/2 = 3/2.
  • A136424 (program): a(n) = floor((x^n - (1-x)^n) / (2x-1) +.5) where x = (sqrt(6)+1)/2 (and hence 2x-1 = sqrt(6)).
  • A136425 (program): a(n) = floor((x^n-(1-x)^n)/sqrt(7)+1/2) where x = (sqrt(7)+1)/2.
  • A136427 (program): a(n) = 3*a(n-1)-4*a(n-2)+6*a(n-3)-4*a(n-4).
  • A136428 (program): First differences of A064770.
  • A136429 (program): a(n) = Sum_{k=0..n} F(k+1)^2*F(n-k+1)^2 where F = Fibonacci numbers (A000045).
  • A136431 (program): Hyperfibonacci square number array a(k,n) = F(n)^(k), read by ascending antidiagonals (k, n >= 0).
  • A136432 (program): a(n)! is the smallest factorial bigger than n^n.
  • A136433 (program): a(n+2)=a(n+1)*(n mod 3 + 1) + (n mod 2 + 1), a(1)=11.
  • A136437 (program): a(n) = prime(n) - k! where k is the greatest number such that k! <= prime(n).
  • A136442 (program): a(3n) = 1, a(3n-1) = 0 and a(3n+1) = a(n).
  • A136443 (program): Numbers m such that A102863(m) = 1.
  • A136444 (program): a(n) = Sum_{k=0..n} k*binomial(n-k, 2*k).
  • A136462 (program): Square table, read by antidiagonals, where T(n,k) = C((n+1)*2^(k-1), k) for n>=0, k>=0.
  • A136463 (program): Diagonal of square array A136462: a(n) = C((n+1)*2^(n-1), n) for n>=0.
  • A136464 (program): C((n+1)*2^(n-1),n)/(n+1).
  • A136465 (program): Row 0 of square array A136462: a(n) = C(2^(n-1), n) for n>=0.
  • A136466 (program): Row 2 of square array A136462: a(n) = C(3*2^(n-1), n) for n>=0.
  • A136480 (program): Number of trailing equal digits in binary representation of n.
  • A136481 (program): Symmetric polynomial matrices that give multivariate determinants as Coefficients of characteristic polynomials: h(n,m)=If[m == 1, n, If[n - m + 1 == 0, 1, If[n - m == 0, 1, If[n - m > 0, 1, 0]]]],n,m<=d.
  • A136482 (program): Triangle read by rows: T(n,k) = 2*A007318(n,k) - A034851(n,k) (i.e., twice Pascal’s triangle - the Losanitch triangle).
  • A136483 (program): Number of unit square lattice cells inside quadrant of origin-centered circle of diameter n.
  • A136484 (program): Number of unit square lattice cells inside quadrant of origin centered circle of diameter 2n+1.
  • A136485 (program): Number of unit square lattice cells enclosed by origin centered circle of diameter n.
  • A136486 (program): Number of unit square lattice cells enclosed by origin centered circle of diameter 2n+1.
  • A136488 (program): a(n) = 2^n - A005418(n).
  • A136489 (program): 3*A007318 - 2*A034851 (i.e., thrice Pascal’s triangle - twice Losanitch’s triangle).
  • A136494 (program): Number of permutation symmetries in the binary expansion of n.
  • A136495 (program): Solution of the complementary equation b(n)=a(a(n))+n.
  • A136496 (program): Solution of the complementary equation b(n)=a(a(n))+n; this is sequence b; sequence a is A136495.
  • A136501 (program): Triangle, read by rows, where T(n,k) = C(2^k,n-k) for n>=k>=0.
  • A136505 (program): a(n) = binomial(2^n + 1, n).
  • A136506 (program): a(n) = binomial(2^n + 2, n).
  • A136507 (program): a(n) = Sum_{k=0..n} binomial(2^(n-k) + k, n-k).
  • A136508 (program): G.f.: A(x) = Sum_{n>=0} (-1)^n * log(1 - x - 2^n*x^2)^n / n! .
  • A136509 (program): G.f.: A(x) = Sum_{n>=0} (-1)^n * (1 -x -2^n*x^2)^(-1) * log(1 -x -2^n*x^2)^n / n!.
  • A136513 (program): Number of unit square lattice cells inside half-plane (two adjacent quadrants) of origin centered circle of diameter n.
  • A136514 (program): Number of unit square lattice cells inside half-plane (two adjacent quadrants) of origin centered circle of radius n.
  • A136515 (program): Number of unit square lattice cells inside half-plane (two adjacent quadrants) of origin centered circle of diameter 2n+1.
  • A136516 (program): a(n) = (2^n+1)^n.
  • A136518 (program): a(n) = A027907(2^n, n), where A027907 = triangle of trinomial coefficients.
  • A136519 (program): a(n) = A027907(2^n+1, n), where A027907 = triangle of trinomial coefficients.
  • A136520 (program): A001263 * A027656.
  • A136521 (program): Triangle read by rows: (1, 2, 2, 2, …) on the main diagonal and the rest zeros.
  • A136522 (program): a(n) = 1 if n is a palindrome, otherwise 0.
  • A136524 (program): a(n) = 2^n*(2^n + n)^(n-1).
  • A136525 (program): a(n) = (2^n + 1)*(2^n + n + 1)^(n-1).
  • A136530 (program): a(n) = 2^n*(3*n^2 + 13*n + 8)/8.
  • A136531 (program): Coefficients of polynomials B(x,n) = ((1+a+b)*x - c)*B(x,n-1) - a*b*B(x,n-2) where B(x,0) = 1, B(x,1) = x, a=-b, b=1, c=1.
  • A136548 (program): a(n) = max {k >= 1 | sigma(k) <= n}.
  • A136550 (program): a(n) = C(2^n + 2*n, n) * 2^n / (2^n + 2*n); a(n) = coefficient of x^n in Catalan(x)^(2^n).
  • A136551 (program): a(n) = C(2^n + 2*n + 1, n)*(2^n + 1)/(2^n + 2*n + 1); a(n) = coefficient of x^n in Catalan(x)^(2^n+1).
  • A136552 (program): a(n) = C(2*2^n + 2*n, n)*2^n/(2^n + n); a(n) = coefficient of x^n in Catalan(x)^(2*2^n).
  • A136554 (program): G.f.: A(x) = Sum_{n>=0} log( (1 + x)*(1 + 2^n*x) )^n / n!.
  • A136555 (program): Square array, read by antidiagonals, where T(n,k) = binomial(2^k + n-1, k).
  • A136556 (program): a(n) = binomial(2^n - 1, n).
  • A136557 (program): a(n) = Sum_{k=0..n} binomial(2^k + n-k-1, k).
  • A136559 (program): G.f.: A(x) = Sum_{n>=0} arctanh( 2^(2n+1)*x )^(2n+1) / (2n+1)!; a power series in x with integer coefficients.
  • A136565 (program): a(n) = sum of the distinct values making up the exponents in the prime-factorization of n.
  • A136567 (program): a(n) is the number of exponents occurring only once each in the prime factorization of n.
  • A136572 (program): Triangle read by rows: row n consists of n zeros followed by n!.
  • A136574 (program): Row sums of triangle A136573.
  • A136575 (program): A triangular sequence using Stan Wagon’s LegendrePhi[a,b] function.
  • A136576 (program): Series reversion of x*c(x)/(1-2x), c(x) the g.f. of A000108.
  • A136577 (program): Conjectured Hankel transform of A136576(n+1).
  • A136579 (program): Triangle read by rows: A128174 * A136572.
  • A136580 (program): Row sums of triangle A136579.
  • A136581 (program): Triangle read by rows: A136572 * A128174.
  • A136591 (program): Column 1 of triangle A136590.
  • A136596 (program): Column 2 of triangle A136595.
  • A136598 (program): G.f.: (2*x^3 + 5) / ( -x^5 + x^3 + 1).
  • A136602 (program): Nonnegative numbers that can be obtained by inserting minus and plus-signs in 123456789.
  • A136606 (program): Reduced denominators in the Maclaurin series for the Gudermannian.
  • A136610 (program): Number of odd digits in Fibonacci numbers.
  • A136612 (program): a(n) = ((prime(n+3) + prime(n+1)) - (prime(n+2) + prime(n))).
  • A136613 (program): Concatenation of (sum of digits of n) and n.
  • A136614 (program): Sum of digits of A108773 and of A136613.
  • A136615 (program): Fold-switch-fold sequence defined by McFarlane and Withers for m=3: Let A(n) = If[Mod[A(n - 1), 2] == 0, A(n - 1)/2, (m - A(n - 1))2]; a(n)= If[ Mod[A(n - 1), 2] == 0, a(n - 1)/2, (Pi - a(n - 1))/2].
  • A136616 (program): a(n) = largest m with H(m) - H(n) <= 1, where H(i) = Sum_{j=1 to i} 1/j, the i-th harmonic number, H(0) = 0.
  • A136617 (program): a(n) = largest k such that the sum of k consecutive reciprocals 1/n + … + 1/(n+k-1) does not exceed 1.
  • A136619 (program): a(1) = 1, then repeat period 3: [1, 4, 2].
  • A136636 (program): a(n) = n * C(2*3^(n-1), n) for n>=1.
  • A136643 (program): Triangle of coefficients of characteristic polynomials of anti-symmetrical tridiagonal matrices: Middle diagonal: a=1; Lower first subdiagonal: b=2; Upper first subdiagonal: c=-2; Example: M(3) {{1, -2, 0}, {2, 1, -2}, {0, 2, 1}}.
  • A136644 (program): Triangle of coefficients of characteristic polynomials of asymmetrical tridiagonal matrices: Middle diagonal: a=1; Lower first subdiagonal: b=2; Upper first subdiagonal: c=1; Example: M(3) {{1, 1, 0}, {2, 1, 1}, {0, 2, 1}}.
  • A136648 (program): Inverse binomial transform of A014070: a(n) = Sum_{k=0..n} (-1)^(n-k)*C(n,k)*C(2^k,k).
  • A136649 (program): Binomial transform of A014070: a(n) = Sum_{k=0..n} C(n,k)*C(2^k,k).
  • A136650 (program): Self-convolution of A006125(n) = 2^{n(n-1)/2}.
  • A136651 (program): Self-convolution of A014070: a(n) = Sum_{k=0..n} C(2^k,k)*C(2^(n-k),n-k).
  • A136652 (program): L.g.f.: A(x) = log( Sum_{n>=0} 2^[n(n-1)/2]*x^n ).
  • A136655 (program): Product of odd divisors of n.
  • A136658 (program): Row sums of unsigned triangle A136656 and also of triangle 2*A136657.
  • A136659 (program): Unsigned third column (k=2) of triangle A136656 divided by 4.
  • A136660 (program): Unsigned fourth column (k=3) of triangle A136656 divided by 8.
  • A136673 (program): Triangle of coefficients from a polynomial recursion for Galois field GF(2^n) polynomials: p(x,n)=(x+1)*p(x,n-1)-x*p(x,n-2); or f(x,n)=x^n+x+1;.
  • A136675 (program): Numerator of Sum_{k=1..n} (-1)^(k+1)/k^3.
  • A136676 (program): Numerator of Sum_{k=1..n} (-1)^(k+1)/k^5.
  • A136677 (program): Numerator of Sum_{k=1..n} (-1)^(k+1)/k^6.
  • A136687 (program): Number of palindromes in the range [0,n] inclusive.
  • A136688 (program): Triangular sequence of q-Fibonacci polynomials for s=2: F(x,n) = x*F(x,n-1) + s*F(x,n-2).
  • A136689 (program): Triangular sequence of q-Fibonacci polynomials for s=3: F(x,n) = x*F(x,n-1) + s*F(x,n-2).
  • A136690 (program): Final nonzero digit of n! in base 3.
  • A136691 (program): Final nonzero digit of n! in base 4.
  • A136692 (program): Final nonzero digit of n! in base 5.
  • A136693 (program): Final nonzero digit of n! in base 6.
  • A136694 (program): Final nonzero digit of n! in base 7.
  • A136695 (program): Final nonzero digit of n! in base 8.
  • A136696 (program): Final nonzero digit of n! in base 9.
  • A136697 (program): Final nonzero digit of n! in base 11.
  • A136698 (program): Final nonzero digit of n! in base 12.
  • A136699 (program): Final nonzero digit of n! in base 13.
  • A136700 (program): Final nonzero digit of n! in base 14.
  • A136701 (program): Final nonzero digit of n! in base 15.
  • A136702 (program): Final nonzero digit of n! in base 16.
  • A136705 (program): Triangle read by rows where the n-th row gives the coefficients of the characteristic polynomial for a Fibonacci-type matrix with a=1 and b=1.
  • A136719 (program): Number of labeled directed trees with n nodes.
  • A136724 (program): Numbers divisible by 4 that are not powers of 2.
  • A136725 (program): Primitive dimensions of Hadamard matrices.
  • A136727 (program): E.g.f.: A(x) = [ exp(x)/(3 - 2*exp(x)) ]^(1/3).
  • A136728 (program): E.g.f.: A(x) = (exp(x)/(4 - 3*exp(x)))^(1/4).
  • A136729 (program): E.g.f.: A(x) = [ exp(x)/(5 - 4*exp(x)) ]^(1/5).
  • A136746 (program): G.f.: (z^12+1-z^11-z^10+z^8-z^6+z^5-z^3+z)/((z+1)*(z-1)^2).
  • A136749 (program): G.f.: Sum_{n>=0} arctanh(2^n*x)^n / n!, a power series in x with integer coefficients.
  • A136754 (program): Leading digit of n! in base 3.
  • A136755 (program): a(n) = leading digit of n! in base 4.
  • A136756 (program): Leading digit of n! in base 5.
  • A136757 (program): Leading digit of n! in base 6.
  • A136758 (program): a(n) = leading digit of n! in base 7.
  • A136759 (program): a(n) = leading digit of n! in base 8.
  • A136760 (program): a(n) = leading digit of n! in base 9.
  • A136761 (program): a(n) = leading digit of n! in base 11.
  • A136762 (program): Leading digit of n! in base 12.
  • A136763 (program): a(n) = leading digit of n! in base 13.
  • A136764 (program): a(n) = leading digit of n! in base 14.
  • A136765 (program): a(n) = leading digit of n! in base 15.
  • A136766 (program): a(n) = leading digit of n! in base 16.
  • A136767 (program): n! never ends in this many 0’s in base 4.
  • A136768 (program): n! never ends in this many 0’s in base 7.
  • A136770 (program): n! never ends in this many 0’s in base 9.
  • A136771 (program): n! never ends in this many 0’s in base 11.
  • A136773 (program): n! never ends in this many 0’s in base 13.
  • A136775 (program): Number of multiplex juggling sequences of length n, base state <1,1> and hand capacity 2.
  • A136776 (program): Number of primitive multiplex juggling sequences of length n, base state <1,1> and hand capacity 2.
  • A136777 (program): Number of multiplex juggling sequences of length n, base state <2,1> and hand capacity 2.
  • A136778 (program): Number of primitive multiplex juggling sequences of length n, base state <2,1> and hand capacity 2.
  • A136779 (program): Number of multiplex juggling sequences of length n, base state <1,1,1> and hand capacity 2.
  • A136780 (program): Number of primitive multiplex juggling sequences of length n, base state <1,1,1> and hand capacity 2.
  • A136783 (program): Number of multiplex juggling sequences of length n, base state <3> and hand capacity 3.
  • A136784 (program): Number of primitive multiplex juggling sequences of length n, base state <3> and hand capacity 3.
  • A136785 (program): Number of multiplex juggling sequences of length n, base state <2,1> and hand capacity 3.
  • A136786 (program): Number of primitive multiplex juggling sequences of length n, base state <2,1> and hand capacity 3.
  • A136787 (program): Triangle read by rows: A107131 * A000012.
  • A136788 (program): Triangle read by rows: A000012 * A107131.
  • A136796 (program): Number of labeled marked rooted trees with n nodes.
  • A136797 (program): Number of labeled marked trees with n nodes.
  • A136798 (program): First term in a sequence of at least 3 consecutive composite integers.
  • A136799 (program): Last term in a sequence of at least 3 consecutive composite integers.
  • A136800 (program): Number of composites in prime gaps of size 3 or larger, in order of appearance.
  • A136853 (program): Numbers k such that k and k^2 use only the digits 0, 1, 3 and 9.
  • A136859 (program): Numbers k such that k and k^2 use only the digits 0, 1, 4 and 6.
  • A136921 (program): Numbers k such that k and k^2 use only the digits 0, 2, 6 and 7.
  • A136926 (program): Numbers k such that k and k^2 use only the digits 0, 2, 7 and 9.
  • A136957 (program): Numbers k such that k and k^2 use only the digits 0, 4, 6 and 9.
  • A136962 (program): Numbers k such that k and k^2 use only the digits 0, 5, 6 and 7.
  • A137120 (program): Numbers k such that k and k^2 use only the digits 3, 4, 5 and 6.
  • A137146 (program): Numbers k such that k and k^2 use only the digits 5, 6, 7 and 8.
  • A137148 (program): a(n) = n*phi(n) for nonprime n.
  • A137149 (program): a(n) = (prime(n)-2)!.
  • A137150 (program): Degree of Lagrange resolvent of polynomial of composite degree.
  • A137153 (program): Triangle, read by rows, where T(n,k) = C(2^k + n-k-1, n-k).
  • A137154 (program): a(n) = Sum_{k=0..n} binomial(2^k + n-k-1, n-k); equals the row sums of triangle A137153.
  • A137155 (program): a(n) = Sum_{k=0..[n/2]} C(2^k + n-2k-1, n-2k); equals the antidiagonal sums of triangle A137153.
  • A137166 (program): Sequence equals its 4th differences shifted by one index.
  • A137171 (program): Interleaved reading of A000749 and its first to third differences.
  • A137173 (program): A006516 at positions with even indices, A007582 at positions with odd indices.
  • A137174 (program): First differences of A138383.
  • A137176 (program): Hyperlucas number array T(r,n) = L(n)^(r), read by ascending antidiagonals (r >= 0, n >= 0).
  • A137180 (program): Number of palindromes in the range [1,n] inclusive.
  • A137199 (program): a(n)=a(n-1)+3a(n-2)+a(n-3).
  • A137200 (program): Number of ways to tile an n X 1 strip with 1 X 1 squares and 2 X 1 dominoes with the restriction that no three consecutive tiles are of the same type.
  • A137203 (program): Number of Fibonacci numbers less than or equal to n^2.
  • A137204 (program): Decimal expansion of e + 1/e.
  • A137206 (program): First differences of A074323.
  • A137208 (program): a(n) = a(n-1) + 4*a(n-2) - 4*a(n-3) for n > 2; a(0)=2, a(1)=3, a(2)=6.
  • A137211 (program): Generalized or s-Catalan numbers.
  • A137212 (program): a(n) = 5*a(n-1) - 5*a(n-2) - 3*a(n-3).
  • A137213 (program): First differences of A137212.
  • A137215 (program): a(n) = 3*(10^n) + (n^2 + 1)*(10^n - 1)/9.
  • A137219 (program): a(n) = (A126086(n) - 3*A001850(n) + 2)/6.
  • A137220 (program): a(n) = (A126086(n) + 3*A001850(n) + 2)/6.
  • A137221 (program): a(n) = 5*a(n-1) - 9*a(n-2) + 8*a(n-3) - 4*a(n-4), with a(0)=0, a(1)=0, a(2)=0, a(3)=1.
  • A137222 (program): Partial sums of A087429.
  • A137223 (program): a(n) = A135574(3*n) + A135574(3*n+1) + A135574(3*n+2).
  • A137224 (program): Mix 4*n^2, 1+4*n^2, 1+(2n+1)^2, (2n+1)^2 (or A016742, A053755, A069894, A016754).
  • A137225 (program): Triangle T(k,q) of minimal q-Niven numbers: smallest number such that the sum of its digits in base q equals k, 2<=q<=k+1.
  • A137228 (program): Minimal total number of edges in a polyiamond consisting of n triangular cells.
  • A137229 (program): Expansion of g.f. x/((1-x)*(1-3*x+2*x^2-x^3)).
  • A137230 (program): Composite numbers that are divisible by the number of their prime factors (counted with multiplicity).
  • A137232 (program): a(n) = -a(n-1) + 7*a(n-2) + 3*a(n-3) with a(0) = a(1) = 0, a(2) = 1.
  • A137233 (program): Number of n-digit even numbers.
  • A137234 (program): Expansion of g.f. 1/((1-x)^2*(1 - 3*x + 2*x^2 - x^3)).
  • A137235 (program): a(n) = (n+1)/2 if n is odd; a(n) = n/2 + 6 if n is even.
  • A137241 (program): Number triples (k,3-k,2-2k), concatenated for k=0, 1, 2, 3,…
  • A137242 (program): Numbers n such that A116127(n) = 2.
  • A137243 (program): Number of coprime pairs (a,b) with -n <= a,b <= n.
  • A137246 (program): a(n) is the ratio of the sum of the squares of the bends (curvatures) of the n-th generation of an Apollonian packing to the sum of the squares of the bends of the initial four-circle configuration.
  • A137247 (program): a(n) = 4*a(n-1) - 6*a(n-2) + 6*a(n-3) - 3*a(n-4), with initial terms 0, 0, 0, 1.
  • A137249 (program): Expansion of g.f. z*(2-2*z+z^2+z^3)/((1+z)*(1-3*z+2*z^2-z^3)).
  • A137255 (program): a(n) = 2*a(n-1) + 4*a(n-2) - 6*a(n-3) - 3*a(n-4) for n > 3, with a(0)=1, a(1)=2, a(2)=4, a(3)=8.
  • A137256 (program): Binomial transform of 2^n, 2^n, 2^n.
  • A137257 (program): A number k is included if there is at least one (nonzero) exponent in the prime factorization of k that is not coprime to k.
  • A137263 (program): Interprimes (A024675) == 2 (mod 3).
  • A137264 (program): Prime number gaps read modulo 3.
  • A137266 (program): a(n) = number of positive integers k where k divides (n - floor(n/k)).
  • A137267 (program): Chung-Graham juggling polynomials as a triangular sequence of positive coefficients.
  • A137268 (program): Triangle T(n, k) = k! * (k+1)^(n-k), read by rows.
  • A137270 (program): Primes p such that p^2 - 6 is also prime.
  • A137276 (program): Triangle T(n,k), read by rows: T(n,k)= 0 if n-k odd. T(n,k)= 2*(-1)^((n-k)/2)*(2k-n)/(n+k)*binomial((n+k)/2,(n-k)/2) if n-k even.
  • A137277 (program): Triangle of the coefficients [x^k] P_n(x) of the polynomials P_n(x) = 1/n * sum(j=0..floor(n/2), (-1)^j * binomial(n,j) * (n-4*j) * x^(n-2*j) ).
  • A137280 (program): a(n) = 3*a(n-1) + 7*a(n-2).
  • A137281 (program): Numbers k such that T(k) is not divisible by T(i), 1 < i < k, where T(k) = k-th triangular number A000217(k).
  • A137282 (program): Final digit of A136408(n).
  • A137285 (program): a(1)=1. a(n+1) = a(n) + (number of terms of this sequence, from among terms a(1) through a(n), that are >= (1/n)sum{k=1 to n} a(k)).
  • A137287 (program): a(n) is the number 2 written (prime(n)-1)/2 times followed by the digit 1; a(1)=2.
  • A137288 (program): Numbers k such that 2*prime(k)-1 is prime.
  • A137290 (program): Fibonacci(n) mod 30.
  • A137291 (program): Numbers n such that prime(n)^2-2 is prime.
  • A137294 (program): A polynomial-time algorithm for moving all seeds into one pot in a class of sowing positions.
  • A137300 (program): 4 X 4 Latin square or “Vigenere” square read by rows.
  • A137301 (program): Decimal expansion of 999/9801.
  • A137305 (program): Write n in base 3, change twos in ones and ones in twos, reverse.
  • A137309 (program): Let T = {1,3,5,7,9,1,3,5,7,9,1,3,5,7,9, … }; a(n) is n-th concatenation of n numbers from T.
  • A137310 (program): Numbers n such that a type-4 Gaussian normal basis over GF(2^n) exists.
  • A137318 (program): Concatenation of segments of the digit sequence 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 3….
  • A137319 (program): Start with the set of natural numbers. Add 1 to every 2nd term, 2 to every 3rd term, 3 to every 4th term, etc.
  • A137321 (program): a(n) = prime(n)^prime(n) - k!, where prime(n) is the n-th prime number, and k is the greatest number for which k! <= prime(n)^prime(n).
  • A137323 (program): a(n) = sum(d divides n, 2^(n/d-1) - 1 ), omitting d=1 and d=n.
  • A137325 (program): Number of terms in the Janet periodic table of the elements 32 columns: ordered 14 2’s, 10 4’s, 6 6’s, 2 8’s.
  • A137327 (program): Fermat(n) modulo n.
  • A137329 (program): a(n)=-4a(n-4).
  • A137331 (program): a(n) = 1 if the binary weight of n is prime, otherwise 0.
  • A137336 (program): Triangle read by rows, with 2-variable g.f. (-2*x*t+t^2)/(1-2*x*t+t^2).
  • A137337 (program): T(i,j) = (-1)^(i+j)*(i+1)*binomial(i,j)*2^(i-j)*4^j.
  • A137340 (program): a(n) = 2*a(n-1) + 3*a(n-2), with a(0) = 1, a(1) = 9.
  • A137341 (program): a(n) = n! * A000110(n) where A000110 is the sequence of Bell numbers.
  • A137344 (program): a(n)=4a(n-2). Also 3*A084221.
  • A137345 (program): a(n) = binomial( n(n+1)/2, n) mod n.
  • A137356 (program): a(n) = Sum_{k <= n/2 } binomial(n-2k, 3k).
  • A137357 (program): a(n) = Sum_{k <= n/2 } binomial(n-2k, 3k+1).
  • A137358 (program): a(n) = Sum_{k <= n/2 } binomial(n-2k, 3k+2).
  • A137359 (program): a(n) = Sum_{k <= n/2 } k*binomial(n-2k, 3k).
  • A137360 (program): a(n) = Sum_{k <= n/2 } k*binomial(n-2k, 3k+1).
  • A137361 (program): a(n) = Sum_{k=0..n/2} k*binomial(n-2*k, 3*k+2).
  • A137362 (program): Positions at which the truncated square root of triangular numbers is unique.
  • A137367 (program): Subset of A037165 (p(n)*p(n+1)-p(n)-p(n+1)) for twin primes.
  • A137370 (program): Brahmagupta matrix in a Markov matrix recursion produces a set of polynomials: the special values of x->Sqrt[z];y->1;t->n gives a set of polynomials as determinants. The triangular sequence of the Coefficients of these polynomials are except for signs A055134.
  • A137377 (program): a(1)=0; for n >= 2, a(n) = a(n-1) + |d(n)-d(n-1)|, where d(n) is the number of positive divisors of n.
  • A137386 (program): Numbers that when mirrored vertically are still valid characters. Only applies when numbers are scribed in Arabic numerals.
  • A137387 (program): Triangular sequence from coefficients of the expansion of p(x,t)=Exp[2*x*t]*t/(1 - t).
  • A137389 (program): a(n) = 2^prime(n) + 2^prime(n+1).
  • A137391 (program): Triangular sequence of coefficients from a Sheffer sequence expansion: f(t) = 1 + t + t^2; g(t) = t + t^2; p(t) = f[t]*Exp[x*g[t]];.
  • A137392 (program): (10-n) * Fibonacci(n).
  • A137396 (program): Triangle read by rows: row n gives the coefficients in the expansion of the chromatic polynomial of the n-cycle graphs.
  • A137398 (program): Let S be a strictly monotonic sequence of length 2n and let p and q be subsequences of S each of length n such that the least element belongs to p and every element of S belongs to either p or q. The number of ways to select p such that for any index i the exchange of p(i) and q(i) makes at least one of p and q non-monotonic, is given by a(n).
  • A137399 (program): a(n)=4a(n-4).
  • A137400 (program): a(n) = A128941(n) + 2.
  • A137402 (program): a(n) = Sum_{k=0..n} binomial(floor(n-2k/3), k).
  • A137409 (program): Numbers that cannot be the value of ‘C’ in a primitive Pythagorean triple (A < B; A^2 + B^2 = C^2).
  • A137410 (program): a(n) = (5^n - 3) / 2.
  • A137412 (program): a(1)=0. If a(m) is odd, then a(2^(m-1)+k) = a(k)-1, for all k where 1<=k<=2^(m-1). If a(m) is even, then a(2^(m-1)+k) = a(k)+1, for all k where 1<=k<=2^(m-1).
  • A137413 (program): a(n) = the number of positive integers that are <= n and are coprime to (the sum of the distinct prime divisors of n).
  • A137421 (program): Decimal expansion of growth constant in random Fibonacci sequence.
  • A137423 (program): Triangle T(n,k) = A053120(n,k)+binomial(n,k) read by rows, 0<=k<=n.
  • A137426 (program): a(n)=-a(n-1)+2a(n-3).
  • A137429 (program): a(n) = -2*a(n-1) - 2*a(n-2), with a(0)=1 and a(1)=-4.
  • A137430 (program): Triangular sequence from coefficients of a cumulative sum of Chebyshev T(x,n) polynomials (A053120): p(x,n)=p(x,n-1)+T(x,n).
  • A137441 (program): Partial sums of partial sums of PrimePi(k).
  • A137444 (program): a(n) = 2*a(n-1) - 2*a(n-2) with a(0)=1, a(1)=4.
  • A137445 (program): a(n) = 2a(n-1)-2a(n-2), with a(0)=3 and a(1)=2.
  • A137452 (program): Triangular array of the coefficients of the sequence of Abel polynomials A(n,x) := x*(x-n)^(n-1).
  • A137457 (program): Consider a row of standard dice as a counter. This sequence enumerates the number of changes (one face rotated over an edge to an adjacent face) from n-1 to n.
  • A137458 (program): Prime(core(n)).
  • A137462 (program): a(n) + a(n-1) = n-th semiprime.
  • A137465 (program): 1 concatenated with n n’s concatenated with 1.
  • A137466 (program): 1 concatenated with n 21’s.
  • A137469 (program): Numbers with an odd number of 1’s in base 5 expansion.
  • A137470 (program): Inverse binomial transform of 1, 2, 2, 4, 10, 20, … = A100088.
  • A137479 (program): Greatest common divisor of (the average of the n-th twin prime pair) and (the average of the (n+1)st twin prime pair).
  • A137480 (program): a(n)=4a(n-2).
  • A137482 (program): Number of permutations of n objects such that no two-element subset is preserved.
  • A137483 (program): a(n+1) = 9*a(n) - 6, a(0) = 2.
  • A137487 (program): Numbers with 24 divisors.
  • A137491 (program): Numbers with 28 divisors.
  • A137493 (program): Numbers with 30 divisors.
  • A137495 (program): A098601(2n)+A098601(2n+1)
  • A137500 (program): Binomial transform of b(n) = (0, 0, A007910).
  • A137501 (program): The even numbers repeated, with alternating signs.
  • A137505 (program): Inverse binomial transform of A007910.
  • A137508 (program): Successive structures of alkaline earth metals (periodic table elements from 2nd column).
  • A137512 (program): The number of nodes visible from underneath a binary tree, where the nodes are placed such that the innermost of the two sprouting nodes should be underneath the mother.
  • A137516 (program): Let 2n = p + q where p and q are primes. Take the p and q that produce the smallest product, then set a(n) = p*q - 2n.
  • A137517 (program): a(0) = 121; for n>0, a(n) = a(n-1) - n + 1.
  • A137521 (program): Prime numbers concatenated with 45.
  • A137526 (program): A triangular sequence of coefficients based on an expansion of a Enneper like Sheffer expansion function: g(t) = t; f(t) = t; p(x,t) = Exp[x*(t)]*(1 - f(t)2).
  • A137529 (program): a(n)=8a(n-4).
  • A137530 (program): Primes of the form 5k^2 + 1.
  • A137531 (program): a(n) = 3*a(n-1) - 2*a(n-2) + a(n-3).
  • A137551 (program): Number of permutations in S_n avoiding {bar 2}413{bar 5} (i.e., every occurrence of 413 is contained in an occurrence of a 24135).
  • A137553 (program): Number of permutations in S_n avoiding {bar 5}{bar 4}231 (i.e., every occurrence of 231 is contained in an occurrence of a 54231).
  • A137554 (program): Number of permutations in S_n avoiding {bar 5}{bar 4}132 (i.e., every occurrence of 132 is contained in an occurrence of a 54132).
  • A137558 (program): A137521(n)/5.
  • A137569 (program): Expansion of f(-x) / f(-x^3) in powers of x where f() is a Ramanujan theta function.
  • A137575 (program): Successive structures central number of Seaborg’s periodic table of the elements (extended to 32 columns) for odd rows.
  • A137581 (program): Number of inner zeros in decimal representation of n!.
  • A137582 (program): Numbers having no inner zeros in decimal representation of their factorial.
  • A137584 (program): a(n) = 3*a(n-1) - 2*a(n-2) + a(n-3), n > 3.
  • A137588 (program): Number of primes not greater than n that are greater than the number of primes not greater than n.
  • A137589 (program): a(n) is the integer that results after deletion of all digits of n-th prime, except the initial digit and the final digit.
  • A137591 (program): Number of parenthesizings of products formed by n factors assuming nonassociativity and partial commutativity: individual factors commute, but bracketed expressions don’t commute with anything.
  • A137605 (program): Consider the sequence: b(0) = n, and for k >= 1, b(k) = b(k-1)/2 if b(k-1) is even, otherwise b(k) = k-(b(k-1)+1)/2. Then a(n) = m, where m is the smallest index such that b(m) = 1.
  • A137606 (program): Numbers m such that all numbers {1…m} appear in the sequence {b(0) = m, b(n+1) = b(n)/2 if even, m-(b(n)+1)/2 otherwise}.
  • A137608 (program): Expansion of (1 - psi(-q)^3 / psi(-q^3)) / 3 in powers of q where psi() is a Ramanujan theta function.
  • A137610 (program): Self-convolution of A014062, where A014062(n) = C(n^2, n).
  • A137624 (program): Complement of A120632.
  • A137634 (program): Square array where T(n,k) = Sum_{j=0..k} C(n+2*j,j)*C(n+2*j,k-j), read by antidiagonals.
  • A137635 (program): a(n) = Sum_{k=0..n} C(2k,k)*C(2k,n-k); equals row 0 of square array A137634.
  • A137636 (program): a(n) = Sum_{k=0..n} C(2k+1,k)*C(2k+1,n-k) ; equals row 1 of square array A137634; also equals the convolution of A137635 and A073157.
  • A137637 (program): a(n) = Sum_{k=0..n} C(2k+2,k)*C(2k+2,n-k) ; equals row 2 of square array A137634 ; also equals the convolution of A137635 and the self-convolution of A073157.
  • A137638 (program): Antidiagonal sums of square array A137634.
  • A137644 (program): a(n) = Sum_{k=0..n} C(n+k,k)*C(n+k,n-k).
  • A137645 (program): a(n) = Sum_{k=0..n} C((n-k)*k, k) * C((n-k)*k, n-k).
  • A137646 (program): a(n) = Sum_{k=0..n} C(k*(k+1)/2, k) * C(k*(k+1)/2, n-k).
  • A137647 (program): a(n) = Sum_{k=0..n} C(k(k+1), k) * C(k(k+1), n-k).
  • A137648 (program): a(n) = Sum_{k=0..n} C(k^2, k) * C(k^2, n-k).
  • A137657 (program): Primes that are simultaneously of the forms 24i+7 and 7j+24.
  • A137658 (program): Values of i from A137657.
  • A137659 (program): Values of j from A137657.
  • A137664 (program): a(n) = (p+1)^p - 1 where p = prime(n).
  • A137665 (program): Quotients ((p+1)^p - 1)/p^2 for p = prime(n).
  • A137669 (program): Prime numbers p such that p +- a and p +- b are prime numbers where a and b are distinct positive integers with a < b < p.
  • A137670 (program): Prime numbers p such that p-b < p-a < p < p+a < p+b are prime for some a and b.
  • A137675 (program): Prime numbers p such that p +- a, p +- b, p +- c and p +- d are prime numbers, where a, b, c and d are distinct positive integers with p > d, d > c, c > b and b > a.
  • A137681 (program): Row sums of triangle A137680.
  • A137682 (program): Left border of triangle A137680.
  • A137685 (program): Expansion of phi(-q^3) / f(-q)^2 in powers of q where phi(), f() are Ramanujan theta functions.
  • A137688 (program): 2^A003056: 2^n appears n+1 times.
  • A137693 (program): Numbers n such that 3n^2-n = 6k^2-2k for some integer k>0.
  • A137694 (program): Numbers k such that 6k^2-2k = 3n^2-n for some integer n>0.
  • A137697 (program): a(n) = x(n) * 2^((n mod 2 - 1)/2), with x(n)=Sum(x(k)*x(n-k-1):0<=k<n), x(0)=SQRT(2).
  • A137701 (program): a(n) = semiprime(n)^prime(n).
  • A137704 (program): Hankel transform of aerated factorial numbers.
  • A137708 (program): Secondary Lower Wythoff Sequence.
  • A137709 (program): Secondary Upper Wythoff Sequence.
  • A137713 (program): Row sums of triangle A137712.
  • A137717 (program): Hankel transform of A106191.
  • A137718 (program): A scaled Hankel transform.
  • A137719 (program): Sequence based on the pattern [3n, 3n, 3n, 3n+2, 3n+1, 3n+2].
  • A137720 (program): Expansion of sqrt(1-4*x)/(1-3*x).
  • A137721 (program): Number of numbers not greater than n with no prime gaps in their factorization.
  • A137725 (program): Number of sequences of length n with elements {-2,-1,+1,+2}, such that the sum of elements of the whole sequence but of no proper subsequence equals 0 modulo n. For n>=4, the number of Hamiltonian (directed) circuits on the circulant graph C_n(1,2).
  • A137726 (program): Number of sequences of length n with elements {-2,-1,+1,+2}, counted up to simultaneous reversal and negation, such that the sum of elements of the whole sequence but of no proper subsequence equals 0 modulo n. For n>=4, the number of Hamiltonian (undirected) cycles on the circulant graph C_n(1,2).
  • A137727 (program): Final digit of prime(n)*prime(n+1).
  • A137728 (program): Second digit from the end of product of first n primes.
  • A137729 (program): Number of circular permutations of the multiset {1,1,2,2,…,n,n} (up to rotations).
  • A137730 (program): Number of circular permutations of the multiset {1,1,2,2,…,n,n} (up to rotations) with odd distances between equal elements.
  • A137734 (program): a(0)=1. a(n) = ceiling(n/b(n)), where b(n) is the largest value among (a(0),a(1),…,a(n-1)).
  • A137735 (program): a(0)=1. a(n) = floor(n/b(n)), where b(n) is the largest value among (a(0),a(1),…,a(n-1)).
  • A137736 (program): Number of set partitions of n(n-1)/2.
  • A137737 (program): Number of circular permutations of the multiset {1,1,2,2,…,n,n} (up to rotations) with even distances between equal elements.
  • A137741 (program): Number of different strings of length n+4 obtained from “123…n” by iteratively duplicating any substring.
  • A137742 (program): a(n) = (n-1)*(n+4)*(n+6)/6 for n>1, a(1)=1.
  • A137749 (program): Number of circular permutations of the multiset {1,1,2,2,…,2n,2n} (up to rotations) with even distances between equal elements.
  • A137754 (program): Numerators (left to right) of Leibniz’s harmonic-like triangle.
  • A137755 (program): Nontrivial numerators (left to right) of Leibniz’s harmonic-like triangle.
  • A137773 (program): Triangular sequence: The Fibonacci sequence on the diagonal, 1’s at all other places
  • A137775 (program): Number of triples of permutations on n letters such that for each j, exactly one of the permutations fixes j and the other two have the same image on j.
  • A137778 (program): Triangular sequence from coefficients of an expansion of a Rankine-Hugoniot relation function for density in terms of thermodynamic gamma as t and pressure ratio as x: p(x,t)=((t + 1)/(t - 1) + x)/(1 + (t + 1)*x/(t - 1)).
  • A137780 (program): a(n) = 1 + 2^( prime(n + 1) - prime(n) ).
  • A137781 (program): a(n) = (2^prime(n) + 2^prime(n+1)) / 4.
  • A137786 (program): a(n) = 4^n - 3^n - 2^n.
  • A137787 (program): a(n) = 5^n - 4^n - 3^n - 2^n.
  • A137788 (program): a(n) = 6^n - 5^n - 4^n - 3^n - 2^n.
  • A137789 (program): a(n) = 7^n - 6^n - 5^n - 4^n - 3^n - 2^n.
  • A137790 (program): a(n) = 8^n-7^n-6^n-5^n-4^n-3^n-2^n.
  • A137794 (program): Characteristic function of numbers having no prime gaps in their factorization.
  • A137797 (program): a(n) = 2*( (n+1) mod 5 ) - 2*( (n+1) mod 2 ).
  • A137798 (program): Partial sums of A137797.
  • A137801 (program): Number of arrangements of 2n couples into n cars such that each car contains 2 men and 2 women but no couple (cars are labeled).
  • A137802 (program): Number of arrangements of 2n couples into n cars such that each car contains 2 men and 2 women but no couple (cars are unlabeled).
  • A137803 (program): a(n) = floor(n*(sqrt(2) + 1/2)).
  • A137804 (program): a(n) = floor(n*(4*sqrt(2)+9)/7).
  • A137807 (program): Final digit of prime(n)^2.
  • A137821 (program): Numbers k such that Sum_{j=1..2k} Catalan(j) == 0 (mod 3).
  • A137822 (program): First differences of A137821 (numbers such that sum( Catalan(k), k=1..2n) = 0 (mod 3)).
  • A137823 (program): Numbers occurring in A137822 : first differences of numbers n such that 3 | sum( Catalan(k), k=1..2n).
  • A137824 (program): Index at which A137823(n) occurs first in A137822 (gaps in numbers m such that 3 | sum( Catalan(k), k=1..2m)).
  • A137827 (program): Prime powers (A246655) congruent to 1 (mod 3).
  • A137829 (program): Expansion of psi(q^2) / f(-q)^2 in powers of q where psi(), f() are Ramanujan theta functions.
  • A137831 (program): (Prime(n)^2 minus its last digit)/20.
  • A137842 (program): Number of paths from (0,0) to (3n,0) that stay in first quadrant (but may touch horizontal axis) and where each step is (2,1), (1,2) or (1,-1).
  • A137851 (program): a(n) = A054525(n) * A061397(n).
  • A137864 (program): a(n) = n^4 - 10n^3 + 35n^2 - 48n + 23.
  • A137866 (program): a(1)=0. For n >= 2, a(n) = gcd(a(n-1)+1, n).
  • A137876 (program): a(n) = (nextprime(18n)-previousprime(18n))/2.
  • A137877 (program): Numbers k such that 18*k - 1 and 18*k + 1 are twin primes.
  • A137878 (program): Perfect squares among 17-gonal numbers A051869(k) = k*(15*k - 13)/2.
  • A137879 (program): Numbers k such that k^2 is a 17-gonal number.
  • A137880 (program): Indices k of perfect squares among 17-gonal numbers A051869(k) = k*(15*k - 13)/2.
  • A137881 (program): a(n) = sqrt(A137880(n)).
  • A137882 (program): Number of (directed) Hamiltonian paths in the n-ladder graph.
  • A137883 (program): Number of (directed) Hamiltonian paths in the n-Möbius ladder graph.
  • A137885 (program): Number of directed Hamiltonian paths in the 2n-crossed prism graph.
  • A137886 (program): Number of (directed) Hamiltonian paths in the n-crown graph.
  • A137893 (program): Fixed point of the morphism 0->100, 1->101, starting from a(1) = 1.
  • A137897 (program): Denominators of a rational triangle related to 1/sqrt(1-x).
  • A137901 (program): Limiting sequence when we start with positive integers (A000027) and at step n >= 1 add to the term at position n + a(n) the value 1.
  • A137904 (program): Rows 1, 3, 5, 7 of Mendeleyev-Seaborg (extended to 32 columns) periodic table elements.
  • A137913 (program): Rows 2, 4, 6 of Mendeleyev-Seaborg (extended to 32 columns) periodic table elements.
  • A137916 (program): Number of n-node labeled graphs whose components are unicyclic graphs.
  • A137919 (program): (Nextprime(24n)-previousprime(24n))/2.
  • A137920 (program): Numbers k such that 24*k-1 and 24*k+1 are twin primes.
  • A137921 (program): Number of divisors d of n such that d+1 is not a divisor of n.
  • A137922 (program): Numbers having exactly two divisors d such that d+1 is not a divisor.
  • A137924 (program): a(n) = the largest divisor of A002808(n) that is coprime to n. (A002808(n) = the n-th composite.).
  • A137925 (program): a(n) = the largest divisor of n that is coprime to A002808(n). (A002808(n) = the n-th composite.)
  • A137926 (program): a(n) = the largest divisor of n that is coprime to A000005(n). (A000005(n) = the number of positive divisors of n.)
  • A137927 (program): a(n) = the largest divisor of A000005(n) that is coprime to n. (A000005(n) = the number of positive divisors of n.).
  • A137928 (program): The even principal diagonal of a 2n X 2n square spiral.
  • A137930 (program): The sum of the principal diagonals of an n X n spiral.
  • A137931 (program): Sum of the principal diagonals of a 2n X 2n square spiral.
  • A137932 (program): Terms in an n X n spiral that do not lie on its principal diagonals.
  • A137933 (program): Least common multiple of n^2 and 2.
  • A137934 (program): Period 6: 2,2,2,2,2,0.
  • A137935 (program): a(n) = 5n + 26*floor(n/5).
  • A137936 (program): a(n) = 5*mod(n,5) + floor(n/5).
  • A137937 (program): A137904(n) - A137575(n).
  • A137943 (program): Triangle of coefficients associate with the expansion of the K_3 graph matric characteristic polynomial as a Sheffer sequence: M = {{0, 1, 1}, {1, 0, 1}, {1, 1, 0}} f(t)=-t^3+3t+2 p(x,t)=Exp[x,t)/(2*t^3+3*t^2-1)=exp(x*t)(t^3*f(1/t)).
  • A137948 (program): Triangle read by rows, A000012 * A136579.
  • A137951 (program): Redundant binary representation (A089591) of n interpreted as ternary number.
  • A137952 (program): G.f. satisfies A(x) = 1 + x*(1 + x*A(x)^3)^2.
  • A137953 (program): G.f. satisfies A(x) = 1 + x*(1 + x*A(x)^2)^3.
  • A137954 (program): G.f. satisfies A(x) = 1 + x + x^2*A(x)^4.
  • A137955 (program): G.f. satisfies A(x) = 1 + x*(1 + x*A(x)^4)^2.
  • A137956 (program): G.f. satisfies A(x) = 1 + x*(1 + x*A(x)^2)^4.
  • A137957 (program): G.f. satisfies A(x) = 1 + x*(1 + x*A(x)^4)^3.
  • A137958 (program): G.f. satisfies A(x) = 1 + x*(1 + x*A(x)^3)^4.
  • A137959 (program): G.f. satisfies A(x) = 1 + x + x^2*A(x)^5.
  • A137960 (program): G.f. satisfies A(x) = 1 + x*(1 + x*A(x)^5)^2.
  • A137961 (program): G.f. satisfies A(x) = 1 + x*(1 + x*A(x)^2)^5.
  • A137962 (program): G.f. satisfies A(x) = 1 + x*(1 + x*A(x)^5)^3.
  • A137963 (program): G.f. satisfies A(x) = 1 + x*(1 + x*A(x)^3)^5.
  • A137964 (program): G.f. satisfies A(x) = 1 + x*(1 + x*A(x)^5)^4.
  • A137965 (program): G.f. satisfies A(x) = 1 + x*(1 + x*A(x)^4)^5.
  • A137966 (program): G.f. satisfies A(x) = 1+x + x^2*A(x)^6.
  • A137967 (program): G.f. satisfies A(x) = 1 + x*(1 + x*A(x)^6)^2.
  • A137968 (program): G.f. satisfies A(x) = 1 + x*(1 + x*A(x)^2)^6.
  • A137969 (program): G.f. satisfies A(x) = 1 + x*(1 + x*A(x)^6)^3.
  • A137970 (program): G.f. satisfies A(x) = 1 + x*(1 + x*A(x)^3)^6.
  • A137971 (program): G.f. satisfies A(x) = 1 + x*(1 + x*A(x)^6)^4.
  • A137972 (program): G.f. satisfies A(x) = 1 + x*(1 + x*A(x)^4)^6.
  • A137973 (program): G.f. satisfies A(x) = 1 + x*(1 + x*A(x)^6)^5.
  • A137974 (program): G.f. satisfies A(x) = 1 + x*(1 + x*A(x)^5)^6.
  • A137976 (program): Fibonacci numbers (A000045) not in A103311.
  • A137977 (program): Primes congruent to {0, 2, 4, 6, 8, 10} modulo 11.
  • A137978 (program): Primes congruent to {1, 3, 5, 7, 9} modulo 11.
  • A137979 (program): Highest coefficient occurring in the factorization of x^n - 1 over the reals.
  • A137992 (program): A014137 (= partial sums of Catalan numbers A000108) mod 3.
  • A137993 (program): A014138 (= partial sums of Catalan numbers starting with 1,2,5) mod 3.
  • A138003 (program): Binomial transform of 1, 1, 0, -1, -1 (periodically continued).
  • A138010 (program): a(n) is the number of positive divisors of n that divide d(n), where d(n) is the number of positive divisors of n, A000005(n); a(n) also equals d(gcd(n, d(n))).
  • A138015 (program): Triangle read by rows, antidiagonals of an array formed by A000012 * A136579. Replace the term “n” in the correlation triangle A003983 with A003422(n).
  • A138016 (program): Row sums of triangle A138015.
  • A138017 (program): Sequence generated by incidence matrix of the Fano plane, PG(2,2).
  • A138019 (program): Period 5: repeat [1, 1, 0, -1, -1].
  • A138020 (program): G.f. satisfies A(x) = sqrt( (1 + 2x*A(x)) / (1 - 2x*A(x)) ).
  • A138022 (program): Triangular array read by rows: e.g.f. sqrt(1-z^2)*exp(x*z)/(1+z).
  • A138026 (program): Where A121561(n) = 3.
  • A138028 (program): The array of the most significant digit of n^k read by antidiagonals.
  • A138029 (program): Main diagonal of A138028; the most significant digit of n^(n-1).
  • A138031 (program): a(n) = prime(n)^13.
  • A138032 (program): a(n) = prime(n)^17.
  • A138033 (program): a(n) = max_{ 1 <= i <= n-1 } min{ wt(i), wt(n-i) }, where wt() = A000120() is the binary weight function; a(1) = 0 by convention.
  • A138034 (program): Expansion of (1+3*x^2)/(1-x+x^2).
  • A138035 (program): Binomial transform of A135416.
  • A138036 (program): Write n = C(i,2)+C(j,1) with i>j>=0; let L[n] = [i,j]; sequence gives list of pairs L[n], n >= 0.
  • A138037 (program): a(0) = 0, a(n+1) = n + a(n)/(2 - a(n) mod 2).
  • A138041 (program): a(1) = 1, a(2) = 10; for n>2, a(n+1) = 4*a(n) + 6*a(n-1). Also a(n) = upper left term in the 2 X 2 matrix [1,3; 3,3].
  • A138055 (program): Period 8: repeat 1, 3, 5, 9, 3, 1, 9, 5.
  • A138057 (program): Triangle read by rows: row n consists of 0 followed by n (n+1)’s with alternating signs.
  • A138068 (program): Triangle read by rows: row n lists the digits of A135634(n), the palindromic number formed from the reflected decimal expansion of e.
  • A138069 (program): Triangle read by rows: row n lists the digits of A135696(n), the palindromic number with odd number of digits formed from the reflected decimal expansion of e.
  • A138070 (program): Triangle read by rows: row n lists the successive digits of A135697(n), the palindromic number formed from the reflected decimal expansion of Pi.
  • A138071 (program): Triangle read by rows: row n lists the digits of A135698(n), the palindromic number with odd number of digits formed from the reflected decimal expansion of Pi.
  • A138072 (program): Triangle read by rows: row n lists the digits of A135700(n), the palindromic number formed from the reflected decimal expansion of golden ratio phi.
  • A138073 (program): Triangle read by rows: row n lists the digits of A135699(n), the palindromic number with odd number of digits formed from the reflected decimal expansion of golden ratio phi.
  • A138076 (program): A signed version of A060187 obtained by taking the Z-transform of p(t,x)=Exp[t*(1+2*x)].
  • A138097 (program): Duplicate of A004956, for n>0.
  • A138099 (program): Irregular triangle read by rows: T(n,k) = k + floor(n/2), 1 <= k <= ceiling(n/2).
  • A138100 (program): The atomic numbers read along the odd-indexed rows of the Janet table of the elements.
  • A138101 (program): The atomic numbers read along the even-indexed rows of the Janet table of the elements.
  • A138102 (program): The number 2*k^2 repeated 2*k^2 times, k=1 to 4.
  • A138103 (program): Numbers with an odd number of 1’s in base 6 expansion.
  • A138104 (program): 2^(n-th semiprime) - 1.
  • A138105 (program): Partial sums of non-Fibonacci numbers A001690.
  • A138106 (program): A triangular sequence of coefficients based on the expansion of a Morse potential type function: p(x,t) = exp(x*t)*(exp(-2*t) - 2*exp(-t)).
  • A138108 (program): A triangular sequence of coefficients based on the expansion of an Hamiltonian resolvent or Green’s function: p(x,t)=Exp[x*t]/(x-t); where t is taken as the Hamiltonian variable and x as the complex variable.
  • A138112 (program): a(n)=3a(n-1)-4a(n-2)+2a(n-3)-a(n-4), a(0)=a(1)=a(2)=0, a(3)=1, a(4)=3.
  • A138114 (program): Triangle read by rows: row n lists the first n digits of the decimal expansion of Pi.
  • A138115 (program): Triangle read by rows: row n lists the first n digits of the decimal expansion of e.
  • A138116 (program): Triangle read by rows: row n lists the first n digits of the decimal expansion of golden ratio phi.
  • A138117 (program): Triangle read by rows: row n lists the first 2n-1 prime numbers.
  • A138118 (program): Concatenation of 2n-1 digits 1 and n digits 0.
  • A138119 (program): Concatenation of n digits 1 and 2n-1 digits 0.
  • A138120 (program): Concatenation of n digits 1, 2n-1 digits 0 and n digits 1.
  • A138122 (program): Cousin primes, the lower of which is 7 (mod 10).
  • A138127 (program): Multiples of 127.
  • A138128 (program): Powers of 127.
  • A138129 (program): Multiples of 1729, the Hardy-Ramanujan number.
  • A138130 (program): Powers of 1729, the Hardy-Ramanujan number.
  • A138134 (program): a(n) = Sum_{i=0..n} Fibonacci(5*i).
  • A138139 (program): Triangle read by rows: row n contains n terms and each column lists the prime numbers A000040.
  • A138143 (program): Triangle read by rows in which row n lists p(1), p(2), …, p(n), p(n-1), …, p(1), where p(i) = i-th prime.
  • A138144 (program): Palindromes formed from the reflected decimal expansion of the concatenation of 1, 1 and infinite 0’s.
  • A138145 (program): Palindromes formed from the reflected decimal expansion of the concatenation of 1, 1, 1 and infinite 0’s.
  • A138146 (program): Palindromes with 2n-1 digits formed from the reflected decimal expansion of the concatenation of 1, 1, 1 and infinite 0’s.
  • A138147 (program): Concatenation of n digits 1 and n digits 0.
  • A138148 (program): Cyclops numbers with binary digits only.
  • A138149 (program): n-th run has length n-th prime, with values 0 and 1 only, starting with 1.
  • A138150 (program): n-th run has length n-th prime, with digits 0 and 1 only, starting with 0.
  • A138156 (program): Sum of the path lengths of all binary trees with n edges.
  • A138164 (program): Row sums of Riordan array (c(-x^2),xc(-x^2)^2)^(-1) where c(x) is the g.f. of A000108.
  • A138171 (program): Odd n where d(n) > d(n+1), where d(n) = number of positive divisors of n.
  • A138172 (program): Even n where d(n) < d(n+1), where d(n) = number of positive divisors of n.
  • A138175 (program): Row sums of the Riordan array (1/(1+x),x(1+2x)/(1+x)^3)^(-1).
  • A138179 (program): Wiener index of the prism graph Y_n on 2n nodes.
  • A138181 (program): Largest Fibonacci number not exceeding the n-th prime.
  • A138182 (program): Smallest summand in the Zeckendorf representation of the n-th prime.
  • A138183 (program): Smallest Fibonacci number not less than the n-th prime.
  • A138187 (program): Hankel transform of binomial(2*n+3, n).
  • A138188 (program): Expansion of (1 - 2*x - 2*x^2 - x^3)/(1 + x + x^2 - x^3 - x^4 - x^5).
  • A138189 (program): Sequence built on pattern (1,-even,-even) beginning 1,-2,-2.
  • A138190 (program): Numerator of (n-1)*n*(n+1)/12.
  • A138191 (program): Denominator of (n-1)*n*(n+1)/12.
  • A138192 (program): A triangular sequence based on expansion of the rational polynomial of A001788 as a Sheffer sequence: p(x,t)=Exp[x*t]*(-1/(2*t - 1)^3).
  • A138199 (program): a(n) = 14^(2*n+1) + 3^(2*n+1).
  • A138200 (program): a(n) = (14^(2*n+1) + 3^(2*n+1)) / 17.
  • A138202 (program): a(n) = A005875(n)^2.
  • A138218 (program): Numbers k such that 180k^2 + 1 is prime.
  • A138219 (program): Integers related to the volume k(n) of a unit hypersphere in n dimensions.
  • A138220 (program): Numbers k such that 900*k^2 + 1 is prime.
  • A138222 (program): a(n) = the largest divisor of n that is <= the number of positive divisors of n.
  • A138229 (program): Expansion of (1-x)/(1-2x+6x^2).
  • A138230 (program): Expansion of (1-x)/(1 - 2*x + 4*x^2).
  • A138231 (program): A009545 alternated with its first differences.
  • A138232 (program): First differences of A138231.
  • A138233 (program): 2^(2*n+1) + 3^(2*n+1).
  • A138235 (program): a(n) = floor(n*(6 + sqrt(6))/5).
  • A138238 (program): Alternating sum of the squares of the first n Jacobsthal numbers.
  • A138240 (program): Expansion of (1/4)(1-sqrt(1-12x)/sqrt(1-4x)).
  • A138242 (program): Prime numbers k such that 12*k - 1, 12*k + 1 are twin primes.
  • A138250 (program): Prime numbers k such that 30*k - 1, 30*k + 1 are twin primes.
  • A138251 (program): Beatty sequence of the positive root of x^3 - x^2 - 1.
  • A138252 (program): Beatty sequence of the number t satisfying 1/s + 1/t = 1, where s is the positive root of x^3 - x^2 - 1.
  • A138255 (program): Smallest positive integer m such that n divides [2^m/m] (=A000799(m)).
  • A138256 (program): Smallest positive integer m such that n divides [3^m/m] (=A092763(m)).
  • A138257 (program): Smallest positive integer m such that n divides [4^m/m] (=A129794(m)).
  • A138258 (program): Smallest positive integer m such that n divides [5^m/m] (=A129795(m)).
  • A138259 (program): Smallest positive integer m such that n divides [6^m/m] (=A129796(m)).
  • A138260 (program): Smallest positive integer m such that n divides [7^m/m] (=A129797(m)).
  • A138261 (program): Smallest positive integer m such that n divides [8^m/m] (=A129798(m)).
  • A138262 (program): Smallest positive integer m such that n divides [9^m/m] (=A129799(m)).
  • A138263 (program): Smallest positive integer m such that n divides [10^m/m] (=A060156(m)).
  • A138268 (program): Negative of the Hankel transform of C(n)-C(n+2), where C(n)=A000108(n).
  • A138269 (program): a(n+1) is the Hankel transform of C(n)+C(n+2), where C(n) = A000108(n).
  • A138277 (program): Total number of active nodes of the Rule 150 cellular automaton on an infinite Bethe lattice with coordination number 4 (with a single 1 as initial condition).
  • A138278 (program): Sequence identical to its third differences in absolute values: a(2n)=3a(2n-1)-3a(2n-2)+2a(2n-3)), a(2n+1)=3a(2n)-3a(2n-1) n > 1.
  • A138279 (program): Last digit of A136324. After 0, 1, period 4: repeat [1, 2, 5, 6] = A131800.
  • A138281 (program): a(n) = floor((sqrt(2) + sqrt(3))^n).
  • A138287 (program): Palindromic period 10: repeat 0, 2, 8, 4, 6, 6, 4, 8, 2, 0.
  • A138288 (program): a(n) = A054320(n) - A001078(n).
  • A138289 (program): Row sums of A138060.
  • A138297 (program): Rows of triangle A138060 converge to this sequence.
  • A138298 (program): First differences of A137976 after having added two leading ones.
  • A138300 (program): Differences of each column for atomic numbers of Mendeleyev-Seaborg 7*32 elements periodic table,first extension,A138096 table.86 terms.Horizontal lecture.
  • A138302 (program): Exponentially 2^n-numbers: 1 together with positive integers k such that all exponents in prime factorization of k are powers of 2.
  • A138322 (program): a(n) = 5*a(n-1) + 10*a(n-2).
  • A138330 (program): Beatty discrepancy (defined in A138253) giving the closeness of the pair (A136497,A136498) to the Beatty pair (A001951,A001952).
  • A138331 (program): a(n) = C(n+5, 5)*(n+3)*(-1)^(n+1)*16/3.
  • A138332 (program): C(n+7, 7)*(n+4)*(-1)^(n+1)*16.
  • A138333 (program): C(n+9, 9)*(n+5)*(-1)^(n+1)*256/5.
  • A138334 (program): C(n+11, 11)*(n+6)*(-1)^(n+1)*512/3.
  • A138338 (program): Primes of the form n^2+8.
  • A138340 (program): Expansion of (1-8x)/(1-4x+16x^2).
  • A138341 (program): Expansion of (1-4x-x^3)/(1-x+x^2)^2.
  • A138342 (program): First differences of A007088.
  • A138344 (program): Absolute values of first differences of A049541.
  • A138349 (program): Moment sequence of tr(A) in USp(4).
  • A138350 (program): Moment sequence of tr(A^2) in USp(4).
  • A138351 (program): Central moment sequence of tr(A^2) in USp(4).
  • A138353 (program): Primes of the form k^2 + 9.
  • A138354 (program): Central moment sequence of tr(A^4) in USp(4).
  • A138355 (program): Primes of the form k^2 + 10.
  • A138356 (program): Moment sequence of t^2 coefficient in det(tI-A) for random matrix A in USp(4).
  • A138357 (program): Floor of sum of the first n^2 square roots.
  • A138361 (program): First differences of A068985.
  • A138362 (program): Primes of the form k^2 + 11.
  • A138364 (program): The number of Motzkin n-paths with exactly one flat step.
  • A138365 (program): a(n) = A006190(n) * A006190(n+2).
  • A138368 (program): Primes of the form k^2 + 12.
  • A138375 (program): Primes of the form k^2 + 13.
  • A138376 (program): a(n+1) = abs[ a(n) + (-1)^(n+1) * Sum_of_digits_of(n+1)], with a(0)=0.
  • A138377 (program): a(0) = 0, a(1) = 1, a(2) = 3, a(3) = 2; thereafter a(n) = -4*a(n-4).
  • A138378 (program): Number of embedded coalitions in an n-person game.
  • A138379 (program): Number of embedded coalitions in an n-person game where the position of the individual player is important.
  • A138380 (program): First differences of A138377.
  • A138382 (program): First differences of A138380. Second differences of A138377.
  • A138383 (program): If prime(i) = i-th prime, a(n) = prime(n)+1 + prime(n)+2 + … + prime(n+1). a(0) = 3 by convention.
  • A138384 (program): Reverse groups of five Fibonacci numbers.
  • A138390 (program): Record values in A138385.
  • A138392 (program): Hankel transform of A062992 with interpolated zeros.
  • A138393 (program): Numbers of form 8k+1 which are not squares.
  • A138395 (program): a(n) = 6*a(n-1) - 3*a(n-2), a(1) = 1, a(2) = 6.
  • A138401 (program): a(n) = prime(n)^4 - prime(n).
  • A138402 (program): a(n) = (n-th prime)^4-(n-th prime)^2.
  • A138403 (program): a(n) = p^3*(p-1), where p = prime(n).
  • A138404 (program): a(n) = prime(n)^5 - prime(n).
  • A138405 (program): a(n) = prime(n)^5 - prime(n)^2.
  • A138406 (program): a(n) = prime(n)^5 - prime(n)^3.
  • A138407 (program): a(n) = p^4*(p-1), where p = prime(n).
  • A138408 (program): a(n) = prime(n)^6 - prime(n).
  • A138409 (program): a(n) = prime(n)^6 - prime(n)^2.
  • A138410 (program): a(n) = prime(n)^6 - prime(n)^3.
  • A138411 (program): a(n) = prime(n)^6 - prime(n)^4.
  • A138412 (program): a(n) = p^5*(p-1) where p =prime(n).
  • A138413 (program): A bisection of A000957.
  • A138414 (program): A bisection of A000957.
  • A138415 (program): Binomial transform of A000957.
  • A138416 (program): a(n) = (p^3 - p^2)/2, where p = prime(n).
  • A138417 (program): a(n) = (prime(n)^4 - prime(n))/2.
  • A138418 (program): a(n) = ((n-th prime)^4-(n-th prime)^2)/2.
  • A138419 (program): a(n) = (prime(n)^4 - prime(n)^2)/3.
  • A138420 (program): a(n) = ((prime(n))^4-(prime(n))^2)/4.
  • A138421 (program): a(n) = (prime(n)^4 - prime(n)^2)/6.
  • A138422 (program): a(n) = (prime(n)^4 - prime(n)^2)/12.
  • A138423 (program): a(n) = (prime(n)^4 - prime(n)^3)/2.
  • A138424 (program): a(n) = (prime(n)^5 - prime(n))/2.
  • A138425 (program): a(n) = (prime(n)^5 - prime(n))/3.
  • A138426 (program): a(n) = ((prime(n))^5-prime(n))/5.
  • A138427 (program): a(n) = (prime(n)^5 - prime(n))/6.
  • A138428 (program): a(n) = (prime(n)^5 - prime(n))/10.
  • A138429 (program): a(n) = (prime(n)^5 - prime(n))/15.
  • A138430 (program): (prime(n)^5 - prime(n))/30.
  • A138431 (program): a(n) = ((n-th prime)^5-(n-th prime)^2)/2.
  • A138432 (program): a(n) = ((n-th prime)^5-(n-th prime)^3)/2.
  • A138433 (program): a(n) = ((n-th prime)^5-(n-th prime)^3)/3.
  • A138434 (program): a(n) = ((n-th prime)^5-(n-th prime)^3)/4.
  • A138435 (program): a(n) = ((n-th prime)^5-(n-th prime)^3)/6.
  • A138436 (program): a(n) = ((n-th prime)^5-(n-th prime)^3)/8.
  • A138437 (program): a(n) = ((n-th prime)^5-(n-th prime)^3)/12.
  • A138438 (program): a(n) = ((n-th prime)^5-(n-th prime)^3)/24.
  • A138439 (program): a(n) = ((n-th prime)^5-(n-th prime)^4)/2.
  • A138440 (program): a(n) = ((n-th prime)^6-(n-th prime))/2.
  • A138441 (program): a(n) = ((n-th prime)^6-(n-th prime^2))/2.
  • A138442 (program): a(n) = ((n-th prime)^6-(n-th prime^2))/3.
  • A138443 (program): a(n) = ((n-th prime)^6-(n-th prime^2))/4.
  • A138444 (program): a(n) = ((n-th prime)^6-(n-th prime^2))/5.
  • A138445 (program): a(n) = ((n-th prime)^6-(n-th prime^2))/6.
  • A138446 (program): a(n) = ((n-th prime)^6-(n-th prime^2))/10.
  • A138447 (program): a(n) = ((n-th prime)^6-(n-th prime^2))/12.
  • A138448 (program): a(n) = (prime(n)^6-prime(n)^2)/15.
  • A138450 (program): a(n) = ((n-th prime)^6-(n-th prime^2))/30.
  • A138451 (program): a(n) = (prime(n)^6-prime(n)^2)/60.
  • A138452 (program): a(n) = ((n-th prime)^6-(n-th prime)^3))/2.
  • A138453 (program): a(n) = ((n-th prime)^6-(n-th prime)^4))/2.
  • A138454 (program): a(n) = ((n-th prime)^6-(n-th prime)^4))/3.
  • A138455 (program): a(n) = ((n-th prime)^6-(n-th prime)^4))/4.
  • A138456 (program): a(n) = ((n-th prime)^6-(n-th prime)^4))/6.
  • A138457 (program): a(n) = ((n-th prime)^6-(n-th prime)^4))/8.
  • A138458 (program): a(n) = ((n-th prime)^6-(n-th prime)^4))/24.
  • A138459 (program): a(n) = ((n-th prime)^6-(n-th prime)^4))/12.
  • A138460 (program): a(n) = ((n-th prime)^6-(n-th prime)^5))/2.
  • A138461 (program): Inverse binomial transform of A000957.
  • A138462 (program): A bisection of A006318.
  • A138463 (program): A bisection of A006318.
  • A138466 (program): a(1)=1, then for n>=2 a(n)=n-floor((1/2)*a(a(n-1))).
  • A138467 (program): a(1)=1, then for n>=2 a(n) = n - floor((1/3)*a(a(n-1))).
  • A138468 (program): Number of even digits in Fibonacci numbers.
  • A138473 (program): a(n) = Fibonacci(8*n).
  • A138477 (program): Mix A084175 and 2*A084175.
  • A138478 (program): Decimal expansion of 101/970299.
  • A138494 (program): a and b are integers > 0 satisfying a^2 + b^2 = c^2. Sequence gives the number of choices for a and b between successive values of c. (Integer solutions for c (Pythagorean triples) are not included.)
  • A138495 (program): First differences of A138477.
  • A138501 (program): Expansion of (eta(q)^2 * eta(q^4)^4 / eta(q^2)^3)^2 in powers of q.
  • A138502 (program): Expansion of q^(-1/2) * (eta(q)^4 * eta(q^4)^2 / eta(q^2)^3)^2 in powers of q.
  • A138503 (program): a(n) = Sum_{d|n} (-1)^(d-1)*d^3.
  • A138504 (program): Expansion of (eta(q^2)^9 / (eta(q)^2 * eta(q^4)^4))^2 in powers of q.
  • A138505 (program): Expansion of ((phi(q) * phi(-q^2)^2)^2 - 1) / 4 in powers of q where phi() is a Ramanujan theta function.
  • A138506 (program): Expansion of f(q)^5 / f(q^5) in powers of q where f() is a Ramanujan theta function.
  • A138507 (program): Expansion of (f(q)^5 / f(q^5) - 1) / 5 in powers of q where f() is a Ramanujan theta function.
  • A138508 (program): Semiprime analog of Riesel problem: start with n; repeatedly double and add 1 until reach a semiprime. Sequence gives number of steps to reach a semiprime or 0 if no semiprime is ever reached.
  • A138511 (program): Semiprimes where the larger prime factor is greater than the square of the smaller prime factor, short: semiprimes p*q, p^2 < q.
  • A138512 (program): Expansion of q * f(q^5)^5 / f(q) in powers of q where f() is a Ramanujan theta function.
  • A138513 (program): a(n) = 8*a(n-1) - 5*a(n-2).
  • A138514 (program): Expansion of q^(-1/8) * eta(q^2)^4 / (eta(q) * eta(q^4)) in powers of q.
  • A138515 (program): Expansion of q^(-1/4) * eta(q^2)^8 / (eta(q) * eta(q^4))^2 in powers of q.
  • A138523 (program): a(n) = Sum_{k=1..n} (2k-1)!.
  • A138524 (program): a(n) = Sum_{k=1..n} (2*k)!.
  • A138525 (program): a(n) = Sum_{k=0..n} (2*k)!.
  • A138531 (program): Decimal expansion of 109739369/111111111.
  • A138534 (program): Super least prime signatures; LCM of all signatures with n factors.
  • A138543 (program): Moment sequence of tr(A^3) in USp(6).
  • A138546 (program): Moment sequence of tr(A^5) in USp(6).
  • A138552 (program): Returning walks of length 2n on the upper half of the square lattice, distinct under reflections about the y-axis.
  • A138557 (program): Expansion of eta(q)^2 * eta(q^4)^2 * eta(q^10)^7 / (eta(q^2)^3 * eta(q^5)^2 * eta(q^20)^2) in powers of q.
  • A138564 (program): a(1) = 1; a(n) = a(n-1) + (n!)^3.
  • A138573 (program): a(n) = 2*a(n-1) + 2*a(n-2) + 2*a(n-3) - a(n-4); a(0)=0, a(1)=1, a(2)=2, a(3)=5.
  • A138574 (program): a(n) = 2*a(n-1) + 2*a(n-2) + 2*a(n-3) - a(n-4); a(0)=0, a(1)=1, a(2)=3, a(3)=9, a(4)=25.
  • A138585 (program): The sequence is formed by concatenating subsequences S1, S2, … each of finite length. S1 consists of the element 1. The n-th subsequence consist of numbers {(n/2)*(n/2 - 1)+ 1, …, (n/2)*(n/2 + 1)} for n even, {((n-1)/2)^2, …, (n-1)/2 * ((n-1)/2 + 2)} for n odd.
  • A138587 (program): The union of all entries of A024495, A131708 and A024493 sorted into natural order.
  • A138589 (program): a(n) = 5^n mod 4^n.
  • A138590 (program): a(n) = Fibonacci(9*n).
  • A138591 (program): Sums of two or more consecutive nonnegative integers.
  • A138606 (program): List first F(1) odd numbers, then first F(2) even numbers (starting from 2), then the next F(3) odd numbers, then the next F(4) even numbers, etc., where F(n) = A000045(n), the n-th Fibonacci number.
  • A138610 (program): Nonsquarefree numbers congruent to 3 mod 4.
  • A138611 (program): 6^n mod 4^n.
  • A138614 (program): Expansion of (2*x-1)*(x^2-x-1) ) / ( 1-2*x^2+2*x^4 ).
  • A138616 (program): a(n) = 7^n mod 2^n.
  • A138617 (program): a(n) = 7^n mod 3^n.
  • A138618 (program): Triangle of exponentials of Mangoldt function M(n) read by rows, in which row products give the natural numbers.
  • A138620 (program): Nonnegative integers n such that 12*n-1 is prime.
  • A138622 (program): Nonnegative integers k such that 14*k-1 is prime.
  • A138623 (program): Primes congruent to 5 mod 17.
  • A138624 (program): Nonnegative integers k such that 17*k+5 is prime.
  • A138625 (program): Primes congruent to 12 mod 17.
  • A138626 (program): Nonnegative integers n such that 17*n-5 is prime.
  • A138627 (program): Primes congruent to 10 mod 17.
  • A138628 (program): Positive integers k such that 17*k-7 is prime.
  • A138629 (program): Primes of form 17*n+7.
  • A138630 (program): Nonnegative integers k such that 17*k+7 is prime.
  • A138631 (program): Primes of the form 17*k + 9.
  • A138632 (program): Nonnegative integers k such that 17*k+9 is prime.
  • A138633 (program): Primes of the form 17*k - 9.
  • A138634 (program): Nonnegative integers k such that 17*k-9 is prime.
  • A138635 (program): a(n) =3*a(n-3)-3*a(n-6)+2*a(n-9).
  • A138636 (program): a(n) = 6 * prime(n).
  • A138638 (program): Primes of form 19*n-1.
  • A138639 (program): Nonnegative integers n such that 19*n-1 is prime.
  • A138640 (program): Primes of form 19*n-2.
  • A138641 (program): Nonnegative integers n such that 19*n-2 is prime.
  • A138642 (program): Primes of form 19*n-3.
  • A138643 (program): Nonnegative integers k such that 19*k-3 is prime.
  • A138645 (program): Primes p such that 7*p+2 is composite.
  • A138648 (program): 7^n mod 5^n.
  • A138649 (program): a(n) = 6^n mod 5^n.
  • A138653 (program): a(n) = 3*a(n-1)-3*a(n-2)+a(n-3)+a(n-4).
  • A138654 (program): 7^n mod 4^n.
  • A138666 (program): Numbers n such that every sum of consecutive positive numbers ending in n is not prime.
  • A138670 (program): Indices of 0’s in Stewart’s choral sequence.
  • A138671 (program): Indices of 1’s in Stewart’s choral sequence.
  • A138672 (program): Prime(n)^3 mod prime(n-1).
  • A138673 (program): Prime(n)^4 mod prime(n-1).
  • A138674 (program): Prime(n)^5 mod prime(n-1).
  • A138675 (program): Prime(n)^6 mod prime(n-1).
  • A138676 (program): a(n) = prime(n)^7 mod prime(n-1).
  • A138677 (program): Prime(n)^8 mod prime(n-1).
  • A138678 (program): Prime(n)^9 mod prime(n-1).
  • A138679 (program): Prime(n)^10 mod prime(n-1).
  • A138680 (program): Prime(n)^11 mod prime(n-1).
  • A138681 (program): Prime(n)^12 mod prime(n-1).
  • A138685 (program): Numbers n such that there is no prime of the form 2n + p^2 for any prime p.
  • A138686 (program): Primes in A138685.
  • A138687 (program): Composite n with no prime of the form 2n + p^2 for any prime p.
  • A138689 (program): Numbers of the form 26+p^2 (where p is a prime).
  • A138690 (program): Numbers of the form 56+p^2 (where p is a prime).
  • A138691 (program): Numbers of the form 68+p^2 (where p is a prime).
  • A138692 (program): Numbers of the form 86+p^2 (where p is a prime).
  • A138693 (program): Numbers of the form 110 + p^2. (where p is a prime).
  • A138694 (program): Numbers n such that the set {2*n+p^2, p any prime} contains exactly one prime.
  • A138708 (program): Numbers m such that A138707(m) = 1.
  • A138709 (program): n-th run has length n-th positive Fibonacci numbers, with digits 0 and 1 only, starting with 1.
  • A138710 (program): n-th run has length n-th positive Fibonacci numbers, with digits 0 and 1 only, starting with 0.
  • A138711 (program): n-th run has length n-th positive triangular number, with digits 0 and 1 only, starting with 1.
  • A138712 (program): n-th run has length n-th positive triangular number, with digits 0 and 1 only, starting with 0.
  • A138714 (program): Add 1, modulo 10, to the decimal expansion of e, A001113.
  • A138718 (program): Group number of the elements of the n-th column of the periodic table of the elements with 18 columns.
  • A138721 (program): Concatenation of n digits 1, n digits 0 and n digits 1.
  • A138741 (program): Expansion of q^(-1/2) * eta(q)^3 * eta(q^4) * eta(q^12) / (eta(q^2)^2 * eta(q^3)) in powers of q.
  • A138745 (program): Expansion of eta(q) * eta(q^3) * eta(q^4)^3 / (eta(q^2)^2 * eta(q^12)) in powers of q.
  • A138746 (program): Expansion of 1 - eta(q) * eta(q^3) * eta(q^4)^3 / (eta(q^2)^2 * eta(q^12)) in powers of q.
  • A138747 (program): a(n) = 4*a(n-1) - 3*a(n-2) + 2*a(n-3) - 1*a(n-4).
  • A138748 (program): a(n) = (n+(n+1)) + (n*(n+1)) + (n^(n+1)).
  • A138749 (program): a(n) = 2*a(n-1) - 5*a(n-2).
  • A138750 (program): a(n) = ceiling(n/2) if n == 2 (mod 3), a(n) = 2n otherwise.
  • A138751 (program): a(n) = nextprime( p(n)/2 if p(n)=2 (mod 3), 2p(n) else ) = A007918( A138750( A000040( n ))).
  • A138754 (program): PrimePi(A138751(n)) - a variation of the Collatz (3n+1) map.
  • A138757 (program): A007918(A138750(n)) = least prime > n/2 if n=2 (mod 3), > 2n otherwise.
  • A138764 (program): E.g.f. A(x) equals the inverse function of log(x)/(x + x^2).
  • A138766 (program): Real part of upper left and lower right terms of [1,(1+I); 1,1]^n * [1,0].
  • A138770 (program): Triangle read by rows: T(n,k) is the number of permutations of {1,2,…,n} such that there are exactly k entries between the entries 1 and 2 (n>=2, 0<=k<=n-2).
  • A138772 (program): Number of entries in the second cycles of all permutations of {1,2,…,n}; each cycle is written with the smallest element first and cycles are arranged in increasing order of their first elements.
  • A138775 (program): Triangle read by rows: T(n,k)=binomial(n-2k,3k) (n>=0, 0<=k<=n/5).
  • A138776 (program): Triangle read by rows: T(n,k)=binomial(n-2k,3k+1) (n>=1, 0<=k<=(n-1)/5).
  • A138777 (program): Triangle read by rows: T(n,k)=binomial(n-2k,3k+2) (n>=2, 0<=k<=(n-2)/5).
  • A138778 (program): Triangle read by rows: T(n,k)=k*binomial(n-2k,3k) (n>=5, 1<=k<=n/5).
  • A138779 (program): Triangle read by rows: T(n,k)=k*binomial(n-2k,3k+1) (n>=6, 0<=k<=(n-1)/5).
  • A138780 (program): Triangle read by rows: T(n,k)=k*binomial(n-2k,3k+2) (n>=7, 1<=k<=(n-2)/5).
  • A138782 (program): a(n) = n*(3*n-1)*n!/2.
  • A138793 (program): a(n) = concatenation of reversed digits of natural numbers from n down to 1.
  • A138794 (program): a(n) = A138793(n+1)-A138793(n).
  • A138796 (program): Least possible k > 0 with T(k) - T(j) = n, j > 0, where T(i) > 0 are the triangular numbers A000217.
  • A138797 (program): Least possible T(k) with T(k)-T(j)=n, where T(i)>0 are the triangular numbers A000217.
  • A138798 (program): Values of j corresponding to least possible k>0 with T(k)-T(j)=n, where T(i)>0 are the triangular numbers A000217.
  • A138799 (program): Values of T(j) corresponding to least possible T(k) with T(k)-T(j)=n, where T(i)>0 are the triangular numbers A000217.
  • A138803 (program): Imaginary parts of terms (1,1), (2,2) of matrix [1,(1+I); 1,1]^n.
  • A138806 (program): Expansion of (theta_3(q) * theta_3(q^27) + theta_2(q) * theta_2(q^27) - 1) / 2 in powers of q.
  • A138808 (program): Number of integer pairs (x,y), x > 0, y > 0, such that x <= p, y <= q for any factorization n = p*q.
  • A138811 (program): Theta series of quadratic form x^2 + x*y + 11*y^2.
  • A138814 (program): Divisors of 4064 (half the 4th perfect number).
  • A138815 (program): Divisors of 16775168 (half the 5th perfect number).
  • A138821 (program): Concatenation of n-th Fibonacci number and n-th prime.
  • A138822 (program): Concatenation of n-th prime and n-th Fibonacci number.
  • A138824 (program): Divisors of 4064 (the 4th perfect number divided by 2), written in base 2.
  • A138829 (program): Bisection of imperfect numbers A132999.
  • A138830 (program): Bisection of imperfect numbers A132999.
  • A138836 (program): Non-Mersenne numbers A001348.
  • A138837 (program): Non-Mersenne primes: A000040 \ A000668.
  • A138840 (program): Concatenation of initial and final digits of n-th prime.
  • A138844 (program): Concatenation of initial and final digits of n-th positive Fibonacci number.
  • A138849 (program): a(n) = AlexanderPolynomial[n] defined as Det[Transpose[S]-n S] where S is Kronecker Product of two 2 X 2 Seifert matrices {{-1, 1}, {0, -1}} [X] {{-1, 1}, {0, -1}} = {{1, -1, -1, 1}, {0, 1, 0, -1}, {0, 0, 1, -1}, {0, 0, 0, 1}}.
  • A138860 (program): E.g.f. satisfies: A(x) = exp( x*(A(x) + A(x)^2)/2 ).
  • A138879 (program): Sum of all parts of the last section of the set of partitions of n.
  • A138880 (program): Sum of all parts of all partitions of n that do not contain 1 as a part.
  • A138884 (program): Numbers that are not even superperfect numbers.
  • A138885 (program): n-th run has length n-th nonprime number, with digits 0 and 1 only, starting with 1.
  • A138886 (program): n-th run has length n-th nonprime number A018252, with digits 0 and 1 only, starting with 0.
  • A138887 (program): Numbers that are not Sophie Germain primes.
  • A138888 (program): Non-Fermat numbers.
  • A138889 (program): Primes that are not Fermat primes.
  • A138890 (program): Non-Padovan numbers.
  • A138891 (program): Non-Motzkin numbers.
  • A138894 (program): Expansion of (1+x)/(1-10*x+9*x^2).
  • A138896 (program): Ratio of (2n-1)! to number of zeros in Sylvester matrix of polynomial of n degree with all nonzero coefficients.
  • A138897 (program): Ratio of (2n-1)! to number of zeros in upper part of Sylvester matrix of polynomial of degree n with all nonzero coefficients.
  • A138898 (program): Ratio of (2n-1)! to number of zeros in lower part of Sylvester matrix for polynomial of degree n with all nonzero coefficients.
  • A138902 (program): a(n) = d!, where d is the number of digits in n.
  • A138903 (program): a(n) = (1/2^n)* Sum_{k=0..n} binomial(n,k)*(n+k)^(n-1).
  • A138905 (program): a(n) is n-th prime == -1 (mod 6n).
  • A138906 (program): a(n) is n-th prime == 1 (mod 6n).
  • A138908 (program): a(n) = d^d, where d is the number of digits in n.
  • A138909 (program): Expansion of e.g.f.: (1+x)/(1-x*exp(x)).
  • A138910 (program): Inverse binomial transform of A138909.
  • A138911 (program): The n-th term of n-th inverse binomial transform of this sequence is 1 for n>=0.
  • A138912 (program): Inverse binomial transform of A138911.
  • A138918 (program): Numbers n such that 18n-1 is prime.
  • A138929 (program): Twice the prime powers A000961.
  • A138946 (program): Positive integers not in A073071.
  • A138949 (program): Expansion of (3 * phi(q^3)^2 - phi(q)^2) / 2 in powers of q where phi() is a Ramanujan theta function.
  • A138950 (program): Expansion of (2 - 3 * phi(q^3)^2 + phi(q)^2) / 4 in powers of q where phi() is a Ramanujan theta function.
  • A138951 (program): Expansion of eta(q^2)^7 * eta(q^3)^2 * eta(q^12) / (eta(q)^2 * eta(q^4)^3 * eta(q^6)^3) in powers of q.
  • A138952 (program): Expansion of (eta(q^2)^7 * eta(q^3)^2 * eta(q^12) / (eta(q)^2 * eta(q^4)^3 * eta(q^6)^3) - 1) / 2 in powers of q.
  • A138955 (program): a(n) = 8^n mod 3^n.
  • A138957 (program): Concatenation of the reversed digits of numbers from 1 to n.
  • A138959 (program): a(n) = 8^n mod 5^n.
  • A138960 (program): a(n) = smallest prime divisor of A138957(n).
  • A138964 (program): a(n) = 8^n mod 6^n.
  • A138966 (program): a(n) = n + (smallest composite > n).
  • A138967 (program): Infinite Fibonacci word on the alphabet {1,2,3,4}.
  • A138968 (program): Positions of the primes congruent to 1 mod 3 when all primes except 3 are listed in order.
  • A138969 (program): Positions of the primes congruent to 2 mod 3 when all primes except 3 are listed in order.
  • A138970 (program): Positions of the primes congruent to 1 mod 4 when all primes except 2 are listed in order.
  • A138971 (program): Positions of the primes congruent to 3 mod 4 when all primes except 2 are listed in order.
  • A138972 (program): Positions of the primes congruent to 1 mod 6 when all primes except 2 and 3 are listed in order.
  • A138973 (program): a(n) = 8^n mod 7^n.
  • A138976 (program): The discriminant of the characteristic polynomial of the O+ and O- submatrix for spin 3 of the nuclear electric quadrupole Hamiltonian is a perfect square for these values.
  • A138977 (program): Number of 2 X n matrices containing a 1 in the top left entry, all entries are integer values and adjacent entries differ by at most 1.
  • A138984 (program): a(n) = Frobenius number for 4 successive numbers = F(n+1,n+2,n+3,n+4).
  • A138985 (program): a(n) = Frobenius number for 5 successive numbers = F(n+1,n+2,n+3,n+4,n+5).
  • A138986 (program): a(n) = Frobenius number for 6 successive numbers = F(n+1,n+2,n+3,n+4,n+5,n+6).
  • A138987 (program): a(n) = Frobenius number for 7 successive numbers = F(n+1,n+2,n+3,n+4,n+5,n+6,n+7).
  • A138988 (program): a(n) is the Frobenius number for 8 successive numbers n+1, n+2, …,n+8.
  • A138995 (program): First differences of Frobenius numbers for 4 successive numbers A138984.
  • A138996 (program): First differences of Frobenius numbers for 5 successive numbers A138985.
  • A138997 (program): First differences of Frobenius numbers for 6 successive numbers A138986.
  • A138998 (program): 9^n mod 2^n.
  • A138999 (program): First differences of Frobenius numbers for 8 successive numbers A138988.
  • A139011 (program): Real part of (2 + i)^n, where i = sqrt(-1).
  • A139030 (program): Real part of (4 + 3i)^n.
  • A139031 (program): Imaginary part of (4 + 3i)^n.
  • A139035 (program): Primes of the form 4*k+3 with primitive root -2.
  • A139038 (program): Centrally symmetric triangle read by rows: t(n,m) = A000931(m+1) if m <= floor(n/2), A000931(n - m+1) otherwise.
  • A139039 (program): A triangular central symmetric sequence based on the sequence A003269: if m <= floor(n/2), t(n,m) = A003269(m+2), otherwise t(n,m) = A003269(n - (m+2)).
  • A139040 (program): Triangle read by rows: each row is an initial segment of the terms of A000930 followed by its reflection.
  • A139049 (program): a(n) = prime(n) + 6.
  • A139069 (program): Number of 3’s in A020458(n).
  • A139076 (program): Let M(n) = maximal value of (n/k)^k over all k = 1, 2, …; a(n) = floor(M(n)).
  • A139077 (program): Let M(n) = maximal value of (n/k)^k over all k = 1, 2, …; a(n) = round(M(n)).
  • A139081 (program): a(n) = (largest prime power dividing n) + (largest prime power dividing (n+1)).
  • A139082 (program): a(n) = (largest power of a prime dividing n) * (largest power of a prime dividing (n+1)).
  • A139083 (program): a(n) = (smallest prime-power among the largest powers of each prime dividing n) + (smallest prime-power among the largest powers of each prime dividing (n+1)).
  • A139084 (program): a(n) = (smallest prime-power among the largest powers dividing n of each prime dividing n) * (smallest prime-power among the largest powers dividing (n+1) of each prime dividing (n+1)).
  • A139093 (program): Expansion of phi(q) * phi(-q^2) in powers of q where phi() is a Ramanujan theta function.
  • A139098 (program): a(n) = 8*n^2.
  • A139099 (program): Numbers 2n+1 for which A002326(n) are record values of A002326.
  • A139101 (program): Numbers that show the distribution of prime numbers up to the n-th prime minus 1, using “0” for primes and “1” for nonprime numbers.
  • A139102 (program): Numbers whose binary representation shows the distribution of prime numbers up to the n-th prime minus 1, using “0” for primes and “1” for nonprime numbers.
  • A139103 (program): Numbers that show the distribution of prime numbers up to the n-th prime using “0” for primes and “1” for nonprime numbers.
  • A139104 (program): Numbers whose binary representation shows the distribution of prime numbers up to the n-th prime, using “0” for primes and “1” for nonprime numbers.
  • A139105 (program): Bisection of A139101.
  • A139106 (program): Bisection of A139101.
  • A139107 (program): Bisection of A139102.
  • A139108 (program): Bisection of A139102.
  • A139111 (program): Bisection of A139104.
  • A139112 (program): Bisection of A139104.
  • A139113 (program): Concatenation of n and n-th Fibonacci number.
  • A139114 (program): Concatenation of n-th Fibonacci number and n.
  • A139118 (program): Numbers with a nonprime number of divisors.
  • A139125 (program): a(0) = 0; a(n) = a(n-1) + binomial( n(n+1)/2, n) mod n.
  • A139130 (program): a(n) = sum{k=1 to n} d(d(k)), where d(k) = number of divisors of k.
  • A139131 (program): Squarefree kernel of n*(n+1)/2.
  • A139135 (program): Expansion of psi(-q^3) / f(q) where psi(), f() are Ramanujan theta functions.
  • A139136 (program): Expansion of psi(-q) / f(q^3) where psi(), f() are Ramanujan theta functions.
  • A139137 (program): Expansion of phi(q) / phi(q^3) in powers of q where phi() is a Ramanujan theta function.
  • A139139 (program): Expansion of (phi(q) / phi(q^3) - 1) / 2 in powers of q where phi() is a Ramanujan theta function.
  • A139140 (program): For n>=1, a(n) = d(p(n)+1) + d(p(n)+2) + d(p(n)+3) + … + d(p(n+1)), where d(m) is the number of positive divisors of m and p(n) is the n-th prime. a(0) = d(1) + d(2).
  • A139143 (program): This sequence and A139142 are complements. a(1)=2. A139142(1)=1. A139142(n+1) = A139142(n) + sum{k=1 to n} a(k).
  • A139147 (program): Triangle read by rows: replace A003983(n,k) with F(n).
  • A139148 (program): Smallest positive integer of the form (m!+n)/n.
  • A139149 (program): a(n) = (n!+2)/2.
  • A139150 (program): Natural numbers of the form (n!+3)/3.
  • A139151 (program): a(n) = (n!+4)/4.
  • A139152 (program): Natural numbers of the form (n!+5)/5.
  • A139153 (program): Natural numbers of the form (n!+6)/6.
  • A139154 (program): Natural numbers of the form (n!+7)/7.
  • A139155 (program): Natural numbers of the form (n!+8)/8.
  • A139156 (program): Natural numbers of the form (n!+9)/9.
  • A139157 (program): Natural numbers of the form (n!+10)/10.
  • A139159 (program): a(n) = prime(n)! + 1.
  • A139160 (program): a(n)=(prime(n)!+2)/2.
  • A139161 (program): a(n)=(prime(n)!+3)/3.
  • A139164 (program): a(n) = (prime(n)!+6)/6.
  • A139169 (program): a(n)=smallest k >= 1 such that n divides prime(k)!.
  • A139171 (program): a(n) = smallest prime number p such that p!/n is an integer.
  • A139172 (program): Natural numbers of the form (n!-2)/2.
  • A139173 (program): a(n) = n!/3 - 1.
  • A139174 (program): a(n) = (n!-4)/4.
  • A139175 (program): a(n) = (n! - 5)/5.
  • A139176 (program): a(n) = (n! - 6)/6.
  • A139177 (program): a(n) = (n! - 7)/7.
  • A139179 (program): Number of non-fourth-powers <= n.
  • A139183 (program): a(n) = (n! - 8)/8.
  • A139184 (program): a(n) = (n! - 9)/9.
  • A139185 (program): a(n) = (n! - 10)/10.
  • A139189 (program): a(n) = prime(n)!-1.
  • A139190 (program): a(n) = (prime(n)!-2)/2.
  • A139191 (program): Natural numbers of the form (prime(n)!-3)/3.
  • A139192 (program): a(n) = (prime(n)! - 4)/4.
  • A139194 (program): Natural numbers of the form (prime(n)!-6)/6.
  • A139196 (program): a(n) = (prime(n)!-8)/8.
  • A139209 (program): Fibonacci bisection minus powers of 2.
  • A139211 (program): Partial sums of A003325.
  • A139213 (program): Expansion of phi(q) * phi(-q^18) / (phi(-q^3) * phi(-q^6)) in powers of q where phi() is a Ramanujan theta function.
  • A139214 (program): Expansion of q * psi(q^2) * psi(-q^9) / (phi(-q^3) * psi(-q^3)) in powers of q where phi(), psi() are Ramanujan theta functions.
  • A139215 (program): Expansion of q^(-1) * psi(q) * phi(q^9) / (psi(q^3) * psi(q^6)) in power of q where phi(), psi() are Ramanujan theta functions.
  • A139216 (program): Expansion of q^(-1) * psi(-q) * phi(-q^9) / (psi(-q^3) * psi(q^6)) in power of q where phi(), psi() are Ramanujan theta functions.
  • A139217 (program): Smallest positive integer of the form 3k+1 such that all subsets of {a(1),…,a(n)} have a different sum.
  • A139218 (program): Smallest positive integer of the form 3k+2 such that all subsets of {a(1),…,a(n)} have a different sum.
  • A139219 (program): Primes of the form 41+(n+n^2)/2=41+A000217(n).
  • A139220 (program): Numbers k such that 41+(k+k^2)/2 = 41+A000217(k) is prime.
  • A139222 (program): a(n) = 30*n - 27.
  • A139238 (program): First differences of Mersenne numbers A001348.
  • A139241 (program): Second differences of Mersenne numbers A001348.
  • A139242 (program): Second differences of Mersenne numbers A001348, divided by 2.
  • A139243 (program): Second differences of Mersenne numbers A001348, divided by 4.
  • A139245 (program): a(n) = 20*n - 16.
  • A139249 (program): a(n) = 30*n - 24.
  • A139250 (program): Toothpick sequence (see Comments lines for definition).
  • A139251 (program): First differences of toothpicks numbers A139250.
  • A139254 (program): Primes that are not toothpick primes.
  • A139255 (program): Complement of toothpick sequence A139250.
  • A139259 (program): Triangle read by rows: row n lists the digits of A139258(n), the palindromic number formed from the reflected decimal expansion of Euler’s constant (or Euler-Mascheroni constant) gamma.
  • A139262 (program): Total number of two-element anti-chains over all ordered trees on n edges.
  • A139263 (program): Number of two element anti-chains in Riordan trees on n edges (also called non-redundant trees, i.e., ordered trees where no vertex has out-degree equal to 1).
  • A139264 (program): a(n) = 70*n - 63.
  • A139267 (program): Twice octagonal numbers: 2*n*(3*n-2).
  • A139268 (program): Twice nonagonal numbers (or twice 9-gonal numbers): a(n) = n(7n-5).
  • A139270 (program): Twice nonprime numbers.
  • A139271 (program): a(n) = 2*n*(4*n-3).
  • A139272 (program): a(n) = n*(8*n-5).
  • A139273 (program): a(n) = n*(8*n - 3).
  • A139274 (program): a(n) = n*(8*n-1).
  • A139275 (program): a(n) = n*(8*n+1).
  • A139276 (program): a(n) = n*(8*n+3).
  • A139277 (program): a(n) = n*(8*n+5).
  • A139278 (program): a(n) = n*(8*n+7).
  • A139279 (program): a(n) = 40*n - 32.
  • A139280 (program): a(n) = 90*n - 81.
  • A139283 (program): Numbers of spots seen on ladybugs.
  • A139286 (program): a(n) = 2^(2*prime(n) - 1).
  • A139287 (program): 2^(2p - 1) - 1, where p is prime.
  • A139288 (program): 2^(2p - 1)/2, where p is prime.
  • A139289 (program): (2^(2p - 1)/2)-1, where p is prime.
  • A139290 (program): 2^(2p - 1)/4, where p is prime.
  • A139291 (program): a(n) = 2^(2*prime(n) - 3) - 1.
  • A139292 (program): 2^(2p - 1)/8, where p is prime.
  • A139293 (program): (2^(2p - 1)/8)-1, where p is prime.
  • A139309 (program): Array by antidiagonals, sum of non-k-gonal numbers between consecutive k-gonal numbers.
  • A139312 (program): Characteristic function of the good primes (version 1).
  • A139316 (program): An integer k, k>=2, is in the sequence if A001222(k) (the sum of the exponents in the prime factorization of k) divides A008472(k) (the sum of the distinct primes dividing k).
  • A139327 (program): Write the first n^2 odd numbers consecutively in n rows of length n: a(n) = maximal number of primes in a row.
  • A139328 (program): Sums of rows of the triangle in A139325.
  • A139329 (program): a(n) = (factorial of the number of 0’s in the binary expansion of n).
  • A139339 (program): Decimal expansion of the square root of the golden ratio.
  • A139340 (program): Decimal expansion of the cube root of the golden ratio. That is, the decimal expansion of ((1+sqrt(5))/2)^(1/3).
  • A139351 (program): Let the binary expansion of n be n = Sum_{k} 2^{r_k}, let e(n) be the number of r_k’s that are even, o(n) the number that are odd; sequence gives e(n).
  • A139352 (program): Let the binary expansion of n be n = Sum_{k} 2^{r_k}, let e(n) be the number of r_k’s that are even, o(n) the number that are odd; sequence gives o(n).
  • A139353 (program): Let the binary expansion of n be n = Sum_{k} 2^{r_k}, let e(n) be the number of r_k’s that are even, o(n) the number that are odd; sequence gives e(n)*o(n).
  • A139354 (program): Let the binary expansion of n be n = Sum_{k} 2^{r_k}, let e(n) be the number of r_k’s that are even, o(n) the number that are odd; sequence gives min{e(n), o(n)}.
  • A139355 (program): Let the binary expansion of n be n = Sum_{k} 2^{r_k}, let e(n) be the number of r_k’s that are even, o(n) the number that are odd; sequence gives max{e(n), o(n)}.
  • A139365 (program): Array of digit sums of factorial representation of numbers 0,1,…,n!-1 for n >= 1.
  • A139370 (program): Let the binary expansion of n be n = Sum_{k} 2^{r_k}, let e(n) be the number of r_k’s that are even, o(n) the number that are odd; sequence lists n such that e(n) < o(n).
  • A139371 (program): Let the binary expansion of n be n = Sum_{k} 2^{r_k}, let e(n) be the number of r_k’s that are even, o(n) the number that are odd; sequence lists n such that e(n) <= o(n).
  • A139372 (program): Let the binary expansion of n be n = Sum_{k} 2^{r_k}, let e(n) be the number of r_k’s that are even, o(n) the number that are odd; sequence lists n such that e(n) >= o(n).
  • A139373 (program): Let the binary expansion of n be n = Sum_{k} 2^{r_k}, let e(n) be the number of r_k’s that are even, o(n) the number that are odd; sequence lists n such that e(n) > o(n).
  • A139374 (program): Digit sum of Lucas numbers.
  • A139376 (program): Expansion of 1/((1-x^2*c(x))(1-x-x^2)) where c(x) is the g.f. of A000108.
  • A139379 (program): A Jacobsthal Catalan convolution.
  • A139389 (program): Powers of ten in factorial base.
  • A139391 (program): Next odd term in Collatz trajectory with starting value n.
  • A139392 (program): Odd noncyclic numbers; odd numbers n such that gcd(n,phi(n)) > 1.
  • A139393 (program): a(n) = Sum_{i=1..m} e(i) * 10^(m-i) where e(1) <= … <= e(m) are the nonzero exponents in the prime factorization of n: a representation of the prime signature of n.
  • A139398 (program): a(n) = Sum_{k >= 0} binomial(n,5*k).
  • A139399 (program): Number of steps to reach a cycle in Collatz problem.
  • A139404 (program): Numbers k such that 24*k + 5 and 24*k + 7 are twin primes.
  • A139405 (program): Numbers k such that 8*k+1 and 8*k+7 are primes.
  • A139406 (program): Numbers k such that 8*k+1 and 8*k+5 are primes.
  • A139407 (program): Numbers k such that 8*k+3 and 8*k+7 are primes.
  • A139413 (program): Triangle read by rows: row n gives the numbers A010888(n*k) for k = 1..n.
  • A139417 (program): Sum of digits of the square of the sum of the preceding numbers.
  • A139418 (program): Complement of A136120.
  • A139420 (program): a(n) = length of n-th run of consecutive numbers in A136120.
  • A139421 (program): a(1)=1; for n>1, a(n) = largest prime divisor of n!!.
  • A139422 (program): a(1)=a(2)=1. For n >= 3, a(n) = a(n-1) + d(a(n-1)) + d(a(n-2)), where d(m) is the number of positive divisors of m.
  • A139423 (program): a(1)=1, a(2)=2. For n >= 3, a(n) = a(n-1) + d(a(n-1)) + d(a(n-2)), where d(m) is the number of positive divisors of m.
  • A139434 (program): Frieze pattern with 4 rows, read by diagonals.
  • A139459 (program): Triangle read by rows: binomial(3*n,3*k), 0 <= k <= n.
  • A139464 (program): n! + 2n - 1.
  • A139468 (program): a(n) = Sum{k=0..n} C(n,3k+1)^2.
  • A139469 (program): a(n) = Sum_{k=0..n} C(n,3k+2)^2.
  • A139477 (program): Number of binary digits in A001109(n).
  • A139478 (program): a(n) = A001109(n) in binary.
  • A139482 (program): Binomial transform of [1, 1, 2, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, …].
  • A139483 (program): Numbers n such that 24n+7 is prime.
  • A139485 (program): a(1)=1. For m >= 0 and 1 <= k <= 2^m, a(2^m +k) = a(k) + Sum_{j=1..2^m} a(j).
  • A139486 (program): a(n) = Product_{j=0..n-1} (2^j + 2).
  • A139487 (program): Numbers k such that 8k + 7 is prime.
  • A139488 (program): Binomial transform of [1, 2, 3, 4, 0, 0, 0, …].
  • A139492 (program): Primes of the form x^2 + 5x*y + y^2 for x and y nonnegative.
  • A139502 (program): Primes of the form x^2 + 22x*y + y^2 for x and y nonnegative.
  • A139506 (program): Primes of the form x^2 + 26x*y + y^2 for x and y nonnegative.
  • A139513 (program): Primes congruent to {1, 3, 7, 9} mod 20.
  • A139524 (program): Triangle T(n,k) read by rows: the coefficient of [x^k] of the polynomial 2*(x+1)^n + 2^n in row n, column k.
  • A139526 (program): Triangle A061356 read right to left.
  • A139527 (program): Numbers n such that numbers 24n+5 are primes.
  • A139528 (program): Numbers n such that numbers 24n+11 are primes.
  • A139529 (program): Numbers n such that numbers 24n+13 are primes.
  • A139530 (program): Primes of the form 24n+13.
  • A139531 (program): Numbers k such that 24*k + 17 is prime.
  • A139532 (program): Numbers n such that numbers 24n+19 are primes.
  • A139533 (program): Numbers k such that numbers 24*k + 11 and 24*k + 13 are twin primes.
  • A139534 (program): Numbers k such that numbers 24*k + 17 and 24*k + 19 are twin primes.
  • A139541 (program): There are 4*n players who wish to play bridge at n tables. Each player must have another player as partner and each pair of partners must have another pair as opponents. The choice of partners and opponents can be made in exactly a(n)=(4*n)!/(n!*8^n) different ways.
  • A139542 (program): a(n) = a(n-1) + largest divisor of a(n-1) <= sqrt(a(n-1)).
  • A139544 (program): Numbers which are not the difference of two squares of positive integers.
  • A139545 (program): Binomial transform of [1, 0, 0, 4, 0, 0, 7, 0, 0, 10, …].
  • A139546 (program): Numbers of form x^2+5y^2 (x>=0,y>=0) with repetition.
  • A139547 (program): Triangle read by rows: T(n,k) = A003418(A010766).
  • A139548 (program): Triangle T(n,k) with the coefficient of [x^k] of the polynomial (2*(x+1)^2)^n in row n, column k, 0<=k<=2n.
  • A139550 (program): a(n) = lcm(1..floor(n/2)).
  • A139552 (program): a(n) = lcm(1..floor(n/3)).
  • A139554 (program): a(n) = lcm(1..floor(n/4)).
  • A139555 (program): a(n) = number of prime-powers (including 1) that each are <= n and are coprime to n.
  • A139556 (program): a(n) = sum of the prime-powers (including 1) that each are <= n and are coprime to n.
  • A139562 (program): Sum of primes < n^2.
  • A139566 (program): a(n) is the sum of squares of digits of a(n-1); a(1)=15.
  • A139570 (program): 2n(n+3).
  • A139576 (program): a(n) = n(2n+9).
  • A139577 (program): a(n) = n*(2*n + 11).
  • A139578 (program): a(n) = n(2n+13).
  • A139579 (program): a(n) = 2*n^2 + 15*n.
  • A139580 (program): a(n) = n(2n+17).
  • A139581 (program): a(n) = n*(2*n + 19).
  • A139582 (program): Twice partition numbers.
  • A139588 (program): Nonprime numbers with Fibonacci number of divisors.
  • A139591 (program): A139275(n) followed by 18-gonal number A051870(n+1).
  • A139592 (program): A033585(n) followed by A139271(n+1).
  • A139593 (program): A139276(n) followed by A139272(n+1).
  • A139594 (program): Number of different n X n symmetric matrices with nonnegative entries summing to 4. Also number of symmetric oriented graphs with 4 arcs on n points.
  • A139595 (program): A139277(n) followed by A139273(n+1).
  • A139596 (program): A033587(n) followed by even hexagonal number A014635(n+1).
  • A139597 (program): A139278(n) followed by A139274(n+1).
  • A139598 (program): A035008(n) followed by A139098(n+1).
  • A139600 (program): Square array T(n,k) = n*(k-1)*k/2+k, of nonnegative numbers together with polygonal numbers, read by antidiagonals upwards.
  • A139601 (program): Square array T(n,k) = (n+1)*(k-1)*k/2+k, of polygonal numbers, read by antidiagonals upwards.
  • A139606 (program): a(n) = 15*n + 6.
  • A139607 (program): a(n) = 21*n + 7.
  • A139608 (program): a(n) = 28*n + 8.
  • A139609 (program): a(n) = 36*n + 9.
  • A139610 (program): a(n) = 45*n + 10.
  • A139611 (program): 55n + 11.
  • A139612 (program): 66n + 12.
  • A139613 (program): 78n + 13.
  • A139614 (program): a(n) = 91*n + 14.
  • A139615 (program): a(n) = 105*n + 15.
  • A139616 (program): a(n) = 120*n + 16.
  • A139617 (program): a(n) = 136*n + 17.
  • A139618 (program): a(n) = 153*n + 18.
  • A139619 (program): a(n) = 171*n + 19.
  • A139620 (program): a(n) = 190*n + 20.
  • A139624 (program): Table read by rows: T(n,k) is the number of connected directed multigraphs with loops and no vertex of degree 0, with n arcs and k vertices, which are transitive (the existence of a path between two points implies the existence of an arc between those two points).
  • A139626 (program): a(n) = binomial(n+4, 4)*6^n.
  • A139633 (program): Triangle read by rows: binomial transform of a diagonalized matrix of A026741.
  • A139634 (program): 10*2^(n-1) - 9.
  • A139635 (program): Binomial transform of [1, 11, 11, 11, …].
  • A139636 (program): If n = the k-th prime, then a(n) = the (k+1)th prime. If n = the k-th composite, then a(n) = the (k+1)th composite.
  • A139639 (program): Numbers n such that 168n+31 is prime.
  • A139641 (program): a(n) = binomial(n+4, 4)*7^n.
  • A139645 (program): Primes of the form x^2 + 112*y^2.
  • A139672 (program): Convolution of A008619 and A001400.
  • A139678 (program): Number of n X n symmetric binary matrices with no row sum greater than 2.
  • A139693 (program): a(n) is the smallest positive integer m where, for k divides m, minimum(|k - m/k|) = n.
  • A139697 (program): Binomial transform of [1, 12, 12, 12, …].
  • A139698 (program): Binomial transform of [1, 25, 25, 25, …].
  • A139700 (program): Binomial transform of [1, 30, 30, 30, …].
  • A139701 (program): Binomial transform of [1, 100, 100, 100, …].
  • A139704 (program): Nearly palindromic numbers: non-palindromes that can be made palindromic by inserting an extra digit.
  • A139706 (program): Take n in binary. Rotate the binary digits to the right until a 1 once again appears as the leftmost digit. Convert back into decimal for a(n).
  • A139707 (program): Take n in binary. Rotate the binary digits to the right until a 1 once again appears as the leftmost digit. a(n) is result written in binary.
  • A139708 (program): Take n in binary. Rotate the binary digits to the left until a 1 once again appears as the leftmost digit. Convert back into decimal for a(n).
  • A139709 (program): Take n in binary. Rotate the binary digits to the left until a 1 once again appears as the leftmost digit. a(n) is result written in binary.
  • A139710 (program): A number n is included if the sum of (the largest divisor of n that is <= sqrt(n)) and (the smallest divisor of n that is >= sqrt(n)) is odd.
  • A139711 (program): A number n is included if the sum of (the largest divisor of n that is <= sqrt(n)) and (the smallest divisor of n that is >= sqrt(n)) is even.
  • A139714 (program): a(n) = Sum_{k>=0} binomial(n,5*k+2).
  • A139716 (program): If k is the largest divisor of n that is <= sqrt(n) then a(n) = n - k^2.
  • A139717 (program): If k is the smallest divisor of n that is >= sqrt(n) then a(n) = k^2 - n.
  • A139729 (program): 9^n mod 4^n.
  • A139730 (program): a(n) = 9^n mod 5^n.
  • A139731 (program): a(n) = 9^n mod 6^n.
  • A139732 (program): a(n) = 9^n mod 7^n.
  • A139733 (program): 9^n mod 8^n.
  • A139734 (program): a(n) = 10^n mod 3^n.
  • A139735 (program): a(n) = 10^n mod 4^n.
  • A139736 (program): a(n) = 10^n mod 6^n.
  • A139737 (program): a(n) = 10^n mod 7^n.
  • A139738 (program): a(n) = 10^n mod 8^n.
  • A139739 (program): a(n) = 10^n mod 9^n.
  • A139740 (program): a(n) = 11^n - 2^n.
  • A139741 (program): a(n) = 11^n - 3^n.
  • A139742 (program): a(n) = 11^n - 4^n.
  • A139743 (program): a(n) = 11^n - 5^n.
  • A139744 (program): a(n) = 11^n - 6^n.
  • A139745 (program): a(n) = 11^n - 7^n.
  • A139746 (program): a(n) = 11^n - 8^n.
  • A139747 (program): a(n) = 11^n - 9^n.
  • A139748 (program): a(n) = Sum_{ k >= 0} binomial(n,5*k+3).
  • A139754 (program): a(n) = floor(n*2*(3^n-2^n)/2^n).
  • A139756 (program): Binomial transform of A004526.
  • A139757 (program): a(n) = (n+1)*(2n+1)^2.
  • A139758 (program): a(n) is the smallest prime such that (a(n) - the n-th prime) is a power of 2.
  • A139760 (program): First quadrisection of A115451.
  • A139761 (program): a(n) = Sum_{ k >= 0} binomial(n,5*k+4).
  • A139763 (program): a(n)=a(n-1)+a(n-2)+a(n-3)+2a(n-4) with a(n)=n+1 for n<=3.
  • A139764 (program): Smallest term in Zeckendorf representation of n.
  • A139770 (program): Smallest number having at least as many divisors as n.
  • A139782 (program): Binomial transform of A077947.
  • A139786 (program): a(n) = 7^n mod 6^n.
  • A139788 (program): Period 5: repeat 1, 7, 3, 9, 5.
  • A139790 (program): a(n) = (5*2^(n+2) - 3*n*2^n - 2*(-1)^n) / 18.
  • A139791 (program): Numbers n for which 2n is a multiple of A002326(n), the multiplicative order of 2 mod 2n+1.
  • A139792 (program): First quadrisection of A139763 (1, 2, 3, 4, 11, …).
  • A139796 (program): Last term of A139687(n) with a fourth leading 1 = 1, 1, 1, 1, 2, 2, 1, 3, 5, 5 rows.
  • A139797 (program): Inverse binomial transform of [0, A133474].
  • A139798 (program): Coefficient of x^5 in (1-x-x^2)^(-n).
  • A139800 (program): a(n)=a(n-1)+a(n-2)+a(n-3)+2a(n-4).
  • A139806 (program): a(n)=a(n-1)+a(n-2)+a(n-3)+2a(n-4), a(0)=1, a(1)=3, a(2)=7, a(3)=15.
  • A139813 (program): A polynomial triangle based on cross binomial Hodge number matrices/ Hodge diamonds that represent Calabi-Yau type binomials and their monomials.
  • A139814 (program): a(n)=a(n-1)+a(n-2)+a(n-3)+2a(n-4); a(0)=0,a(1)=1,a(2)=3,a(3)=7.
  • A139816 (program): Final nonzero terms in rows of A139801.
  • A139817 (program): 2^n - number of digits of 2^n.
  • A139818 (program): Squares of Jacobsthal numbers.
  • A139819 (program): Complement of repdigit numbers A010785.
  • A139820 (program): Expansion of (phi(-q) / phi(q))^2 in powers of q where phi() is a Ramanujan theta function.
  • A139821 (program): Triangle T(i,j) read by rows: T(i,1) = Fibonacci(i) for all i; T(i,i) = i for all i; T(i,j) = T(i-1,j) + T(i-2,j) + T(i-1,j-1) - T(i-2,j-1).
  • A139829 (program): Primes of the form 4x^2+4xy+11y^2.
  • A139830 (program): Primes of the form 7x^2+6xy+7y^2.
  • A139831 (program): Primes of the form 2x^2+2xy+23y^2.
  • A139832 (program): Primes of the form 7x^2+4xy+7y^2.
  • A139851 (program): Primes of the form 4x^2+4xy+29y^2.
  • A139854 (program): Primes of the form 3x^2 + 40y^2.
  • A139855 (program): Primes of the form 4x^2+4xy+31y^2.
  • A139857 (program): Primes of the form 8x^2 + 15y^2.
  • A139858 (program): Primes of the form 8x^2+8xy+17y^2.
  • A139859 (program): Primes of the form 11x^2+2xy+11y^2.
  • A139860 (program): Primes of the form 12x^2+12xy+13y^2.
  • A139897 (program): Primes of the form 3*x^2+80*y^2.
  • A139898 (program): Primes of the form 4x^2+4xy+61y^2.
  • A139899 (program): Primes of the form 5x^2+48y^2.
  • A139902 (program): Primes of the form 16x^2+16xy+19y^2.
  • A140048 (program): a(n) = (1/2)*Sum_{j=0..2^n-1} j^(n-1) for n>=1.
  • A140050 (program): L.g.f.: A(x) = log(G(x)) where G(x) = g.f. of A014070(n) = C(2^n,n).
  • A140051 (program): L.g.f.: A(x) = log(G(x)) where G(x) = g.f. of A060690(n) = C(2^n+n-1,n).
  • A140056 (program): Triangle of coefficients: f(x,y,n) = x^n - y^(n-1)*x - y^n; p(x,y,z,n) = f(x,y,n) + f(y,z,n) + f(z,x,n).
  • A140058 (program): Numbers > 24 that are congruent to {5,6,7,8,9} mod 10.
  • A140062 (program): 101*2^(n-1) - 100.
  • A140063 (program): Binomial transform of [1, 3, 7, 0, 0, 0, …].
  • A140064 (program): a(n) = (9*n^2 - 23*n + 16)/2.
  • A140065 (program): a(n) = (7*n^2 - 17*n + 12)/2.
  • A140066 (program): a(n) = (5*n^2 - 11*n + 8)/2.
  • A140068 (program): Triangle read by rows, n-th row = (n-1)-th power of the matrix X * [1,0,0,0,…] where X = an infinite lower triangular matrix with [1,2,1,2,1,2,…] in the main diagonal and [1,1,1,…] in the subdiagonal.
  • A140069 (program): Triangle read by rows, n-th row = (n-1)-th power of the matrix X * [1,0,0,0,…]; where X = an infinite lower triangular bidiagonal matrix with [2,1,2,1,2,1,…] and [1,1,1,…] in the subdiagonal.
  • A140070 (program): Triangle read by rows, iterates of matrix X * [1,0,0,0,…], where X = an infinite lower bidiagonal matrix with [1,3,1,3,1,3,…] in the main diagonal and [1,1,1,…] in the subdiagonal.
  • A140071 (program): Triangle read by rows: iterates of X * [1,0,0,0,…]; where X = an infinite lower bidiagonal matrix with [3,1,3,1,3,1…] in the main diagonal and [1,1,1,…] in the subdiagonal.
  • A140077 (program): Numbers n such that n and n+1 have 3 distinct prime factors.
  • A140081 (program): Period 4: repeat [0, 1, 1, 2].
  • A140085 (program): Period 8: repeat [0,1,1,2,1,2,2,3].
  • A140090 (program): a(n) = n*(3*n + 7)/2.
  • A140091 (program): a(n) = 3*n*(n + 3)/2.
  • A140096 (program): a(n) = A000045(n) - A113405(n).
  • A140098 (program): A Beatty sequence: a(n) = [n*(1+1/t)], where t = tribonacci constant (A058265); complement of A140099.
  • A140099 (program): A Beatty sequence: a(n) = [n*(1+t)], where t = tribonacci constant (A058265); complement of A140098.
  • A140100 (program): Start with Y(0)=0, X(1)=1, Y(1)=2. For n > 1, choose least positive integers Y(n) > X(n) such that neither Y(n) nor X(n) appear in {Y(k), 1 <= k < n} or {X(k), 1 <= k < n} and such that Y(n) - X(n) does not appear in {Y(k) - X(k), 1 <= k < n} or {Y(k) + X(k), 1 <= k < n}; sequence gives X(n) (for Y(n) see A140101).
  • A140101 (program): Start with Y(0)=0, X(1)=1, Y(1)=2. For n > 1, choose least positive integers Y(n) > X(n) such that neither Y(n) nor X(n) appear in {Y(k), 1 <= k < n} or {X(k), 1 <= k < n} and such that Y(n)-X(n) does not appear in {Y(k)-X(k), 1 <= k < n} or {Y(k)+X(k), 1 <= k < n}; sequence gives Y(n) (for X(n) see A140100).
  • A140102 (program): Term-by-term differences of A140101 and A140100; also, equals the complement of A140103, which is the term-by-term sums of A140101 and A140100, where A140101 is the complement of A140100.
  • A140103 (program): Term-by-term sums of A140101 and A140100; also, equals the complement of A140102, which is the term-by-term differences of A140101 and A140100, where A140101 is the complement of A140100.
  • A140105 (program): Trailing zeros removed from n! in binary.
  • A140106 (program): Number of noncongruent diagonals in a regular n-gon.
  • A140107 (program): a(n) = binomial(n+3, 3)*7^n.
  • A140113 (program): a(1)=1, a(n)=a(n-1)+n if n odd, a(n)=a(n-1)+ n^2 if n is even.
  • A140114 (program): Number of semiprimes strictly between n^2 and (n+1)^2.
  • A140118 (program): Extrapolation for (n + 1)-st odd prime made by fitting least-degree polynomial to first n odd primes.
  • A140119 (program): Extrapolation for (n + 1)-st prime made by fitting least-degree polynomial to first n primes.
  • A140124 (program): a(n) = degree in N of the number of orbits under S_N of the set of n-tuples of partitions of {1,…,N} into n subsets.
  • A140126 (program): Partial sums of A001912.
  • A140128 (program): A positive integer n is included if d(d(n)) = d(d(n+1)), where d(n) is the number of divisors of n.
  • A140130 (program): a(n) = denominator(c(n)) where c(n) = 1 if n=1, otherwise if n < 3*2^floor(log_2(n)-1) then c(n) = (c(floor(n/2))+c(floor((n+1)/2)))/2 otherwise c(n) = c(n-2^floor(log_2(n)))+1.
  • A140131 (program): a(n)=a(n-1)+a(n-2)+Sum_digits[a(n-1)]+Sum_digits[a(n-2)], with a(0)=0 and a(1)=1.
  • A140132 (program): a(n)=Sum_digits{a(n-1)+a(n-2)+Sum_digits[a(n-1)]+Sum_digits[a(n-2)]}, with a(0)=0 and a(1)=1.
  • A140139 (program): Binomial transform of [1, 1, 2, -3, 4, -5, 6, -7, …].
  • A140142 (program): a(1)=1, a(n)=a(n-1)+n^0 if n odd, a(n)=a(n-1)+ n^4 if n is even.
  • A140143 (program): a(1)=1, a(n)=a(n-1)+n^0 if n odd, a(n)=a(n-1)+ n^5 if n is even.
  • A140144 (program): a(1)=1, a(n)=a(n-1)+n^1 if n odd, a(n)=a(n-1)+ n^0 if n is even.
  • A140145 (program): a(1)=1, a(n)=a(n-1)+n^1 if n odd, a(n)=a(n-1)+ n^3 if n is even.
  • A140146 (program): a(1)=1, a(n)=a(n-1)+n^1 if n odd, a(n)=a(n-1)+ n^4 if n is even.
  • A140147 (program): a(1)=1, a(n)=a(n-1)+n^1 if n odd, a(n)=a(n-1)+ n^5 if n is even.
  • A140148 (program): a(1)=1, a(n)=a(n-1)+n^2 if n odd, a(n)=a(n-1)+ n^0 if n is even.
  • A140149 (program): a(1)=1, a(n)=a(n-1)+n^2 if n odd, a(n)=a(n-1)+ n^3 if n is even.
  • A140150 (program): a(1)=1, a(n)=a(n-1)+n^2 if n odd, a(n)=a(n-1)+ n^4 if n is even.
  • A140151 (program): a(1)=1, a(n)=a(n-1)+n^2 if n odd, a(n)=a(n-1)+ n^5 if n is even.
  • A140152 (program): a(1)=1, a(n)=a(n-1)+n^3 if n odd, a(n)=a(n-1)+ n^0 if n is even.
  • A140153 (program): a(1)=1, a(n) = a(n-1) + n^3 if n odd, a(n) = a(n-1) + n^1 if n is even.
  • A140154 (program): a(1)=1, a(n) = a(n-1) + n^3 if n odd, a(n) = a(n-1) + n^2 if n is even.
  • A140155 (program): a(1)=1, a(n)=a(n-1)+n^3 if n odd, a(n)=a(n-1)+ n^4 if n is even.
  • A140156 (program): a(1)=1, a(n) = a(n-1) + n^3 if n odd, a(n) = a(n-1) + n^5 if n is even.
  • A140157 (program): a(1)=1, a(n) = a(n-1) + n^4 if n odd, a(n) = a(n-1) + n^0 if n is even.
  • A140158 (program): a(1)=1, a(n) = a(n-1) + n^4 if n odd, a(n) = a(n-1) + n^1 if n is even.
  • A140159 (program): a(1)=1, a(n) = a(n-1) + n^4 if n odd, a(n) = a(n-1) + n^2 if n is even.
  • A140160 (program): a(1)=1, a(n) = a(n-1) + n^4 if n odd, a(n) = a(n-1) + n^3 if n is even.
  • A140161 (program): a(1)=1, a(n) = a(n-1) + n^4 if n odd, a(n) = a(n-1) + n^5 if n is even.
  • A140162 (program): a(1)=1, a(n) = a(n-1) + n^5 if n odd, a(n) = a(n-1) + n^0 if n is even.
  • A140163 (program): a(1)=1, a(n) = a(n-1) + n^5 if n odd, a(n) = a(n-1) + n if n is even.
  • A140164 (program): Binomial transform of [1, 1, 1, 1, -1, -1, 5, -11, 19, -29, 41, …].
  • A140165 (program): a(n) = -a(n-1) + 3*a(n-2), starting a(1)=1, a(2)=2.
  • A140166 (program): Triangle read by rows, iterates of X * [1,0,0,0,…]; where X = an infinite bidiagonal matrix with [1,-2,1,-2,1,…] in the main diagonal, [1,1,1,…] in the subdiagonal and the rest zeros.
  • A140167 (program): a(n) = (-1)*a(n-1) + 3*a(n-2) with a(1)=-1 and a(2)=1.
  • A140168 (program): Triangle read by rows, iterates of X * [1,0,0,0,…]; where X = an infinite bidiagonal matrix with [2, -1, 2, -1, 2, …] in the main diagonal, [1, 1, 1, …] in the subdiagonal and rest zeros.
  • A140180 (program): A number n is included if the smallest prime that is congruent to 1 (mod n) is <= the smallest prime that is congruent to -1 (mod n).
  • A140181 (program): A number n is included if the smallest prime that is congruent to 1 (mod n) is >= the smallest prime that is congruent to -1 (mod n).
  • A140182 (program): Binomial transform of an infinite bidiagonal matrix with (1,3,1,3,1,3,…) in the main diagonal, (1,1,1,…) in the subdiagonal, the rest zeros.
  • A140184 (program): a(n) = 2*a(n-1) + 16*a(n-2) + 16*a(n-3).
  • A140191 (program): Fix e = 3; a(n) gives number of multiples ke (0 <= k <= n/e) which are children of n.
  • A140192 (program): Same as A140191 except here e=5.
  • A140193 (program): Same as A140191 except here e=6.
  • A140194 (program): Same as A140191 except here e=7.
  • A140195 (program): Same as A140191 except here e=9.
  • A140197 (program): A137576((k-1)/2) for composite numbers k from A141229.
  • A140198 (program): A002326((k-1)/2) for composite numbers k from A141229.
  • A140199 (program): a(n) = the number of pairs of (not necessarily distinct) positive integers j and k where j <= n and k <= n such that k+j is prime.
  • A140200 (program): Partial sums of A140080.
  • A140201 (program): Partial sums of A140081.
  • A140205 (program): Partial sums of A140085.
  • A140207 (program): Triangle read by rows in which row n (n>=0) gives the first n terms of A000041.
  • A140208 (program): Floor n*Pi(n)/2.
  • A140210 (program): a(n) = Product_{h == 1 (mod 4) and h|n} h.
  • A140211 (program): a(n) = Product_{d == 3 (mod 4) and d|n} d.
  • A140213 (program): Product_{h|n and h mod 6 = 1} h; product of divisors of n of the form 6*k + 1.
  • A140214 (program): a(n) = Product_{h == 5 (mod 6) and h|n} h.
  • A140215 (program): A140213(n)*A140214(n).
  • A140219 (program): Denominator of the coefficient [x^1] of the Bernoulli twin number polynomial C(n,x).
  • A140220 (program): a(n) = binomial(n+7, 7)*5^n.
  • A140221 (program): A number n is included if n is coprime to sum{k=1 to n} d(k), where d(k) is the number of divisors of k.
  • A140222 (program): A number j is included if (Sum_{k=1..j} d(k)) is prime, where d(k) is the number of divisors of k.
  • A140226 (program): Binomial transform of [1, 3, 3, 1, 1, -1, 1, -1, 1, …].
  • A140227 (program): Binomial transform of [1, 4, 6, 4, 1, 1, -1, 1, -1, 1, …].
  • A140228 (program): Binomial transform of [1, 5, 10, 10, 5, 1, 1, -1, 1, -1, 1, …].
  • A140229 (program): Binomial transform of [1, 3, 3, 1, -2, 3, -4, 5, …].
  • A140230 (program): Binomial transform of [1, 2, -3, -4, 5, 6, -7, -8, 9, 10, …].
  • A140233 (program): a(n)=Floor[n*e^((1+sqrt(5))/2)] = floor[n*A139341].
  • A140234 (program): Sum of the semiprimes <= n.
  • A140235 (program): Partial sum of non-semiprimes A100959.
  • A140236 (program): Double tetrahedral numbers (or double pyramidal numbers): a(n) = k(k+1)(k+2)/6 where k = n(n+1)(n+2)/6.
  • A140239 (program): Decimal expansion of 3*sqrt(15)/4.
  • A140240 (program): Decimal expansion of arccos(7/8).
  • A140246 (program): Decimal expansion of sqrt(15)/6.
  • A140247 (program): Decimal expansion of 8/sqrt(15).
  • A140248 (program): Decimal expansion of 0.3 * sqrt(15).
  • A140249 (program): Decimal expansion of 3*sqrt(15)/2.
  • A140252 (program): Inverse binomial transform of A140420.
  • A140253 (program): a(2*n) = 2*(2*4^(n-1)-1) and a(2*n-1) = 2*4^(n-1)-1.
  • A140254 (program): Mobius transform of A014963.
  • A140255 (program): Inverse Mobius transform of A014963.
  • A140256 (program): Triangle read by columns: Column k is A014963 aerated with groups of (k-1) zeros.
  • A140260 (program): Those n for which A140259(n) = A002264(n+11).
  • A140261 (program): The length of Sapro’s necklace at successive years in Werneck’s Black Pearl Necklace problem.
  • A140262 (program): A140260 reduced modulo 9.
  • A140264 (program): Inverse permutation to A140263.
  • A140266 (program): Inverse permutation to A140265.
  • A140267 (program): Nonnegative integers in balanced ternary representation (with 2 standing for -1 digit).
  • A140268 (program): a(n) = negative integer -n presented in balanced ternary system.
  • A140271 (program): Least divisor of n that is > sqrt(n), with a(1) = 1.
  • A140280 (program): Product of digits of values in Pascal’s triangle, by rows.
  • A140282 (program): Numbers k such that A000330(k) is multiple of 3.
  • A140289 (program): First quadrisection of A140287.
  • A140290 (program): Fourth quadrisection of A140287.
  • A140295 (program): a(n)=a(n-1)+a(n-2)+2a(n-3).
  • A140298 (program): a(0)=1; a(3n+1) = a(3n)+1, a(3n+2) = a(3n+1) + a(3n) (=3*A000244), a(3n+3) = a(3n+2) + a(3n) (=A003462(n+2)).
  • A140299 (program): a(n) = A100626(n+1)/A100626(n).
  • A140300 (program): a(n) = 1024^n.
  • A140303 (program): Triangle T(n,k) = 3^(n-k) read by rows.
  • A140313 (program): First differences of A140298.
  • A140316 (program): Write n in base 3, delete 0’s.
  • A140317 (program): Smallest n-digit number divisible by n^2.
  • A140318 (program): Period 18: repeat 0, 1, -1, 1, 0, -1, 1, -1, 0, 0, -1, 1, -1, 0, 1, -1, 1, 0.
  • A140320 (program): a(n) = A137576((3^n-1)/2).
  • A140321 (program): Decimal expansion of x-coordinate of fixed point of Henon Map for a=7/5 and b=3/10 where x is a positive.
  • A140322 (program): a(n) = -1/6 + (-1)^n/2 + 2*4^n/3.
  • A140323 (program): First differences of A140322.
  • A140325 (program): a(n) = binomial(n+8,8) * 2^n.
  • A140341 (program): The number of bits needed to write the universal code for an Elias delta coding, the simplest asymptotically optimal code.
  • A140342 (program): a(n)=5a(n-1)-11a(n-2)+13a(n-3)-9a(n-4)+3a(n-5)-a(n-6).
  • A140343 (program): a(n)=4a(n-1)-7a(n-2)+6a(n-3)-3a(n-4), n>4.
  • A140344 (program): Catalan triangle A009766 prepended by n zeros in its n-th row.
  • A140345 (program): a(n)=a(n-1)^2-a(n-2)-a(n-3)-a(n-4), a(1)=a(2)=a(3)=a(4)=1.
  • A140346 (program): a(n) = binomial(n+8, 8)*5^n.
  • A140347 (program): Composites of the form ((x+y)/3+2)/(x-y), where x=composite and y=prime.
  • A140353 (program): a(n) = prime(n) + 9.
  • A140354 (program): a(n) = binomial(n+9,9)*2^n.
  • A140356 (program): Triangle T(n,m) read by rows: m! if m <= floor(n/2), and (n-m)! otherwise.
  • A140357 (program): a(1)=1; a(n)=floor(4*a(n-1)*(n-a(n-1) / n) for n > 1.
  • A140358 (program): Smallest nonnegative integer k such that n = +-1+-2+-…+-k for some choice of +’s and -‘s.
  • A140359 (program): a(n) = 2*a(n-1) + a(n-2) - 2*a(n-3).
  • A140360 (program): Inverse binomial transform of A140359.
  • A140365 (program): a(n) = sum of primes in {6*n-5, 6*n-1}.
  • A140366 (program): a(n) = isprime(6n-1) + 2*isprime(6n-5), where isprime = A010051.
  • A140367 (program): Composites of the form 26k + 5.
  • A140368 (program): Composites of the form 26k + 17.
  • A140369 (program): Composites of the form 26k + 19.
  • A140370 (program): Composites of the form 26k + 21.
  • A140371 (program): Primes of the form 26k + 7.
  • A140372 (program): Primes of the form 26k + 9.
  • A140373 (program): Primes of the form 26*n+11.
  • A140374 (program): Primes of the form 26k + 15.
  • A140375 (program): Primes of the form 26n+23.
  • A140376 (program): Nonprimes of the form 26n+1.
  • A140377 (program): Composites of the form 26k + 3.
  • A140379 (program): Nonprimes of the form 14k+1.
  • A140380 (program): Composites of the form 14k + 3.
  • A140381 (program): Composites of the form 14k + 9.
  • A140390 (program): Nonprimes of the form 21k+1.
  • A140397 (program): a(n) = floor(3*phi*n) - 3*floor(phi*n) where phi = (1+sqrt(5))/2.
  • A140398 (program): Numbers n such that A140397(n) = 0.
  • A140399 (program): Numbers n such that A140397(n) = 1.
  • A140400 (program): Numbers n such that A140397(n) = 2.
  • A140402 (program): Expansion of x^4/((1-x)^2*(1-x^3)) + x^5/((1-x)*(1-x^2)*(1-x^5)).
  • A140403 (program): Expansion of 8*x^4/((1-x)^2*(1-x^3)) + 8*x^5/((1-x)*(1-x^2)*(1-x^5)).
  • A140404 (program): a(n) = binomial(n+5, 5)*7^n.
  • A140405 (program): a(n) = binomial(n+6, 6)*5^n.
  • A140406 (program): a(n) = binomial(n+6, 6)*8^n.
  • A140407 (program): A000225 interleaved with A000051.
  • A140408 (program): Irregular triangle T(n,k) read by rows: n repetitions of -1 followed by (n+1) repetitions of n+1.
  • A140413 (program): a(2n) = A000045(6n) + 1, a(2n+1) = A000045(6n+3) - 1.
  • A140414 (program): Triangle T(p,s) showing the coefficients of sequences which are half their p-th differences.
  • A140420 (program): Binomial transform of 0, 1, 1, 7, 7, 31, 31, …, zero followed by duplicated A083420.
  • A140426 (program): Number of multi-symmetric Steinhaus matrices of size n.
  • A140427 (program): Arises in relating doubly-even error-correcting codes, graphs and irreducible representations of N-extended supersymmetry.
  • A140428 (program): a(n) = A000045(n) + A113405(n).
  • A140429 (program): a(n) = floor(3^(n-1)).
  • A140430 (program): Period 6: repeat [3, 2, 4, 1, 2, 0].
  • A140431 (program): 2*A094555(n).
  • A140432 (program): a(1)=1, a(2)=2, a(3)=3, a(4)=4, a(5)=5, a(n+1)=a(1)*a(2)*…*a(n)-1 for n>=5.
  • A140433 (program): Primes of the form n^0+(n+1)^1+(n+2)^2+(n+3)^3+(n+4)^4.
  • A140434 (program): Number of new visible points created at each step in an n X n grid.
  • A140435 (program): Number of new lattice points created at each step in an n X n grid that are not visible.
  • A140438 (program): Number of letters in word for the number n in Tamil.
  • A140439 (program): Array, by antidiagonals, arises in counting <= k facets in d-dimensional n-point sets.
  • A140442 (program): Primes congruent to 9 mod 14.
  • A140444 (program): Primes congruent to 1 (mod 14).
  • A140445 (program): List of prime pairs of form p, p + 10.
  • A140455 (program): 13-Fibonacci sequence.
  • A140456 (program): a(n) is the number of indecomposable involutions of length n.
  • A140461 (program): Numbers in A008364 but not in A038511.
  • A140462 (program): Turan’s upper bound on the number of triangles of a simplicial complex of dimension two for which every minimal non-face has three vertices.
  • A140466 (program): a(n) = 4*A002088(n).
  • A140472 (program): Chaotic sequence related to A004001: a(n) = a(n - a(n-1)) + a(floor(n/2)).
  • A140475 (program): 1 along with primes greater than 3.
  • A140477 (program): Binomial(127,n).
  • A140479 (program): n^2 - number of digits of n^2.
  • A140481 (program): a(1) = 1; for n >= 1, a(n+1) is obtained by adding to a(n) the a(n)-th smallest number not dividing a(n).
  • A140482 (program): a(n) = 2*n + tau(n).
  • A140496 (program): a(n) = p - number of digits of p^4, where p = n-th prime.
  • A140498 (program): a(n) = 3*a(n-1)-3*a(n-2)+3*a(n-3) with a(0)=1, a(1)=3, a(2)=7.
  • A140500 (program): Period 18: repeat [1, 1, -2, 2, -1, -1, 1, -2, 1, -1, -1, 2, -2, 1, 1, -1, 2, -1].
  • A140503 (program): Triangle T(d,n) read by rows, the n-th term of the d-th differences of the Jacobsthal sequence A001045.
  • A140504 (program): a(n) = 2^n + 4.
  • A140505 (program): Second differences of Jacobsthal sequence A001045, pairs with even and odd indices swapped.
  • A140506 (program): Primes congruent to 11 or 19 mod 30.
  • A140508 (program): Mobius transform applied twice to A001414.
  • A140511 (program): a(n) = ((prime(n))^2 + prime(n+1))/2.
  • A140513 (program): Repeat 2^n n times.
  • A140520 (program): a(n) = binomial(n+9, 9)*5^n.
  • A140524 (program): a(1)=2. For n >=2, a(n) = the least integer >= n that is non-coprime to both n and a(n-1).
  • A140525 (program): a(1)=2. For n >=2, a(n) = the least integer >= a(n-1) that is not coprime to both a(n-1)+1 and a(n-1).
  • A140529 (program): a(n) = 6*4^n - 1.
  • A140530 (program): Triangle read by rows of coefficients of polynomials defined in comments lines.
  • A140531 (program): Concatenate subsequences 0, 1, 2, 4, …, 2^k.
  • A140533 (program): Primes congruent to 13 or 17 mod 30.
  • A140538 (program): Greatest prime factor of 2*n^4 + 1.
  • A140540 (program): Primes of form 17*n - 3.
  • A140541 (program): Primes of the form 17*k - 1.
  • A140542 (program): Primes of form 17*n - 6.
  • A140543 (program): Primes congruent to 15 mod 17.
  • A140544 (program): Primes of form 17*k + 2.
  • A140545 (program): Primes of form 17n + 6.
  • A140554 (program): First differences of A066841.
  • A140555 (program): Primes p such that p + 6 is not a prime.
  • A140556 (program): Primes p such that p + 10 is not a prime.
  • A140557 (program): Primes p such that p + 14 is composite.
  • A140558 (program): Primes p such that p + 22 is not a prime.
  • A140559 (program): Primes p such that p + 34 is not a prime.
  • A140560 (program): Primes p such that p + 30 is not a prime.
  • A140562 (program): Primes p such that p + 26 is not a prime.
  • A140563 (program): Primes p such that p + 38 is not a prime.
  • A140575 (program): Triangle read by rows: the coefficient of [x^k] of the polynomial 1-(x-1)^n in row n and column k, 0<=k<n.
  • A140576 (program): Numbers of the form i*9^j-1 (i=1..8, j >= 0).
  • A140579 (program): Triangle read by rows, A014963(n) * 0^(n-k); 1<=k<=n.
  • A140580 (program): a(n) = (n^2)/A048671(n), = n*A014963(n) = A140579 * [1, 2, 3, …].
  • A140584 (program): Row sums of A140583.
  • A140588 (program): a(n) = Bell(n) * Fibonacci(n).
  • A140589 (program): Triangle A(k,n) = (-2)^k+2^n read by rows.
  • A140590 (program): Exchange successive pairs of terms of A000051.
  • A140592 (program): a(n) = 2n if A010060(n-1) is 0, and a(n) = 2n+1 if A010060(n-1) is 1.
  • A140612 (program): Integers k such that both k and k+1 are the sum of 2 squares.
  • A140633 (program): Primes of the form 7x^2+4xy+52y^2.
  • A140642 (program): Triangle of sorted absolute values of Jacobsthal successive differences.
  • A140643 (program): First differences of A140642.
  • A140647 (program): Number of car parking assignments of n cars in n spaces, if one car does not park.
  • A140649 (program): Triangle whose rows are decreasing powers of 2, followed by 0.
  • A140651 (program): A140579^(-1) * A000290, the squares starting (1, 4, 9, …).
  • A140652 (program): Partial sums of A062968.
  • A140653 (program): A triangular sequence of cyclotomic polynomial doubling: For cyclotomic polynomial:c(x,n) p(x,n)=c(x,Prime[n])*c(x,2*Prime[n]).
  • A140655 (program): Primes congruent to 53 or 157 mod 210.
  • A140657 (program): Powers of 2 with 3 alternatingly added and subtracted.
  • A140659 (program): a(n) = floor(A140657(n+2)/10).
  • A140660 (program): a(n) = 3*4^n + 1.
  • A140662 (program): Number of possible column states for self-avoiding polygons in a slit of width n.
  • A140664 (program): a(n) = A014963(n)*mobius(n).
  • A140668 (program): a(n) = n + A140664(n).
  • A140670 (program): a(n) = 1 if n is odd; otherwise, a(n) = 2^k - 1 where 2^k is the largest power of 2 that divides n.
  • A140672 (program): a(n) = n*(3*n + 13)/2.
  • A140673 (program): a(n) = 3*n*(n + 5)/2.
  • A140674 (program): a(n) = n*(3*n + 17)/2.
  • A140675 (program): a(n) = n*(3*n + 19)/2.
  • A140676 (program): a(n) = n*(3*n + 4).
  • A140677 (program): a(n) = n*(3*n + 8).
  • A140678 (program): a(n) = n*(3*n + 10).
  • A140679 (program): a(n) = n*(3*n+14).
  • A140680 (program): a(n) = n*(3*n+16).
  • A140681 (program): a(n) = 3*n*(n+6).
  • A140682 (program): Triangle T(n,k) = gcd(n,k)-binomial(n,k), 0<=k<=n.
  • A140683 (program): a(n) = 3*(-1)^(n+1)*2^n - 1.
  • A140684 (program): A037481 mod 10.
  • A140685 (program): Triangle T(n,k) read by rows: T = 1 if n is odd and k=(n-1)/2; T = 2 otherwise.
  • A140689 (program): a(n) = n*(3*n + 20).
  • A140694 (program): A014963(n) * A063659(n).
  • A140697 (program): Mobius transform of A000082.
  • A140699 (program): Triangle read by rows: A054524*A140256.
  • A140700 (program): Row products of A140699.
  • A140701 (program): Product of first n centered triangular numbers.
  • A140702 (program): Main diagonal of array A(k,n) = product of first n centered n-gonal numbers.
  • A140703 (program): A000012 * A051731^3.
  • A140706 (program): A054525 * A014683; a(n) = Sum_{d|n} mu(d)*A014683(n/d).
  • A140707 (program): A positive integer n is included if n written in binary contains the same number of 0’s as the number of distinct primes that divide n.
  • A140709 (program): Triangle read by rows: T(n,k) is the number of deco polyominoes of height n in which the maximal number of initial consecutive columns ending at the same level is k (1 <= k <= n).
  • A140710 (program): Number of maximal initial consecutive columns ending at the same level, summed over all deco polyominoes of height n.
  • A140712 (program): Number of white corners in all permutations of {1,2,…,n} (for definition see the Eriksson-Linusson references).
  • A140716 (program): Blocky integers, i.e., integers m > 1 such that there is a run of m consecutive integer squares the average of which is a square.
  • A140719 (program): Primes of form n^3-(n+1)^2.
  • A140720 (program): The length of the n-th run of identical consecutive values of A112325.
  • A140721 (program): Alternated reading of A000302 and negated A002042.
  • A140724 (program): Period 10: 1, 5, 9, 7, 7, 9, 5, 1, 3, 3 repeated.
  • A140725 (program): Inverse binomial transform of (0 followed by A037481).
  • A140727 (program): Expansion of (phi(q) * phi(q^15) - phi(q^3) * phi(q^5)) / 2 in powers of q where phi() is a Ramanujan theta function.
  • A140728 (program): Expansion of (phi(-q^3) * phi(-q^5) - phi(-q) * phi(-q^15)) / 2 in powers of q where phi() is a Ramanujan theta function.
  • A140729 (program): Diagonal A(n,n) of array A(k,n) = Product of first n of k-gonal pyramidal numbers.
  • A140730 (program): a(4*n)=5^n, a(4*n+1)=2*5^n, a(4*n+2)=3*5^n, a(4*n+3)=4*5^n.
  • A140736 (program): Triangle read by rows, X^n * [1,0,0,0,…]; where X = a tridiagonal matrix with (1,0,1,0,1,…) in the main diagonal and (1,1,1,…) in the sub- and subsubdiagonals.
  • A140737 (program): Triangle read by rows, X^n * [1,0,0,0,…]; where X = an infinite tridiagonal matrix with (1,1,1,…) in the main and subdiagonals and (1,0,1,0,1,…) in the subsubdiagonal.
  • A140740 (program): Triangle read by rows: T(n,n) = 1 and for k with 1 <= k < n: T(n+1,k) = T(n,k) + T(n - n mod k, k).
  • A140741 (program): Sums of rows of the triangle in A140740.
  • A140743 (program): Primes congruent to 79 or 131 mod 210.
  • A140747 (program): a(n) is the number of divisors of n that are coprime to the next larger divisor of n.
  • A140748 (program): a(n) is the number of divisors of n that are not coprime to the next larger divisor of n.
  • A140750 (program): Triangle read by rows, X^n * [1,0,0,0,…]; where X = an infinite tridiagonal matrix with (1,0,1,0,1,…) in the main and subsubdiagonals and (1,1,1,…) in the subdiagonal.
  • A140751 (program): Triangle read by rows, X^n * [1,0,0,0,…] where X = an infinite tridiagonal matrix with (1,0,1,0,1,…) in the main and subdiagonals and (1,1,1,…) in the subsubdiagonal.
  • A140756 (program): Count up to k sequence with alternating signs (k always positive).
  • A140757 (program): Cumulative sums of A140756.
  • A140758 (program): a(n) = floor(n*Pi/2).
  • A140765 (program): Array T(n,k) = binomial(k+2, k-1) + n*binomial(k+2, k) read by antidiagonals.
  • A140766 (program): a(n) = 6*a(n-1) - 6*a(n-2).
  • A140770 (program): 3D analog of A081113: the number of (n-1)-step paths a 3D chess king can make starting from one face of the n X n X n cube to the opposite one.
  • A140773 (program): Consider the products of all pairs of (not necessarily distinct) positive divisors of n. a(n) is the number of these products that divide n. a(n) also is the number of the products that are divisible by n.
  • A140776 (program): A number n is included if (p + n/p) is prime, where p is the largest prime that divides n.
  • A140777 (program): a(n) = 2*prime(n) - 4.
  • A140780 (program): a(n) = 10*a(n-1) - a(n-2).
  • A140781 (program): a(n) = 10*a(n-1) - a(n-2).
  • A140782 (program): a(n) = sigma(n) * Kronecker(13, n).
  • A140783 (program): Digit sum of A091137(n).
  • A140785 (program): a(n) = the single integer k, where p(n) <= k <= p(n+1), that is divisible by (p(n+1)-p(n)+1), where p(n) is the n-th prime.
  • A140787 (program): Expansion of 1 / ( (1+x)*(2*x+1)*(-1+2*x)^2 ).
  • A140788 (program): a(n) = 6*4^n + 2.
  • A140796 (program): a(n)=a(n-1)+6a(n-2), n>2.
  • A140801 (program): a(0)=360, a(n)=a(n-1)+720 for n>=1.
  • A140802 (program): a(n) = binomial(n+3, 3)*8^n.
  • A140805 (program): Positive triangular sequence of coefficients inspired by the Belyi transform: x’->(m + n)^(n + m)*x^m*(1 - x)^n/(m^m*n^n): t(n,m)=Binomial[n, m]^Binomial[n, m].
  • A140806 (program): Expansion of x *(1+x) *(x^2+1) *(15*x^4+1) / ( (x^4-2*x^3+2*x^2+2*x+1) *(x^4+2*x^3+2*x^2-2*x+1) ).
  • A140807 (program): a(n) is the largest integer such that n^k is palindromic in binary for all nonnegative integers k that are <= a(n).
  • A140808 (program): a(n) is the smallest composite of the form n*k - 1.
  • A140811 (program): a(n) = 6*n^2 - 1.
  • A140812 (program): a(n) = A051717(2n) + A051717(2n+1).
  • A140814 (program): a(0)=3, a(n)=A002445(n) for n >= 1.
  • A140816 (program): A third of digital roots of Bernoulli number denominators.
  • A140818 (program): Coefficients of Hodge diamond binomial ‘X’ matrices as polynomials: matrix example; M={{1,0,1}. {0,2,0], {1,0,1}: M(d, x, y)= Sum[Sum[If[n == m, Binomial[d - 1, m - 1], If[n == d - m + 1, Binomial[d - 1, n - 1], 0]]*x^(n - 1)*y^(m - 1), {n, 1, d}], {m, 1, d}] .
  • A140819 (program): Coefficients of Hodge diamond GCD ‘X’ matrices as polynomials: matrix example; M={{2,0,2}. {0,1,0], {2,0,2}: M(d, x, y)= Sum[Sum[If[n == m, GCD[d - 1, m - 1], If[n == d - m + 1, GCD[d - 1, n - 1], 0]]*x^(n - 1)*y^(m - 1), {n, 1, d}], {m, 1, d}] .
  • A140822 (program): Triangle T(n,m) = binomial(n,gcd(n,m)) read by rows, 0<=m<=n.
  • A140823 (program): Natural numbers which are not perfect fourth powers.
  • A140824 (program): Expansion of (x-x^3)/(1-3*x+2*x^2-3*x^3+x^4).
  • A140826 (program): Arithmetic nondivisor means.
  • A140827 (program): Interleave denominators and numerators of convergents to sqrt(3).
  • A140828 (program): a(0)=1, a(n) = ceiling(prime(n)/a(n-1)), where prime(n) is the n-th prime.
  • A140829 (program): a(0)=1; for n >= 1, a(n) = ceiling(Fibonacci(n)/a(n-1)).
  • A140832 (program): a(0) = 1; if a(n) is even, a(n + 1) = 5a(n)/2; if a(n) is odd, a(n + 1) is 5a(n)/2 rounded to the nearest even integer.
  • A140833 (program): Sum of Fibonacci numbers between F(-n)….F(n), inclusive.
  • A140835 (program): A triangular sequence from a vector a(n) times a triangular tensor t(n,m): T(n,m)=a(n).t(n,m); a(n)=Fibonacci(n);A000045(n): t(n,m)=Binomial(n,GCD(n,m)).
  • A140840 (program): Primes of the form 210n+11.
  • A140841 (program): Primes of the form 210n + 13.
  • A140842 (program): Primes of the form 210k + 17.
  • A140843 (program): Primes of the form 210k + 19.
  • A140844 (program): Primes of the form 210k + 23.
  • A140845 (program): Primes of the form 210k + 29.
  • A140846 (program): Primes of the form 210k + 31.
  • A140847 (program): Primes of the form 210k + 37.
  • A140848 (program): Primes of the form 210k + 41.
  • A140849 (program): Primes of the form 210k + 43.
  • A140850 (program): Primes of the form 210k + 47.
  • A140851 (program): Primes of the form 210k + 53.
  • A140852 (program): Primes of the form 210k + 59.
  • A140853 (program): a(n) = prime(prime(n) - 1) - 1, where prime(n) is the n-th prime.
  • A140854 (program): Primes of the form 210k + 61.
  • A140855 (program): Primes of the form 210k + 67.
  • A140856 (program): Primes of the form 210n+71.
  • A140857 (program): Primes of the form 210k + 73.
  • A140868 (program): a(n) = floor(floor(n*alpha)*alpha) where alpha = 1+sqrt(2) = A014176.
  • A140869 (program): Triangle read by rows where T(m,n) = floor((2mn+m+n-2)/2), m >= n >= 1.
  • A140870 (program): 8*P_4(2n), 8 times the Legendre Polynomial of order 4 at 2n.
  • A140874 (program): Triangle T(n,k) = binomial(n,k+2)-2*binomial(n,k+1)-binomial(n,k) read by rows, 0<=k<=n-2, n>=2.
  • A140880 (program): Triangle read by rows, T(n,k) = Gamma(n+3)/(Gamma(k+1)*Gamma(n-k+1)) for n>=0 and 0<=k<=n.
  • A140883 (program): Triangle T(n,k) = A053120(n,k)+A053120(n,n-k) of symmetrized Chebyshev coefficients, read by rows, 0<=k<=n.
  • A140887 (program): Number of nonprimes in [30n - 30, 30n] coprime to 30.
  • A140890 (program): a(n) = sum of primes in {10*n-9, 10*n-7, 10*n-3, 10*n-1}.
  • A140898 (program): Expansion of -x^2/(136*x^2+2*x-1).
  • A140899 (program): A140724(n+4). Period 10: repeat 7, 9, 5, 1, 3, 3, 1, 5, 9, 7.
  • A140900 (program): A nonnegative integer n is included if the binary representation of n and the digit-reversal (with leading 0’s) of the binary representation of n do not have any 1’s in the same position.
  • A140901 (program): Number of 3 X 5 matrices with elements in 0..n with each row and each column in nondecreasing order. 3,5,n can be permuted, see formula.
  • A140902 (program): Number of 4 X 5 matrices with elements in 0..n with each row and each column in nondecreasing order. 4,5,n can be permuted, see formula.
  • A140903 (program): Number of 3 X 6 matrices with elements in 0..n with each row and each column in nondecreasing order. 3,6,n can be permuted, see formula.
  • A140904 (program): Number of 4 X 6 matrices with elements in 0..n with each row and each column in nondecreasing order. 4,6,n can be permuted, see formula.
  • A140905 (program): Number of 5 X 6 matrices with elements in 0..n with each row and each column in nondecreasing order. 5,6,n can be permuted, see formula.
  • A140906 (program): Number of 6 X 6 matrices with elements in 0..n with each row and each column in nondecreasing order. 6,6,n can be permuted, see formula.
  • A140907 (program): Number of 3 X 7 matrices with elements in 0..n with each row and each column in nondecreasing order. 3,7,n can be permuted, see formula.
  • A140908 (program): Number of 4 X 7 matrices with elements in 0..n with each row and each column in nondecreasing order. 4,7,n can be permuted, see formula.
  • A140909 (program): Number of 5 X 7 matrices with elements in 0..n with each row and each column in nondecreasing order. 5,7,n can be permuted, see formula.
  • A140910 (program): Number of 6 X 7 matrices with elements in 0..n with each row and each column in nondecreasing order. 6,7,n can be permuted, see formula.
  • A140911 (program): Number of 7 X 7 matrices with elements in 0..n with each row and each column in nondecreasing order. 7,7,n can be permuted, see formula.
  • A140912 (program): Number of 3 X 8 matrices with elements in 0..n with each row and each column in nondecreasing order. 3,8,n can be permuted, see formula.
  • A140913 (program): Number of 4 X 8 matrices with elements in 0..n with each row and each column in nondecreasing order. 4,8,n can be permuted, see formula.
  • A140914 (program): Number of 5 X 8 matrices with elements in 0..n with each row and each column in nondecreasing order. 5,8,n can be permuted, see formula.
  • A140915 (program): Number of 6 X 8 matrices with elements in 0..n with each row and each column in nondecreasing order. 6,8,n can be permuted, see formula.
  • A140918 (program): Number of 3 X 9 matrices with elements in 0..n with each row and each column in nondecreasing order. 3,9,n can be permuted, see formula.
  • A140919 (program): Number of 4 X 9 matrices with elements in 0..n with each row and each column in nondecreasing order. 4,9,n can be permuted, see formula.
  • A140920 (program): Number of 5 X 9 matrices with elements in 0..n with each row and each column in nondecreasing order. 5,9,n can be permuted, see formula.
  • A140921 (program): Number of 6 X 9 matrices with elements in 0..n with each row and each column in nondecreasing order. 6,9,n can be permuted, see formula.
  • A140925 (program): a(n) = binomial(m+n-1,n)^2 - binomial(m+n,n+1)*binomial(m+n-2,n-1) with m=12.
  • A140926 (program): Number of 3 X 10 matrices with elements in 0..n with each row and each column in nondecreasing order. 3,10,n can be permuted, see formula.
  • A140927 (program): Number of 4 X 10 matrices with elements in 0..n with each row and each column in nondecreasing order. 4,10,n can be permuted, see formula.
  • A140928 (program): Number of 5 X 10 matrices with elements in 0..n with each row and each column in nondecreasing order. 5,10,n can be permuted, see formula.
  • A140934 (program): Number of 2 X 11 matrices with elements in 0..n with each row and each column in nondecreasing order. 2,11,n can be permuted, see formula.
  • A140935 (program): Number of 3 X 11 matrices with elements in 0..n with each row and each column in nondecreasing order.
  • A140936 (program): Number of 4 X 11 matrices with elements in 0..n with each row and each column in nondecreasing order. 4,11,n can be permuted, see formula.
  • A140937 (program): Number of 5 X 11 matrices with elements in 0..n with each row and each column in nondecreasing order. 5,11,n can be permuted, see formula.
  • A140938 (program): Number of 6 X 11 matrices with elements in 0..n with each row and each column in nondecreasing order. 6,11,n can be permuted, see formula.
  • A140944 (program): Triangle T(d,n) read by rows, the n-th term of the d-th differences of the Jacobsthal sequence A001045.
  • A140946 (program): Triangle T(n,k) = (-2)^n*(-1)^k if k<n; T(n,n) = (-1)^(n+1)*A001045(n+1).
  • A140949 (program): a(n) = number of iterations of k -> k-1/k until we reach a negative number, starting at n.
  • A140950 (program): a(n) = A140944(n+1) - 3*A140944(n).
  • A140951 (program): Based on Jacobsthal numbers. Increasing order of different positive terms of A140950.
  • A140952 (program): Expansion of 1/((1-x^2)*(1-x^3)*(1-x^5)*(1-x^7)*(1-x^11)).
  • A140953 (program): Expansion of 1/((1-x^2)*(1-x^3)*(1-x^5)*(1-x^7)*(1-x^11)*(1-x^13)).
  • A140957 (program): a(n) = A140951(n+1) - A140951(n).
  • A140960 (program): a(n) = (2*(-1)^n - 2^(n+1) + 3*n*2^n)/9.
  • A140961 (program): Number of 3 X n {0,1}-matrices such that: (a) first and second row have a common 1, (b) second and third row have a common 1.
  • A140962 (program): Negative values of the Inverse binomial transform of A045883.
  • A140966 (program): a(n) = (5 + (-2)^n)/3.
  • A140969 (program): Prime numbers whose hexadecimal representation uses only the digits A,B,C,D,E,F (and not the decimal digits).
  • A140971 (program): Numbers n such that arithmetic mean of squares of the first n nonzero Fibonacci numbers is an integer.
  • A140975 (program): Period length 20: repeat 1, 3, 8, 8, 9, 1, 6, 6, 7, 9, 4, 4, 5, 7, 2, 2, 3, 5, 0, 0.
  • A140976 (program): Period length 10: repeat 8, 8, 6, 6, 4, 4, 2, 2, 0, 0.
  • A140978 (program): Repeat (n+1)^2 n times.
  • A140979 (program): a(n) = floor(2*phi*floor(n*phi)) where phi = A001622.
  • A140980 (program): Number of (4,2)-noncrossing partitions of [n].
  • A140990 (program): Half the number of n X n binary matrices having equal row sums.
  • A140991 (program): a(n) = (1/9)*(7*2^n + (-1)^n*(3*n+2)) - (n-1)^2.
  • A140992 (program): a(0) = 0, a(1) = 1; for n > 1, a(n) = a(n-2) + a(n-1) + A000071(n+1).
  • A141012 (program): a(0) = 0, a(n) = 13^(n-1) + 1.
  • A141013 (program): E.g.f. Sum_{d|M} (exp(d*x)-1)/d, M=14.
  • A141014 (program): E.g.f. Sum_{d|M} (exp(d*x)-1)/d, M=15.
  • A141015 (program): a(0) = 0, a(1) = 1, a(2) = 2; for n > 2, a(n) = a(n-1) + 2*a(n-2) + a(n-3).
  • A141022 (program): a(n) = n mod ((sum of digits of n)+1).
  • A141023 (program): a(n) = 2^n - (3-(-1)^n)/2.
  • A141025 (program): a(n) = (2^(2+n)-(-1)^n)/3 - 2*n.
  • A141026 (program): Numbers n such that (n,n+8) forms a pair of consecutive primes ending respectively in 1 and 9.
  • A141032 (program): a(n) = 4*(16^n-1)/15.
  • A141035 (program): Period 10: repeat 0, 0, 4, 2, -2, 4, 2, -4, -4, -2.
  • A141036 (program): Tribonacci-like sequence; a(0)=2, a(1)=1, a(2)=1, a(n) = a(n-1) + a(n-2) + a(n-3).
  • A141038 (program): Padovan-like sequence; a(0)=2, a(1)=1, a(2)=1, a(n) = a(n-2) + a(n-3).
  • A141041 (program): a(n) = ((3 + 2*sqrt(3))^n + (3 - 2*sqrt(3))^n)/2.
  • A141042 (program): Product of n and the n-th gap between primes: a(n) = n*A001223(n).
  • A141043 (program): Number of sequences of length n whose terms are positive integers less than or equal to n in which the i-th term is greater than both the (i-2)nd and (i-3)rd terms.
  • A141044 (program): Two 2’s followed by all 1’s.
  • A141046 (program): a(n) = 4*n^4.
  • A141052 (program): Number of runs or rising sequences of length 2 among all permutations of n.
  • A141053 (program): Most-significant decimal digit of Fibonacci(5n+3).
  • A141054 (program): 8-idempotent numbers: a(n) = binomial(n+8,8)*8^n.
  • A141055 (program): The n-th differences of the row A141045(n,.).
  • A141056 (program): 1 followed by A027760, a variant of Bernoulli number denominators.
  • A141057 (program): Number of Abelian cubes of length 3n over an alphabet of size 3. An Abelian cube is a string of the form x x’ x’’ with |x| = |x’| = |x’’| and x is a permutation of x’ and x’’.
  • A141059 (program): Number of numbers m such that n = 0 (mod usigma(m)), where usigma(m) is the sum of unitary divisors of m (A034448).
  • A141060 (program): Fourth quadrisection of Jacobsthal numbers A001045: a(n)=16a(n-1)-5.
  • A141061 (program): Number of primes between n*p(n) and (n+1)*p(n+1), where p(n) is the n-th prime.
  • A141062 (program): a(n) = (prime(n) - 1) mod (sum of digits of prime(n)).
  • A141063 (program): a(n) = n mod (sum of digits of prime(n)).
  • A141071 (program): a(n) = prime(n) mod (sum of base-10 digits of n) where prime(n) is the n-th prime.
  • A141072 (program): Sum of diagonal numbers in a Pascal-like triangle with index of asymmetry y = 3 and index of obliquity z = 0 (going upwards, left to right).
  • A141083 (program): a(n) = 2^(p - 2)*(2^p - 2), where p = prime(n).
  • A141086 (program): a(n) = prime(2*n^2) - 2*n^2.
  • A141093 (program): p(p(2*n)-n*2)-n*2, where p(n)=n-th prime.
  • A141094 (program): Expansion of b(q) / b(q^2) in powers of q where b() is a cubic AGM theta function.
  • A141099 (program): Number of unordered pairs of odd nonprime numbers that sum to 2n.
  • A141100 (program): Number of unordered pairs of odd composite numbers that sum to 2n.
  • A141101 (program): a(n) = prime(2n) - 2n.
  • A141104 (program): Lower Even Swappage of Upper Wythoff Sequence.
  • A141105 (program): Upper Even Swappage of Upper Wythoff Sequence.
  • A141106 (program): Lower Odd Swappage of Upper Wythoff Sequence.
  • A141107 (program): Upper Odd Swappage of Upper Wythoff Sequence.
  • A141109 (program): Even numbers 2n such that for every prime p in [n,2n-2], 2n-p is also prime.
  • A141113 (program): Positive integers k such that d(d(k)) divides k, where d(k) is the number of divisors of k.
  • A141114 (program): Positive integers k where d(d(k)) is coprime to k, where d(k) is the number of divisors of k.
  • A141123 (program): Primes of the form -x^2+2*x*y+2*y^2 (as well as of the form 3*x^2+6*x*y+2*y^2).
  • A141124 (program): Hankel transform of a transform of Jacobsthal numbers.
  • A141125 (program): Hankel transform of a transform of Fibonacci numbers.
  • A141129 (program): a(n) = prime(n^2) - n^2.
  • A141133 (program): p(p(p(A028815(n)-1)-1)-1)-1, where p(n)=n-th prime.
  • A141134 (program): Hankel transform of C(2n+4,n+4).
  • A141135 (program): Minimal number of unit edges required to construct n regular pentagons when allowing edge-sharing.
  • A141136 (program): p(p(A028815(n)-1)-1)-1, where p(n)=n-th prime.
  • A141138 (program): p(A028815(n)-1)-1, where p(n)=n-th prime.
  • A141147 (program): Number of linear arrangements of n blue, n red and n green items such that the first item is blue and there are no adjacent items of the same color (first and last elements considered as adjacent).
  • A141151 (program): L.g.f.: A(x) = log( Sum_{n>=0} n^n*x^n ) = Sum_{n>=1} a(n)*x^n/n.
  • A141152 (program): L.g.f.: A(x) = log( 1 + Sum_{n>=1} n^(n-1)*x^n ) = Sum_{n>=1} a(n)*x^n/n.
  • A141154 (program): L.g.f.: A(x) = log( 1 + Sum_{n>=1} (n-1)!*x^n ) = Sum_{n>=1} a(n)*x^n/n.
  • A141155 (program): Triangle read by rows, A140207 * A000012.
  • A141156 (program): Row sums of triangle A141155.
  • A141159 (program): Duplicate of A139492.
  • A141160 (program): Primes of the form -x^2 + 3*x*y + 3*y^2 (as well as of the form 5*x^2 + 9*x*y + 3*y^2).
  • A141164 (program): Numbers having exactly 1 divisor of the form 8*k + 7.
  • A141169 (program): Triangle of Fibonacci numbers, read by rows: T(n,k) = A000045(k), 0<=k<=n.
  • A141170 (program): Primes of the form x^2+4*x*y-2*y^2 (as well as of the form 3*x^2+6*x*y+y^2).
  • A141171 (program): Primes of the form -x^2+4*x*y+2*y^2 (as well as of the form 5*x^2+8*x*y+2*y^2).
  • A141172 (program): Primes of the form 2*x^2+2*x*y-3*y^2 (as well as of the form 2*x^2+6*x*y+y^2).
  • A141173 (program): Primes of the form -2*x^2+2*x*y+3*y^2 (as well as of the form 6*x^2+10*x*y+3*y^2).
  • A141187 (program): Primes of the form -x^2+6*x*y+3*y^2 (as well as of the form 8*x^2+12*x*y+3*y^2).
  • A141194 (program): Primes of the form 16k+7.
  • A141195 (program): Primes of the form 16k+11.
  • A141196 (program): Primes of the form 16k+13.
  • A141197 (program): a(n) = the number of divisors of n that are each one less than a power of a prime.
  • A141198 (program): a(n) = the number of divisors of n that are each one more than a power of a prime.
  • A141208 (program): a(n) = prime(prime(prime(n) - 1) - 1) - 1, where prime(n) = n-th prime.
  • A141210 (program): Triangle read by rows, A140207^2.
  • A141211 (program): Row sums of triangle A141210.
  • A141212 (program): a(n) = 1, if n == {1,3,4} mod 6; otherwise 0.
  • A141213 (program): Defining A to be the interior angle of a regular polygon, the number of constructible regular polygons such that A is in a field extension = degree 2^n, starting with n=0. This is also the number of values of x such that phi(x)/2 = 2^n (where phi is Euler’s phi function), also starting with n=0.
  • A141214 (program): Defining A to be the interior angle of a regular polygon, the number of constructible regular polygons such that A is in a field extension <= degree 2^n, starting with n=0. This is also the number of values of x such that phi(x)/2 is a power of 2 <= 2^n (where phi is Euler’s phi function), also starting with n=0.
  • A141217 (program): a(n) = prime(prime(prime(prime(n) - 1) - 1) - 1) - 1, where prime(n) is the n-th prime.
  • A141221 (program): Number of ways for each of 2n (labeled) people in a circle to look at either a neighbor or the diametrally opposite person, such that no eye contact occurs.
  • A141222 (program): Expansion of -1/(2*x) + (2*x-1)^2/(2*x*(1-4x)^(3/2)).
  • A141223 (program): Expansion of 1/(sqrt(1-4*x)*(1-3*x*c(x))), where c(x) is the g.f. of A000108.
  • A141241 (program): a(n) = number of divisors of n-th positive integer with a nonprime number of divisors. a(n) = the number of divisors of A139118(n).
  • A141242 (program): a(n) is the number of divisors of the n-th positive integer with a prime number of divisors. In other words a(n) is the number of divisors of A009087(n).
  • A141244 (program): Numerators in the expansion of (1-sqrt(1-x^2))/(1-x).
  • A141245 (program): Numerators in expansion of (1+x-sqrt(1-x^2))/(x(1-x)).
  • A141253 (program): Number of permutations that lie in the cyclic closure of Av(132)–i.e., at least one cyclic rotation of the permutation avoids the pattern 132.
  • A141259 (program): a(n) == {0,1,3,4,5,7,9,11} mod 12; n>0.
  • A141260 (program): a(n) = 1 if n == {0,1,3,4,5,7,9,11} mod 12, otherwise a(n) = 0.
  • A141262 (program): Mancala numbers that are prime numbers.
  • A141275 (program): Composite indices associated with A141274.
  • A141276 (program): a(n) = A338038(A002808(n)).
  • A141285 (program): Largest part of the n-th partition of j in the list of colexicographically ordered partitions of j, if 1 <= n <= A000041(j).
  • A141289 (program): Triangle read by rows, n-th row = (n-2)-th row appended to the beginning of (n-1)-th row, + n.
  • A141290 (program): Triangle read by rows, descending antidiagonals of a (1, 3, 5, …) * (1, 4, 16, …) multiplication table.
  • A141291 (program): a(n) = 4*a(n-1) + 2*n-1
  • A141293 (program): Primes p of the form 4*k+1 which are not of the form r^2 + 1.
  • A141295 (program): Largest m<=n such that all k with 1<=k<=m are divisors of n or coprime to n.
  • A141302 (program): Primes of the form -x^2+6*x*y+6*y^2 (as well as of the form 11*x^2+18*x*y+6*y^2).
  • A141303 (program): Primes of the form 2*x^2+6*x*y-3*y^2 (as well as of the form 5*x^2+10*x*y+2*y^2).
  • A141304 (program): Primes of the form -2*x^2+6*x*y+3*y^2 (as well as of the form 7*x^2+12*x*y+3*y^2).
  • A141307 (program): Number of bicolored connected permutations.
  • A141310 (program): The odd numbers interlaced with the constant-2 sequence.
  • A141313 (program): Number of connected 2-colored parking functions.
  • A141317 (program): a(n) = A000244(n) - A010684(n).
  • A141321 (program): a(n) = -A141055(n)/(n+1)!.
  • A141324 (program): Sum of digits of A002452(n).
  • A141325 (program): a(n) = A000045(n) + A131531(n+3).
  • A141326 (program): Subsequence of ‘Fermat near misses’ which is generated by a simple formula based on the cubic binomial expansion along with formulas for the corresponding terms in the expression, x^3 + y^3 = z^3 + 1.
  • A141340 (program): Positive integers n such that A061358(n) = #{primes p | n/2 <= p < n-1}.
  • A141341 (program): Totally Goldbach numbers: Positive integers n such that for all primes p < n-1 with p not dividing n, n-p is prime.
  • A141342 (program): A transform of the Fibonacci numbers.
  • A141344 (program): Expansion of (2-sqrt(1+4x))/(2-x-sqrt(1+4x)).
  • A141351 (program): a(n)=C(n)+1-0^n where C(n)=A000108(n).
  • A141352 (program): Expansion of (1-2x-5x^2-7x^3+x^6)/((1-x)(1-x^3)^2).
  • A141353 (program): a(n) = Catalan(n) + 2^n - 0^n.
  • A141354 (program): Expansion of (1-5*x-x^2+x^3)/((1+x)*(1-x)^3).
  • A141355 (program): The Jacobsthal sequence, dropping each third term.
  • A141364 (program): a(n)=C(n)-1+0^n where C(n)=A000108(n).
  • A141365 (program): Expansion of (1-5x^2-7x^3-2x^4+x^6)/((1-x)(1-x^3)^2).
  • A141368 (program): G.f.: Sum_{n>=0} arctanh(4^n*x)^n/n!, a power series in x having only integer coefficients.
  • A141369 (program): E.g.f. satisfies: A(x) = exp(x*A(-x)).
  • A141373 (program): Primes of the form 3*x^2+16*y^2. Also primes of the form 4*x^2+4*x*y-5*y^2 (as well as primes the form 4*x^2+12*x*y+3*y^2).
  • A141375 (program): Primes of the form x^2 + 8*x*y - 8*y^2 (as well as of the form x^2 + 10*x*y + y^2).
  • A141376 (program): Primes of the form -x^2 + 8*x*y + 8*y^2 (as well as of the form 15*x^2 + 24*x*y + 8*y^2).
  • A141384 (program): Trace of the n-th power of a certain 8X8 adjacency matrix.
  • A141385 (program): a(n) = 7*a(n-1) - 9*a(n-2) + a(n-3) with a(0)=3, a(1)=7, a(2)=31.
  • A141387 (program): Triangle read by rows: T(n,m) = n + 2*m*(n - m) (0 <= m <= n).
  • A141388 (program): Triangle T(n, k) = ( k*(n-k+1) )^3 - 2^(n-1), read by rows.
  • A141396 (program): Triangle read by rows, antidiagonals of a multiplication table: 3^n * (numbers not multiples of 3).
  • A141397 (program): a(n) = 3*a(n-1) + A001651(n+1).
  • A141402 (program): Triangle T(n, k) = n^2 + (2*k*(n-k))^2, read by rows.
  • A141407 (program): a(n) = binomial(n+7,7)*6^n.
  • A141410 (program): Denominator of A027760(n+1)/n.
  • A141413 (program): Inverse binomial transform of A140962.
  • A141416 (program): First differences of A133730.
  • A141418 (program): Triangle read by rows: T(n,k) = k * (2*n - k - 1) / 2, 1 <= k <= n.
  • A141419 (program): Triangle read by rows: T(n, k) = A000217(n) - A000217(n - k) with 1 <= k <= n.
  • A141421 (program): First bisection of A091137.
  • A141425 (program): Period 6: repeat [1, 2, 4, 5, 7, 8].
  • A141426 (program): Count of numbers smaller than and coprime to the prime A140555(n).
  • A141427 (program): a(n) = phi(A067775(n).
  • A141429 (program): Triangle T(n, k) = (k+1)*(n-k+1), read by rows.
  • A141430 (program): a(n) = A000111(n) mod 9.
  • A141431 (program): Triangle T(n,k) = (k-1)*(3*n-k+1), read by rows.
  • A141432 (program): Triangle T(n,k) = (k+1)*(n-k-1) read by rows.
  • A141433 (program): Triangle T(n, k) = (k-1)*(3*n-k), read by rows.
  • A141434 (program): Triangle T(n, k) = (k-1)*(3*n-k-1), read by rows.
  • A141446 (program): A102055(n) mod 9.
  • A141448 (program): Generalized Pell numbers P(n,5,5).
  • A141449 (program): A005439 mod 9.
  • A141454 (program): A Legendre symbol type assignment of the modulo ten primes to the polynomial: Expand[(x-1)*(x+1)*(x-2)*(x+2)*(x-0)]=4 x - 5 x^3 + x^5; c(n) = If[Mod[n, 10] == 1, 1, If[Mod[n, 10] == 9, -1, If[Mod[n, 10] == 3, 2, If[Mod[n, 10] == 7, -2, 0]]]] such that n is a prime[n].
  • A141458 (program): a(n) = A000111(2n) + A000111(2n+1).
  • A141459 (program): a(n) = Product_{p-1 divides n} p, where p is an odd prime.
  • A141460 (program): A086892(11*n).
  • A141468 (program): Zero together with the nonprime numbers A018252.
  • A141476 (program): Triangle T(n,k) = A000142(n-k)*A003319(k+1) read by rows.
  • A141478 (program): a(n) = Binomial(n+2,3)*4^3.
  • A141479 (program): a(n) = A000111(n) + A014695(n).
  • A141480 (program): a(n) = binomial(n+2,3)*5^3.
  • A141489 (program): Numbers n such that n^2 + n + 257 is prime.
  • A141495 (program): a(n) = 3*a(n-1) for n>2; a(0)=1, a(1)=3, a(2)=7.
  • A141496 (program): a(0)=1; a(1)=5; a(2)=11; a(n)=a(1)*a(n-1).
  • A141498 (program): A010696(n-1)* A086892(n).
  • A141499 (program): a(0)=0; a(1)=1; a(n) = triangular number at index 5*2^(n-2)-1.
  • A141501 (program): a(n) is smallest integer for which the number of integers from 1 to a(n) that are not divisors of n is greater than the number of integers from 1 to a(n) that are divisors of n.
  • A141515 (program): a(n) = phi(A067774(n)) where phi is Euler totient function.
  • A141516 (program): The main diagonal of the array of A141425 and its higher order differences.
  • A141518 (program): Period 5: repeat [1, 3, 5, 7, 9].
  • A141519 (program): Period 10: repeat [-1, 1, -3, 7, -5, 3, -7, 9, -9, 5].
  • A141520 (program): a(1) = 0, a(2) = a(3) = 1; a(n) = a(n-1)*a(n-2) + a(n-2)*a(n-3) for n > 3.
  • A141522 (program): a(1) = 0, a(2) = a(3) = 1; a(n) = a(n-1)*a(n-2) + a(n-1)*a(n-3) for n > 3.
  • A141523 (program): Expansion of (3-2*x-3*x^2)/(1-x-x^2-x^3).
  • A141527 (program): Expansion of x*(2 + x)/(1 + x + 41*x^2).
  • A141528 (program): Expansion of x/(1 + x + 41*x^2).
  • A141529 (program): A cyclotomic Binet solution for the first 11 primes: solution of a set of linear equations with cyclotomic polynomial roots; roots: r[i]->(x^11-1): a(n)=Sum[r(i)^n*c(i),{i,1,11}].
  • A141530 (program): a(n) = 4*n^3 - 6*n^2 + 1.
  • A141531 (program): Inverse binomial transform of A001651.
  • A141532 (program): Inverse binomial transform of A141425.
  • A141533 (program): The first subdiagonal of the array of A141425 and its higher order differences.
  • A141534 (program): Derived from the centered polygonal numbers: start with the first triangular number, then the sum of the first square number and the second triangular number, then the sum of first pentagonal number, the second square number and the third triangular number, and so on and so on…
  • A141537 (program): An example of a simple prime-generating formula similar to Rowland’s ( a(1) = 7, n>1, a(n) = a(n-1) + gcd(n,a(n-1) ) that is a particular instance of a more general formula. The sequence submitted is the first 20 values that do not equal ‘1’:.
  • A141539 (program): Square array A(n,k) of numbers of length n binary words with at least k “0” between any two “1” digits (n,k >= 0), read by antidiagonals.
  • A141543 (program): Triangle T(n,k) read by brows: T(n,2k)=k, T(n,2k+1) = k-n, for 0<=k<=n.
  • A141544 (program): Odd numbers k such that 2k+5 is a prime.
  • A141557 (program): Nonprimes of form (p(c(n))-c(p(n))), where c(n)=n-th composite and p(n)=n-th prime.
  • A141560 (program): Nonprimes of form (prime(n)-r(n)), where A141468(n)=r(n)=n-th nonprime and prime(n)=n-th prime.
  • A141563 (program): Primes of the form 2*3*5*7*n+79.
  • A141570 (program): Primes of the form 2*3*5*7*n+83.
  • A141571 (program): Decimal expansion of 11999/99900.
  • A141576 (program): An alternating sequence of a difference type: a(0)=-1, a(1)=0, a(2)=1, a(n) = a(n-1) - 2*a(n-2) + a(n-3).
  • A141577 (program): Alternating difference recursion: a(0) = -1; a(1) = 0; a(2) = 1; a(3) = -1; a(n) = a(n-1) - 3*a(n-2) + 3*a(n-3) - a(n-4).
  • A141582 (program): a(n) = number of ways to dispose two pawns on a chessboard of size n X n (two dispositions are equivalent if one can be rotated or reflected to give the other one).
  • A141583 (program): Squares of tribonacci numbers A000213.
  • A141588 (program): Take numerators of expansion for Debye function (D(1,x)) A120082 with 1’s instead of 0’s. Then (Bernoulli numbers numerators) A027641(n)/a(n) is an integer sequence.
  • A141590 (program): Bisection of A120082.
  • A141596 (program): Triangle T(n,k) = 4*binomial(n,k)^2-3, read by rows, 0<=k<=n.
  • A141597 (program): Triangle T(n,k) = 2*binomial(n,k)^2-1, read by rows, 0<=k<=n.
  • A141609 (program): a(n)=(a(n - 1)*a(n - 2) + a(n - 1)^2)/a(n - 3).
  • A141611 (program): A symmetrical triangle of coefficients read by rows: t(n,m)=(n - m + 1)*(m + 1)*binomial[n, m].
  • A141612 (program): Write down 0,1,2,3,…n each in binary. Total up the number of 1’s in each bit-position (total number of 1’s in 1’s position, total number of 1’s in 2’s position, total number of 1’s in 4’s position, etc.). a(n) = the number of such totals that each do not equal any other such total.
  • A141614 (program): First differences of A008846.
  • A141615 (program): Inverse binomial transform of A120070.
  • A141616 (program): Even terms in A120070.
  • A141617 (program): Triangle t(n,m) = prime(m)*prime(n-m)*binomial(n,m) read by rows, 0<=m<=n.
  • A141618 (program): Triangle read by rows: number of nilpotent partial transformations (of an n-element set) of height r (height(alpha) = |Im(alpha)|), 0 <= r < n.
  • A141619 (program): a(n) = 3*(n+1)/2 if n is odd, a(n) = prime(n/2) if n is even.
  • A141620 (program): First differences of A120070.
  • A141631 (program): a(n) = 3*n^2 - 4*n + 3.
  • A141641 (program): Digital sum of n is an even composite.
  • A141642 (program): Composite numbers whose sum of digits is a prime.
  • A141660 (program): Triangle read by rows: T(n,k) = 2^k*A123125(n,k).
  • A141662 (program): Triangle read by rows, T(n,m) = abs(n - m^2).
  • A141663 (program): Regular triangle T(n,m) = abs(prime(n) - m^2), 0 <= m <= n-1.
  • A141665 (program): A signed half of Pascal’s triangle A007318: p(x,n) = (1+I*x)^n; t(n,m) = real part of coefficients(p(x,n)).
  • A141667 (program): Number of partitions of n times number of divisors of n.
  • A141668 (program): a(n) = tau(n) * (NumberOfPartitions(n) - 1).
  • A141670 (program): a(n) = NumberOfPartitions(n) * ( tau(n)-1 ).
  • A141671 (program): A triangle of coefficients as a modular shifted triangular sequence: t(n,m) = If[m == 0, n + 1, If[Mod[n, m] == 0, n/m, 0]].
  • A141677 (program): Number of divisors of n times the number of primes <= n.
  • A141678 (program): Symmetrical triangle of coefficients based on invert transform of A001906.
  • A141679 (program): Triangle of coefficients of the inverse of A058071.
  • A141680 (program): Triangle read by rows: T(n,m) = (n/m)*binomial(n,m) if m divides n, otherwise 0.
  • A141683 (program): a(n) = Sum_{k=1..n} b(k)*a(n - k) for n >= 1, where b(n) = b(n-2) + b(n-3) for n >= 3 with b(0) = 0 and b(1) = b(2) = 1.
  • A141685 (program): a(1) = 1, a(n) = Sum_{k=1..n} (k mod 3) * a(n-k) for n >= 2.
  • A141686 (program): Triangle T(n,m) = A008292(n,m)*binomial(n-1,m-1) read by rows.
  • A141687 (program): Triangle read by rows: t(n,m) = 1 - ((prime(n) - prime(m))/2 mod 2).
  • A141689 (program): Average of Eulerian numbers (A008292) and Pascal’s triangle (A007318): t(n,m) = (A008292(n,m) + A007318(n,m))/2.
  • A141690 (program): Triangle t(n,m) = 2*A008292(n+1,m+1) - A007318(n,m), a linear combination of Eulerian numbers and Pascal’s triangle, 0 <= m <= n.
  • A141691 (program): A linear combination of Eulerian numbers (A008292) and Pascal’s triangle (A007318); t(n,m)=(3*A008292(n,m)-A007318(n,m))/2.
  • A141692 (program): Triangle read by rows: T(n,k) = n*(binomial(n - 1, k - 1) - binomial(n - 1, k)), 0 <= k <= n.
  • A141694 (program): a(n) = 22*n + 12.
  • A141695 (program): Triangle T(n,m) = A120070(n,m)-A143814(n,m) read by rows, 1<=m<n.
  • A141696 (program): Triangle read by rows, T(n, k) = ( ( 6 * Sum_{j=0..k+1} (-1)^j * binomial(n+1, j) * (k-j+1)^n ) - 4 * binomial(n-1, k) ) / 2.
  • A141697 (program): T(n,k) = (q*Sum_{j=0..k+1} (-1)^j*binomial(n+1, j)*(k+1-j)^n - p*binomial(n-1, k))/2 where p=12 and q=14.
  • A141700 (program): Triangle read by rows: A120007 interleaved with (k-1) zeros.
  • A141701 (program): Triangle read by rows: A001414 interleaved with (k-1) zeros.
  • A141719 (program): Triangle online: 4, A140978(n+1) - A133819 .
  • A141721 (program): A141631(n) mod 10.
  • A141722 (program): a(n) = 8*4^n - 7.
  • A141723 (program): Triangle T(n, k) = Sum_{j=0..n} (2*n)!/((2*n-k-j)!*j!*k!), read by rows.
  • A141725 (program): a(n) = 4^(n+1) - 3.
  • A141726 (program): Sawtooth with period length 9: repeat 8, 7, 6, 5, 4, 3, 2, 1, 0.
  • A141742 (program): Starting from the 1 in the first line of triangle A141728 choose one of the three digits below it. Repeat down to the other rows. Sequence gives the numbers in base 10 expressed by the collected digits that cannot be reached following any possible path.
  • A141747 (program): a(n) is the number of nonnegative integer pairs i,j such that n = 2^i + 3^j.
  • A141748 (program): a(n) = n-th nonnegative integer k such that there is a unique nonnegative integer pair (i,j) for which n = 2^i + 3^j.
  • A141751 (program): Triangle, read by rows, where T(n,k) = [T(n-1,k-1)*T(n-1,k) + 1]/T(n-2,k-1) for 0<k<n with T(n,n) = 1 for n>=0 and T(n,0) = Fibonacci(2*n-1) for n>=1.
  • A141752 (program): a(n) = Sum_{k=0..n} ( Fibonacci(2*k-1) + (n-k)*Fibonacci(2*k) ).
  • A141759 (program): a(n) = 16n^2 + 32n + 15.
  • A141765 (program): Triangle T, read by rows, such that row n equals column 0 of matrix power M^n where M is a triangular matrix defined by M(k+m,k) = binomial(k+m,k) for m=0..2 and zeros elsewhere. Width-2-restricted finite functions.
  • A141771 (program): Expansion of (1-sqrt(1-4*x))/(2*x) + 8*x^3/((sqrt(1-4*x))*(1+sqrt(1-4*x))^3).
  • A141775 (program): Binomial transform of (1, 2, 0, 1, 2, 0, 1, 2, 0, …).
  • A141782 (program): Number of connected graphs with one cycle of length m = n-4 and n nodes.
  • A141783 (program): Number of bracelets (turn over necklaces) with n beads: 1 blue, 12 green, and r = n - 13 red.
  • A141784 (program): Primes of the form A141468(n)-n, where A141468(n)=n-th nonprime.
  • A141785 (program): Primes of the form -x^2 + 5*x*y + 5*y^2 (as well as of the form 9*x^2 + 15*x*y + 5*y^2).
  • A141791 (program): Primes of the form c(n)-n, where c(n)=n-th composite.
  • A141792 (program): Primes of the form A018252(n)-n, where A018252(n)=n-th nonprime.
  • A141803 (program): Triangle read by rows derived from generalized Thue-Morse sequences.
  • A141804 (program): Row sums of triangle A141803.
  • A141811 (program): Partial Catalan numbers: triangle read by rows n = 1, 2, 3, … and columns k = 0, 1, …, n-1.
  • A141827 (program): a(n) = (n^3*a(n-1) - 1)/(n - 1) for n >= 2, with a(0) = 1, a(1) = 4.
  • A141828 (program): a(n) = (n^4*a(n-1)-1)/(n-1) for n >= 2, with a(0) = 1, a(1) = 5.
  • A141834 (program): Sum of the lengths of the cycles at a vertex of the complete graph K_n.
  • A141844 (program): Expansion of (1+x)*(1+x^2)/((1-x)^2*(1+x+x^2)*(1-4*x)).
  • A141845 (program): a(n) = 5*a(n-1) + A047201(n), a(1) = 1. A047201 = numbers not divisible by 5: (1, 2, 3, 4, 6, 7, 8, 9, 11, …).
  • A141846 (program): Triangle read by rows: A051731 * A051953^(n-k) * 0^(n-k), 1 <= k <= n.
  • A141849 (program): Primes congruent to 1 mod 11.
  • A141850 (program): Primes congruent to 3 mod 11.
  • A141851 (program): Primes congruent to 4 mod 11.
  • A141852 (program): Primes congruent to 5 mod 11.
  • A141853 (program): Primes congruent to 6 mod 11.
  • A141854 (program): Primes congruent to 7 mod 11.
  • A141855 (program): Primes congruent to 8 mod 11.
  • A141856 (program): Primes congruent to 9 mod 11.
  • A141857 (program): Primes congruent to 10 mod 11.
  • A141858 (program): Primes congruent to 2 mod 13.
  • A141859 (program): Primes congruent to 12 mod 13.
  • A141860 (program): Primes congruent to 2 mod 15.
  • A141865 (program): Primes congruent to 13 mod 17.
  • A141866 (program): Primes of the form 2*3*5*7*k+89, k >= 0.
  • A141868 (program): Primes congruent to 1 mod 19.
  • A141869 (program): Primes congruent to 2 mod 19.
  • A141870 (program): Primes congruent to 4 mod 19.
  • A141871 (program): Primes congruent to 6 mod 19.
  • A141872 (program): Primes congruent to 7 mod 19.
  • A141873 (program): Primes congruent to 8 mod 19.
  • A141874 (program): Primes congruent to 9 mod 19.
  • A141875 (program): Primes congruent to 10 mod 19.
  • A141876 (program): Primes congruent to 11 mod 19.
  • A141877 (program): Primes congruent to 12 mod 19.
  • A141878 (program): Primes congruent to 13 mod 19.
  • A141879 (program): Primes congruent to 14 mod 19.
  • A141880 (program): Primes congruent to 15 mod 19.
  • A141881 (program): Primes congruent to 1 mod 20.
  • A141882 (program): Primes congruent to 7 mod 20.
  • A141883 (program): Primes congruent to 9 mod 20.
  • A141884 (program): Primes congruent to 11 mod 20.
  • A141885 (program): Primes congruent to 13 mod 20.
  • A141886 (program): Primes congruent to 17 mod 20.
  • A141887 (program): Primes congruent to 19 mod 20.
  • A141888 (program): Primes congruent to 2 mod 21.
  • A141889 (program): Primes congruent to 4 mod 21.
  • A141890 (program): Primes congruent to 5 mod 21.
  • A141891 (program): Primes congruent to 8 mod 21.
  • A141892 (program): Primes congruent to 10 mod 21.
  • A141893 (program): Primes congruent to 11 mod 21.
  • A141894 (program): Primes congruent to 13 mod 21.
  • A141895 (program): Primes congruent to 16 mod 21.
  • A141896 (program): Primes congruent to 17 mod 21.
  • A141897 (program): Primes congruent to 19 mod 21.
  • A141898 (program): Primes congruent to 20 mod 21.
  • A141899 (program): Primes of the form 2*3*5*7*k + 97.
  • A141905 (program): Triangle read by rows, T(n, k) = binomial(n, k)*A052509(n, k) for 0 <= k <= n.
  • A141906 (program): Triangle t(n,m) = (n*m)!/(m!^n) read by rows, 0<=m<=n.
  • A141908 (program): Primes congruent to 2 mod 23.
  • A141909 (program): Primes congruent to 4 mod 23.
  • A141910 (program): Primes congruent to 6 mod 23.
  • A141911 (program): Primes congruent to 7 mod 23.
  • A141912 (program): Primes congruent to 8 mod 23.
  • A141913 (program): Primes congruent to 9 mod 23.
  • A141914 (program): Primes congruent to 10 mod 23.
  • A141915 (program): Primes congruent to 11 mod 23.
  • A141916 (program): Primes congruent to 12 mod 23.
  • A141917 (program): Primes congruent to 13 mod 23.
  • A141918 (program): Primes congruent to 14 mod 23.
  • A141919 (program): Primes congruent to 15 mod 23.
  • A141920 (program): Primes congruent to 16 mod 23.
  • A141921 (program): Primes congruent to 17 mod 23.
  • A141922 (program): Primes congruent to 18 mod 23.
  • A141923 (program): Primes congruent to 19 mod 23.
  • A141924 (program): Primes congruent to 20 mod 23.
  • A141925 (program): Primes congruent to 21 mod 23.
  • A141926 (program): Primes congruent to 22 mod 23.
  • A141927 (program): Primes congruent to 1 mod 25.
  • A141928 (program): Primes congruent to 2 mod 25.
  • A141929 (program): Primes congruent to 3 mod 25.
  • A141930 (program): Primes congruent to 4 mod 25.
  • A141931 (program): Primes congruent to 6 mod 25.
  • A141932 (program): Primes congruent to 7 mod 25.
  • A141933 (program): Primes congruent to 8 mod 25.
  • A141934 (program): Primes congruent to 9 mod 25.
  • A141935 (program): Primes congruent to 11 mod 25.
  • A141936 (program): Primes congruent to 12 mod 25.
  • A141937 (program): Primes congruent to 13 mod 25.
  • A141938 (program): Primes congruent to 14 mod 25.
  • A141939 (program): Primes congruent to 16 mod 25.
  • A141940 (program): Primes congruent to 17 mod 25.
  • A141941 (program): Primes congruent to 18 mod 25.
  • A141942 (program): Primes congruent to 19 mod 25.
  • A141943 (program): Primes congruent to 21 mod 25.
  • A141944 (program): Primes congruent to 22 mod 25.
  • A141945 (program): Primes congruent to 23 mod 25.
  • A141946 (program): Primes congruent to 24 mod 25.
  • A141948 (program): Primes congruent to 1 mod 27.
  • A141949 (program): Primes congruent to 2 mod 27.
  • A141950 (program): Primes congruent to 4 mod 27.
  • A141951 (program): Primes congruent to 5 mod 27.
  • A141952 (program): Primes congruent to 7 mod 27.
  • A141953 (program): Primes congruent to 8 mod 27.
  • A141954 (program): Primes congruent to 10 mod 27.
  • A141955 (program): Primes congruent to 11 mod 27.
  • A141956 (program): Primes congruent to 13 mod 27.
  • A141957 (program): Primes congruent to 14 mod 27.
  • A141958 (program): Primes congruent to 16 mod 27.
  • A141959 (program): Primes congruent to 17 mod 27.
  • A141960 (program): Primes congruent to 19 mod 27.
  • A141961 (program): Primes congruent to 20 mod 27.
  • A141962 (program): Primes congruent to 22 mod 27.
  • A141963 (program): Primes congruent to 23 mod 27.
  • A141964 (program): Primes congruent to 25 mod 27.
  • A141965 (program): Primes congruent to 26 mod 27.
  • A141966 (program): Primes congruent to 3 mod 28.
  • A141967 (program): Primes congruent to 5 mod 28.
  • A141968 (program): Primes congruent to 9 mod 28.
  • A141969 (program): Primes congruent to 11 mod 28.
  • A141970 (program): Primes congruent to 13 mod 28.
  • A141971 (program): Primes congruent to 15 mod 28.
  • A141972 (program): Primes congruent to 17 mod 28.
  • A141973 (program): Primes congruent to 19 mod 28.
  • A141974 (program): Primes congruent to 23 mod 28.
  • A141975 (program): Primes congruent to 25 mod 28.
  • A141976 (program): Primes congruent to 27 mod 28.
  • A141977 (program): Primes congruent to 1 mod 29.
  • A141978 (program): Primes congruent to 2 mod 29.
  • A141979 (program): Primes congruent to 3 mod 29.
  • A141980 (program): Primes congruent to 4 mod 29.
  • A141981 (program): Primes congruent to 5 mod 29.
  • A141982 (program): Primes congruent to 6 mod 29.
  • A141983 (program): Primes congruent to 7 mod 29.
  • A141984 (program): Primes congruent to 8 mod 29.
  • A141985 (program): Primes congruent to 9 mod 29.
  • A141986 (program): Primes congruent to 10 mod 29.
  • A141987 (program): Primes congruent to 11 mod 29.
  • A141988 (program): Primes congruent to 12 mod 29.
  • A141989 (program): Primes congruent to 13 mod 29.
  • A141990 (program): Primes congruent to 14 mod 29.
  • A141991 (program): Primes congruent to 15 mod 29.
  • A141992 (program): Primes congruent to 16 mod 29.
  • A141993 (program): Primes congruent to 17 mod 29.
  • A141994 (program): Primes congruent to 18 mod 29.
  • A141995 (program): Primes congruent to 19 mod 29.
  • A141996 (program): Primes congruent to 20 mod 29.
  • A141997 (program): Primes congruent to 21 mod 29.
  • A141998 (program): Primes congruent to 22 mod 29.
  • A141999 (program): Primes congruent to 23 mod 29.
  • A142000 (program): Primes congruent to 24 mod 29.
  • A142001 (program): Primes congruent to 25 mod 29.
  • A142002 (program): Primes congruent to 26 mod 29.
  • A142003 (program): Primes congruent to 27 mod 29.
  • A142004 (program): Primes congruent to 28 mod 29.
  • A142005 (program): Primes congruent to 1 mod 31.
  • A142006 (program): Primes congruent to 2 mod 31.
  • A142007 (program): Primes congruent to 3 mod 31.
  • A142008 (program): Primes congruent to 4 mod 31.
  • A142009 (program): Primes congruent to 5 mod 31.
  • A142010 (program): Primes congruent to 6 mod 31.
  • A142011 (program): Primes congruent to 7 mod 31.
  • A142012 (program): Primes congruent to 8 mod 31.
  • A142013 (program): Primes congruent to 9 mod 31.
  • A142014 (program): Primes congruent to 10 mod 31.
  • A142015 (program): Primes congruent to 11 mod 31.
  • A142016 (program): Primes congruent to 12 mod 31.
  • A142017 (program): Primes congruent to 13 mod 31.
  • A142018 (program): Primes congruent to 14 mod 31.
  • A142019 (program): Primes congruent to 15 mod 31.
  • A142020 (program): Primes congruent to 16 mod 31.
  • A142021 (program): Primes congruent to 17 mod 31.
  • A142022 (program): Primes congruent to 18 mod 31.
  • A142023 (program): Primes congruent to 19 mod 31.
  • A142024 (program): Primes congruent to 20 mod 31.
  • A142025 (program): Primes congruent to 21 mod 31.
  • A142026 (program): Primes congruent to 22 mod 31.
  • A142027 (program): Primes congruent to 23 mod 31.
  • A142028 (program): Primes congruent to 24 mod 31.
  • A142029 (program): Primes congruent to 25 mod 31.
  • A142030 (program): Primes congruent to 26 mod 31.
  • A142031 (program): Primes congruent to 27 mod 31.
  • A142032 (program): Primes congruent to 28 mod 31.
  • A142033 (program): Primes congruent to 29 mod 31.
  • A142034 (program): Primes congruent to 30 mod 31.
  • A142035 (program): Primes congruent to 3 mod 32.
  • A142036 (program): Primes congruent to 5 mod 32.
  • A142037 (program): Primes congruent to 7 mod 32.
  • A142038 (program): Primes congruent to 9 mod 32.
  • A142039 (program): Primes congruent to 11 mod 32.
  • A142040 (program): Primes congruent to 13 mod 32.
  • A142041 (program): Primes congruent to 15 mod 32.
  • A142042 (program): Primes congruent to 19 mod 32.
  • A142043 (program): Primes congruent to 21 mod 32.
  • A142044 (program): Primes congruent to 23 mod 32.
  • A142045 (program): Primes congruent to 25 mod 32.
  • A142046 (program): Primes congruent to 27 mod 32.
  • A142047 (program): Primes congruent to 29 mod 32.
  • A142049 (program): Primes congruent to 1 mod 33.
  • A142050 (program): Primes congruent to 2 mod 33.
  • A142051 (program): Primes congruent to 4 mod 33.
  • A142052 (program): Primes congruent to 5 mod 33.
  • A142053 (program): Primes congruent to 7 mod 33.
  • A142054 (program): Primes congruent to 8 mod 33.
  • A142055 (program): Primes congruent to 10 mod 33.
  • A142056 (program): Primes congruent to 13 mod 33.
  • A142057 (program): Primes congruent to 14 mod 33.
  • A142058 (program): Primes congruent to 16 mod 33.
  • A142059 (program): Primes congruent to 17 mod 33.
  • A142060 (program): Primes congruent to 19 mod 33.
  • A142061 (program): Primes congruent to 20 mod 33.
  • A142062 (program): Primes congruent to 23 mod 33.
  • A142063 (program): Primes congruent to 25 mod 33.
  • A142064 (program): Primes congruent to 26 mod 33.
  • A142065 (program): Primes congruent to 28 mod 33.
  • A142066 (program): Primes congruent to 29 mod 33.
  • A142067 (program): Primes congruent to 31 mod 33.
  • A142068 (program): Primes congruent to 32 mod 33.
  • A142069 (program): Period length 9: repeat 3, 7, 2, 6, 1, 5, 0, 4, 8 .
  • A142071 (program): Expansion of the exponential generating function 1 - log(1 - x*(exp(z) - 1)), triangle read by rows, T(n,k) for n >= 0 and 0 <= k <= n.
  • A142072 (program): Primes congruent to 19 mod 34.
  • A142075 (program): Triangle T(n, k) = 2^(k-1) * E(n, k-1) where E(n,k) are the Eulerian numbers A173018, read by rows.
  • A142076 (program): Primes congruent to 1 mod 35.
  • A142077 (program): Primes congruent to 2 mod 35.
  • A142078 (program): Primes congruent to 3 mod 35.
  • A142079 (program): Primes congruent to 4 mod 35.
  • A142080 (program): Primes congruent to 6 mod 35.
  • A142081 (program): Primes congruent to 8 mod 35.
  • A142082 (program): Primes congruent to 9 mod 35.
  • A142083 (program): Primes congruent to 11 mod 35.
  • A142084 (program): Primes congruent to 12 mod 35.
  • A142085 (program): Primes congruent to 13 mod 35.
  • A142086 (program): Primes congruent to 16 mod 35.
  • A142087 (program): Primes congruent to 17 mod 35.
  • A142088 (program): Primes congruent to 18 mod 35.
  • A142089 (program): Primes congruent to 19 mod 35.
  • A142090 (program): Primes congruent to 22 mod 35.
  • A142091 (program): Primes congruent to 23 mod 35.
  • A142092 (program): Primes congruent to 24 mod 35.
  • A142093 (program): Primes congruent to 26 mod 35.
  • A142094 (program): Primes congruent to 27 mod 35.
  • A142095 (program): Primes congruent to 29 mod 35.
  • A142096 (program): Primes congruent to 31 mod 35.
  • A142097 (program): Primes congruent to 32 mod 35.
  • A142098 (program): Primes congruent to 33 mod 35.
  • A142099 (program): Primes congruent to 34 mod 35.
  • A142101 (program): Primes congruent to 5 mod 36.
  • A142102 (program): Primes congruent to 7 mod 36.
  • A142103 (program): Primes congruent to 11 mod 36.
  • A142104 (program): Primes congruent to 13 mod 36.
  • A142105 (program): Primes congruent to 17 mod 36.
  • A142106 (program): Primes congruent to 19 mod 36.
  • A142107 (program): Primes congruent to 23 mod 36.
  • A142108 (program): Primes congruent to 25 mod 36.
  • A142109 (program): Primes congruent to 29 mod 36.
  • A142110 (program): Primes congruent to 31 mod 36.
  • A142111 (program): Primes congruent to 35 mod 36.
  • A142112 (program): Primes congruent to 2 mod 37.
  • A142113 (program): Primes congruent to 4 mod 37.
  • A142114 (program): Primes congruent to 5 mod 37.
  • A142115 (program): Primes congruent to 6 mod 37.
  • A142116 (program): Primes congruent to 7 mod 37.
  • A142117 (program): Primes congruent to 8 mod 37.
  • A142118 (program): Primes congruent to 9 mod 37.
  • A142119 (program): Primes congruent to 10 mod 37.
  • A142120 (program): Primes congruent to 11 mod 37.
  • A142121 (program): Primes congruent to 12 mod 37.
  • A142122 (program): Primes congruent to 13 mod 37.
  • A142123 (program): Primes congruent to 14 mod 37.
  • A142124 (program): Primes congruent to 15 mod 37.
  • A142125 (program): Primes congruent to 16 mod 37.
  • A142126 (program): Primes congruent to 17 mod 37.
  • A142127 (program): Primes congruent to 18 mod 37.
  • A142128 (program): Primes congruent to 19 mod 37.
  • A142129 (program): Primes congruent to 20 mod 37.
  • A142130 (program): Primes congruent to 21 mod 37.
  • A142131 (program): Primes congruent to 22 mod 37.
  • A142132 (program): Primes congruent to 23 mod 37.
  • A142133 (program): Primes congruent to 24 mod 37.
  • A142134 (program): Primes congruent to 25 mod 37.
  • A142135 (program): Primes congruent to 26 mod 37.
  • A142136 (program): Primes congruent to 27 mod 37.
  • A142137 (program): Primes congruent to 28 mod 37.
  • A142138 (program): Primes congruent to 29 mod 37.
  • A142139 (program): Primes congruent to 30 mod 37.
  • A142140 (program): Primes congruent to 31 mod 37.
  • A142141 (program): Primes congruent to 32 mod 37.
  • A142142 (program): Primes congruent to 33 mod 37.
  • A142143 (program): Primes congruent to 34 mod 37.
  • A142144 (program): Primes congruent to 35 mod 37.
  • A142145 (program): Primes congruent to 36 mod 37.
  • A142149 (program): a(n) = XOR{k OR (n-k): 0<=k<=n}.
  • A142150 (program): The nonnegative integers interleaved with 0’s.
  • A142151 (program): a(n) = OR{k XOR (n-k): 0<=k<=n}.
  • A142152 (program): Primes congruent to 21 mod 38.
  • A142155 (program): Expansion of x/( 1+x-x^2-x^4-x^5-x^6-x^7+x^9+x^10 ).
  • A142156 (program): Triangle T(n,k)= n! if k=0, T(n,k) = -(n-k)!*A003319(k) if k > 0.
  • A142157 (program): Last digit of A003319(n).
  • A142159 (program): Primes congruent to 1 mod 39.
  • A142160 (program): Primes congruent to 2 mod 39.
  • A142161 (program): Primes congruent to 4 mod 39.
  • A142162 (program): Primes congruent to 5 mod 39.
  • A142163 (program): Primes congruent to 7 mod 39.
  • A142164 (program): Primes congruent to 8 mod 39.
  • A142165 (program): Primes congruent to 10 mod 39.
  • A142166 (program): Primes congruent to 11 mod 39.
  • A142167 (program): Primes congruent to 14 mod 39.
  • A142168 (program): Primes congruent to 16 mod 39.
  • A142169 (program): Primes congruent to 17 mod 39.
  • A142170 (program): Primes congruent to 19 mod 39.
  • A142171 (program): Primes congruent to 20 mod 39.
  • A142172 (program): Primes congruent to 22 mod 39.
  • A142173 (program): Primes congruent to 23 mod 39.
  • A142174 (program): Primes congruent to 25 mod 39.
  • A142176 (program): Primes congruent to 29 mod 39.
  • A142177 (program): Primes congruent to 31 mod 39.
  • A142178 (program): Primes congruent to 32 mod 39.
  • A142179 (program): Primes congruent to 34 mod 39.
  • A142180 (program): Primes congruent to 35 mod 39.
  • A142181 (program): Primes congruent to 37 mod 39.
  • A142182 (program): Primes congruent to 38 mod 39.
  • A142183 (program): Primes congruent to 1 mod 40.
  • A142184 (program): Primes congruent to 3 mod 40.
  • A142185 (program): Primes congruent to 7 mod 40.
  • A142186 (program): Primes congruent to 9 mod 40.
  • A142187 (program): Primes congruent to 11 mod 40.
  • A142188 (program): Primes congruent to 13 mod 40.
  • A142189 (program): Primes congruent to 17 mod 40.
  • A142190 (program): Primes congruent to 19 mod 40.
  • A142191 (program): Primes congruent to 21 mod 40.
  • A142192 (program): Primes congruent to 23 mod 40.
  • A142193 (program): Primes congruent to 27 mod 40.
  • A142194 (program): Primes congruent to 29 mod 40.
  • A142195 (program): Primes congruent to 31 mod 40.
  • A142196 (program): Primes congruent to 33 mod 40.
  • A142197 (program): Primes congruent to 37 mod 40.
  • A142198 (program): Primes congruent to 39 mod 40.
  • A142199 (program): Primes congruent to 2 mod 41.
  • A142200 (program): Primes congruent to 3 mod 41.
  • A142201 (program): Primes congruent to 4 mod 41.
  • A142202 (program): Primes congruent to 5 mod 41.
  • A142203 (program): Primes congruent to 6 mod 41.
  • A142204 (program): Primes congruent to 7 mod 41.
  • A142205 (program): Primes congruent to 8 mod 41.
  • A142206 (program): Primes congruent to 9 mod 41.
  • A142207 (program): Primes congruent to 10 mod 41.
  • A142208 (program): Primes congruent to 11 mod 41.
  • A142209 (program): Primes congruent to 12 mod 41.
  • A142210 (program): Primes congruent to 13 mod 41.
  • A142211 (program): Primes congruent to 14 mod 41.
  • A142212 (program): Primes congruent to 15 mod 41.
  • A142213 (program): Primes congruent to 16 mod 41.
  • A142214 (program): Primes congruent to 17 mod 41.
  • A142215 (program): Primes congruent to 18 mod 41.
  • A142216 (program): Primes congruent to 19 mod 41.
  • A142217 (program): Primes congruent to 20 mod 41.
  • A142218 (program): Primes congruent to 21 mod 41.
  • A142219 (program): Primes congruent to 22 mod 41.
  • A142220 (program): Primes congruent to 23 mod 41.
  • A142221 (program): Primes congruent to 24 mod 41.
  • A142222 (program): Primes congruent to 25 mod 41.
  • A142223 (program): Primes congruent to 26 mod 41.
  • A142224 (program): Primes congruent to 27 mod 41.
  • A142225 (program): Primes congruent to 28 mod 41.
  • A142226 (program): Primes congruent to 29 mod 41.
  • A142227 (program): Primes congruent to 30 mod 41.
  • A142228 (program): Primes congruent to 31 mod 41.
  • A142229 (program): Primes congruent to 32 mod 41.
  • A142230 (program): Primes congruent to 33 mod 41.
  • A142231 (program): Primes congruent to 34 mod 41.
  • A142232 (program): Primes congruent to 35 mod 41.
  • A142233 (program): Primes congruent to 36 mod 41.
  • A142234 (program): Primes congruent to 37 mod 41.
  • A142235 (program): Primes congruent to 38 mod 41.
  • A142236 (program): Primes congruent to 39 mod 41.
  • A142237 (program): Primes congruent to 40 mod 41.
  • A142238 (program): Numerators of continued fraction convergents to sqrt(3/2).
  • A142239 (program): Denominators of continued fraction convergents to sqrt(3/2).
  • A142240 (program): A triangular sequence from the pattern in row sums of Pascal’s triangle A007318, Eulerian numbers A008292 and A060187: Delta_diagonal=m; m={0,1,2,3,…k}.
  • A142241 (program): a(n) = 24*n + 14.
  • A142242 (program): Row sums of A143200.
  • A142243 (program): Triangle T(n,k) = binomial(2*n,k) *binomial(2*n-2*k,n-k), read by rows; 0<=k<=n.
  • A142244 (program): Primes congruent to 23 mod 42.
  • A142245 (program): Expansion of 2*x*(6 + 5*x) / ((1 - x)*(1 - x - x^2)).
  • A142248 (program): Odd numbers in A138123.
  • A142250 (program): Primes congruent to 1 mod 43.
  • A142251 (program): Primes congruent to 2 mod 43.
  • A142252 (program): Primes congruent to 3 mod 43.
  • A142253 (program): Primes congruent to 4 mod 43.
  • A142254 (program): Primes congruent to 5 mod 43.
  • A142255 (program): Primes congruent to 6 mod 43.
  • A142256 (program): Primes congruent to 7 mod 43.
  • A142257 (program): Primes congruent to 8 mod 43.
  • A142258 (program): Primes congruent to 9 mod 43.
  • A142259 (program): Primes congruent to 10 mod 43.
  • A142260 (program): Primes congruent to 11 mod 43.
  • A142261 (program): Primes congruent to 12 mod 43.
  • A142262 (program): Primes congruent to 13 mod 43.
  • A142263 (program): Primes congruent to 14 mod 43.
  • A142264 (program): Primes congruent to 15 mod 43.
  • A142265 (program): Primes congruent to 16 mod 43.
  • A142266 (program): Primes congruent to 17 mod 43.
  • A142267 (program): Primes congruent to 18 mod 43.
  • A142268 (program): Primes congruent to 19 mod 43.
  • A142269 (program): Primes congruent to 20 mod 43.
  • A142270 (program): Primes congruent to 21 mod 43.
  • A142271 (program): Primes congruent to 22 mod 43.
  • A142272 (program): Primes congruent to 23 mod 43.
  • A142273 (program): Primes congruent to 24 mod 43.
  • A142274 (program): Primes congruent to 25 mod 43.
  • A142275 (program): Primes congruent to 26 mod 43.
  • A142276 (program): Primes congruent to 27 mod 43.
  • A142277 (program): Primes congruent to 28 mod 43.
  • A142278 (program): Primes congruent to 29 mod 43.
  • A142279 (program): Primes congruent to 30 mod 43.
  • A142280 (program): Primes congruent to 31 mod 43.
  • A142281 (program): Primes congruent to 32 mod 43.
  • A142282 (program): Primes congruent to 33 mod 43.
  • A142283 (program): Primes congruent to 34 mod 43.
  • A142284 (program): Primes congruent to 35 mod 43.
  • A142285 (program): Primes congruent to 36 mod 43.
  • A142286 (program): Primes congruent to 37 mod 43.
  • A142287 (program): Primes congruent to 38 mod 43.
  • A142288 (program): Primes congruent to 39 mod 43.
  • A142289 (program): Primes congruent to 40 mod 43.
  • A142290 (program): Primes congruent to 41 mod 43.
  • A142291 (program): Primes congruent to 42 mod 43.
  • A142292 (program): Primes congruent to 1 mod 44.
  • A142293 (program): Primes congruent to 3 mod 44.
  • A142294 (program): Primes congruent to 5 mod 44.
  • A142295 (program): Primes congruent to 7 mod 44.
  • A142296 (program): Primes congruent to 9 mod 44.
  • A142297 (program): Primes congruent to 13 mod 44.
  • A142298 (program): Primes congruent to 15 mod 44.
  • A142299 (program): Primes congruent to 17 mod 44.
  • A142300 (program): Primes congruent to 19 mod 44.
  • A142301 (program): Primes congruent to 21 mod 44.
  • A142302 (program): Primes congruent to 23 mod 44.
  • A142303 (program): Primes congruent to 25 mod 44.
  • A142304 (program): Primes congruent to 27 mod 44.
  • A142305 (program): Primes congruent to 29 mod 44.
  • A142306 (program): Primes congruent to 31 mod 44.
  • A142307 (program): Primes congruent to 35 mod 44.
  • A142308 (program): Primes congruent to 37 mod 44.
  • A142309 (program): Primes congruent to 39 mod 44.
  • A142310 (program): Primes congruent to 41 mod 44.
  • A142311 (program): Primes congruent to 43 mod 44.
  • A142312 (program): Primes congruent to 1 mod 45.
  • A142313 (program): Primes congruent to 2 mod 45.
  • A142314 (program): Primes congruent to 4 mod 45.
  • A142315 (program): Primes congruent to 7 mod 45.
  • A142316 (program): Primes congruent to 8 mod 45.
  • A142317 (program): Primes congruent to 11 mod 45.
  • A142318 (program): Primes congruent to 13 mod 45.
  • A142319 (program): Primes congruent to 14 mod 45.
  • A142320 (program): Primes congruent to 16 mod 45.
  • A142321 (program): Primes congruent to 17 mod 45.
  • A142322 (program): Primes congruent to 19 mod 45.
  • A142323 (program): Primes congruent to 22 mod 45.
  • A142324 (program): Primes congruent to 23 mod 45.
  • A142325 (program): Primes congruent to 26 mod 45.
  • A142326 (program): Primes congruent to 28 mod 45.
  • A142327 (program): Primes congruent to 29 mod 45.
  • A142328 (program): Primes congruent to 31 mod 45.
  • A142329 (program): Primes congruent to 32 mod 45.
  • A142330 (program): Primes congruent to 34 mod 45.
  • A142331 (program): Primes congruent to 37 mod 45.
  • A142332 (program): Primes congruent to 38 mod 45.
  • A142333 (program): Primes congruent to 41 mod 45.
  • A142334 (program): Primes congruent to 43 mod 45.
  • A142335 (program): Primes congruent to 44 mod 45.
  • A142337 (program): Numbers n such that sum(i=1..n, sigma(i)) is prime.
  • A142342 (program): a(n) = 10*prime(n).
  • A142344 (program): Primes congruent to 25 mod 46.
  • A142354 (program): A triangular sequence “representation” of the modulo 10 Integer field: t(+)(n,m)=Mod[n + m, 10]; t(x)(n,m)=Mod[n*m, 10]; t(n,m)=Mod[t(=)(n,m)*t(X)(n,m),10].
  • A142355 (program): Primes congruent to 2 mod 47.
  • A142356 (program): Primes congruent to 4 mod 47.
  • A142357 (program): Primes congruent to 6 mod 47.
  • A142358 (program): Primes congruent to 7 mod 47.
  • A142359 (program): Primes congruent to 8 mod 47.
  • A142360 (program): Primes congruent to 9 mod 47.
  • A142361 (program): Primes congruent to 10 mod 47.
  • A142362 (program): Primes congruent to 11 mod 47.
  • A142363 (program): Primes congruent to 12 mod 47.
  • A142364 (program): Primes congruent to 13 mod 47.
  • A142365 (program): Primes congruent to 14 mod 47.
  • A142366 (program): Primes congruent to 15 mod 47.
  • A142367 (program): Primes congruent to 16 mod 47.
  • A142368 (program): Primes congruent to 17 mod 47.
  • A142369 (program): Primes congruent to 18 mod 47.
  • A142370 (program): Primes congruent to 19 mod 47.
  • A142371 (program): Primes congruent to 20 mod 47.
  • A142372 (program): Primes congruent to 21 mod 47.
  • A142373 (program): Primes congruent to 22 mod 47.
  • A142374 (program): Primes congruent to 23 mod 47.
  • A142375 (program): Primes congruent to 24 mod 47.
  • A142376 (program): Primes congruent to 25 mod 47.
  • A142377 (program): Primes congruent to 26 mod 47.
  • A142378 (program): Primes congruent to 27 mod 47.
  • A142379 (program): Primes congruent to 28 mod 47.
  • A142380 (program): Primes congruent to 29 mod 47.
  • A142381 (program): Primes congruent to 30 mod 47.
  • A142382 (program): Primes congruent to 31 mod 47.
  • A142383 (program): Primes congruent to 32 mod 47.
  • A142384 (program): Primes congruent to 33 mod 47.
  • A142385 (program): Primes congruent to 34 mod 47.
  • A142386 (program): Primes congruent to 35 mod 47.
  • A142387 (program): Primes congruent to 36 mod 47.
  • A142388 (program): Primes congruent to 37 mod 47.
  • A142389 (program): Primes congruent to 38 mod 47.
  • A142390 (program): Primes congruent to 39 mod 47.
  • A142391 (program): Primes congruent to 40 mod 47.
  • A142392 (program): Primes congruent to 41 mod 47.
  • A142393 (program): Primes congruent to 42 mod 47.
  • A142394 (program): Primes congruent to 43 mod 47.
  • A142395 (program): Primes congruent to 44 mod 47.
  • A142396 (program): Primes congruent to 45 mod 47.
  • A142397 (program): Primes congruent to 46 mod 47.
  • A142398 (program): Primes congruent to 1 mod 48.
  • A142399 (program): Primes congruent to 5 mod 48.
  • A142400 (program): Primes congruent to 7 mod 48.
  • A142401 (program): Primes congruent to 11 mod 48.
  • A142402 (program): Primes congruent to 13 mod 48.
  • A142403 (program): Primes congruent to 17 mod 48.
  • A142404 (program): Primes congruent to 19 mod 48.
  • A142405 (program): Primes congruent to 23 mod 48.
  • A142406 (program): Primes congruent to 25 mod 48.
  • A142407 (program): Primes congruent to 29 mod 48.
  • A142408 (program): Primes congruent to 31 mod 48.
  • A142409 (program): Primes congruent to 35 mod 48.
  • A142410 (program): Primes congruent to 37 mod 48.
  • A142411 (program): Primes congruent to 41 mod 48.
  • A142412 (program): Primes congruent to 43 mod 48.
  • A142413 (program): Primes congruent to 47 mod 48.
  • A142414 (program): Primes congruent to 1 mod 49.
  • A142415 (program): Primes congruent to 2 mod 49.
  • A142416 (program): Primes congruent to 3 mod 49.
  • A142417 (program): Primes congruent to 4 mod 49.
  • A142418 (program): Primes congruent to 5 mod 49.
  • A142419 (program): Primes congruent to 6 mod 49.
  • A142420 (program): Primes congruent to 8 mod 49.
  • A142421 (program): Primes congruent to 9 mod 49.
  • A142422 (program): Primes congruent to 10 mod 49.
  • A142423 (program): Primes congruent to 11 mod 49.
  • A142424 (program): Primes congruent to 12 mod 49.
  • A142425 (program): Primes congruent to 13 mod 49.
  • A142426 (program): Primes congruent to 15 mod 49.
  • A142427 (program): Primes congruent to 16 mod 49.
  • A142428 (program): Primes congruent to 17 mod 49.
  • A142429 (program): Primes congruent to 18 mod 49.
  • A142430 (program): Primes congruent to 19 mod 49.
  • A142431 (program): Primes congruent to 20 mod 49.
  • A142432 (program): Primes congruent to 22 mod 49.
  • A142433 (program): Primes congruent to 23 mod 49.
  • A142434 (program): Primes congruent to 24 mod 49.
  • A142435 (program): Primes congruent to 25 mod 49.
  • A142436 (program): Primes congruent to 26 mod 49.
  • A142437 (program): Primes congruent to 27 mod 49.
  • A142438 (program): Primes congruent to 29 mod 49.
  • A142439 (program): Primes congruent to 30 mod 49.
  • A142440 (program): Primes congruent to 31 mod 49.
  • A142441 (program): Primes congruent to 32 mod 49.
  • A142442 (program): Primes congruent to 33 mod 49.
  • A142443 (program): Primes congruent to 34 mod 49.
  • A142444 (program): Primes congruent to 36 mod 49.
  • A142445 (program): Primes congruent to 37 mod 49.
  • A142446 (program): Primes congruent to 38 mod 49.
  • A142447 (program): Primes congruent to 39 mod 49.
  • A142448 (program): Primes congruent to 40 mod 49.
  • A142449 (program): Primes congruent to 41 mod 49.
  • A142450 (program): Primes congruent to 43 mod 49.
  • A142451 (program): Primes congruent to 44 mod 49.
  • A142452 (program): Primes congruent to 45 mod 49.
  • A142453 (program): Primes congruent to 46 mod 49.
  • A142454 (program): Primes congruent to 47 mod 49.
  • A142455 (program): Primes congruent to 48 mod 49.
  • A142457 (program): A triangular sequence “representation” of the modulo 11 Integer field: t(+)(n,m)=Mod[n + m, 11]; t(x)(n,m)=Mod[n*m, 11]; t(n,m)=Mod[t(=)(n,m)*t(X)(n,m),11].
  • A142463 (program): a(n) = 2*n^2 + 2*n - 1.
  • A142464 (program): Decimal expansion of 13/36.
  • A142466 (program): Primes congruent to 27 mod 50.
  • A142471 (program): a(0) = a(1) = 0; thereafter a(n) = a(n-1)*a(n-2) + 2.
  • A142474 (program): 1 followed by A141015.
  • A142476 (program): Primes congruent to 1 mod 51.
  • A142477 (program): Primes congruent to 2 mod 51.
  • A142478 (program): Primes congruent to 4 mod 51.
  • A142479 (program): Primes congruent to 5 mod 51.
  • A142480 (program): Primes congruent to 7 mod 51.
  • A142481 (program): Primes congruent to 8 mod 51.
  • A142482 (program): Primes congruent to 10 mod 51.
  • A142483 (program): Primes congruent to 11 mod 51.
  • A142484 (program): Primes congruent to 13 mod 51.
  • A142485 (program): Primes congruent to 14 mod 51.
  • A142486 (program): Primes congruent to 16 mod 51.
  • A142487 (program): Primes congruent to 19 mod 51.
  • A142488 (program): Primes congruent to 20 mod 51.
  • A142489 (program): Primes congruent to 22 mod 51.
  • A142490 (program): Primes congruent to 23 mod 51.
  • A142491 (program): Primes congruent to 25 mod 51.
  • A142492 (program): Primes congruent to 26 mod 51.
  • A142493 (program): Primes congruent to 28 mod 51.
  • A142494 (program): Primes congruent to 29 mod 51.
  • A142495 (program): Primes congruent to 31 mod 51.
  • A142496 (program): Primes congruent to 32 mod 51.
  • A142497 (program): Primes congruent to 35 mod 51.
  • A142498 (program): Primes congruent to 37 mod 51.
  • A142499 (program): Primes congruent to 38 mod 51.
  • A142500 (program): Primes congruent to 40 mod 51.
  • A142501 (program): Primes congruent to 41 mod 51.
  • A142502 (program): Primes congruent to 43 mod 51.
  • A142503 (program): Primes congruent to 44 mod 51.
  • A142504 (program): Primes congruent to 46 mod 51.
  • A142505 (program): Primes congruent to 47 mod 51.
  • A142506 (program): Primes congruent to 49 mod 51.
  • A142507 (program): Primes congruent to 50 mod 51.
  • A142508 (program): Primes congruent to 1 mod 52.
  • A142509 (program): Primes congruent to 3 mod 52.
  • A142510 (program): Primes congruent to 5 mod 52.
  • A142511 (program): Primes congruent to 7 mod 52.
  • A142512 (program): Primes congruent to 9 mod 52.
  • A142513 (program): Primes congruent to 11 mod 52.
  • A142514 (program): Primes congruent to 15 mod 52.
  • A142515 (program): Primes congruent to 17 mod 52.
  • A142516 (program): Primes congruent to 19 mod 52.
  • A142517 (program): Primes congruent to 21 mod 52.
  • A142518 (program): Primes congruent to 23 mod 52.
  • A142519 (program): Primes congruent to 25 mod 52.
  • A142520 (program): Primes congruent to 27 mod 52.
  • A142521 (program): Primes congruent to 29 mod 52.
  • A142522 (program): Primes congruent to 31 mod 52.
  • A142523 (program): Primes congruent to 33 mod 52.
  • A142524 (program): Primes congruent to 35 mod 52.
  • A142525 (program): Primes congruent to 37 mod 52.
  • A142526 (program): Primes congruent to 41 mod 52.
  • A142527 (program): Primes congruent to 43 mod 52.
  • A142528 (program): Primes congruent to 45 mod 52.
  • A142529 (program): Primes congruent to 47 mod 52.
  • A142530 (program): Primes congruent to 49 mod 52.
  • A142531 (program): Primes congruent to 51 mod 52.
  • A142532 (program): Primes congruent to 2 mod 53.
  • A142533 (program): Primes congruent to 3 mod 53.
  • A142534 (program): Primes congruent to 4 mod 53.
  • A142535 (program): Primes congruent to 5 mod 53.
  • A142536 (program): Primes congruent to 6 mod 53.
  • A142537 (program): Primes congruent to 7 mod 53.
  • A142538 (program): Primes congruent to 8 mod 53.
  • A142539 (program): Primes congruent to 9 mod 53.
  • A142540 (program): Primes congruent to 10 mod 53.
  • A142541 (program): Primes congruent to 11 mod 53.
  • A142542 (program): Primes congruent to 12 mod 53.
  • A142543 (program): Primes congruent to 13 mod 53.
  • A142544 (program): Primes congruent to 14 mod 53.
  • A142545 (program): Primes congruent to 15 mod 53.
  • A142546 (program): Primes congruent to 16 mod 53.
  • A142547 (program): Primes congruent to 17 mod 53.
  • A142548 (program): Primes congruent to 18 mod 53.
  • A142549 (program): Primes congruent to 19 mod 53.
  • A142550 (program): Primes congruent to 20 mod 53.
  • A142551 (program): Primes congruent to 21 mod 53.
  • A142552 (program): Primes congruent to 22 mod 53.
  • A142553 (program): Primes congruent to 23 mod 53.
  • A142554 (program): Primes congruent to 24 mod 53.
  • A142555 (program): Primes congruent to 25 mod 53.
  • A142556 (program): Primes congruent to 26 mod 53.
  • A142557 (program): Primes congruent to 27 mod 53.
  • A142558 (program): Primes congruent to 28 mod 53.
  • A142559 (program): Primes congruent to 29 mod 53.
  • A142560 (program): Primes congruent to 30 mod 53.
  • A142561 (program): Primes congruent to 31 mod 53.
  • A142562 (program): Primes congruent to 32 mod 53.
  • A142563 (program): Primes congruent to 33 mod 53.
  • A142564 (program): Primes congruent to 34 mod 53.
  • A142565 (program): Primes congruent to 35 mod 53.
  • A142566 (program): Primes congruent to 36 mod 53.
  • A142567 (program): Primes congruent to 37 mod 53.
  • A142568 (program): Primes congruent to 38 mod 53.
  • A142569 (program): Primes congruent to 39 mod 53.
  • A142570 (program): Primes congruent to 40 mod 53.
  • A142571 (program): Primes congruent to 41 mod 53.
  • A142572 (program): Primes congruent to 42 mod 53.
  • A142573 (program): Primes congruent to 43 mod 53.
  • A142574 (program): Primes congruent to 44 mod 53.
  • A142575 (program): Primes congruent to 45 mod 53.
  • A142576 (program): Primes congruent to 46 mod 53.
  • A142577 (program): Primes congruent to 47 mod 53.
  • A142578 (program): Primes congruent to 48 mod 53.
  • A142579 (program): Primes congruent to 49 mod 53.
  • A142580 (program): Primes congruent to 50 mod 53.
  • A142581 (program): Primes congruent to 51 mod 53.
  • A142582 (program): Primes congruent to 52 mod 53.
  • A142584 (program): a(n) = A014217(n+1) - A115360(n+2).
  • A142585 (program): Inverse binomial transform of A014217.
  • A142586 (program): Binomial transform of A014217.
  • A142588 (program): A trisection of A000129, the Pell numbers.
  • A142589 (program): Square array T(n,m) = Product_{i=0..m} (1+n*i) read by antidiagonals.
  • A142590 (program): First trisection of A061037 (Balmer line series of the hydrogen atom).
  • A142592 (program): Primes congruent to 29 mod 54.
  • A142599 (program): Second trisection of A061037.
  • A142600 (program): Third trisection of A061037.
  • A142601 (program): Primes congruent to 1 mod 55.
  • A142602 (program): Primes congruent to 2 mod 55.
  • A142603 (program): Primes congruent to 3 mod 55.
  • A142604 (program): Primes congruent to 4 mod 55.
  • A142605 (program): Primes congruent to 6 mod 55.
  • A142606 (program): Primes congruent to 7 mod 55.
  • A142607 (program): Primes congruent to 8 mod 55.
  • A142608 (program): Primes congruent to 9 mod 55.
  • A142609 (program): Primes congruent to 12 mod 55.
  • A142610 (program): Primes congruent to 13 mod 55.
  • A142611 (program): Primes congruent to 14 mod 55.
  • A142612 (program): Primes congruent to 16 mod 55.
  • A142613 (program): Primes congruent to 17 mod 55.
  • A142614 (program): Primes congruent to 18 mod 55.
  • A142615 (program): Primes congruent to 19 mod 55.
  • A142616 (program): Primes congruent to 21 mod 55.
  • A142617 (program): Primes congruent to 23 mod 55.
  • A142618 (program): Primes congruent to 24 mod 55.
  • A142619 (program): Primes congruent to 26 mod 55.
  • A142620 (program): Primes congruent to 27 mod 55.
  • A142621 (program): Primes congruent to 28 mod 55.
  • A142622 (program): Primes congruent to 29 mod 55.
  • A142623 (program): Primes congruent to 31 mod 55.
  • A142624 (program): Primes congruent to 32 mod 55.
  • A142625 (program): Primes congruent to 34 mod 55.
  • A142626 (program): Primes congruent to 36 mod 55.
  • A142627 (program): Primes congruent to 37 mod 55.
  • A142628 (program): Primes congruent to 38 mod 55.
  • A142629 (program): Primes congruent to 39 mod 55.
  • A142630 (program): Primes congruent to 41 mod 55.
  • A142631 (program): Primes congruent to 42 mod 55.
  • A142632 (program): Primes congruent to 43 mod 55.
  • A142633 (program): Primes congruent to 46 mod 55.
  • A142634 (program): Primes congruent to 47 mod 55.
  • A142635 (program): Primes congruent to 48 mod 55.
  • A142636 (program): Primes congruent to 49 mod 55.
  • A142637 (program): Primes congruent to 51 mod 55.
  • A142638 (program): Primes congruent to 52 mod 55.
  • A142639 (program): Primes congruent to 53 mod 55.
  • A142640 (program): Primes congruent to 54 mod 55.
  • A142641 (program): Primes congruent to 1 mod 56.
  • A142642 (program): Primes congruent to 3 mod 56.
  • A142643 (program): Primes congruent to 5 mod 56.
  • A142644 (program): Primes congruent to 9 mod 56.
  • A142645 (program): Primes congruent to 11 mod 56.
  • A142646 (program): Primes congruent to 13 mod 56.
  • A142647 (program): Primes congruent to 15 mod 56.
  • A142648 (program): Primes congruent to 17 mod 56.
  • A142649 (program): Primes congruent to 19 mod 56.
  • A142650 (program): Primes congruent to 23 mod 56.
  • A142651 (program): Primes congruent to 25 mod 56.
  • A142652 (program): Primes congruent to 27 mod 56.
  • A142653 (program): Primes congruent to 29 mod 56.
  • A142654 (program): Primes congruent to 31 mod 56.
  • A142655 (program): Primes congruent to 33 mod 56.
  • A142656 (program): Primes congruent to 37 mod 56.
  • A142657 (program): Primes congruent to 39 mod 56.
  • A142658 (program): Primes congruent to 41 mod 56.
  • A142659 (program): Primes congruent to 43 mod 56.
  • A142660 (program): Primes congruent to 45 mod 56.
  • A142661 (program): Primes congruent to 47 mod 56.
  • A142662 (program): Primes congruent to 51 mod 56.
  • A142663 (program): Primes congruent to 53 mod 56.
  • A142664 (program): Primes congruent to 55 mod 56.
  • A142665 (program): Primes congruent to 1 mod 57.
  • A142666 (program): Primes congruent to 2 mod 57.
  • A142667 (program): Primes congruent to 4 mod 57.
  • A142668 (program): Primes congruent to 5 mod 57.
  • A142669 (program): Primes congruent to 7 mod 57.
  • A142670 (program): Primes congruent to 8 mod 57.
  • A142671 (program): Primes congruent to 10 mod 57.
  • A142672 (program): Primes congruent to 11 mod 57.
  • A142673 (program): Primes congruent to 13 mod 57.
  • A142674 (program): Primes congruent to 14 mod 57.
  • A142675 (program): Primes congruent to 16 mod 57.
  • A142676 (program): Primes congruent to 17 mod 57.
  • A142677 (program): Primes congruent to 20 mod 57.
  • A142678 (program): Primes congruent to 22 mod 57.
  • A142679 (program): Primes congruent to 23 mod 57.
  • A142680 (program): Primes congruent to 25 mod 57.
  • A142681 (program): Primes congruent to 26 mod 57.
  • A142682 (program): Primes congruent to 28 mod 57.
  • A142683 (program): Primes congruent to 29 mod 57.
  • A142684 (program): Primes congruent to 31 mod 57.
  • A142685 (program): Primes congruent to 32 mod 57.
  • A142686 (program): Primes congruent to 34 mod 57.
  • A142687 (program): Primes congruent to 35 mod 57.
  • A142688 (program): Primes congruent to 37 mod 57.
  • A142689 (program): Primes congruent to 40 mod 57.
  • A142690 (program): Primes congruent to 41 mod 57.
  • A142691 (program): Primes congruent to 43 mod 57.
  • A142692 (program): Primes congruent to 44 mod 57.
  • A142693 (program): Primes congruent to 46 mod 57.
  • A142694 (program): Primes congruent to 47 mod 57.
  • A142695 (program): Primes congruent to 49 mod 57.
  • A142696 (program): Primes congruent to 50 mod 57.
  • A142697 (program): Primes congruent to 52 mod 57.
  • A142698 (program): Primes congruent to 53 mod 57.
  • A142699 (program): Primes congruent to 55 mod 57.
  • A142700 (program): Primes congruent to 56 mod 57.
  • A142702 (program): Period 4: repeat [5, 2, 5, 8].
  • A142703 (program): a(n) = 2*(n-1)*( a(n-1)+a(n-2) ) starting a(1)=a(2)=1.
  • A142704 (program): A generalized factorial level recursion of a Padovan type: a(n) = b(n)*(a(n-2) + a(n-3)) with b(n) = b(n-1) + k and k=2.
  • A142705 (program): Numerator of 1/4 - 1/(2n)^2.
  • A142710 (program): a(n) = A142585(n) + A142586(n).
  • A142714 (program): A determinant sequence: M={{a(-1 + n), a(-2 + n)}, {a(-2 + n), a(-3 + n)}}; a(n)=Det[M].
  • A142715 (program): Primes congruent to 31 mod 58.
  • A142717 (program): First (leftmost) odd term in the n-th row of triangle A120070.
  • A142718 (program): Odds terms in A014217.
  • A142719 (program): a(n) = if n < 41 then n^2 - n + 41, otherwise n^2 - 81*n + 1681.
  • A142720 (program): A triangle sequence of coefficients of odd sum polynomials: p(x,n)=x^(2*n - 1) - Sum[x^(2*i + 1), {i, 0, n - 1}] - 1.
  • A142721 (program): An even-odd sequence: a(n) = n/2 if n is even, or a(n-1) + 2^floor(log_2(n+1)) otherwise.
  • A142722 (program): a(0)=a(1)=1 and a(n) = -(2*n-1)*a(n-1) + a(n-2) for n>=2.
  • A142729 (program): Primes congruent to 2 mod 59.
  • A142730 (program): Primes congruent to 3 mod 59.
  • A142731 (program): Primes congruent to 4 mod 59.
  • A142732 (program): Primes congruent to 5 mod 59.
  • A142733 (program): Primes congruent to 6 mod 59.
  • A142734 (program): Primes congruent to 7 mod 59.
  • A142735 (program): Primes congruent to 8 mod 59.
  • A142736 (program): Primes congruent to 9 mod 59.
  • A142737 (program): Primes congruent to 10 mod 59.
  • A142738 (program): Primes congruent to 11 mod 59.
  • A142739 (program): Primes congruent to 12 mod 59.
  • A142740 (program): Primes congruent to 13 mod 59.
  • A142741 (program): Primes congruent to 14 mod 59.
  • A142742 (program): Primes congruent to 15 mod 59.
  • A142743 (program): Primes congruent to 16 mod 59.
  • A142744 (program): Primes congruent to 17 mod 59.
  • A142745 (program): Primes congruent to 18 mod 59.
  • A142746 (program): Primes congruent to 19 mod 59.
  • A142747 (program): Primes congruent to 20 mod 59.
  • A142748 (program): Primes congruent to 21 mod 59.
  • A142749 (program): Primes congruent to 22 mod 59.
  • A142750 (program): Primes congruent to 23 mod 59.
  • A142751 (program): Primes congruent to 24 mod 59.
  • A142752 (program): Primes congruent to 25 mod 59.
  • A142753 (program): Primes congruent to 26 mod 59.
  • A142754 (program): Primes congruent to 27 mod 59.
  • A142755 (program): Primes congruent to 28 mod 59.
  • A142756 (program): Primes congruent to 29 mod 59.
  • A142757 (program): Primes congruent to 30 mod 59.
  • A142758 (program): Primes congruent to 31 mod 59.
  • A142759 (program): Primes congruent to 32 mod 59.
  • A142760 (program): Primes congruent to 33 mod 59.
  • A142761 (program): Primes congruent to 34 mod 59.
  • A142762 (program): Primes congruent to 35 mod 59.
  • A142763 (program): Primes congruent to 36 mod 59.
  • A142764 (program): Primes congruent to 37 mod 59.
  • A142765 (program): Primes congruent to 38 mod 59.
  • A142766 (program): Primes congruent to 39 mod 59.
  • A142767 (program): Primes congruent to 40 mod 59.
  • A142768 (program): Primes congruent to 41 mod 59.
  • A142769 (program): Primes congruent to 42 mod 59.
  • A142770 (program): Primes congruent to 43 mod 59.
  • A142771 (program): Primes congruent to 44 mod 59.
  • A142772 (program): Primes congruent to 45 mod 59.
  • A142773 (program): Primes congruent to 46 mod 59.
  • A142774 (program): Primes congruent to 47 mod 59.
  • A142775 (program): Primes congruent to 48 mod 59.
  • A142776 (program): Primes congruent to 49 mod 59.
  • A142777 (program): Primes congruent to 50 mod 59.
  • A142778 (program): Primes congruent to 51 mod 59.
  • A142779 (program): Primes congruent to 52 mod 59.
  • A142780 (program): Primes congruent to 53 mod 59.
  • A142781 (program): Primes congruent to 54 mod 59.
  • A142782 (program): Primes congruent to 55 mod 59.
  • A142783 (program): Primes congruent to 56 mod 59.
  • A142784 (program): Primes congruent to 57 mod 59.
  • A142785 (program): Primes congruent to 58 mod 59.
  • A142786 (program): Primes congruent to 7 mod 60.
  • A142787 (program): Primes congruent to 13 mod 60.
  • A142788 (program): Primes congruent to 17 mod 60.
  • A142789 (program): Primes congruent to 19 mod 60.
  • A142790 (program): Primes congruent to 23 mod 60.
  • A142791 (program): Primes congruent to 29 mod 60.
  • A142792 (program): Primes congruent to 31 mod 60.
  • A142793 (program): Primes congruent to 37 mod 60.
  • A142794 (program): Primes congruent to 41 mod 60.
  • A142795 (program): Primes congruent to 43 mod 60.
  • A142796 (program): Primes congruent to 47 mod 60.
  • A142797 (program): Primes congruent to 49 mod 60.
  • A142798 (program): Primes congruent to 53 mod 60.
  • A142799 (program): Primes congruent to 59 mod 60.
  • A142800 (program): Primes congruent to 2 mod 61.
  • A142801 (program): Primes congruent to 3 mod 61.
  • A142802 (program): Primes congruent to 4 mod 61.
  • A142803 (program): Primes congruent to 5 mod 61.
  • A142804 (program): Primes congruent to 6 mod 61.
  • A142805 (program): Primes congruent to 7 mod 61.
  • A142806 (program): Primes congruent to 8 mod 61.
  • A142807 (program): Primes congruent to 9 mod 61.
  • A142808 (program): Primes congruent to 10 mod 61.
  • A142809 (program): Primes congruent to 11 mod 61.
  • A142810 (program): Primes congruent to 12 mod 61.
  • A142811 (program): Primes congruent to 13 mod 61.
  • A142812 (program): Primes congruent to 14 mod 61.
  • A142813 (program): Primes congruent to 15 mod 61.
  • A142814 (program): Primes congruent to 16 mod 61.
  • A142815 (program): Primes congruent to 17 mod 61.
  • A142816 (program): Primes congruent to 18 mod 61.
  • A142817 (program): Primes congruent to 19 mod 61.
  • A142818 (program): Primes congruent to 20 mod 61.
  • A142819 (program): Primes congruent to 21 mod 61.
  • A142820 (program): Primes congruent to 22 mod 61.
  • A142821 (program): Primes congruent to 23 mod 61.
  • A142822 (program): Primes congruent to 24 mod 61.
  • A142823 (program): Primes congruent to 25 mod 61.
  • A142824 (program): Primes congruent to 26 mod 61.
  • A142825 (program): Primes congruent to 27 mod 61.
  • A142826 (program): Primes congruent to 28 mod 61.
  • A142827 (program): Primes congruent to 29 mod 61.
  • A142828 (program): Primes congruent to 30 mod 61.
  • A142829 (program): Primes congruent to 31 mod 61.
  • A142830 (program): Primes congruent to 32 mod 61.
  • A142831 (program): Primes congruent to 33 mod 61.
  • A142832 (program): Primes congruent to 34 mod 61.
  • A142833 (program): Primes congruent to 35 mod 61.
  • A142834 (program): Primes congruent to 36 mod 61.
  • A142835 (program): Primes congruent to 37 mod 61.
  • A142836 (program): Primes congruent to 38 mod 61.
  • A142837 (program): Primes congruent to 39 mod 61.
  • A142838 (program): Primes congruent to 40 mod 61.
  • A142839 (program): Primes congruent to 41 mod 61.
  • A142840 (program): Primes congruent to 42 mod 61.
  • A142841 (program): Primes congruent to 43 mod 61.
  • A142842 (program): Primes congruent to 44 mod 61.
  • A142843 (program): Primes congruent to 45 mod 61.
  • A142844 (program): Primes congruent to 46 mod 61.
  • A142845 (program): Primes congruent to 47 mod 61.
  • A142846 (program): Primes congruent to 48 mod 61.
  • A142847 (program): Primes congruent to 49 mod 61.
  • A142848 (program): Primes congruent to 50 mod 61.
  • A142849 (program): Primes congruent to 51 mod 61.
  • A142850 (program): Primes congruent to 52 mod 61.
  • A142851 (program): Primes congruent to 53 mod 61.
  • A142852 (program): Primes congruent to 54 mod 61.
  • A142853 (program): Primes congruent to 55 mod 61.
  • A142854 (program): Primes congruent to 56 mod 61.
  • A142855 (program): Primes congruent to 57 mod 61.
  • A142856 (program): Primes congruent to 58 mod 61.
  • A142857 (program): Primes congruent to 59 mod 61.
  • A142858 (program): Primes congruent to 60 mod 61.
  • A142874 (program): Primes congruent to 33 mod 62.
  • A142879 (program): a(n) = 5*a(n-3) - a(n-6) with terms 1..6 as 0, 1, 2, 5, 7, 9.
  • A142880 (program): a(n) = 7*a(n-3) - a(n-6).
  • A142881 (program): a(0) = 0, a(1) = 1, after which, if n=3k: a(n) = 2*a(n-1) - a(n-2), if n=3k+1: a(n) = a(n-1) + a(n-2), if n=3k+2: a(n) = 2*a(n-1) + a(n-2).
  • A142882 (program): First trisection of A120070.
  • A142883 (program): a(n) = A142590(n)/3.
  • A142888 (program): First differences of A142705.
  • A142889 (program): Primes congruent to 1 mod 63.
  • A142890 (program): Primes congruent to 2 mod 63.
  • A142891 (program): Primes congruent to 4 mod 63.
  • A142892 (program): Primes congruent to 5 mod 63.
  • A142893 (program): Primes congruent to 8 mod 63.
  • A142894 (program): Primes congruent to 10 mod 63.
  • A142895 (program): Primes congruent to 11 mod 63.
  • A142896 (program): Primes congruent to 13 mod 63.
  • A142897 (program): Primes congruent to 16 mod 63.
  • A142898 (program): Primes congruent to 17 mod 63.
  • A142899 (program): Primes congruent to 19 mod 63.
  • A142900 (program): Primes congruent to 20 mod 63.
  • A142901 (program): Primes congruent to 22 mod 63.
  • A142902 (program): Primes congruent to 23 mod 63.
  • A142903 (program): Primes congruent to 25 mod 63.
  • A142904 (program): Primes congruent to 26 mod 63.
  • A142905 (program): Primes congruent to 29 mod 63.
  • A142906 (program): Primes congruent to 31 mod 63.
  • A142907 (program): Primes congruent to 32 mod 63.
  • A142908 (program): Primes congruent to 34 mod 63.
  • A142909 (program): Primes congruent to 37 mod 63.
  • A142910 (program): Primes congruent to 38 mod 63.
  • A142911 (program): Primes congruent to 40 mod 63.
  • A142912 (program): Primes congruent to 41 mod 63.
  • A142913 (program): Primes congruent to 43 mod 63.
  • A142914 (program): Primes congruent to 44 mod 63.
  • A142915 (program): Primes congruent to 46 mod 63.
  • A142916 (program): Primes congruent to 47 mod 63.
  • A142917 (program): Primes congruent to 50 mod 63.
  • A142918 (program): Primes congruent to 52 mod 63.
  • A142919 (program): Primes congruent to 53 mod 63.
  • A142920 (program): Primes congruent to 55 mod 63.
  • A142921 (program): Primes congruent to 58 mod 63.
  • A142922 (program): Primes congruent to 59 mod 63.
  • A142923 (program): Primes congruent to 61 mod 63.
  • A142924 (program): Primes congruent to 62 mod 63.
  • A142925 (program): Primes congruent to 1 mod 64.
  • A142926 (program): Primes congruent to 3 mod 64.
  • A142927 (program): Primes congruent to 5 mod 64.
  • A142928 (program): Primes congruent to 7 mod 64.
  • A142929 (program): Primes congruent to 9 mod 64.
  • A142930 (program): Primes congruent to 11 mod 64.
  • A142931 (program): Primes congruent to 13 mod 64.
  • A142932 (program): Primes congruent to 15 mod 64.
  • A142933 (program): Primes congruent to 17 mod 64.
  • A142934 (program): Primes congruent to 19 mod 64.
  • A142935 (program): Primes congruent to 23 mod 64.
  • A142936 (program): Primes congruent to 25 mod 64.
  • A142937 (program): Primes congruent to 27 mod 64.
  • A142938 (program): Primes congruent to 29 mod 64.
  • A142939 (program): Primes congruent to 31 mod 64.
  • A142940 (program): Primes congruent to 35 mod 64.
  • A142941 (program): Primes congruent to 37 mod 64.
  • A142942 (program): Primes congruent to 39 mod 64.
  • A142943 (program): Primes congruent to 41 mod 64.
  • A142944 (program): Primes congruent to 43 mod 64.
  • A142945 (program): Primes congruent to 45 mod 64.
  • A142946 (program): Primes congruent to 47 mod 64.
  • A142947 (program): Primes congruent to 49 mod 64.
  • A142948 (program): Primes congruent to 51 mod 64.
  • A142949 (program): Primes congruent to 53 mod 64.
  • A142950 (program): Primes congruent to 55 mod 64.
  • A142951 (program): Primes congruent to 57 mod 64.
  • A142952 (program): Primes congruent to 59 mod 64.
  • A142953 (program): Primes congruent to 61 mod 64.
  • A142954 (program): a(n) = 2*n+3+3*(-1)^n.
  • A142962 (program): Scaled convolution of (n^3)*A000984(n) with A000984(n). A000984(n) = binomial(2*n,n) (central binomial coefficients).
  • A142964 (program): a(n) = 6*2^n - 2*n - 5.
  • A142965 (program): One fourth of third column (m=2) of triangle A142963.
  • A142969 (program): Numerators of approximants of a continued fraction for 4/Pi - 1 = (4 - Pi)/Pi.
  • A142970 (program): Numerators of n-th approximants of a continued fraction for Pi-3.
  • A142971 (program): Triangle read by rows: A061397 with negative signs interleaved with (k-1) zeros.
  • A142974 (program): A007318 * [1, 1, -1, 1, 1, 1, …].
  • A142975 (program): n-th term of the Fibonacci-type sequence x(1)=1, x(2)=Fibonacci(n), x(k+1)=x(k)+x(k-1) for k>1.
  • A142976 (program): a(n) = (1/18)*(9*n^2 + 21*n + 10 - 4^(n+2)*(3*n+5) + 10*7^(n+1)).
  • A142977 (program): Table of coefficients in the expansion of the rational function 1/{(1-x)^2 - y*(1+x)^2}.
  • A142978 (program): Table of figurate numbers for the n-dimensional cross polytopes.
  • A142979 (program): a(1) = 1, a(2) = 3, a(n+2) = 3*a(n+1) + (n+1)^2*a(n).
  • A142980 (program): a(1) = 1, a(2) = 5, a(n+2) = 5*a(n+1) + (n+1)^2*a(n).
  • A142981 (program): a(1) = 1, a(2) = 7, a(n+2) = 7*a(n+1) + (n+1)^2*a(n).
  • A142982 (program): a(1) = 1, a(2) = 9, a(n+2) = 9*a(n+1) + (n+1)^2*a(n).
  • A142983 (program): a(1) = 1, a(2) = 2, a(n+2) = 2*a(n+1) + (n+1)*(n+2)*a(n).
  • A142984 (program): a(1) = 1, a(2) = 4, a(n+2) = 4*a(n+1) + (n+1)*(n+2)*a(n).
  • A142985 (program): a(1) = 1, a(2) = 6, a(n+2) = 6*a(n+1) + (n+1)*(n+2)*a(n).
  • A142986 (program): a(1) = 1, a(2) = 8, a(n+2) = 8*a(n+1) + (n+1)*(n+2)*a(n).
  • A142987 (program): a(1) = 1, a(2) = 10, a(n+2) = 10*a(n+1) + (n+1)*(n+2)*a(n).
  • A142988 (program): a(1) = 1, a(2) = 3, a(n+2) = 3*a(n+1)+(n+1)*(n+3)*a(n).
  • A142989 (program): a(1) = 1, a(2) = 5, a(n+2) = 5*a(n+1)+(n+1)*(n+3)*a(n).
  • A142990 (program): a(1) = 1, a(2) = 7, a(n+2) = 7*a(n+1)+(n+1)*(n+3)*a(n).
  • A142991 (program): a(1) = 1, a(2) = 9, a(n+2) = 9*a(n+1)+(n+1)*(n+3)*a(n).
  • A142992 (program): Square array, read by ascending antidiagonals, of the crystal ball sequences for the root lattices of type C_n.
  • A142993 (program): Crystal ball sequence for the lattice C_4.
  • A142994 (program): Crystal ball sequence for the lattice C_5.
  • A142995 (program): a(0) = 0, a(1) = 1, a(n+1) = (2*n^2 + 2*n + 3)*a(n) - n^4*a(n-1), n >= 1.
  • A142996 (program): a(0) = 0, a(1) = 1, a(n+1) = (2*n^2+2*n+7)*a(n) - n^4*a(n-1), n >= 1.
  • A142997 (program): a(0) = 0, a(1) = 1, a(n+1) = (2*n^2+2*n+13)*a(n) - n^4*a(n-1).
  • A142998 (program): a(0) = 0, a(1) = 1, a(n+1) = (2*n^2+2*n+21)*a(n) - n^4*a(n-1).
  • A142999 (program): a(0) = 0, a(1) = 1; for n>1, a(n+1) = (2*n+1)*a(n) + n^4*a(n-1).
  • A143007 (program): Square array, read by antidiagonals, where row n equals the crystal ball sequence for the 2*n-dimensional lattice A_n x A_n.
  • A143008 (program): Crystal ball sequence for the A2 x A2 lattice.
  • A143009 (program): Crystal ball sequence for the A3 x A3 lattice.
  • A143010 (program): Crystal ball sequence for the A4 x A4 lattice.
  • A143011 (program): Crystal ball sequence for the A_5 x A_5 lattice.
  • A143012 (program): Numbers of the form (4^p + 2^p + 1)/7, where p > 3 is prime.
  • A143017 (program): Number of {2-1-3, 2’^e-31}-avoiding permutations of size n (see definition in the Elizalde paper).
  • A143018 (program): Triangle read by rows: T(n,k) (n >= 2, k >= 1) is the number of non-crossing connected graphs on n nodes on a circle such that the distance from a fixed node (root) to the next node is k. Rows are indexed 2,3,4,…; columns are indexed 1,2,3, … .
  • A143019 (program): Infinite square array read by antidiagonals: a(q,n) is the coefficient of z^n in the series expansion of C(z)^q/(1-4z)^(3/2), where C(z) = (1-sqrt(1-4z))/(2z) is the Catalan function (q,n = 0,1,2,…).
  • A143020 (program): Sum of the distances from a fixed node (root) to the next node in all non-crossing graphs on n nodes on a circle.
  • A143021 (program): Number of vertices of degree 1 in all non-crossing connected graphs on n points on a circle.
  • A143023 (program): Sum of the root degrees over all non-crossing connected graphs on n nodes on a circle (by root we mean a distinguished node).
  • A143025 (program): Period length 4: repeat [1, 8, 2, 8].
  • A143037 (program): Triangle read by rows, A000012 * A127773 * A000012. A000012 is an infinite lower triangular matrix with all 1’s, A127773 = (1; 0,3; 0,0,6; 0,0,0,10; …).
  • A143038 (program): Triangle read by rows, A000012 * A134309 * A000012, where A134309 = an infinite lower triangular matrix with (1, 1, 2, 4, 8, 16, …) in the main diagonal and the rest zeros.
  • A143051 (program): Smallest number not occurring earlier and smaller than the largest square so far, the next square if no such number exists.
  • A143052 (program): Inverse permutation to A143051.
  • A143053 (program): A143051(A143051(n)).
  • A143054 (program): A143052(A143052(n)).
  • A143055 (program): The real part of complex sequence: a(n) = a(n-1) + (1+i)*a(n-2).
  • A143056 (program): a(n) = Re(b(n)) where b(n)=(1+i)*b(n-1)+b(n-2), with b(1)=0, b(2)=1.
  • A143058 (program): A007318 * [1, 6, 7, 1, 0, 0, 0, …].
  • A143059 (program): A007318 * [1, 10, 25, 15, 1, 0, 0, 0, …].
  • A143061 (program): Triangle read by rows, A000012 * A127647 * A000012.
  • A143062 (program): Expansion of false theta series variation of Euler’s pentagonal number series in powers of x.
  • A143064 (program): Expansion of a Ramanujan false theta series variation of A089801 in powers of x.
  • A143070 (program): A positive integer n is included if the number of 0’s in the binary representation of n is a power of 2 (including being possibly 1).
  • A143071 (program): A positive integer n is included if the number of 1’s in the binary representation of n is a power of 2 (including being possibly 1).
  • A143072 (program): A positive integer n is included if both the number of 0’s and the number of 1’s in the binary representation of n are powers of 2 (including being possibly 1).
  • A143074 (program): Numerator of Euler(n,2).
  • A143075 (program): Polynomial expansion sequence: p(x)=1/(1 - 4x + 5x^2 - 6x^4 + 6x^5 - x^6 - 2x^7 + x^8).
  • A143077 (program): a(n) is the n-th term of a pseudo-Fibonacci sequence created by applying the function fib(1,…,n) to itself n times.
  • A143079 (program): a(n) = ((9+sqrt(9))^n + (9-sqrt(9))^n)/2.
  • A143080 (program): Triangular sequence of coefficients from an exponential based polynomial: p(x,n)=If[n == 0, 1, -(2*n - 1)!*x^(2*n)*(Sum[x^i/(i + 2*n)!, {i, 0, Infinity}] - Exp[x]/x^(2*n))].
  • A143083 (program): A triangle of coefficients: T(n,m) = (2*n + 2*m + 3)! / (2*(2*m + 1)!*(2*n + 1)!).
  • A143084 (program): Triangle read by rows: T(n,m) = (n + m)!.
  • A143085 (program): Triangle sequence: t(n,m)=(n+1)*(n+m)!.
  • A143086 (program): Symmetrical triangle sequence: t(n,m)=If[m < = ( less than or equal) Floor[n/2], 2^(m + 1) - 1, 2^(n - m + 1) - 1].
  • A143087 (program): Symmetrical triangle sequence: t(n,m)=If[m <= Floor[n/2], 2^(m + 1) - 1, 2^(n - m + 1) - 1]*Binomial[n, m].
  • A143088 (program): Triangle T(n,m)=( 2^(m+1)-1 ) * ( 2^(n-m+1)-1 ), read by rows, 0<=m<=n.
  • A143090 (program): Aliquot sequence starting at 12.
  • A143095 (program): (1, 2, 4, 8, …) interleaved with (4, 8, 16, 32, …).
  • A143096 (program): a(n) = 2*a(n-1)-1, with a(1)=1, a(2)=4, a(3)=5.
  • A143097 (program): 3*k - 2 interleaved with 3*k - 1 and 3*k.
  • A143098 (program): First differences of A143097.
  • A143099 (program): A007318 * A143097.
  • A143100 (program): A007318 * A143098.
  • A143101 (program): Partial sums of A143097.
  • A143103 (program): Row sums of triangle A143102.
  • A143104 (program): Infinite Redheffer matrix read by upwards antidiagonals.
  • A143110 (program): Triangle read by rows, A051731 * A000034 * 0^(n-k), 1<=k<=n.
  • A143112 (program): A051731 * A032742 = sum of largest proper divisors of the divisors of n.
  • A143121 (program): Triangle read by rows, T(n,k) = Sum_{j=k..n} prime(j), 1 <= k <= n.
  • A143122 (program): Triangle read by rows, T(n,k) = Sum_{j=k..n} j!, 0 <= k <= n.
  • A143125 (program): Sum {j=1..n} j*A001462(j).
  • A143126 (program): a(n) = (1-2n)*2^n.
  • A143127 (program): a(n) = Sum_{k=1..n} k*d(k) where d(k) is the number of divisors of k.
  • A143128 (program): a(n) = Sum_{k=1..n} k*sigma(k).
  • A143129 (program): Triangle read by rows, T(n,k) = sum {j=k..n} A000292(j) = A000012 * (A000292 * 0^(n-k)) * A000012, 1<=k<=n.
  • A143130 (program): Triangle read by rows, A000012 * (A000332 * 0^(n-k)) * A000012, 0<=k<=n.
  • A143131 (program): Binomial transform of [1, 4, 10, 20, 0, 0, 0, …].
  • A143132 (program): Binomial transform of [1, 5, 15, 35, 70, 0, 0, 0, …].
  • A143146 (program): a(n) is the smallest positive multiple of n that has the same number of 0’s as 1’s in its binary representation.
  • A143149 (program): Decimal expansion of 5*sqrt(2*Pi)/4.
  • A143151 (program): Triangle read by rows, A051731 * (A020639 * 0^(n-k)), 1<=k<=n.
  • A143152 (program): Inverse Möbius transform of the least prime factor of n: A051731 * A020639.
  • A143153 (program): Triangle read by rows, A054525 * (A020639 * 0^(n-k)), 1<=k<=n.
  • A143156 (program): Triangle read by rows, T(n,k) = Sum_{j=k..n} A001511(j); = A000012 * (A001511 * 0^(n-k)) * A000012; 1<=k<=n.
  • A143157 (program): Partial sums of A091512.
  • A143158 (program): Triangle read by rows, T(n,k) = Sum_{j=k..n} mu(j).
  • A143159 (program): Expansion of q^(-13/24) * eta(q^2) * eta(q^3) * eta(q^4)^2 in powers of q.
  • A143164 (program): Numbers with digitsum 13, in increasing order.
  • A143165 (program): Expansion of the exponential generating function arcsin(2*x)/(2*(1-2*x)^(3/2)).
  • A143166 (program): a(n) = n*(8*n^2 + 1)/3.
  • A143167 (program): Second column of triangle A000369: |S2(-3;n+2,2)|.
  • A143168 (program): Third column of triangle A000369: |S2(-3; n+3, 3)|.
  • A143169 (program): Fourth column of triangle A000369: |S2(-3;n+4,4)|.
  • A143182 (program): Triangle T(n,m) = 1 + abs(n-2*m), read by rows, 0<=m<=n.
  • A143183 (program): Triangle t(n,m) = 1 + (2+n)*abs(n-2m) read by rows, 0<=m<=n.
  • A143187 (program): A symmetrical triangle sequence with low, even center: t(n,m)=If[(n - m)*m == 0, 1, If[m <= Floor[n/2] && Mod[m, 2] == 1, 2*m, If[m <= Floor[n/2] && Mod[m, 2] == 0, m, If[m > Floor[n/2] && Mod[n - m, 2] == 1, 2*(n - m), If[m > Floor[n/2] && Mod[n - m, 2] == 0, (n - m), n - m]]]]].
  • A143188 (program): A symmetrical triangle sequence with low, even center: t(n,m)=If[(n - m)*m == 0, 1, If[m <= Floor[n/2] && Mod[m, 2] == 1, 2*m, If[m <= Floor[n/2] && Mod[m, 2] == 0, m, If[m > Floor[n/2] && Mod[n - m, 2] == 1, 2*(n - m), If[m > Floor[n/2] && Mod[n - m, 2] == 0, (n - m), n - m]]]]]*Binomial[n, m].
  • A143198 (program): Triangle t(n,m) = n +(n+1)*(m-1)*(m+2)/2 read by rows, 0<=m<=n.
  • A143199 (program): A symmetrical triangular sequence based on a generalization of A142463 at n=3: a(n)=a(n-1)+n;A000096; t(n,m)=If[m <= Floor[n/2], (n + 1)*a[m] + n, (n + 1)*a[n - m] + n].
  • A143200 (program): Triangle read by rows: t(n,m) is -1 if binomial(n, m) is greater than 1 and odd, otherwise t(n,m) = binomial(n, m) mod 2.
  • A143201 (program): Product of distances between prime factors in factorization of n.
  • A143206 (program): Product of the n-th cousin prime pair.
  • A143207 (program): Numbers with distinct prime factors 2, 3, and 5.
  • A143208 (program): a(1)=2; for n>1, a(n) = (4-9*n+3*n^2)/2.
  • A143211 (program): Triangle read by rows, T(n,k) = F(n)*F(k); 1<=k<=n.
  • A143212 (program): a(n) = F(n) * (F(n+2)-1) = A000045(n) * A000071(n+2) = row sums of triangle A143211.
  • A143214 (program): Gray code applied to Pascal’s triangle: T(n,m)=GrayCode(binomial(n,m)).
  • A143215 (program): a(n) = prime(n) * Sum_{i=1..n} prime(i).
  • A143216 (program): Triangle read by rows: T(n,k) = n!*k!, 0 <= k <= n.
  • A143217 (program): a(n) = n! * (!(n+1)) = n! * Sum_{k=0..n} k!.
  • A143218 (program): Triangle read by rows, A127775 * A000012 * A127775; 1<=k<=n.
  • A143219 (program): Triangle read by rows, A127648 * A000012 * A127773, 1 <= k <= n.
  • A143229 (program): a(n) = A000041(n) * A000070(n).
  • A143230 (program): Triangle read by rows, A130207 * A000012 * A130207.
  • A143231 (program): a(n) = A000010(n) * A002088(n).
  • A143236 (program): a(n) = A000005(n) * A006218(n).
  • A143238 (program): a(n) = A000203(n) * A024916(n).
  • A143239 (program): Triangle read by rows, A126988 * A128407 as infinite lower triangular matrices.
  • A143250 (program): Reverse binary expansion of the Fibonacci numbers.
  • A143253 (program): Irregular triangle by rows, squares mod primes; 1<=k<=n.
  • A143254 (program): Triangle read by rows, T(n,k) = (4n-3)*(4k-3); 1<=k<=n.
  • A143255 (program): Triangle read by rows, A128407 * A126988; 1<=k<=n.
  • A143256 (program): Triangle read by rows, matrix multiplication A051731 * A128407 * A127648, 1<=k<=n.
  • A143257 (program): Reverse binary expansion of the factorial numbers.
  • A143259 (program): a(n) = 1 if n is a nonzero square, -1 if n is twice a nonzero square, 0 otherwise.
  • A143261 (program): Triangle read by rows: binary reversed Gray code of binomial(n,m).
  • A143267 (program): Triangle read by rows, A130207 * A000012 * A127648.
  • A143268 (program): a(n) = phi(n)*T(n), where phi(n) is Euler’s totient function (A000010) and T(n) = n*(n+1)/2 is the n-th triangular number (A000217).
  • A143269 (program): Triangle read by rows, A127648 * A000012 * A130207, 1<=k<=n.
  • A143270 (program): a(n) = n*A002088(n).
  • A143272 (program): a(n) = d(n)*T(n), where d(n) is the number of divisors of n (A000005) and T(n)=n(n+1)/2 are the triangular numbers (A000217).
  • A143274 (program): a(n) = n * A006218(n).
  • A143275 (program): A054525 * A029935.
  • A143278 (program): Convolution of A006352 and A010815.
  • A143281 (program): Number of binary words of length n containing at least one subword 101 and no subword 11.
  • A143282 (program): Number of binary words of length n containing at least one subword 1001 and no subwords 10^{i}1 with i<2.
  • A143292 (program): Gray code of prime(n) (decimal representation).
  • A143293 (program): Partial sums of A002110, the primorial numbers.
  • A143298 (program): Decimal expansion of Gieseking’s constant.
  • A143299 (program): Number of terms in the Zeckendorf representation of every number in row n of the Wythoff array.
  • A143310 (program): Triangle read by rows, A000012 * A127446, 1 <= k <= n.
  • A143311 (program): Triangle read by rows, A127648 * A126988; 1<=k<=n.
  • A143329 (program): Primes in A143292.
  • A143330 (program): G.f. satisfies: A(x) = (1 + x*A(x)^2)/(1 - x^2).
  • A143331 (program): Lengths of successive runs of 0’s in the Thue-Morse sequence A010060.
  • A143332 (program): Related to Gray code representation of Fibonacci(n) in base 10.
  • A143333 (program): Pascal’s triangle binomial(n,m) read by rows, all even elements replaced by zero.
  • A143336 (program): Expansion of K(k) * (2 * E(k) - K(k)) / (Pi/2)^2 in powers of q where E(k), K(k) are complete elliptic integrals and q = exp(-Pi * K(k’) / K(k)).
  • A143337 (program): Expansion of K(k) * (6 * E(k) - (1 + 4*k’^2) * K(k)) / (Pi/2)^2 in powers of q where E(k), K(k) are complete elliptic integrals and q = exp(-Pi * K(k’) / K(k)).
  • A143339 (program): G.f. satisfies: A(x) = 1 + x*A(x)^2/A(-x).
  • A143348 (program): a(n) = -(-1)^n times sum of divisors of n.
  • A143352 (program): Triangle read by rows, A051731 * A054524 = (A051731)^2 * A128407; 1<=k<=n.
  • A143356 (program): A051731 * A006218.
  • A143357 (program): Floor((n-1)!/[n(n+1)]).
  • A143358 (program): Triangle read by rows: T(n,k) = 2^k*binomial(n,k)*binomial(n-k, floor((n-k)/2)), 0 <= k <= n.
  • A143360 (program): Sum of root degrees of all symmetric ordered trees with n edges.
  • A143361 (program): Triangle read by rows: T(n,k) is the number of 010-avoiding binary words of length n containing k 00 subwords (0<=k<=n-1).
  • A143363 (program): Number of ordered trees with n edges and having no protected vertices. A protected vertex in an ordered tree is a vertex at least 2 edges away from its leaf descendants.
  • A143365 (program): Numbers n such that (prime(n)-11)/10 is a prime.
  • A143368 (program): Triangle read by rows: T(n,k) is the Wiener index of a k X n grid (i.e., P_k X P_n, where P_m is the path graph on m vertices; 1 <= k <= n).
  • A143370 (program): Triangle read by rows: T(n,k) is the number of unordered pairs of vertices at distance k in the grid P_2 x P_n (1 <= k <= n). P_m is the path graph on m vertices.
  • A143373 (program): Expansion of x/(1 - x - 2*x^3 - 2*x^5 - x^7).
  • A143374 (program): G.f.: eta(q)*eta(q^3)*eta(q^9)*eta(q^27)*eta(q^81)*eta(q^243)*…, where eta(q) = Product((1-q^m), m=1..oo).
  • A143376 (program): Triangle read by rows: T(n,k) is the number of unordered pairs of vertices at distance k in the cube Q_n of dimension n (1 <= k <= n).
  • A143377 (program): Expansion of q^(-1/6) * eta(q)^2 * eta(q^4) / eta(q^2) in powers of q.
  • A143378 (program): Expansion of q^(-1/24) * eta(q^2)^5 / (eta(q) * eta(q^4)^2) in powers of q.
  • A143379 (program): Expansion of q^(-7/24) * eta(q) * eta(q^4)^2 / eta(q^2) in powers of q.
  • A143380 (program): Expansion of q^(-1/6) * eta(q^2)^5 / (eta(q)^2 * eta(q^4)) in powers of q.
  • A143388 (program): a(n) = Sum_{k=0..n} A033184(n,k)*A033184(n,n-k), where Catalan triangle entry A033184(n,k) = C(2*n-k,n-k)*(k+1)/(n+1).
  • A143392 (program): A quadratic recursion sequence: a(n)=a(n - 1)^2 - 2*a(n - 1) - a(n - 2)^2 + 2*a(n - 2).
  • A143399 (program): Expansion of x^k/Product_{t=k..2k} (1-tx) for k=4.
  • A143400 (program): Expansion of x^k/Product_{t=k..2k} (1-tx) for k=5.
  • A143401 (program): Expansion of x^k/Product_{t=k..2k} (1-tx) for k=6.
  • A143402 (program): Expansion of x^k/Product_{t=k..2k} (1-tx) for k=7.
  • A143403 (program): Expansion of x^k/Product_{t=k..2k} (1-tx) for k=8.
  • A143409 (program): Square array read by antidiagonals: form the Euler-Seidel matrix for the sequence {k!} and then divide column k by k!.
  • A143410 (program): Form the difference table of the sequence {2^k*k!}, then divide k-th column entries by 2^k*k!. Array read by ascending antidiagonals, T(n, k) for n, k >= 0.
  • A143411 (program): Square array, read by antidiagonals: form the Euler-Seidel matrix for the sequence {2^k*k!} and then divide column k by 2^k*k!.
  • A143412 (program): Main diagonal of A143410.
  • A143413 (program): Apéry-like numbers for the constant e: a(n) = 1/(n-1)!*Sum_{k = 0..n+1} (-1)^k*C(n+1,k)*(2*n-k)! for n >= 1.
  • A143414 (program): Apéry-like numbers for the constant 1/e: a(n) = (1/(n-1)!)*Sum_{k = 0..n-1} binomial(n-1,k)*(2*n-k)!.
  • A143415 (program): Another sequence of Apery-like numbers for the constant 1/e: a(n) = 1/(n+1)!*Sum_{k = 0..n-1} C(n-1,k)*(2*n-k)!.
  • A143418 (program): Triangle read by rows. T(n,k) = binomial(n,k)*(binomial(n,k)-1)/2.
  • A143424 (program): Triangle read by rows, A054525 * A130123, 1<=k<=n.
  • A143425 (program): Triangle read by rows A051731 * A130123, 1<=k<=n.
  • A143431 (program): Periodic length 8 sequence [1, -1, 1, -1, -1, 1, -1, 1, …].
  • A143432 (program): Ultimately periodic length 4 sequence [ 2, 2, 0, 0, …] with a(0) = a(1) = 1.
  • A143433 (program): Expansion of f(-x, x^3) in powers of x where f(,) is Ramanujan’s general theta function.
  • A143434 (program): Expansion of f(x, -x^3) in powers of x where f(,) is Ramanujan’s two-variable theta function.
  • A143438 (program): a(n) = a(n-2) + a(n-3) + a(n-4) - a(n-6), with a(0) = a(2) = a(3) = 1, a(1) = 0 and a(4) = a(5) = 2.
  • A143442 (program): Triangle read by rows, A127648 * A000012 * A128407, 1 <= k <= n.
  • A143443 (program): a(n) = n * A002321(n).
  • A143445 (program): Triangle read by rows, A051731 * (A001318 * 0^(n-k)); 1<=k<=n.
  • A143447 (program): Expansion of 1/(x^k*(1-x-2*x^(k+1))) for k=4.
  • A143448 (program): Expansion of 1/(x^k*(1-x-2*x^(k+1))) for k=5.
  • A143449 (program): Expansion of 1/(x^k*(1-x-2*x^(k+1))) for k=6.
  • A143450 (program): Expansion of 1/(x^k*(1-x-2*x^(k+1))) for k=7.
  • A143451 (program): Expansion of 1/(x^k*(1-x-2*x^(k+1))) for k=8.
  • A143452 (program): Expansion of 1/(x^k*(1-x-2*x^(k+1))) for k=9.
  • A143454 (program): Expansion of 1/(x^k*(1 - x - 3*x^(k+1))) for k=3.
  • A143455 (program): Expansion of 1/(x^k*(1-x-3*x^(k+1))) for k=4.
  • A143456 (program): Expansion of 1/(x^k*(1-x-3*x^(k+1))) for k=5.
  • A143457 (program): Expansion of 1/(x^k*(1-x-3*x^(k+1))) for k=6.
  • A143458 (program): Expansion of 1/(x^k*(1-x-3*x^(k+1))) for k=7.
  • A143459 (program): Expansion of 1/(x^k*(1-x-3*x^(k+1))) for k=8.
  • A143460 (program): Expansion of 1/(x^k*(1-x-3*x^(k+1))) for k=9.
  • A143462 (program): Expansion of 1/(1 + 4*x + 8*x^2).
  • A143464 (program): Catalan transform of the Pell sequence.
  • A143466 (program): Odious count triangle, T(n,k) = A010060(n) * A010060(k); 1 <= k <= n.
  • A143468 (program): Triangle read by rows, A054525 * A127775, 1<=k<=n.
  • A143472 (program): Expansion of 1/(1 - x^3 - x^5 - x^7 + x^10), inverse of a Salem polynomial.
  • A143497 (program): Triangle of unsigned 2-Lah numbers.
  • A143498 (program): Triangle of unsigned 3-Lah numbers.
  • A143499 (program): Triangle of unsigned 4-Lah numbers.
  • A143502 (program): n occurs d(n-1) times.
  • A143513 (program): Numbers of the form 2^a 3^b 5^c 17^d 257^e 65537^f; products of 2 and the Fermat primes.
  • A143517 (program): Triangle read by rows, A054525 * (A061397 * 0^(n-k)), 1<=k<=n.
  • A143518 (program): Triangle read by rows, A054525 * (A010051 * 0^(n-k)), 1<=k<=n.
  • A143519 (program): Moebius transform of A010051, the characteristic function of the primes: a(n) = Sum_{d|n} mu(n/d)*A010051(d); A054525 * A010051.
  • A143520 (program): a(n) is n times number of divisors of n if n is odd, zero if n is twice odd, n times number of divisors of n/4 if n is divisible by 4.
  • A143521 (program): G.f.: Sum_{k>0} k * x^k / (1 + (-x)^k)^2.
  • A143536 (program): Triangle read by rows, T(n,k) = 1 if n is prime, 0 otherwise.
  • A143537 (program): Triangle read by rows: T(n,k) = number of primes in the interval [k..n], n >= 1, 1 <= k <= n.
  • A143538 (program): Triangle read by rows, T(n,k) = 1 if k is prime, 0 otherwise; 1 <= k <= n.
  • A143539 (program): Number of ways to express 2n-1 as p+2a^2; p prime, a > 0.
  • A143541 (program): Triangle read by rows, T(n,k) = 1 if both n and k are prime, 0 otherwise; 1 <= k <= n.
  • A143544 (program): Triangle read by rows, T(n,k) = 2 if n is prime, 1 otherwise; 1<=k<=n.
  • A143545 (program): a(n) = n unless n is a prime, in which case a(n) = 2n.
  • A143546 (program): G.f. satisfies: A(x) = 1 + x*A(x)^3*A(-x)^2.
  • A143547 (program): G.f. satisfies: A(x) = 1 + x*A(x)^4*A(-x)^3.
  • A143549 (program): G.f. satisfies: A(x) = 1 + x*A(x)^4*A(-x).
  • A143554 (program): G.f. satisfies: A(x) = 1 + x*A(x)^5*A(-x)^4.
  • A143555 (program): G.f. satisfies: A(x) = 1 + x*A(x)^2/A(-x)^2.
  • A143574 (program): Sum of all distinct squares occurring when partitioning n into two squares.
  • A143575 (program): Numbers m such that A143574(m) = m.
  • A143579 (program): Permutation of the natural numbers (0,1,2,3,…): Odious numbers (A000069) interleaved with Evil numbers (A001969).
  • A143581 (program): Numerators of coefficient of x^(n+1/2) in the series expansion of the haversine.
  • A143582 (program): Denominators of coefficient of x^(n+1/2) in the series expansion of the haversine.
  • A143583 (program): Apéry-like numbers: a(n) = (1/C(2n,n))*Sum_{k=0..n} C(2k,k)*C(4k,2k)*C(2n-2k,n-k)*C(4n-4k,2n-2k).
  • A143593 (program): Triangle read by rows, square of an infinite lower triangular matrix with 1’s in the first column and the rest 2’s.
  • A143594 (program): Triangle read by rows, A051731 * (an infinite lower triangular matrix with 1’s in the first column and the rest 2’s).
  • A143595 (program): Triangle read by rows, A000012 * (an infinite lower triangular matrix with 1’s in the first column and the rest 2’s); 1<=k<=n.
  • A143596 (program): A symmetrical triangle sequence of coefficients of a difference polynomial’ p(x,n)=((x + 1)^(2*n) - (x^2 + 1)^n)/(2*x).
  • A143603 (program): Triangle, read by rows, such that the g.f. of column k = G(x)^(2k+1) where G(x) = 1 + x*G(x)^3 is the g.f. of A001764 (ternary trees).
  • A143605 (program): Polynomial expansion sequence : p(x)=1 + x - x^5 + x^9 + x^10.
  • A143607 (program): Numerators of principal and intermediate convergents to 2^(1/2).
  • A143608 (program): A005319 and A002315 interleaved.
  • A143609 (program): Numerators of the upper principal and intermediate convergents to 2^(1/2).
  • A143611 (program): Expansion of x/((1-x)^2(1+x-x^3-x^4-x^5-x^6-x^7+x^9+x^10)).
  • A143612 (program): Triangle read by rows, A127368 * A000012, 1<=k<=n.
  • A143615 (program): Triangle A054521 * A000005 as a vector.
  • A143616 (program): Record values in A010371.
  • A143618 (program): Decimal expansion of 127/216.
  • A143621 (program): a(n) = (-1)^binomial(n,4): Periodic sequence 1,1,1,1,-1,-1,-1,-1,… .
  • A143622 (program): a(n) = (-1)^binomial(n,8): Periodic sequence 1,1,1,1,1,1,1,1,-1,-1,-1,-1,-1,-1,-1,-1,… .
  • A143623 (program): Decimal expansion of the constant cos(1) + sin(1) = 1.38177 32906 … .
  • A143624 (program): Decimal expansion of the negated constant cos(1) - sin(1) = -0.3011686789…
  • A143625 (program): Decimal expansion of the constant E_3(0) := sum {n = 0.. inf} (-1)^floor(n/3)/n! = 1 + 1/1! + 1/2! - 1/3! - 1/4! - 1/5! + + + - - - … = 2.28494 23824 … .
  • A143626 (program): Decimal expansion of the constant E_3(1) := sum {k = 0.. inf} (-1)^floor(k/3)*k/k! = 1/1! + 2/2! - 3/3! - 4/4! - 5/5! + + + - - - … = 1.30155 94959 … .
  • A143642 (program): Numerators of principal and intermediate convergents to 3^(1/2).
  • A143643 (program): Numerators of the lower principal convergents and the lower intermediate convergents to 3^(1/2).
  • A143645 (program): Aliquot sequence starting at 24.
  • A143646 (program): Catalan transform of the 3-Fibonacci sequence A006190.
  • A143647 (program): a(n) = ((5 + sqrt(3))^n + (5 - sqrt(3))^n)/2.
  • A143648 (program): a(n) = ((4 + sqrt 6)^n + (4 - sqrt 6)^n)/2.
  • A143655 (program): Triangle read by rows, primes not dividing n; A054521 * (A061397 * 0^(n-k)), 1<=k<=n.
  • A143662 (program): a(n) is the number of n-tosses having a run of 6 or more heads for a fair coin (i.e., probability is a(n)/2^n).
  • A143667 (program): Digits of the infinite Fibonacci word A003849 grouped 2 by 2 and interpreted as a binary value.
  • A143668 (program): Result of the morphing 01->01021212, 02->0102121201, 12->01021201, iterated from ‘01’. Sequence of the Fibonacci word fractal.
  • A143669 (program): a(n) = binomial((n+1)^2, n) / (n+1)^2.
  • A143681 (program): Duplicate of A081582.
  • A143683 (program): Pascal-(1,8,1) array.
  • A143684 (program): a(0) = a(1) = 0; thereafter a(n) = 2*a(n-1)*a(n-2) + 1.
  • A143685 (program): Pascal-(1,9,1) array.
  • A143689 (program): a(n) = (3*n^2 - n + 2)/2.
  • A143690 (program): a(n) = A007318 * [1, 6, 14, 9, 0, 0, 0, …].
  • A143698 (program): 12 times hexagonal numbers: 12*n*(2*n-1).
  • A143712 (program): Numbers with at least two digits in which all digits except the rightmost are even and the rightmost is odd.
  • A143721 (program): Aliquot sequence starting at 38.
  • A143722 (program): Aliquot sequence starting at 48.
  • A143723 (program): Aliquot sequence starting at 52.
  • A143724 (program): Triangle read by rows, inverse Möbius transform of a diagonalized matrix of A116470.
  • A143730 (program): a(n) = A141616(n) - A100181(n).
  • A143731 (program): Characteristic function of numbers with at least two distinct prime factors (A024619).
  • A143733 (program): Aliquot sequence starting at 62.
  • A143737 (program): Aliquot sequence starting at 68.
  • A143740 (program): E.g.f.: A(x) = exp(x + x^2*A(x)/2).
  • A143741 (program): Aliquot sequence starting at 72.
  • A143749 (program): Series reversion of x * (1 - x) / (1 + 9*x).
  • A143750 (program): a(n)=10^C(n,2)*(1-10^n)/9.
  • A143753 (program): Irregular triangle: A120070 read downwards antidiagonals.
  • A143754 (program): Aliquot sequence starting at 75.
  • A143755 (program): Aliquot sequence starting at 80.
  • A143756 (program): Aliquot sequence starting at 81.
  • A143757 (program): Aliquot sequence starting at 82.
  • A143758 (program): Aliquot sequence starting at 84.
  • A143759 (program): Aliquot sequence starting at 86.
  • A143761 (program): a(n+1) = a(n)^2 - n*a(n) + n^2, a(1) = 1.
  • A143763 (program): a(n+1) = (a(n)-n)^2, a(1) = 1.
  • A143765 (program): a(n+1) = a(n)^2 - 3*n*a(n) + n^2, a(1) = 1.
  • A143767 (program): Aliquot sequence starting at 87.
  • A143768 (program): E.g.f. satisfies: A(x) = exp(x + x^2*A(x)^2).
  • A143769 (program): Expansion of 3*x*(3*x+1)*(2*x-1) / ( (1+x)*(3*x^2+1) ).
  • A143771 (program): a(n) = gcd(k + n/k), where k is over all divisors of n.
  • A143772 (program): If m is the n-th composite, then a(n) = gcd(k + m/k), where k is over all divisors of m.
  • A143779 (program): Numbers of the form k=k^2-n^2.
  • A143785 (program): Antidiagonal sums of the triangle A120070.
  • A143786 (program): Number of arithmetic progressions from m to n; a rectangular array, m>=0, n>=0, by antidiagonals.
  • A143787 (program): Number of compositions of n into floor((3*j)/2) kinds of j’s for all j>=1.
  • A143795 (program): a(1) = 1, then for n > 1, a(n) = a(n - 1) + 1 for n even, or a(n) = a(n - 1) + 10 for n odd.
  • A143800 (program): In acoustics, using 12-tone equal temperament, the rounded number of semitones in the interval perceived when a vibrating string is divided into n congruent segments.
  • A143802 (program): Triangle read by rows, “n” followed by (n-1) terms of (1, 3, 7, 15, …).
  • A143803 (program): a(n) = 2*A001614(n) - 1 where A001614 lists the Connell numbers.
  • A143804 (program): Triangle read by rows, thrice the Connell numbers (A001614) - 2.
  • A143808 (program): Triangle read by rows, first n terms of the sequence (1, 2, 4, 10, …) followed by P(n), where (2, 4, 10, 12, …) = twice Pell numbers.
  • A143810 (program): Eigentriangle of A051731, the inverse Mobius transform.
  • A143812 (program): Maximal number of halving and tripling steps to reach 1 in ‘3x+1’ problem for range (1, …, n).
  • A143814 (program): Triangle T(n,m) read along rows: T(n,m) = n^2 - (m+1)^2 for 1<=m<n-1, T(n,n-1) = n^2-1.
  • A143818 (program): Let R(n) = sum {k = 0..inf} (3k)^n/(3k)! for n = 0,1,2,… . Then the real number R(n) is an integral linear combination of R(0), R(1) and R(2). This sequence gives the coefficients of R(1).
  • A143819 (program): Decimal expansion of Sum_{k>=0} 1/(3*k)!.
  • A143820 (program): Decimal expansion of the constant 1/1! + 1/4! + 1/7! + … = 1.04186 53550 98909 … .
  • A143821 (program): Decimal expansion of the constant 1/2! + 1/5! + 1/8! + … = 0.50835 81599 84216 … .
  • A143826 (program): Numbers n such that 6n^2 - 1 is prime.
  • A143827 (program): Numbers n such that 8n^2 - 1 is prime.
  • A143828 (program): Primes of the form 10*k^2 - 1.
  • A143829 (program): Numbers n such that 10n^2 - 1 is prime.
  • A143830 (program): Primes of the form 12*n^2-1
  • A143831 (program): Numbers n such that 12n^2 - 1 is prime.
  • A143832 (program): Primes of the form 14 n^2-1
  • A143833 (program): Numbers n such that 14n^2 - 1 is prime.
  • A143834 (program): Numbers k such that 2k^2 - 1 is not prime.
  • A143836 (program): Triangle read by rows of n such that n(r,c)=(p(r+2)-1)/2+(p(c+1)-1)/2+1.
  • A143838 (program): Ulam’s spiral (SSW spoke).
  • A143839 (program): Ulam’s spiral (SSE spoke).
  • A143844 (program): Triangle T(n,k) = k^2 read by rows.
  • A143845 (program): Periodic with period 8: repeat 0, 8, 12, 14, 15, 7, 3, 1.
  • A143846 (program): Aliquot sequence starting at 88.
  • A143847 (program): Aliquot sequence starting at 96.
  • A143854 (program): Ulam’s spiral (WSW spoke).
  • A143855 (program): Ulam’s spiral (ESE spoke).
  • A143856 (program): Ulam’s spiral (ENE spoke).
  • A143857 (program): a(n) = n + (n+1)*(n+2)^(n+3).
  • A143858 (program): Number of pairwise disjoint unions of m integer-to-integer subintervals of [0,n]; a rectangular array by antidiagonals, n>=2m-1, m>=1.
  • A143859 (program): Ulam’s spiral (WNW spoke).
  • A143860 (program): Ulam’s spiral (NNW spoke).
  • A143861 (program): Ulam’s spiral (NNE spoke).
  • A143862 (program): Number of compositions of n such that every part is divisible by number of parts.
  • A143865 (program): Eigentriangle of A099375 (odd number subsequences decrescendo)
  • A143869 (program): An integer k is called regular (mod n) if there is an integer x such that k^2 x == k (mod n). Then these numbers are the sum of regular integers k (mod n) such that 1 <= k <= n for n=1,2,… .
  • A143901 (program): Rectangular array R by antidiagonals: R(m,n) = floor((m*n+1)/2).
  • A143902 (program): Rectangular array R by antidiagonals: R(m,n) = number of black squares
  • A143905 (program): Positive integers n that are palindromic in base 2 and whose binary representation has the same number of 0’s as 1’s.
  • A143906 (program): a(n) is A143905(n) written in binary.
  • A143908 (program): Eigentriangle by rows, n terms of (3 * A026150) followed by A026150(n).
  • A143909 (program): A positive integer n is included if the number of digits in the binary representation of n is a multiple of the number of zeros in the binary representation of n.
  • A143918 (program): G.f. A(x) satisfies: A(x) = 1/(1-x)^2 + x^2*A’(x).
  • A143919 (program): Aliquot sequence starting at 100.
  • A143926 (program): G.f. satisfies: A(x) = 1 + x*A(x)*A(-x) + x^2*A(x)^2*A(-x)^2.
  • A143927 (program): G.f. satisfies: A(x) = [1 + x*A(x) + x^2*A(x)^2]^2.
  • A143928 (program): 2*p^2, for p an odd prime.
  • A143929 (program): Eigentriangle by rows, termwise products of the natural numbers decrescendo and the bisected Fibonacci series.
  • A143938 (program): The Wiener index of a benzenoid consisting of a linear chain of n hexagons.
  • A143939 (program): Triangle read by rows: T(n,k) is the number of unordered pairs of vertices at distance k in the cycle C_n (1 <= k <= floor(n/2)).
  • A143940 (program): Triangle read by rows: T(n,k) is the number of unordered pairs of vertices at distance k in a linear chain of n triangles (i.e., joined like VVV..VV; here V is a triangle!), 1 <= k <= n.
  • A143941 (program): The Wiener index of a chain of n triangles (i.e., joined like VVV..VV; here V is a triangle!).
  • A143943 (program): The Wiener index of a chain of n squares joined at vertices (i.e., joined like <><><>…<>; here <> is a square!).
  • A143945 (program): Wiener index of the grid P_n x P_n, where P_n is the path graph on n vertices.
  • A143954 (program): Number of peaks in the peak plateaux of all Dyck paths of semilength n.
  • A143955 (program): Sum of the altitudes of the leftmost valleys of all Dyck paths of semilength n (if path has no valley, then this altitude is taken to be 0).
  • A143956 (program): Triangle read by rows, A000012 * A136521 * A000012; 1<=k<=n.
  • A143959 (program): Final digit of n^(n+1)-(n+1)^n for n>2
  • A143960 (program): a(n) = the n-th positive integer with exactly n zeros and n ones in its binary representation.
  • A143961 (program): Binomial transform of A010054 (characteristic function of triangular numbers).
  • A143962 (program): Binomial transform of A066247.
  • A143963 (program): Binomial transform of A012245.
  • A143966 (program): Eigentriangle with row sums = A001333 starting (1, 3, 7, 17, 41, 99, …).
  • A143967 (program): Numbers containing only digits 3 or 7 in decimal representation.
  • A143968 (program): Denominators of numbers with g.f. exp(1-(1-x)^(1/2)).
  • A143970 (program): Eigentriangle by rows, n terms of (10 * A002535) followed by A002535(n)
  • A143971 (program): Triangle read by rows, (3n-2) subsequences decrescendo
  • A143973 (program): Distances between multiples of 3 in A000010.
  • A143974 (program): Rectangular array R by antidiagonals: label each unit square in the first quadrant lattice by its northeast vertex (x,y) and mark those having x+y=1(mod 3); then R(m,n) is the number of marked unit squares in the rectangle [0,m]x[0,n].
  • A143975 (program): a(n) = floor(n*(n+3)/3).
  • A143976 (program): Rectangular array R by antidiagonals: label each unit square in the first quadrant lattice by its northeast vertex (x,y) and mark squares having x + y == 1 (mod 3); then R(m,n) is the number of UNmarked squares in the rectangle [0,m] X [0,n].
  • A143977 (program): Rectangular array R by antidiagonals: label each unit square in the first quadrant lattice by its northeast vertex (x,y) and mark squares having |x-y| == 0 (mod 3); then R(m,n) is the number of marked squares in the rectangle [0,m] X [0,n].
  • A143978 (program): a(n) = floor(2*n*(n+1)/3).
  • A143979 (program): Rectangular array R by antidiagonals: label each unit square in the first quadrant lattice by its northeast vertex (x,y) and mark squares having |x-y| = 0 (mod 3); then R(m,n) is the number of UNmarked squares in the rectangle [0,m] X [0,n].
  • A143980 (program): Binomial transform of A079260.
  • A143984 (program): a(0) = 0; thereafter, a(n+1) = (a(n) - 2)^2 - n.
  • A143988 (program): Numbers congruent to {5, 13} mod 18.
  • A143989 (program): Numbers having a unique representation as a sum of a prime and a square.
  • A143990 (program): n!*A001515(n-1) with a(0) = 1.
  • A143991 (program): Numerators of numbers with g.f. exp(1-(1-x)^(1/2)).
  • A143994 (program): Years in which there are five Tuesdays in the month of February.
  • A143995 (program): Years in which there are five Thursdays in the month of February, in the Gregorian calendar.
  • A143996 (program): Rectangular array by antidiagonals: label each unit square in the first quadrant lattice by its northeast vertex (x,y) and mark squares for which (x,y) is congruent mod 4 to one of the following: (1,4), (2,2), (3,3), (4,1); then R(m,n) is the number of marked squares in the rectangle [0,m]x[0,n].
  • A143997 (program): Rectangular array by antidiagonals: label each unit square in the first quadrant lattice by its northeast vertex (x,y) and mark squares for which (x,y) is congruent mod 4 to one of the following: (1,4), (2,2), (3,3), (4,1); then R(m,n) is the number of UNmarked squares in the rectangle [0,m]x[0,n].
  • A143998 (program): Rectangular array by antidiagonals: label each unit square in the first quadrant lattice by its northeast vertex (x,y) and mark squares for which (x,y) is congruent mod 4 to one of the following: (1,1), (2,3), (3,2), (4,0); then R(m,n) is the number of marked squares in the rectangle [0,m]x[0,n].
  • A143999 (program): Rectangular array by antidiagonals: label each unit square in the first quadrant lattice by its northeast vertex (x,y) and mark squares for which (x,y) is congruent mod 4 to one of the following: (1,1), (2,3), (3,2), (4,0); then R(m,n) is the number of UNmarked squares in the rectangle [0,m]x[0,n].
  • A144000 (program): Rectangular array by antidiagonals: label each unit square in the first quadrant lattice by its northeast vertex (x,y) and mark squares for which x + y == 0 (mod 3); then R(m,n) is the number of marked squares in the rectangle [0,m]x[0,n].
  • A144001 (program): Rectangular array read by antidiagonals: label each unit square in the first quadrant lattice by its northeast vertex (x,y) and mark squares for which x + y == 0 (mod 3); then R(m,n) is the number of unmarked squares in the rectangle [0,m] X [0,n].
  • A144020 (program): Numbers of the form 1+i^2+j^2+k^2 with 1 <= i <= j <= k.
  • A144023 (program): INVERT transform of the rabbit sequence, A005614.
  • A144026 (program): An INVERT transform of the Thue-Morse sequence.
  • A144028 (program): INVERT transform of A055615, n*mu(n).
  • A144030 (program): Numbers n such that : a=a^2-n^3; a=a-2.
  • A144031 (program): INVERT transform of A002321, Mertens’s function.
  • A144043 (program): a(2n-1) = 2*prime(n), a(2n) = prime(n) + prime(n+1).
  • A144044 (program): a(n) = ((1+sqrt(11))^n-(1-sqrt(11))^n)^2/44.
  • A144065 (program): Values of k such that the expression sqrt(4!*(k+1) + 1) yields an integer.
  • A144066 (program): T(n, k) is the number of order-preserving partial transformations (of an n-element chain) of height k (height(alpha) = |Im(alpha)|); triangle T read by rows.
  • A144075 (program): Duplicate of A008621.
  • A144077 (program): a(n) = z(n^2,n) with z(x,y) = if x>y then z(x-y,y+1) else y.
  • A144078 (program): a(n) = the number of digits in the binary representation of n that differ from the corresponding digit in the binary reversal of n. (I.e., a(n) = number of 1’s in n XOR A030101(n).)
  • A144079 (program): a(n) = the number of digits in the binary representation of n that equal the corresponding digit in the binary reversal of n. (I.e., a(n) = number of 0’s in n XOR A030101(n).)
  • A144082 (program): Eigentriangle generated from inverse of 6th cyclotomic polynomial, row sums = n+1.
  • A144083 (program): Triangle read by rows, partial sums from the right an A010892 subsequences decrescendo triangle
  • A144084 (program): T(n,k) is the number of partial bijections of height k (height(alpha) = |Im(alpha)|) of an n-element set.
  • A144085 (program): a(n) is the number of partial bijections (or subpermutations) of an n-element set without fixed points (also called partial derangements).
  • A144086 (program): Number of partial bijections (or subpermutations) of an n-element set with exactly 1 fixed point.
  • A144087 (program): a(n) is the number of partial bijections (or subpermutations) of an n-element set with exactly 2 fixed points.
  • A144088 (program): T(n,k) is the number of partial bijections (or subpermutations) of an n-element set with exactly k fixed points.
  • A144089 (program): T(n,k) is the number of partial bijections (or subpermutations) of an n-element set of height k (height(alpha) = |Im(alpha)|) and without fixed points.
  • A144090 (program): Triangle read by rows: T(n,k) is the number of partial bijections (or subpermutations) of an n-element set of height k (height(alpha) = |Im(alpha)|) and with exactly 1 fixed point.
  • A144091 (program): T(n,k) is the number of partial bijections (or subpermutations) of an n-element set of height k (height(alpha) = |Im(alpha)|) and with exactly 2 fixed points
  • A144097 (program): The 4-Schroeder numbers: a(n) = number of lattice paths (Schroeder paths) from (0,0) to (3n,n) with unit steps N=(0,1), E=(1,0) and D=(1,1) staying weakly above the line y = 3x.
  • A144100 (program): Numbers k such that k is strictly greater than f(k), where f(k) = 1 if k is prime, 2 * rad(k) if 4 divides k and rad(k) otherwise.
  • A144101 (program): Characteristic sequence for A144100.
  • A144107 (program): Eigentriangle, row sums = n!
  • A144109 (program): INVERT transform of the cubes A000578.
  • A144110 (program): Period 6: repeat [2, 2, 2, 1, 1, 1].
  • A144112 (program): Weight array W={w(i,j)} of the natural number array A000027.
  • A144113 (program): Weight array W={w(i,j)} of the natural number array A038722.
  • A144124 (program): P_4(2n+1), the Legendre polynomial of order 4 at 2n+1.
  • A144125 (program): Primes of the form P_4(n) where P_4(n) is the Legendre polynomial of order 4 at n.
  • A144126 (program): P_6(2n+1), the Legendre polynomial of order 6 at 2n+1.
  • A144128 (program): Chebyshev U(n,x) polynomial evaluated at x=18.
  • A144129 (program): ChebyshevT(3, n).
  • A144130 (program): a(n) = ChebyshevT(4, n).
  • A144131 (program): Primes of the form T_4(n), where T_4(x) = 8x^4 - 8x^2 + 1 is the fourth Chebyshev polynomial (of the first kind).
  • A144133 (program): Gegenbauer polynomial C_n^2(3).
  • A144135 (program): GegenbauerC[n,2,8].
  • A144138 (program): Chebyshev polynomial of the second kind U(3,n).
  • A144139 (program): Chebyshev polynomial of the second kind U(4,n).
  • A144141 (program): a(n) = Hermite(n,2).
  • A144142 (program): a(n) = Hermite(n,3).
  • A144143 (program): a(n) = Hermite(n,4).
  • A144146 (program): A positive integer n is included if every nonzero exponent in the prime factorization of n is coprime to n.
  • A144151 (program): Triangle T(n,k), n>=0, 0<=k<=n, read by rows: T(n,k) = number of ways an undirected cycle of length k can be built from n labeled nodes.
  • A144161 (program): Triangle read by rows: T(n,k) = number of simple graphs on n labeled nodes with k edges that are node-disjoint unions of undirected cycle subgraphs.
  • A144165 (program): JacobiP[n,1,2,5].
  • A144166 (program): JacobiP[n,1,3,5].
  • A144180 (program): Number of ways of placing n labeled balls into n unlabeled (but 5-colored) boxes.
  • A144181 (program): INVERT transform of A118434, = row sums of triangle A144182.
  • A144186 (program): Numerators of series expansion of the e.g.f. for the Catalan numbers.
  • A144187 (program): Denominators of series expansion of the e.g.f. for the Catalan numbers.
  • A144193 (program): Square array (5 X 5) read by rows.
  • A144194 (program): Square array (6 X 6) read by rows.
  • A144195 (program): Square array (6 X 6) read by rows.
  • A144196 (program): Square array (6 X 6) read by rows.
  • A144197 (program): Square array 7 x 7 read by rows.
  • A144204 (program): Array A(k,n) = (n+k-2)*(n-1) - 1 (k >= 1, n >= 1) read by antidiagonals.
  • A144206 (program): Numbers A141427(k) such that the three numbers A141427(k) -/+ 3 and A141427(k) + 1 are all prime.
  • A144213 (program): Primes with a prime number of 0’s in their binary representations.
  • A144216 (program): C(m,2)+C(n,2), m>=1, n>=1: a rectangular array R read by antidiagonals.
  • A144217 (program): Weight array of A144216: a rectangular array by antidiagonals.
  • A144222 (program): Floor of the volumes of the first sixteen Lobell polyhedra.
  • A144223 (program): Number of ways of placing n labeled balls into n unlabeled (but 6-colored) boxes.
  • A144225 (program): Bordered Pascal’s triangle in rectangular format.
  • A144248 (program): Partial sums of A000594.
  • A144249 (program): Apply partial sum operator twice to A000594.
  • A144250 (program): Eigentriangle, row sums = A125275, shifted.
  • A144251 (program): Eigensequence of triangle A054142.
  • A144255 (program): Semiprimes of the form k^2+1.
  • A144257 (program): Weight array of A086270.
  • A144259 (program): Number of forests of trees on n or fewer nodes using a subset of labels 1..n, also row sums of triangle A144258.
  • A144263 (program): Number of ways of placing n labeled balls into n unlabeled (but7-colored) boxes.
  • A144272 (program): Second column (m=2) of triangle S2hat(-1) = A144270.
  • A144277 (program): Second column (m=2) of triangle S2hat(-2) = A144275.
  • A144282 (program): Second column (m=2) of triangle S2hat(-3) = A144280.
  • A144291 (program): Triangular numbers n*(n-1)/2 with n and n -1 nonprime.
  • A144297 (program): BINOMIAL transform of A001515.
  • A144298 (program): Number of cycles of length 3 in the queen’s graph associated with an n X n chessboard.
  • A144299 (program): Triangle of Bessel numbers read by rows. Row n gives T(n,n), T(n,n-1), T(n,n-2), …, T(n,0) for n >= 0.
  • A144300 (program): Number of partitions of n minus number of divisors of n.
  • A144301 (program): a(0) = a(1) = 1; thereafter a(n) = (2*n-3)*a(n-1) + a(n-2).
  • A144302 (program): Odd members of A049445.
  • A144304 (program): Square array A(n,m), n>=0, m>=0, read by antidiagonals: A(n,m) = n-th number of the m-th iteration of the hyperbinomial transform on sequence A001858.
  • A144312 (program): a(n) = 5*n*(5*n + 1)/2.
  • A144314 (program): a(n) = 3*n*(6*n + 1).
  • A144327 (program): Prime numbers p such that p - 1 is the fourth a-figurate number and nineteenth b-figurate number for some a and b.
  • A144328 (program): A002260 preceded by a column of 1’s: a (1, 1, 2, 3, 4, 5, …) crescendo triangle by rows.
  • A144329 (program): Triangle read by rows, A000012 * A144328
  • A144330 (program): Triangle read by rows, A144328 * A000012
  • A144331 (program): Triangle b(n,k) read by rows (n >= 0, 0 <= k <= 2n). See A144299 for definition and properties.
  • A144332 (program): Triangle read by rows, A144328 * A007318
  • A144333 (program): Triangle read by rows, A007318 * A144328
  • A144334 (program): Triangle read by rows, A144328^2
  • A144335 (program): Row sums of triangle A144334, binomial transform of [1, 2, 6, 7, 3, 0, 0, 0, …].
  • A144336 (program): Triangle read by rows, 2*A144328 - A007318^(-1)
  • A144338 (program): Squarefree numbers > 1.
  • A144339 (program): Second column (m=2) of triangle S2hat(-4) = A144285.
  • A144344 (program): Second column (m=2) of triangle S2hat(-5) = A144342.
  • A144345 (program): Second column (m=2) of triangle S2p(-2) = A004747.
  • A144346 (program): Third column (m=3) of triangle S2p(-2) = A004747.
  • A144347 (program): Second column (m=2) of triangle S2p(-4) = A011801.
  • A144349 (program): Second column (m=2) of triangle S2p(-5) = A013988.
  • A144379 (program): Triangle read by rows, first n terms of an array formed by A054521 * A054521(transform).
  • A144384 (program): T(1,k) = 1 and T(n,k) = [t^k] (1 - t)/(1 - t^n) for n >= 2, square array read by ascending antidiagonals (n >= 1, k >= 0).
  • A144388 (program): Triangle T(n,k) = binomial(n, k) + ((-1)^(n + k))*n*binomial(n - 1, k), T(0,0) = 1, read by rows, 0 <= k <= n.
  • A144389 (program): Triangle T(n,k) = n*binomial(n - 1, k) - (-1)^(n - k)*binomial(n, k), T(0,0) = 1, read by rows, 0 <= k <= n.
  • A144390 (program): a(n) = 3*n^2 - n - 1.
  • A144391 (program): a(n) = 3*n^2 + n - 1.
  • A144392 (program): Inverse binomial transform of A061037 (read as with offset 0).
  • A144393 (program): Triangle read by rows (n >= 0, 0 <= k <= n): row n gives the coefficients in the expansion of x^n + n*x^(n - 1) + n*x + 1.
  • A144394 (program): Triangle read by rows (n >= 4, 0 <= k <= n - 4): row n gives the coefficients in the expansion of ((x + 1)^n - (x^n + n*x^(n - 1) + n*x + 1))/x^2.
  • A144395 (program): A designed polynomial set that gives a {1,6,1} quadratic and gives a symmetrical triangle of coefficients: p(x,n)=If[n == 2, 1, ((x + 1)^n -If[n == 0, 1, x^n + (n - 1)*x^(n - 1) + (n - 1)*x + 1])/x],.
  • A144396 (program): The odd numbers greater than 1.
  • A144398 (program): Coefficients of a symmetrical polynomial set:( Pascal’s triangle with central zeros) p(x,n)=If[n <= 4, Sum[Binomial[n, i]*x^i, {i, 0, n}], x^n + n*x^(n - 1) + Binomial[n, 2]*x^(n - 2) + n*x + Binomial[n, 2]*x^2 + 1].
  • A144401 (program): Padovan ( A000931) version of A038137: expansion of polynomials as antidiagonal: p(x,n)=1/(1-x-x^3)^n.
  • A144403 (program): Triangle T(n, k) = binomial(n, k)^2 - binomial(n, k) - 1, read by rows.
  • A144404 (program): Triangle T(n,k) = 3*binomial(n, k)^2 - binomial(n, k) - 1, read by rows.
  • A144405 (program): Triangle T(n,k) = binomial(n, k)*(3*binomial(n, k)^2 - binomial(n, k) - 1), read by rows.
  • A144407 (program): A058529(n+1)^2.
  • A144408 (program): Last digit of A135266(n).
  • A144410 (program): a(n) = 4*(3*n+1)*(3*n+2).
  • A144411 (program): Odd nonprime gaps adjusted to be {2,1,0,-1}: a(n)=A067970(n)/2-2.
  • A144412 (program): Invert transform of odd nonprime gaps adjusted to be from the set {2,1,0,-1}: b(n)=A067970(n)/2-2; a(n)=Sum[b(n + 1)*a(n - k), {k, 1, n}].
  • A144413 (program): a(n) = Sum_{k=0..n} (-1)^k * binomial(n, k) * A000931(n-k+4).
  • A144414 (program): a(n) = 2*(4^n - 1)/3 - n.
  • A144419 (program): Primes of the form prime(k) - 2*k (terms can be repeated).
  • A144429 (program): Starts 1 2 3 then successive terms have differences 1 2 3.
  • A144430 (program): a(n) = 1 + A144429(n).
  • A144433 (program): Multiples of 8 interleaved with the sequence of odd numbers >= 3.
  • A144437 (program): Period 3: repeat [3, 3, 1].
  • A144448 (program): First bisection of A061039.
  • A144449 (program): a(n) = 36*n^2 + 60*n + 16.
  • A144450 (program): Second bisection of A061039.
  • A144453 (program): a(n) = A061039(8*n+5).
  • A144454 (program): First trisection of A061039.
  • A144459 (program): a(n) = (3*n+1)*(5*n+1).
  • A144463 (program): Triangle T(n,m) read by rows: T(n,m)= A013609(n,m) if m <= n/2, T(n,m)= T(n,n-m) otherwise.
  • A144464 (program): Triangle T(n,m) read by rows: T(n,m) = 2^min(m,n-m).
  • A144465 (program): a(n) = 5^n - 2^(n - 1) for n > 0; a(0) = 1.
  • A144468 (program): Final digit of multiples of 7.
  • A144470 (program): Triangle t(n,m) read by rows: t(n,m) = binomial(n,m)*3^m if m <= n/2, else t(n,m) = t(n,n-m).
  • A144471 (program): Inverse binomial transform of A020806.
  • A144472 (program): Negative values along the main diagonal of the array defined by A020806 and its differences.
  • A144473 (program): A triangle sequence of determinants: a(n)=If[Mod[n, 3] == 0, 1, If[Mod[n, 3] == 1, -1, If[Mod[n, 3] == 2, 0]]]; b(n,m)=If[m < n && Mod[n, 3] == 0, 0, If[m < n && Mod[n, 3] == 1, 0, If[m < n && Mod[n, 3] == 2 && Mod[n, 2] == 0, 1, If[m < n && Mod[n, 3] == 2 && Mod[n, 2] == 1, -1, If[m == n, -1, 0]]]]]; M={{a(m), b(n, m)}, {a(n), b(n, n)}}; t(n,m)=Det[M].
  • A144474 (program): A triangle sequence of determinants: a(n)=If[Mod[n, 2] == 0, 1, If[Mod[n, 2] == 1, -1, 0]]; b(n,m)=If[m < n && Mod[n, 3] == 0, 0, If[m < n && Mod[n, 3] == 1, 0, If[m < n && Mod[n, 3] == 2 && Mod[n, 2] == 0, 1, If[m < n && Mod[n, 3] == 2 && Mod[n, 2] == 1, -1, If[m == n, -1, 0]]]]]; M={{a(m), b(n, m)}, {a(n), b(n, n)}}; t(n,m)=Det[M].
  • A144477 (program): a(n) = minimal number of 0’s that must be changed to 1’s in the binary expansion of the n-th prime in order to make it into a palindrome.
  • A144478 (program): Period 9: repeat 1,0,5,7,6,2,4,3,8.
  • A144479 (program): a(0)=1, a(1)=3, a(n) = 8*a(n-1) - a(n-2).
  • A144480 (program): T(n,k) = binomial(n, k)*min(k + 1, n - k + 1), triangle read by rows (n >= 0, 0 <= k <= n).
  • A144481 (program): A078371(n-1) mod 9.
  • A144483 (program): A144481(4n-3).
  • A144484 (program): Triangle read by rows: T(n, k) = binomial(3*n+1-k, n-k) for n, k >= 0.
  • A144485 (program): a(n) = (3n + 2)*binomial(3n + 1,n).
  • A144486 (program): Triangular numbers n*(n+1)/2 with n and n+1 composite, where number of prime factors in n = number of prime factors in n+1. (Prime factors are counted with multiplicity.)
  • A144489 (program): Partial sums of A087624.
  • A144494 (program): a(n) = 0 if n is prime, otherwise A001222(n).
  • A144495 (program): Row 2 of array in A144502.
  • A144496 (program): Row 3 of array in A144502.
  • A144497 (program): Row 4 of array in A144502.
  • A144498 (program): Column 2 of array in A144502.
  • A144499 (program): Column 3 of array in A144502.
  • A144503 (program): Sum of n-th antidiagonal of array in A144502.
  • A144506 (program): Column 3 of triangle in A144505, negated.
  • A144507 (program): Column 4 of triangle in A144505.
  • A144513 (program): a(n) = Sum_{k=0..n} (n+k+2)!/((n-k)!*k!*2^k).
  • A144514 (program): a(n) = Sum_{k=0..n} (n+k+3)!/((n-k)!*k!*2^k).
  • A144515 (program): Triangle read by rows: A051731 * A103451.
  • A144516 (program): a(n) = (15*n^2+45*n-70)*binomial(n+4,6)/8.
  • A144519 (program): Triangular numbers n*(n+1)/2 with n prime and n+1 nonprime.
  • A144522 (program): Sums of pairs of successive digits after the decimal point in the decimal expansion of 2^(1/2) = 1.41421356…
  • A144526 (program): Denominators of expansion of exp(1-sqrt(1-3*x)).
  • A144532 (program): Continued fraction for sqrt(8/9).
  • A144533 (program): Numerators of continued fraction convergents to sqrt(8/9).
  • A144534 (program): Denominators of continued fraction convergents to sqrt(8/9).
  • A144535 (program): Numerators of continued fraction convergents to sqrt(3)/2.
  • A144536 (program): Denominators of continued fraction convergents to sqrt(3)/2.
  • A144537 (program): a(0) = 3; for n > 0, a(n) = sqrt(3)*(P^(2*n)-M^(2*n))/8 + (3/4)*(P^n+M^n) + 1/2), where P = 7+4*sqrt(3), M = 7-4*sqrt(3).
  • A144545 (program): a(n) = 2^(n*(n-1))*(2^n + 1)*Product_{i=1..n-1} (4^i - 1).
  • A144551 (program): a(n) = nonprime(n)*nonprime(n+1)/2, where nonprime(n) = A141468(n).
  • A144555 (program): a(n) = 14*n^2.
  • A144560 (program): Ten times hexagonal numbers: 10*n*(2*n-1).
  • A144562 (program): Triangle read by rows: T(n, k) = 2*n*k + n + k - 1.
  • A144564 (program): Bisection of A147757.
  • A144567 (program): Primes of the form: smallest prime factor of n + largest prime factor of n, n > 1.
  • A144570 (program): Nonprime(prime(n)).
  • A144571 (program): Primes of the form 81n^2 - 90n + 26.
  • A144572 (program): Primes of the form nonprime(prime(n))+1, where n-th nonprime = A141468(n) and first nonprime = 0.
  • A144573 (program): Smallest prime greater than nonprime(prime(n)).
  • A144574 (program): Largest prime < nonprime(prime(n)).
  • A144575 (program): E,g.f.: exp(1-sqrt(1-2*x-3*x^2)).
  • A144589 (program): Prime(n-th “prime nonprime”).
  • A144590 (program): Number of ordered ways of writing 2n+1 = i + j, where i is a prime and j is of the form k*(k+1), k > 0.
  • A144595 (program): Christoffel word of slope 4/7.
  • A144596 (program): Christoffel word of slope 2/7.
  • A144597 (program): Christoffel word of slope 3/7.
  • A144598 (program): Christoffel word of slope 5/7.
  • A144599 (program): Christoffel word of slope 6/7.
  • A144600 (program): Christoffel word of slope 2/11.
  • A144601 (program): Christoffel word of slope 3/11.
  • A144602 (program): Christoffel word of slope 4/11.
  • A144603 (program): Christoffel word of slope 5/11.
  • A144604 (program): Christoffel word of slope 6/11.
  • A144605 (program): Christoffel word of slope 7/11.
  • A144606 (program): Christoffel word of slope 8/11.
  • A144607 (program): Christoffel word of slope 9/11.
  • A144608 (program): Christoffel word of slope 10/11.
  • A144609 (program): Sturmian word of slope Pi.
  • A144610 (program): Sturmian word of slope e.
  • A144611 (program): Sturmian word of slope 2-sqrt(2).
  • A144612 (program): Sturmian word of slope (3-sqrt(3))/2.
  • A144613 (program): a(n) = sigma(3*n) = A000203(3*n).
  • A144614 (program): Sum of divisors of 3*n + 1.
  • A144615 (program): a(n) = A000203(3n+2).
  • A144619 (program): a(n) = 19n + 8.
  • A144620 (program): Numbers k such that k and 19*k + 8 are both prime.
  • A144627 (program): Initial members of triples listed in A144625.
  • A144628 (program): Central members of triples listed in A144625.
  • A144629 (program): Last members of triples listed in A144625.
  • A144635 (program): a(n) = 5^n*Sum_{ k=0..n } binomial(2*k,k)/5^k.
  • A144640 (program): Row sums from A144562.
  • A144646 (program): a(n) = Bell(n) - 2^n + n.
  • A144647 (program): Second differences of A001515 (or A144301).
  • A144650 (program): Triangle read by rows where T(m,n) = 2m*n + m + n + 1.
  • A144652 (program): Triangle, read by rows, where T(m,n) = floor((2mn+m+n)/2) with m >= n >= 1.
  • A144654 (program): Numerator of Sum_{k=1..n} k*H_{n+k} where H_m = Sum_{i=1..m}.
  • A144655 (program): Denominator of Sum_{k=1..n} k*H_{n+k} where H_m = Sum_{i=1..m}.
  • A144656 (program): a(n) = (n mod 2) if n <= 3, otherwise a(n) = (n^2-5n+7)*(n-2)*a(n-1)/(n-3) + (n^2-5n+7)*a(n-2) - (n-2)*a(n-3)/(n-3).
  • A144657 (program): a(n) = Sum[Sum[(i+j)!/(i!*j!),{i,1,n}],{j,1,n}].
  • A144659 (program): a(n) = A001516(n)/2.
  • A144660 (program): a(n) = Sum_{i=0..n} Sum_{j=0..n} Sum_{k=0..n} (i+j+k)!/(i!*j!*k!).
  • A144670 (program): Triangle read by rows where T(m,n)=2mn+m+n-7
  • A144677 (program): Related to enumeration of quantum states (see reference for precise definition).
  • A144678 (program): Related to enumeration of quantum states (see reference for precise definition).
  • A144679 (program): a(n) = [n/5 + 1]*[n/5 + 2]*(3*n - 10*[n/5] + 3)/6, where [.] = floor.
  • A144680 (program): Triangle read by rows, lower half of an array formed by A004736 * A144328 (transform).
  • A144685 (program): Size of acyclic domain of size n based on the alternating scheme.
  • A144693 (program): Triangle read by rows, A000012 * (3*A144328 - 2*A000012), where A000012 means a lower triangular matrix of all 1’s.
  • A144696 (program): Triangle of 2-Eulerian numbers.
  • A144697 (program): Triangle of 3-Eulerian numbers.
  • A144698 (program): Triangle of 4-Eulerian numbers.
  • A144700 (program): Generalized (3,-1) Catalan numbers.
  • A144704 (program): a(n) = 4^n*(1-2*n).
  • A144706 (program): Central coefficients of the triangle A132047.
  • A144707 (program): Diagonal sums of the triangle A132047.
  • A144708 (program): a(n) = 6^n * (1-4*n).
  • A144720 (program): a(0) = 2, a(1) = 3, a(n) = 4 * a(n-1) - a(n-2).
  • A144721 (program): a(0) = 2, a(1) = 5, a(n) = 4 * a(n-1) - a(n-2).
  • A144732 (program): Triangle of numerator coefficients, reading across rows, of Sum_{k=1..n} (1/(1 + r^2 - 2*r*cos(k*Pi/n))).
  • A144739 (program): 7-factorial numbers A114799(7*n+3): Partial products of A017017(k) = 7*k+3, a(0) = 1.
  • A144740 (program): Partial totient function phi(c, n) for c = 2: number of semiprimes less than and coprime to n.
  • A144741 (program): Partial cototient function Phi(c, n) for c = 2: number of semiprimes less than or equal and not coprime to n.
  • A144750 (program): A098777 mod 9.
  • A144751 (program): a(1) = 3, a(n + 1) = 1 + a(n) + least odd prime factor of a(n).
  • A144754 (program): Integers that have a prime number of 0’s in their binary expansion.
  • A144756 (program): Partial products of successive terms of A017101; a(0)=1 .
  • A144758 (program): Partial products of successive terms of A017197.
  • A144764 (program): Partial totient function phi(c, n) for c = 3: number of 3-semiprimes less than and coprime to n.
  • A144768 (program): a(n) = n! - n^9.
  • A144769 (program): a(n) = floor(prime(n)/3).
  • A144773 (program): 10-fold factorials: Product_{k=0..n-1} (10*k+1).
  • A144777 (program): Integers having decimal digital mean equal to zero.
  • A144786 (program): If n is an oblong number A002378, then a(n)=a(j) where j is the number of oblong numbers in (0,n], otherwise a(n)=n.
  • A144795 (program): A positive integer n is included if every 1 in binary n is next to at least one other 1.
  • A144796 (program): Expansion of x(5+215x-1253x^2-23x^3)/((1+34x+x^2)(1-34x+x^2)).
  • A144797 (program): Numbers k such that 2*k^2 + 17 is a square.
  • A144816 (program): Denominators of triangle T(n,k), n>=0, 0<=k<=n, read by rows: T(n,k) is the coefficient of x^(2*k+1) in polynomial t_n(x), used to define continuous and n times differentiable sigmoidal transfer functions.
  • A144827 (program): Partial products of successive terms of A017029; a(0)=1.
  • A144828 (program): Partial products of successive terms of A017113; a(0)=1.
  • A144829 (program): Partial products of successive terms of A017209; a(0)=1 .
  • A144831 (program): (n+1)^2 - (smallest prime > n^2).
  • A144832 (program): Distance from nxtprm(n^2) to (n+1)^2 in A144831 is prime.
  • A144834 (program): Numbers n such that the two numbers n+1 and n+3 are both prime.
  • A144840 (program): Numbers k such that the three numbers k-1, k+3 and k+5 are all prime.
  • A144842 (program): Numbers k such that the three numbers k+3, k-3 and k+5 are all prime.
  • A144843 (program): a(n) = (6^n - 2^n)^2 / 16.
  • A144844 (program): a(n) = ((2 + sqrt(2))^n - (2 - sqrt(2))^n)^2/8.
  • A144855 (program): Number of paths from (1,1) to (n,n) in an n X n grid using only the steps +(1,0), -(1,0), +(0,1) and -(0,1) which do not self-intersect and which avoid any point (p,q) satisfying “(p-1)*n + q is prime”.
  • A144864 (program): a(n) = (4*16^(n-1)-1)/3.
  • A144865 (program): Shadow transform of C(n+3,4) = A000332(n+3).
  • A144866 (program): Shadow transform of C(n+4,5) = A000389(n+4).
  • A144867 (program): Shadow transform of C(n+5,6) = A000579(n+5).
  • A144868 (program): Shadow transform of C(n+6,7) = A000580(n+6).
  • A144869 (program): Shadow transform of C(n+7,8) = A000581(n+7).
  • A144870 (program): Shadow transform of C(n+8,9) = A000582(n+8).
  • A144874 (program): Coefficients of the series expansion of q^(-1/4) pi_q.
  • A144876 (program): Maximal number of distinct polyominoes into which an n X n square can be divided.
  • A144883 (program): Second column (m=2) of triangle A144881 (S1hat(3).
  • A144888 (program): Second column (m=2) of triangle A144886 (S1hat(4)).
  • A144893 (program): Second column (m=2) of triangle A144891 (S1hat(5)).
  • A144895 (program): Second column of triangle A134134 (S2’(2) = S1hat(2)).
  • A144897 (program): Expansion of x/(1 - 4*x + 6*x^2 - 5*x^3 + 4*x^4 - 3*x^5).
  • A144898 (program): Expansion of x/((1-x-x^3)*(1-x)^4).
  • A144899 (program): Expansion of x/((1-x-x^3)*(1-x)^5).
  • A144900 (program): Expansion of x/((1-x-x^3)*(1-x)^6).
  • A144901 (program): Expansion of x/((1-x-x^3)*(1-x)^7).
  • A144902 (program): Expansion of x/((1-x-x^3)*(1-x)^8).
  • A144903 (program): Square array A(n,k), n>=0, k>=0, read by antidiagonals, where column k is the expansion of x/((1-x-x^3)*(1-x)^(k-1)).
  • A144904 (program): Coefficient of x^n in expansion of x/((1-x-x^3)*(1-x)^(n-1)), also diagonal of A144903.
  • A144905 (program): a(0) = 1; thereafter a(n) = A105749(n)/n.
  • A144907 (program): a(n) = 1 if n is prime, 2 * rad(n) if four divides n and rad(n) otherwise.
  • A144913 (program): Integers which are the product of even powers of primes up to 13.
  • A144916 (program): Integers k for which |A144912| attains a new maximal odd value.
  • A144917 (program): a(n) is the maximal odd value attained by A144916(n).
  • A144925 (program): Number of nontrivial divisors of the n-th composite number.
  • A144927 (program): Numbers n such that there exists an integer k with (n+7)^3-n^3=k^2.
  • A144928 (program): Values of k arising in A144927.
  • A144929 (program): Numbers n such that there exists an integer k with (n+1)^3 - n^3 = 7*k^2.
  • A144930 (program): Numbers k arising in A144929.
  • A144931 (program): a(n) is the Mersenne number exponent for A144932(n).
  • A144932 (program): Integers n such that n^2 + k is a Mersenne number 2^m - 1 for some k < n and m odd.
  • A144933 (program): a(n) is the Mersenne number exponent for A144934(n).
  • A144934 (program): Integers n such that n^2 + k is a Mersenne number 2^m - 1 for some k such that n < k < 2 * n and m odd.
  • A144941 (program): Numbers k such that 6*k-1 = A144796(k).
  • A144942 (program): Expansion of x^2*(3*x^3+145*x^2-507*x-25) / ((x-1)*(x^2-34*x+1)*(x^2+34*x+1)).
  • A144943 (program): a(n) = number of divisors of n^3 (excluding 1 and n^3).
  • A144944 (program): Super-Catalan triangle (read by rows) = triangular array associated with little Schroeder numbers (read by rows): T(0,0)=1, T(p,q)=T(p,q-1) if 0<p=q, T(p,q) = T(p,q-1) + T(p-1,q) + T(p-1,q-1) if -1<p<q and T(p,q)=0 otherwise.
  • A144945 (program): Number of ways to place 2 queens on an n X n chessboard so that they attack each other.
  • A144952 (program): Total walk count of molecular graphs for linear alkanes with n carbon atoms.
  • A144953 (program): Primes of form n^3 + 2.
  • A144965 (program): a(n) = 4*n*(4*n^2+1).
  • A144968 (program): Number of squares between consecutive cubes.
  • A144969 (program): Stirling numbers of second kind S(n,n-6).
  • A144971 (program): Integers of the form sum_{i=2521..j} i/(i-2520) for any upper limit j.
  • A144974 (program): Centered heptagonal prime numbers.
  • A144980 (program): Natural numbers k such that k+1 is divisible by the sum of the decimal digits of k.
  • A144981 (program): Decimal expansion of cos(Pi/8) = cos(22.5 degrees).
  • A145004 (program): Values of n at which the number of roots of the function x+n*cos(x) increases.
  • A145005 (program): Values of n at which the number of roots of the function x+n*sin(x) increases.
  • A145009 (program): Array read by antidiagonals: array of odd integers found in |A144912| with axes b = {4, 6, 8, …} and n = {b^2, b^4, b^6, …}.
  • A145011 (program): First differences of A007775.
  • A145018 (program): a(n) = (n^2 - n + 8)/2.
  • A145020 (program): a(n) = ((7 + sqrt(7))^n - (7 - sqrt(7))^n)^2/28.
  • A145021 (program): a(n) = number of different positive integers that can be formed from different groupings of expressions of the form n op1 n op2 n op3 n, where each of op1, op2 and op3 are addition, subtraction, multiplication or division.
  • A145027 (program): a(n) = a(n-1) + a(n-2) + a(n-3) with a(1) = 2, a(2) = 3, a(3) = 4.
  • A145028 (program): Tetranacci numbers: a(n)=a(n-1)+a(n-2)+a(n-3)+a(n-4), {1,2,3,4…}.
  • A145029 (program): Pentanacci numbers: a(n)=a(n-1)+a(n-2)+a(n-3)+a(n-4)+a(n-5), {1,2,3,4,5…}.
  • A145030 (program): Hexanacci numbers: a(n)=a(n-1)+a(n-2)+a(n-3)+a(n-4)+a(n-5)+a(n-6), {0,1,2,3,4,5…}.
  • A145032 (program): If t(n) is the maximal triangular number not exceeding n, then a(n) is the n-th prime for which a(n)-t(a(n)) is a triangular number
  • A145033 (program): T(n,k) is the number of amenable quasi-idempotent order-decreasing partial one-one transformations (of an n-chain) of height k (height(alpha) = |Im(alpha)|).
  • A145036 (program): T(n,k) is the number of idempotent order-decreasing and order-preserving partial transformations (of an n-chain) of waist k (waist(alpha) = max(Im(alpha))).
  • A145037 (program): Number of 1’s minus number of 0’s in the binary representation of n.
  • A145051 (program): Numerator of the first convergent to sqrt(n) using the recursion x = (n/x + x)/2.
  • A145052 (program): One-third of the number of n X n nonnegative integer arrays with every 3 X 3 subblock summing to 1.
  • A145057 (program): First differences of A031443.
  • A145058 (program): Second differences of A031443.
  • A145059 (program): Sum of successive values in A031443.
  • A145060 (program): Cumulative sums of A031443.
  • A145061 (program): Number of pairs of odd numbers that separate two consecutive twin prime pairs
  • A145063 (program): Hankel transform of A145062.
  • A145064 (program): Reduced numerators of the first convergent to the cube root of n using the recursion x = (2*x+n/x^2)/3.
  • A145066 (program): Partial sums of A002522, starting at n=1.
  • A145067 (program): Zero followed by partial sums of A008865.
  • A145068 (program): Zero followed by partial sums of A059100, starting at n=1.
  • A145069 (program): a(n) = n*(n^2 + 3*n + 5)/3.
  • A145070 (program): Partial sums of A006127, starting at n=1.
  • A145071 (program): Partial sums of A000051, starting at n=1.
  • A145091 (program): a(n) = n if n is a term of A301776, otherwise a(n) = 0.
  • A145094 (program): Coefficients in expansion of Eisenstein series q*E’_4.
  • A145095 (program): Coefficients in expansion of Eisenstein series -q*E’_6.
  • A145102 (program): a(0) = a(1) = 1. a(n+1) = floor(n*a(n)/a(n-1)), for n >= 1.
  • A145103 (program): a(0) = a(1) = 1. a(n+1) = ceiling(n*a(n)/a(n-1)), for n >= 1.
  • A145105 (program): a(n) = n if n is prime or a perfect number, otherwise a(n) = 0.
  • A145109 (program): a(n) = 2*n * core(2*n).
  • A145110 (program): Number of elements in the Redheffer matrix that contribute to the Moebius function.
  • A145112 (program): Numbers of length n binary words with fewer than 4 0-digits between any pair of consecutive 1-digits.
  • A145113 (program): Numbers of length n binary words with fewer than 5 0-digits between any pair of consecutive 1-digits.
  • A145114 (program): Numbers of length n binary words with fewer than 6 0-digits between any pair of consecutive 1-digits.
  • A145115 (program): Numbers of length n binary words with fewer than 7 0-digits between any pair of consecutive 1-digits.
  • A145116 (program): Numbers of length n binary words with fewer than 8 0-digits between any pair of consecutive 1-digits.
  • A145117 (program): Numbers of length n binary words with fewer than 9 0-digits between any pair of consecutive 1-digits.
  • A145119 (program): a(n) = Product_{k=1..n-1} (ceiling(n/k) - ceiling(n/k) mod 2).
  • A145120 (program): Numbers X such that (X^2-19)/57 is a square
  • A145121 (program): Numbers n such that there exists x in N : (x+19)^3-x^3=n^2.
  • A145122 (program): Numbers X such that (X+19)^3-X^3 is a square
  • A145123 (program): Numbers n such that there exists x in N : (x+1)^3-x^3=19*n^2.
  • A145124 (program): Numbers x such that there exists n in N : (x+1)^3-x^3=19*n^2.
  • A145126 (program): a(n) = 1 + (6 + (11 + (6 + n)*n)*n)*n/24.
  • A145127 (program): a(n) = 1 + (144 + (50 + (35 + (10 + n)*n)*n)*n)*n/120.
  • A145128 (program): 1 + (1200 + (634 + (225 + (85 + (15 + n)*n)*n)*n)*n)*n/720.
  • A145129 (program): 1 + (9960 + (6804 + (2464 + (735 + (175 + (21 + n)*n)*n)*n)*n)*n)*n/5040.
  • A145130 (program): 2 + (89040 + (71868 + (29932 + (8449 + (1960 + (322 + (28 + n)*n)*n)*n)*n)*n)*n)*n/40320.
  • A145131 (program): Expansion of x/((1 - x - x^4)*(1 - x)^2).
  • A145132 (program): Expansion of x/((1 - x - x^4)*(1 - x)^3).
  • A145133 (program): Expansion of x/((1 - x - x^4)*(1 - x)^4).
  • A145134 (program): Expansion of x/((1 - x - x^4)*(1 - x)^5).
  • A145135 (program): Expansion of x/((1 - x - x^4)*(1 - x)^6).
  • A145136 (program): Expansion of x/((1 - x - x^4)*(1 - x)^7).
  • A145137 (program): Expansion of x/((1 - x - x^4)*(1 - x)^8).
  • A145138 (program): Main diagonal of square array A145153.
  • A145139 (program): Antidiagonal sums of A145153.
  • A145153 (program): Square array A(n,k), n >= 0, k >= 0, read by antidiagonals, where sequence a_k of column k is the expansion of x/((1 - x - x^4)*(1 - x)^(k - 1)).
  • A145154 (program): Coefficients in expansion of Eisenstein series E_1.
  • A145155 (program): Coefficients in expansion of Delta’(q).
  • A145171 (program): Triangle read by rows: left half of trinomial triangle (A027907) modulo 3.
  • A145172 (program): Number of pentagonal numbers needed to represent n with greedy algorithm.
  • A145193 (program): Omega(6n-1) + Omega(6n+1).
  • A145197 (program): Partial sums of number of primes < n-th prime p such that p+2 is prime.
  • A145199 (program): Nonsquarefree numbers k such that k+1 is prime.
  • A145204 (program): Numbers whose representation in base 3 (A007089) ends in an odd number of zeros.
  • A145216 (program): Self-convolution of (1^3, 2^3, 3^3, 4^3, … ).
  • A145217 (program): a(n) is the self-convolution series of the sum of 4th powers of the first n natural numbers.
  • A145218 (program): a(n) is the self-convolution series of the sum of 5th powers of the first n natural numbers.
  • A145219 (program): a(n) is the number of even permutations (of an n-set) with exactly 1 fixed point.
  • A145220 (program): a(n) is the number of even permutations (of an n-set) with exactly 2 fixed points.
  • A145222 (program): a(n) is the number of odd permutations (of an n-set) with exactly 1 fixed point.
  • A145223 (program): a(n) is the number of odd permutations (of an n-set) with exactly 2 fixed points.
  • A145224 (program): Triangle read by rows: T(n,k) is the number of even permutations (of an n-set) with exactly k fixed points.
  • A145225 (program): T(n,k) is the number of odd permutations (of an n-set) with exactly k fixed points.
  • A145229 (program): Coefficients in expansion of E’_1(q).
  • A145264 (program): a(n) is the positive integer such that Sum_{k>=0} floor(n/(a(n)+k)) = n, or 0 if there is no such positive integer.
  • A145265 (program): A positive integer n is included if there exists a positive integer m such that Sum_{k>=0} floor(n/(m+k)) = n.
  • A145266 (program): A positive integer n is included if there does not exist a positive integer m such that Sum{k>=0} floor(n/(m+k)) = n.
  • A145282 (program): a(n) = number of monomials in n-th power of polynomial x^2-x-1
  • A145285 (program): a(n) is the number of monomials in the n-th power of polynomial x^4-x^3-x^2-x-1.
  • A145292 (program): Composite numbers generated by the Euler polynomial x^2 + x + 41.
  • A145301 (program): a(n) = 12*a(n-1) - 30*a(n-2) with a(0)=1 and a(1)=6.
  • A145302 (program): a(n) = ((7 + sqrt(7))^n + (7 - sqrt(7))^n)/2.
  • A145303 (program): a(n) = ((8 + sqrt(8))^n + (8 - sqrt(8))^n)/2.
  • A145312 (program): Coefficients in expansion of E’‘_4(q), where E_4 is the Eisenstein series in A004009.
  • A145318 (program): Numbers X such that exists Y in N with X^2 = 93*Y^2+31.
  • A145319 (program): Numbers Y such that 93*Y^2+31 is a square.
  • A145322 (program): Numbers n such that there exists x in N : (x+1)^3-x^3=31*n^2.
  • A145323 (program): Numbers x such that there exists n in N : (x+1)^3-x^3=31*n^2.
  • A145325 (program): Least k such that f(n,k) is not a prime, where f(n,1)=2n+1 and f(n,k)=f(f(n,k-1)) for k>=2.
  • A145328 (program): Partial sums of A007925, starting at n=1.
  • A145329 (program): Partial sums of A051442, starting at n=1.
  • A145335 (program): Numbers n such that there exists x in N : (x+1)^3-x^3=43*n^2.
  • A145336 (program): Numbers x such that there exists n in N : (x+1)^3-x^3=43*n^2.
  • A145341 (program): Convert 2n-1 to binary. Reverse its digits. Convert back to decimal to get a(n).
  • A145342 (program): a(n) = (A145341(n) + 1)/2.
  • A145346 (program): A145312(n)/1440.
  • A145354 (program): It is conjectured that for each m >= 1 there exist primes Q=Q(m) and P=P(m) with (2m)^2 + 1 <= Q <= (2m+1)^2 - 2m <= P <= (2m+1)^2; then set a(2m-1) = Q, a(2m) = P.
  • A145359 (program): Second column (m=2) of triangle A145357 (S1hat(6)).
  • A145362 (program): Lower triangular array, called S1hat(-1), related to partition number array A145361.
  • A145365 (program): Row sums of triangle A145364 (S1hat(-2)) and partition array A145363 (M31hat(-2)).
  • A145375 (program): Numerators of partial sums of the alternating series of inverse central binomial coefficients.
  • A145377 (program): a(n) = A002324(n) mod 2.
  • A145378 (program): a(n) = Sum_{d|n} sigma(d) - 2*Sum_{2c|n} sigma(c) + 4*Sum_{4b|n} sigma(b).
  • A145379 (program): Square array read by antidiagonals upwards.
  • A145382 (program): Write the n-th prime in binary. Change all 0’s to 1’s and all 1’s to 0’s. a(n) is the decimal equivalent of the result.
  • A145388 (program): Sum of (k,n)_* for k=1,2,…,n, where (k,n)_* is the greatest divisor of k which is a unitary divisor of n.
  • A145389 (program): Digital roots of triangular numbers.
  • A145390 (program): Number of sublattices of index n of a centered rectangular lattice fixed by a reflection.
  • A145391 (program): Number of inequivalent sublattices of index n in centered rectangular lattice.
  • A145392 (program): Number of inequivalent sublattices of index n in square lattice, where two sublattices are considered equivalent if one can be rotated by a multiple of Pi/2 to give the other.
  • A145393 (program): Number of inequivalent sublattices of index n in square lattice, where two sublattices are considered equivalent if one can be rotated or reflected to give the other, with that rotation or reflection preserving the parent square lattice.
  • A145394 (program): Number of inequivalent sublattices of index n in hexagonal lattice, where two sublattices are considered equivalent if one can be rotated by a multiple of Pi/3 to give the other.
  • A145395 (program): Complement of the primes of form 4k+3 (A002145).
  • A145396 (program): a(n) = Sum_{d|n} sigma(d) + 3*Sum_{2c|n} sigma(c).
  • A145397 (program): Numbers not of the form m*(m+1)*(m+2)/6, the non-tetrahedral numbers.
  • A145398 (program): a(n) = Sum_{d|n} sigma(d) - Sum_{2c|n} sigma(c) + 4*Sum_{4b|n} sigma(b).
  • A145399 (program): Dirichlet g.f.: (1+4/2^s+1/4^s)*zeta(s)^3.
  • A145422 (program): Decimal expansion of sum_{n=0..infinity} (-1)^n/(2^(3n)*(3n+1)).
  • A145423 (program): Decimal expansion of Sum_{n>=1} (-1)^(n-1)/(n^2-1/4)^2.
  • A145426 (program): Decimal expansion of Sum_{k>=0} (k!/(k+2)!)^2.
  • A145429 (program): Decimal expansion of Sum_{n > 0} n*(n!)^2/(2n)!.
  • A145430 (program): Decimal expansion of sum_{n=1..inf} n^2*(n!)^2/(2n)!.
  • A145432 (program): Decimal expansion of sum_{n=1..inf} (-1)^(n-1)*2^n/binomial(2n,n).
  • A145433 (program): Decimal expansion of Sum_{n>=1} (-1)^(n-1)*n/binomial(2n,n).
  • A145434 (program): Decimal expansion of Sum_{n>=1} (-1)^(n-1)*n^2/binomial(2n,n).
  • A145436 (program): Decimal expansion of sum_{n=0..inf} (-1)^n/((2n+1)^2*binomial(2n,n)).
  • A145438 (program): Decimal expansion of sum_{n=1..inf} 1/(n^3*binomial(2n,n)).
  • A145439 (program): Decimal expansion of Sum_{k>=0} binomial(4*k, 2*k)/2^(6*k).
  • A145441 (program): Exponents of multipliers 10^a(n) of SI prefixes, in increasing order.
  • A145442 (program): Multipliers of SI prefixes, in increasing order.
  • A145444 (program): Dirichlet g.f.: (1+3/4^s+2/8^s)*zeta(s)^3.
  • A145445 (program): a(n) = the smallest square > n-th prime.
  • A145446 (program): a(n) = the smallest cube > n-th prime
  • A145448 (program): a(n) = 12^n*n!.
  • A145461 (program): Numbers that can be written with a single digit in base 10 as well as in some base b<10.
  • A145466 (program): Expansion of q^(1/6) * eta(q) / eta(q^5) in powers of q.
  • A145467 (program): Convolution square of A003114.
  • A145468 (program): Convolution square of A003106.
  • A145471 (program): Primes p such that (5+p)/2 is prime.
  • A145472 (program): Primes p such that (p+7)/2 is prime.
  • A145473 (program): Primes p such that (11 + p)/2 is prime.
  • A145474 (program): Primes p such that (13+p)/2 is prime.
  • A145475 (program): Primes p such that (17+p)/2 is prime.
  • A145476 (program): Primes p such that (19 + p)/2 is prime.
  • A145477 (program): Primes p such that (23 + p)/2 is prime.
  • A145478 (program): Primes p such that (29 + p)/2 is prime.
  • A145479 (program): Primes p such that (31+p)/2 is prime.
  • A145480 (program): Primes p such that (p+37)/2 is prime.
  • A145481 (program): Primes p such that 2p - 17 is prime.
  • A145482 (program): Primes p such that 2p - 19 is prime.
  • A145483 (program): Primes p such that 2p - 23 is prime.
  • A145484 (program): Primes p such that 2p - 29 is a positive prime.
  • A145485 (program): Primes p such that 2p - 31 is prime.
  • A145486 (program): Primes p such that 2p - 37 is prime.
  • A145487 (program): Numbers k such that 6k+5 is prime and 12k+5 is also prime
  • A145488 (program): Numbers k such that 6k+13 is prime and 12k+13 is also prime.
  • A145489 (program): Numbers k such that 6k + 11 is prime and 12k + 5 is also prime.
  • A145491 (program): In these bases, there exist numbers written with only one distinct digit whose translation in binary is also written with the same lonely digit.
  • A145511 (program): Dirichlet g.f.: (1-2/2^s+7/4^s)*zeta(s)^3.
  • A145516 (program): 11^1,22^2,33^3,44^4,…
  • A145525 (program): Numbers X such that there exists Y in N : X^2=273*Y^2+91.
  • A145526 (program): Numbers Y such that 273*Y^2+91 is a square.
  • A145527 (program): Numbers n such that there exists x in N : (x+91)^3-x^3=n^2.
  • A145528 (program): Numbers x such that (x+91)^3 - x^3 is a square.
  • A145529 (program): Numbers n such that there exists x in N : (x+1)^3-x^3=91*n^2.
  • A145530 (program): Numbers x such that there exists n in N with (x+1)^3-x^3=91*n^2.
  • A145542 (program): Numerators in continued fraction expansion of sqrt(3/5).
  • A145543 (program): Denominators in continued fraction expansion of sqrt(3/5).
  • A145544 (program): 4*(4^n-3^n).
  • A145556 (program): Denominators of partial sums of the alternating series of inverse central binomial coefficients.
  • A145557 (program): Numerators of partial sums of a certain alternating series of inverse central binomial coefficients.
  • A145558 (program): Denominators of partial sums of a certain alternating series of inverse central binomial coefficients.
  • A145559 (program): Numerators of partial sums of a certain alternating series of inverse central binomial coefficients.
  • A145560 (program): Denominators of partial sums of a certain alternating series of inverse central binomial coefficients.
  • A145562 (program): Second column (m=2) of triangle A049029 (S2(5)).
  • A145563 (program): a(0)=0 and a(n+1) = 3*a(n) + 2^(n+2).
  • A145564 (program): a(n) = numerator(Sum_{k=0..n} 1/(binomial(2*k,k)*(k+1))).
  • A145565 (program): Denominators of partial sums of a certain series of inverse central binomial coefficients.
  • A145566 (program): a(n) = numerator(6 * Sum_{k=2..n} 1/(binomial(2*k, k)*(k-1))).
  • A145567 (program): Denominators of partial sums of a certain series of inverse central binomial coefficients.
  • A145568 (program): Characteristic function of numbers relatively prime to 11.
  • A145569 (program): Multiples of 6 appear in pairs.
  • A145577 (program): A045944 mod 9. Period 9: repeat 0,5,7,6,2,4,3,8,1.
  • A145593 (program): Inverse binomial transform of A144472.
  • A145594 (program): A145593(n) mod 9.
  • A145596 (program): Triangular array of generalized Narayana numbers: T(n, k) = 2*binomial(n + 1, k + 1)*binomial(n + 1, k - 1)/(n + 1).
  • A145597 (program): Generalized Narayana numbers, T(n, k) = 3/(n + 1)*binomial(n + 1, k + 2)*binomial(n + 1, k - 1), triangular array read by rows.
  • A145598 (program): Triangular array of generalized Narayana numbers: T(n, k) = 4*binomial(n+1, k+3)*binomial(n+1, k-1)/(n+1).
  • A145599 (program): Triangular array of generalized Narayana numbers: T(n,k) = 5/(n+1)*binomial(n+1,k+4)*binomial(n+1,k-1).
  • A145600 (program): a(n) is the number of walks from (0,0) to (0,1) that remain in the upper half-plane y >= 0 using (2*n - 1) unit steps either up (U), down (D), left (L) or right (R).
  • A145601 (program): a(n) is the number of walks from (0,0) to (0,2) that remain in the upper half-plane y >= 0 using 2*n unit steps either up (U), down (D), left (L) or right (R).
  • A145602 (program): a(n) is the number of walks from (0,0) to (0,3) that remain in the upper half-plane y >= 0 using 2*n +1 unit steps either up (U), down (D), left (L) or right (R).
  • A145603 (program): a(n) is the number of walks from (0,0) to (0,4) that remain in the upper half-plane y >= 0 using 2*n +2 unit steps either up (U), down (D), left (L) or right (R).
  • A145607 (program): Numbers k such that (3*(2*k + 1)^2 + 2)/5 is a square.
  • A145608 (program): Numbers a(n)=k such that (1/3)*(5*(2k+1)^2-2) is A057080(n)^2.
  • A145609 (program): Numerator of the polynomial A_l(x) = sum_{d=1..l-1} x^(l-d)/d for index l=2n+1 evaluated at x=1.
  • A145610 (program): Denominator of the polynomial A_l(x) = Sum_{d=1..l-1} x^(l-d)/d for index l=2n+1 evaluated at x=1.
  • A145611 (program): Numerator of the polynomial A_l(x) = sum_{d=1..l-1} x^(l-d)/d for index l=2n+1 evaluated at x=2.
  • A145612 (program): Denominator of the polynomial A_l(x) = Sum_{d=1..l-1} x^(l-d)/d for index l=2n+1 evaluated at x=2.
  • A145613 (program): Numerator of the polynomial A_l(x) = sum_{d=1..l-1} x^(l-d)/d for index l=2n+1 evaluated at x=3.
  • A145614 (program): Denominator of the polynomial A_l(x) = sum_{d=1..l-1} x^(l-d)/d for index l=2n+1 evaluated at x=3.
  • A145615 (program): Numerator of the polynomial A_l(x) = sum_{d=1..l-1} x^(l-d)/d for index l=2n+1 evaluated at x=4.
  • A145616 (program): Denominator of the polynomial A_l(x) = sum_{d=1..l-1} x^(l-d)/d for index l=2n+1 evaluated at x=4.
  • A145617 (program): Numerator of the polynomial A_l(x) = sum_{d=1..l-1} x^(l-d)/d for index l=2n+1 evaluated at x=5.
  • A145618 (program): Denominator of the polynomial A_l(x) = sum_{d=1..l-1} x^(l-d)/d for index l=2n+1 evaluated at x=5.
  • A145619 (program): Numerator of the polynomial A_l(x) = sum_{d=1..l-1} x^(l-d)/d for index l=2n+1 evaluated at x=6.
  • A145620 (program): Denominator of the polynomial A_l(x) = sum_{d=1..l-1} x^(l-d)/d for index l=2n+1 evaluated at x=6.
  • A145621 (program): Numerator of the polynomial A_l(x) = sum_{d=1..l-1} x^(l-d)/d for index l=2n+1 evaluated at x=7.
  • A145622 (program): Denominator of the polynomial A_l(x) = sum_{d=1..l-1} x^(l-d)/d for index l=2n+1 evaluated at x=7.
  • A145623 (program): Numerator of the polynomial A_l(x) = Sum_{d=1..l-1} x^(l-d)/d for index l=2n+1 evaluated at x=8.
  • A145624 (program): Denominator of the polynomial A_l(x) = Sum_{d=1..l-1} x^(l-d)/d for index l=2n+1 evaluated at x=8.
  • A145625 (program): Numerator of the polynomial A_l(x) = sum_{d=1..l-1} x^(l-d)/d for index l=2n+1 evaluated at x=9.
  • A145626 (program): Denominator of the polynomial A_l(x) = sum_{d=1..l-1} x^(l-d)/d for index l=2n+1 evaluated at x=9.
  • A145627 (program): Numerator of the polynomial A_l(x) = sum_{d=1..l-1} x^(l-d)/d for index l=2n+1 evaluated at x=10.
  • A145628 (program): Numerator of the polynomial A_l(x) = sum_{d=1..l-1} x^(l-d)/d for index l=2n+1 evaluated at x=11.
  • A145629 (program): Denominator of the polynomial A_l(x) = Sum_{d=1..l-1} x^(l-d)/d for index l=2n+1 evaluated at x=10.
  • A145630 (program): Denominator of the polynomial A_l(x) = sum_{d=1..l-1} x^(l-d)/d for index l=2n+1 evaluated at x=11.
  • A145631 (program): Numerator of the polynomial A_l(x) = sum_{d=1..l-1} x^(l-d)/d for index l=2n+1 evaluated at x=12.
  • A145632 (program): Denominator of the polynomial A_l(x) = sum_{d=1..l-1} x^(l-d)/d for index l=2n+1 evaluated at x=12.
  • A145633 (program): Numerator of the polynomial A_l(x) = sum_{d=1..l-1} x^(l-d)/d for index l=2n+1 evaluated at x=13.
  • A145634 (program): Denominator of the polynomial A_l(x) = sum_{d=1..l-1} x^(l-d)/d for index l=2n+1 evaluated at x=13.
  • A145635 (program): Numerator of the polynomial A_l(x) = sum_{d=1..l-1} x^(l-d)/d for index l=2n+1 evaluated at x=14.
  • A145636 (program): Denominator of the polynomial A_l(x) = sum_{d=1..l-1} x^(l-d)/d for index l=2n+1 evaluated at x=15.
  • A145637 (program): Numerator of the polynomial A_l(x) = sum_{d=1..l-1} x^(l-d)/d for index l=2n+1 evaluated at x=15.
  • A145638 (program): Denominator the polynomial A_l(x) = sum_{d=1..l-1} x^(l-d)/d for index l=2n+1 evaluated at x=14.
  • A145639 (program): Numerator of the polynomial A_l(x) = sum_{d=1..l-1} x^(l-d)/d for index l=2n+1 evaluated at x=16.
  • A145640 (program): Denominator the polynomial A_l(x) = sum_{d=1..l-1} x^(l-d)/d for index l=2n+1 evaluated at x=16.
  • A145641 (program): Numbers whose binary representation is the concatenation of n 1’s, n 0’s and n 1’s.
  • A145642 (program): Cubefree part of n!.
  • A145644 (program): Cubefree part of 10^n.
  • A145646 (program): Wavelength (in ångströms) of the series limit of the Hydrogen spectrum for main quantum number n.
  • A145647 (program): First differences of A145646.
  • A145654 (program): Partial sums of A000918, starting from index 1.
  • A145655 (program): Partial sums of A080674.
  • A145656 (program): a(n) = numerator of polynomial of genus 1 and level n for m = 2
  • A145658 (program): a(n) = numerator of polynomial of genus 1 and level n for m = 3
  • A145660 (program): a(n) = numerator of polynomial of genus 1 and level n for m = 4 = A1,n.
  • A145661 (program): Triangle T(n,k) = (-1)^k * A119258(n,k) read by rows, 0 <= k <= n.
  • A145662 (program): a(n) = numerator of polynomial of genus 1 and level n for m = 5 = A1,n.
  • A145664 (program): a(n) = numerator of polynomial of genus 1 and level n for m = 6 = A1,n.
  • A145666 (program): a(n) = numerator of polynomial of genus 1 and level n for m = 7 : A1,n.
  • A145677 (program): Triangle T(n, k) read by rows: T(n, 0) = 1, T(n, n) = n, n>0, T(n,k) = 0, 0 < k < n-1.
  • A145678 (program): a(n) = 441*n^2 - 21.
  • A145679 (program): Lower limit of backward value of 2^n and n!.
  • A145693 (program): Numbers X such that there exists Y in N with X^2=21*Y^2+7.
  • A145694 (program): Numbers Y such that 57*Y^2+19 is a square.
  • A145695 (program): Numbers X such that there exists Y in N with X^2=111*Y^2+37.
  • A145696 (program): Numbers Y such that 111*Y^2+37 is a square.
  • A145697 (program): Numbers n such that there exists x in N with (x+37)^3-x^3=n^2.
  • A145698 (program): Numbers x such that (x+37)^3-x^3 is a square.
  • A145699 (program): Numbers n such that there exists x in N with (x+1)^3-x^3=37*n^2
  • A145700 (program): Numbers x such that there exists n in N with (x+1)^3-x^3=37*n^2.
  • A145701 (program): Lesser p of twin primes (p,q) such that there exists an integer between sqrt(2p) and sqrt(2q)
  • A145714 (program): a(n) = ceiling(sqrt(2*A145701(n))).
  • A145715 (program): Numbers X such that there exists Y in N with X^2 = 381*Y^2 + 127.
  • A145716 (program): Numbers Y such that 381*Y^2+127 is a square.
  • A145717 (program): Numbers n such that there exists x in N with (x+127)^3-x^3=n^2.
  • A145718 (program): Numbers x such that there exists n in N with (x+127)^3-x^3=n^2.
  • A145720 (program): Numbers x such that there exists n in N with (x+1)^3-x^3=127*n^2.
  • A145721 (program): Numbers n such that there exists x in N with (x+1)^3-x^3=127*n^2.
  • A145722 (program): Expansion of f(q) * f(q^5) / phi(-q^2)^2 in powers of q where f(), phi() are Ramanujan theta functions.
  • A145729 (program): Partial sums of A052379.
  • A145730 (program): Partial sums of A108019.
  • A145733 (program): Indices of palindromes in A001127
  • A145737 (program): a(n) = square part of A145609(n).
  • A145756 (program): a(n) = ((2^prime(n+2)-2)/prime(n+2))/3, where n >= 1
  • A145766 (program): Partial sums of A020988.
  • A145784 (program): Numbers with property that the number of prime factors is a multiple of 3.
  • A145787 (program): Number of times you have to move n cards from one pile to another doing one up, one down, until you obtain the initial sequence.
  • A145801 (program): Number of islands of ones fitting in an n X n array with all ones connected only either two adjacent vertically or two adjacent horizontally.
  • A145804 (program): 1/2 the number of islands of ones fitting in an n X n array symmetric about main diagonal with all ones connected only either two adjacent vertically or two adjacent horizontally.
  • A145805 (program): 1/4 of the number of islands of ones fitting in an n X n array symmetric about the diagonal and under 90-degree rotation with all ones connected only either two adjacent vertically or two adjacent horizontally.
  • A145806 (program): 1/4 of the number of islands of ones fitting in an n X n array symmetric under 90-degree rotation with all ones connected only either two adjacent vertically or two adjacent horizontally.
  • A145807 (program): 1/2 the number of islands of ones fitting in an n X n array symmetric under 180 degree rotation with all ones connected only either two adjacent vertically or two adjacent horizontally.
  • A145809 (program): Number of islands of ones fitting in an n X n array with all ones connected only either three adjacent vertically or three adjacent horizontally.
  • A145812 (program): Odd positive integers a(n) such that for every odd integer m > 1 there exists a unique representation of m as a sum of the form a(l) + 2a(s).
  • A145813 (program): 1/2 the number of islands of ones fitting in an n X n array symmetric about main diagonal with all ones connected only either three adjacent vertically or three adjacent horizontally.
  • A145816 (program): 1/4 of the number of islands of ones fitting in an n X n array symmetric under 90-degree rotation with all ones connected only either three adjacent vertically or three adjacent horizontally.
  • A145818 (program): Odd positive integers a(n) such that for every integer m == 3 (mod 4) there exists a unique representation of the form m = a(l) + 2*a(s), but there are no such representations for m == 1 (mod 4).
  • A145819 (program): Union of A145812 and A145818 with double repetition of 1, so that a(1)=1, a(2)=1
  • A145823 (program): Squares of the form p1 - 1 where p1 is a lower twin prime.
  • A145824 (program): Lower twin primes p1 such that p1-1 is a square.
  • A145825 (program): a(n) is in A145818 such that (4n-1-a(n))/2 is in A145818 as well
  • A145826 (program): Arises from critical number of finite Abelian groups.
  • A145834 (program): a(n) = difference between the n-th composite number and the sum of its prime factors with repetition.
  • A145837 (program): Indices of primes in A005891(n).
  • A145838 (program): Primes in A005891 = Centered pentagonal numbers: (5n^2 + 5n + 2)/2.
  • A145839 (program): Number of 3-compositions of n.
  • A145840 (program): Number of 4-compositions of n.
  • A145841 (program): Number of 5-compositions of n.
  • A145845 (program): Number of permutations of length 2n+1 which are invariant under the reverse-complement map and have no decreasing subsequences of length 5.
  • A145847 (program): Number of involutions of length 2n which are invariant under the reverse-complement map and have no decreasing subsequences of length 6.
  • A145849 (program): a(n) = A145812(2n-1).
  • A145850 (program): a(n) = A145818(2n-1).
  • A145865 (program): a(0) = 0, a(1) = 1, a(2n) = a(n), a(2n+1) = a(n) - a(n+1).
  • A145867 (program): Number of involutions of length 2n which are invariant under the reverse-complement map and have no decreasing subsequence of length 7.
  • A145885 (program): a(n) = (n-1)^2*binomial(2n,n)/(2*(n+1)).
  • A145886 (program): Number of excedances in all odd permutations of {1,2,…,n} with no fixed points.
  • A145887 (program): Number of excedances in all even permutations of {1,2,…,n} with no fixed points.
  • A145888 (program): Triangle read by rows: T(n,k) is the number of permutations of {1,2,…,n} in which k is the largest entry in the cycle containing 1 (1 <= k <= n).
  • A145889 (program): Number of even entries that are followed by a smaller entry in all permutations of {1,2,…,n}.
  • A145890 (program): Triangle read by rows: T(n,k) = B(k)C(n-k), where B(j) is the central binomial coefficient binomial(2j,j) (A000984) and C(j) is the Catalan number binomial(2j,j)/(j+1) (A000108); 0 <= k <= n).
  • A145897 (program): Starting prime (and 1): where number of consecutive squares m^2 satisfy r=p+4*m^2, prime
  • A145901 (program): Triangle of f-vectors of the simplicial complexes dual to the permutohedra of type B_n.
  • A145903 (program): Generalized Narayana numbers for root systems of type D_n. Triangle of h-vectors of type D associahedra.
  • A145905 (program): Square array read by antidiagonals: Hilbert transform of triangle A060187.
  • A145909 (program): First 6-fold decimation of A061039. First bisection of A144454.
  • A145910 (program): a(n) = (1 + 3*n)*(4 + 3*n)/2.
  • A145911 (program): a(n) = A145909(n)/8.
  • A145917 (program): Triangle read by rows: to get n-th row, start with -4n and successively add 5, 7, 9, 11, 13, … until reaching a square.
  • A145919 (program): A000332(n) = a(n)*(3*a(n) - 1)/2.
  • A145920 (program): List of numbers that are both pentagonal (A000326) and binomial coefficients C(n,4) (A000332).
  • A145921 (program): Numerator of n*B(n,1+1/n), where B(.,.) is the Beta Function.
  • A145923 (program): Second bisection of A061041: a(n) = A061041(2n+1) = (2n+1)*(2n+9).
  • A145924 (program): Last digit of A145923(n).
  • A145934 (program): Expansion of 1/(1-x*(1-6*x)).
  • A145960 (program): Decimal expansion of 2*log(5/3) used in BBP Pi formula.
  • A145976 (program): Expansion of 1/(1-x*(1-7*x)).
  • A145977 (program): Expansion of c(q^3) / (c(q^3) + c(q^6)) where c() is a cubic AGM function.
  • A145978 (program): Expansion of 1/(1-x*(1-8*x)).
  • A145979 (program): a(n) = (2*n + 4)/gcd(n,4).
  • A145980 (program): a(n) = 29 + 73*n + 37*n^2.
  • A145984 (program): Number of “universes” built from n entities according to the following rules: 1. Each of the entities can be an element or a set. 2. Sets are entities that do have another entity as an element. 3. There must exist an element. 4. Two sets are identical when they own the same elements.
  • A145995 (program): a(n) = 8 - 12*n + 5*n^2.
  • A146005 (program): a(n) = n*Lucas(n).
  • A146023 (program): Triangle read by rows, square of A027293.
  • A146029 (program): Numbers that can be written from base 2 to base 17 using only the digits 0 to 8 (conjectured to be complete).
  • A146071 (program): Consider A145834 as the first step of the sieving (subtracting the sum of its prime factors with repetition from the composite numbers). This sequence is the result of the subsequent application of above described sieving - thus all terms of this sequence arise as prime numbers.
  • A146076 (program): Sum of even divisors of n.
  • A146078 (program): Expansion of 1/(1-x*(1-9*x)).
  • A146079 (program): Period 9: repeat 2,4,8,5,4,5,8,4,2.
  • A146080 (program): Expansion of 1/(1-x*(1-10*x)).
  • A146081 (program): First differences of A145980.
  • A146082 (program): a(n) = A146081(n) mod 9.
  • A146083 (program): Expansion of 1/(1 - x*(1 - 11*x)).
  • A146084 (program): Expansion of 1/(1-x(1-12x)).
  • A146085 (program): Positive integers a(n) such that for every integer m == 1 (mod 3), m >= 4, there exists a unique representation of m as a sum of the form a(l) + 3*a(s).
  • A146086 (program): Number of n-digit numbers with each digit odd where the digits 1 and 3 occur an even number of times.
  • A146087 (program): a(n) = 3*A146085(n) - 1.
  • A146091 (program): a(n) = 3*A146085(n) - 2.
  • A146093 (program): Bell numbers (A000110) read mod 3.
  • A146094 (program): Bell numbers (A000110) mod 4.
  • A146095 (program): Bell numbers (A000110) read mod 5.
  • A146096 (program): Bell numbers (A000110) read mod 6.
  • A146097 (program): Bell numbers (A000110) read mod 7.
  • A146098 (program): Bell numbers (A000110) read mod 8.
  • A146099 (program): Bell numbers (A000110) read mod 9.
  • A146100 (program): Bell numbers (A000110) read mod 10.
  • A146101 (program): Bell numbers (A000110) read mod 11.
  • A146102 (program): Bell numbers (A000110) read mod 12.
  • A146103 (program): Bell numbers (A000110) read mod 13.
  • A146104 (program): Bell numbers (A000110) read mod 14.
  • A146105 (program): Bell numbers (A000110) read mod 15.
  • A146106 (program): Bell numbers (A000110) read mod 16.
  • A146107 (program): Bell numbers (A000110) read mod 17.
  • A146108 (program): Bell numbers (A000110) read mod 18.
  • A146109 (program): Bell numbers (A000110) read mod 19.
  • A146110 (program): Bell numbers (A000110) read mod 20.
  • A146111 (program): Bell numbers (A000110) read mod 21.
  • A146112 (program): Bell numbers (A000110) read mod 22.
  • A146113 (program): Bell numbers (A000110) read mod 23.
  • A146114 (program): Bell numbers (A000110) read mod 24.
  • A146115 (program): Bell numbers (A000110) read mod 25.
  • A146116 (program): Bell numbers (A000110) read mod 26.
  • A146117 (program): Bell numbers (A000110) read mod 27.
  • A146118 (program): Bell numbers (A000110) read mod 28.
  • A146119 (program): Bell numbers (A000110) read mod 29.
  • A146120 (program): Bell numbers (A000110) read mod 30.
  • A146121 (program): Bell numbers (A000110) read mod 31.
  • A146122 (program): Bell numbers (A000110) read mod 32.
  • A146135 (program): Positive integers a(n) such that for every integer m==1(mod 4),m>=5, there exists a unique representation of m as a sum of the form a(l)+4a(s).
  • A146160 (program): Period 4: repeat [1, 4, 1, 16].
  • A146161 (program): a(n) is the number of n X n matrices with entries in {1,2,3} such that all adjacent entries (in the same row or column) differ by 1 or -1.
  • A146163 (program): Expansion of q^(-3/4) * eta(q^2)^2 * eta(q^20) / (eta(q)^2 * eta(q^4)) in powers of q.
  • A146179 (program): Digit sums of Cullen numbers.
  • A146205 (program): Number of paths of the simple random walk on condition that the median applied to the partial sums S_0=0, S_1,…,S_n, n odd (n=15 in this example), is equal to half-integer values k+1/2, -[n/2]-1<=k<=[n/2].
  • A146211 (program): Fermat quotient of the n-th prime with base 3.
  • A146298 (program): Difference between the cubes and 2*tetrahedral numbers; A000578(n) - 2*A000292(n).
  • A146301 (program): a(n) = (8*n+3)*(8*n+7).
  • A146302 (program): a(n) = (8*n+5)*(8*n+9).
  • A146306 (program): a(n) = numerator of (n-6)/(2n)
  • A146307 (program): a(n) = denominator of (n-6)/(2n) = denominator of (n+6)/(2n).
  • A146308 (program): a(n) is the smallest k such that the numerator of (k-6)/(2k) equals n.
  • A146309 (program): a(n) = indices where primes occurred in A146306.
  • A146311 (program): a(n) = cos(2*n*arcsin(sqrt(3)) = (-1)^n*cosh(2*n*arcsinh(sqrt(2)).
  • A146312 (program): a(n) = -cos((2 n - 1) arcsin(sqrt(3)))^2 = -1 + cosh((2 n - 1) arcsinh(sqrt(2)))^2.
  • A146313 (program): a(n) = cosh( (2n - 1)*arcsinh(sqrt(2)) )^2 = 1 - cos( (2n - 1)*arcsin(sqrt(3)) )^2.
  • A146314 (program): Inverse of Riordan array A127543.
  • A146316 (program): Prime subtrahends of nearest squares producing prime differences
  • A146321 (program): Inverse binomial transform of A070366.
  • A146322 (program): a(n) = A061039(n) mod 9.
  • A146325 (program): Period 3: repeat [1, 4, 1].
  • A146501 (program): Period 6: repeat [4,8,7,5,1,2].
  • A146507 (program): Numbers congruent to {1, 13} mod 42.
  • A146509 (program): Numbers that are congruent to {1, 5} mod 18.
  • A146510 (program): Numbers congruent to {1, 4} mod 15.
  • A146511 (program): Numbers congruent to {5, 17} modulo 66.
  • A146512 (program): Numbers congruent to {1, 3} mod 12.
  • A146523 (program): Binomial transform of A010685.
  • A146524 (program): a(n) is the largest nonnegative integer m such that 2*n*k+1 is prime for all k where 1<=k<=m. a(n) = 0 if 2n+1 is composite.
  • A146525 (program): a(n) is the largest nonnegative integer m such that 2*n*k-1 is prime for all k where 1<=k<=m. a(n) = 0 if 2n-1 is composite.
  • A146528 (program): a(0) = 4; for n >= 1, a(n) = 2^n + 4.
  • A146529 (program): A two level sequence: v(n)=2*(If[n == 0, 0, 2^(n - 1)] + 2); a(n)=If[n == 0, 6, (v[n] + v[n - 1] - 2)].
  • A146533 (program): Catalan transform of A135092.
  • A146534 (program): 4*C(2n,n)-3*0^n.
  • A146535 (program): Numerator of (2*n-1)/3.
  • A146537 (program): a(n) = A144453(n)/16.
  • A146538 (program): Even numbers n such that n+3 is not a prime.
  • A146539 (program): A061045 mod 9.
  • A146540 (program): The PolyLog functional part of A008292 (the Eulerian numbers) is treated as a curvature to give a set of polynomial triangle sequence coefficients: p(x,n)=Sum[A008292(n,m)*x^(m-1),{m,0,n}]; q(x,n)=k from Solve[FullSimplify[ExpandAll[p[x, n]/(x - 1)^n]] - (1 + k/x^2) == 0, k].
  • A146541 (program): Binomial transform of A010688.
  • A146543 (program): The LerchPhi functional part of A060187 MacMahon numbers is treated/ solved for as a curvature to give a set of polynomial triangle sequence coefficients: p(x,n)=Sum[A060187(n,m)*x^(m-1),{m,0,n}]; q(x,n)=k from Solve[FullSimplify[ExpandAll[p[x, n]/(x - 1)^n]] - (1 + k/x^2) == 0, k].
  • A146559 (program): Expansion of (1-x)/(1 - 2*x + 2*x^2).
  • A146562 (program): ‘Erratic’ numbers in A064353 [Kolakoski (1,3)]
  • A146564 (program): a(n) is the number of solutions of the equation k*n/(k-n) = c. k,c integers.
  • A146566 (program): Numbers k such that k*sigma_0(k) is divisible by (k - sigma_0(k)).
  • A146749 (program): Coefficients of the Pascal sequence minus the Eulerian numbers: q(x,n)= = (1 - x)^(n + 1)*PolyLog[ -n, x]; p(x,n) = (q(x, n)/x - (x + 1)^(n - 1))/x.
  • A146753 (program): a(n) = denominator((1/2)*(1 + Product_{k=0..n-1} 2*(1 + 3*k)/(5 + 6*k))).
  • A146761 (program): Period 6: repeat [0, 0, 6, 6, 3, 3].
  • A146762 (program): Numbers in A061039 ending with 0.
  • A146763 (program): Rank of terms ending in 0 in A061039.
  • A146765 (program): Triangle read by rows: expansion of p(x,n)=If[n == 0, 1, (x + 1)^n + 2^(n - 1)*Sum[Binomial[n, m]*x^m*(1 + x^(n - 2*m)), {m, 1, n - 1}]].
  • A146766 (program): Triangle read by rows: expansion of p(x,n)=If[n == 0, 1, (x + 1)^n + 2^(n - 2)*Sum[Binomial[n, m]*x^m*(1 + x^(n - 2*m)), {m, 1, n - 1}]].
  • A146767 (program): Triangle read by rows: expansion of p(x,n)=If[n == 0, 1, (x + 1)^n + 2^(n - 3)*Sum[Binomial[n, m]*x^m*(1 + x^(n - 2*m)), {m, 1, n - 1}]].
  • A146769 (program): Coefficients of polynomial P(n) by rows, with P(n) = (x+1)^n + 2^(n-3)*((x+1)^n - x^n - 1) for n > 0 and P(0) = 1.
  • A146880 (program): A symmetrical triangle sequence of coefficients : p(x,n)=If[n == 0, 1, (x + 1)^n + Sum[(1 + Mod[Binomial[n, m], 2])*x^m*(1 + x^(n - 2*m)), {m, 1, n - 1}]].
  • A146881 (program): A symmetrical triangle sequence of coefficients : p(x,n)=If[n == 0, 1, (x + 1)^n + Sum[(1 + Mod[Binomial[n, m], 4])*x^m*(1 + x^(n - 2*m)), {m, 1, n - 1}]].
  • A146882 (program): a(n) = 5*(4^(n+1) - 1)/3.
  • A146883 (program): a(n) = 6 * Sum_{m=0..n} 5^m.
  • A146884 (program): a(n) = 7*Sum_{k=0..n} 6^k.
  • A146885 (program): a(n) = 8*Sum_{k=0..n} 7^k.
  • A146887 (program): a(n) = prime(n)*a(n-1) - a(n-2).
  • A146898 (program): Lower polynomial approximation of Eulerian numbers: t0(n,m)=If[Mod[2*Binomial[n, m], 2] - Mod[Binomial[n, m], 2] == 0, Binomial[n, m]/2, Binomial[n, m] + 1]; p(x,n)=If[n == 0, 1, (x + 1)^n + Sum[t0(n,m)*x^m*(1 + x^(n - 2*m)), {m, 1, n - 1}]].
  • A146899 (program): An additive term polynomial as a stand-alone polynomial: t(n,m) = binomial(n, m)/2 if binomial(n, m) is even, binomial(n, m) + 1 otherwise; p(x,n) = (Sum_{m=1..n-1} t(n, m)*x^m*(1 + x^(n - 2*m)))/(2*x).
  • A146900 (program): Symmetrical polynomial: t0(n,m)=If[Mod[2*Binomial[n, m], 2] - Mod[Binomial[n, m], 2] == 0, Binomial[n, m]/2, Binomial[n, m] + 1]; p(x,n)=If[n == 0, 1, (x + 1)^n + Sum[t0(n,m)*x^m*(1 + x^(n - 2*m)), {m, 1, n - 1}]/2].
  • A146950 (program): Terms of A061047 ending in 0.
  • A146951 (program): Numbers that are congruent to 0 or 6 mod 10.
  • A146952 (program): a(n) = A146950(n)/40.
  • A146962 (program): a(n) = 10*a(n-1) - 19*a(n-2) with a(0)=1, a(1)=5.
  • A146963 (program): a(n) = ((3 + sqrt(7))^n + (3 - sqrt(7))^n)/2.
  • A146964 (program): a(n) = ((4 + sqrt(7))^n + (4 - sqrt(7))^n))/2.
  • A146965 (program): a(n) = 10*a(n-1) - 18*a(n-2) with a(0)=1, a(1)=5.
  • A146966 (program): a(n) = ((6 + sqrt(7))^n + (6 - sqrt(7))^n) / 2.
  • A146969 (program): A prime sequence form based on A003602: a(1)=3, a(2)=1, a(n) = (n+1)/2 if n is an odd prime, and a(n) = a(floor(n/2)) otherwise.
  • A146970 (program): Created from A135506 by adding successive terms as: a(n) = a(n - 1) + lcm(n, a(n - 1)); f(n) = (a(n)/a(n - 1) - 1) + (a(n + 1)/a(n) - 1).
  • A146975 (program): First quintisection of A061043: A061043(5n).
  • A146977 (program): a(n) = Sum_{k=1..prime(n)} binomial(2k,k).
  • A146980 (program): Nonsquarefree numbers such that n-1 is prime and n+1 is square.
  • A146981 (program): Numbers k of the form q^2, q = prime, such that k-2 is a prime.
  • A146983 (program): a(n) = A002531(n)*A002531(n+1).
  • A146985 (program): I call this sequence “symmetrical spooky primes” as two prime combinations are used in cryptography: f(n)=If[n==0,1,Prime[n]]; t(n,m)=f(n-m)*f(n).
  • A146989 (program): Periodic sequence with period {15,2,1,13,1}.
  • A146994 (program): a(n) = (n+1)^2/4 + (floor((n+5)/6) - 1/4) * ((n+1) mod 2).
  • A147158 (program): Number of n X n binary arrays symmetric about both diagonal and antidiagonal with all ones connected only in a 1000-1100-0111-0100 pattern in any orientation.
  • A147291 (program): a(n) = Sum_{k=1..n^2-1} binomial(2k,k).
  • A147293 (program): Triangle read by rows, A011782 convolved with A001519.
  • A147295 (program): Pascal triangle shifted MacMahon numbers: p(x,n)=If[n < 2, -(-2)^n*(x - 1)^(n + 1)*LerchPhi[x, -n, 1/2], 2*x*(x + 1)^(n - 2) - (-2)^n*(x - 1)^(n + 1)*LerchPhi[x, -n, 1/2]].
  • A147296 (program): a(n) = n*(9*n+2).
  • A147297 (program): Primes of the form (2k)^2 + 3(2k + 1)^2.
  • A147310 (program): A golden mean based polynomials set that behaves like an even powered Pascal triangle: p(x,n) = (x - phi)^floor(n/2)*(x + phi)^floor(n/2).
  • A147313 (program): Decimal expansion of sqrt(11)/2.
  • A147316 (program): Fibonacci numbers (A000045) starting at offset -20.
  • A147513 (program): Numbers such that the n-th and (n+1)st terms are the successors of prime numbers and primes themselves and n+1 > n.
  • A147518 (program): Expansion of (1-x)/(1-4*x-6*x^2).
  • A147534 (program): a(n) is congruent to (1,1,2) mod 3.
  • A147535 (program): A counting vertex substitution vector matrix Markov 3x3 with characteristic polynomial:24 - 26 x + 9 x^2 - x^3
  • A147536 (program): A counting vertex substitution vector matrix Markov 2x2 with characteristic polynomial:12 - 7 x + x=^2
  • A147537 (program): Numbers whose binary representation is the concatenation of 2n-1 digits 1 and n digits 0.
  • A147538 (program): Numbers whose binary representation is the concatenation of n 1’s and 2n-1 digits 0.
  • A147539 (program): Numbers whose binary representation is the concatenation of n 1’s, 2n-1 digits 0 and n 1’s.
  • A147540 (program): Numbers whose binary representation is the concatenation of 2n-1 digits 1, n digits 0 and 2n-1 digits 1.
  • A147543 (program): a(n) = (8*5^n + 5*3^(n+1) - 5*2^n)/3.
  • A147546 (program): Vertex counting using a vector matrix Markov with characteristic polynomial: 36 - 36 x + 11 x^2 - x^3.
  • A147560 (program): a(n) = 4*A046162(n+1).
  • A147562 (program): Number of “ON” cells at n-th stage in the “Ulam-Warburton” two-dimensional cellular automaton.
  • A147565 (program): Triangle, T(n, k) = coefficients x^k, where p(x, n) = (1/2)*( (1+x)^n + 2^n*(1-x)^(n+1)*LerchPhi(x, -n, 1/2) ), read by rows.
  • A147568 (program): a(n) = 2*A000695(n)+3.
  • A147571 (program): Numbers with exactly 4 distinct prime divisors {2,3,5,7}.
  • A147572 (program): Numbers with exactly 5 distinct prime divisors {2,3,5,7,11}.
  • A147573 (program): Numbers with exactly 6 distinct prime divisors {2,3,5,7,11,13}.
  • A147574 (program): Numbers with exactly 7 distinct prime divisors {2,3,5,7,11,13,17}.
  • A147576 (program): Numbers with exactly 3 distinct odd prime divisors {3,5,7}.
  • A147577 (program): Numbers with exactly 4 distinct odd prime divisors {3,5,7,11}.
  • A147578 (program): Numbers with exactly 5 distinct odd prime divisors {3,5,7,11,13}.
  • A147579 (program): Numbers with exactly 6 distinct odd prime divisors {3,5,7,11,13,17}.
  • A147582 (program): First differences of A147562.
  • A147585 (program): a(1) = 1; a(n) = (7*n-9)*a(n-1) for n > 1.
  • A147586 (program): a(n) = A142710(n)/2.
  • A147587 (program): a(n) = 14*n + 7.
  • A147589 (program): Concatenation of 2n-1 digits 1 and n-1 digits 0.
  • A147590 (program): Numbers whose binary representation is the concatenation of 2n-1 digits 1 and n-1 digits 0.
  • A147592 (program): Expansion of 1/(1 + x - x^2 - 3*x^3 - x^4 + x^5 + x^6).
  • A147593 (program): Expansion of 1/(1 - x + x^3 - 3*x^4 + x^5 - x^7 + x^8).
  • A147594 (program): a(1)=1, a(n)= sigma_0 (n+a(n-1)).
  • A147595 (program): a(n) is the number whose binary representation is A138144(n).
  • A147596 (program): a(n) is the number whose binary representation is A138145(n).
  • A147597 (program): a(n) is the number whose binary representation is A138146(n).
  • A147599 (program): Expansion of Product_{i>=1} (1+x^(4*i-1)).
  • A147600 (program): Expansion of 1/(1 - 3*x^2 + x^4).
  • A147601 (program): First differences of A132355.
  • A147604 (program): Expansion of g.f.: (1 + x^2 - x^3)/(1 - x - x^2 + x^3 - x^5).
  • A147609 (program): a(n) = A000290(n-1) - A065893(n).
  • A147610 (program): a(n) = 3^(wt(n-1)-1), where wt() = A000120().
  • A147611 (program): The 3rd Witt transform of A000027.
  • A147612 (program): If n is a Jacobsthal number then 1 else 0.
  • A147613 (program): Numbers that are not Jacobsthal numbers.
  • A147615 (program): a(n) = 13 + Sum_{j=4..n+3} j!.
  • A147623 (program): The 3rd Witt transform of A040000.
  • A147625 (program): Octo-factorial numbers(4).
  • A147626 (program): Octo-factorial numbers(5).
  • A147629 (program): 9-factorial numbers (4).
  • A147630 (program): a(1) = 1; for n>1, a(n) = Product_{k = 1..n-1} (9k - 3).
  • A147631 (program): 9-factorial numbers (6).
  • A147644 (program): Triangle read by rows: t(n,m)=Binomial[n, m] + If[n > 2, 2*Binomial[n - 2, m - 1], 0]; Mod[If[n > 2, 2*Binomial[n - 2, m - 1], 0],2]=0.
  • A147645 (program): Number of distinct Mersenne primes dividing n.
  • A147646 (program): If A139251 is written as a triangle with rows of lengths 1, 2, 4, 8, 16, …, the n-th row begins with 2^n followed by the first 2^n-1 terms of the present sequence.
  • A147648 (program): Number of distinct even superperfect numbers dividing n.
  • A147649 (program): Binary prejudiced single Sierpinski modulo two Pascal shift: Prejudice function: p(n,m)=If[Mod[Binomial[n - 2, m - 1], 2] == 0, Round[Log[2]]/2, 1]; t(n,m)=Binomial[n, m] + If[n > 2, 2*Binomial[n - 2, m - 1]*p(n, m), 0]; Mod[If[n > 2, 2*Binomial[n - 2, m - 1]*p(n,m), 0],2]=0.
  • A147650 (program): First trisection of A061040.
  • A147651 (program): First trisection of A028560.
  • A147652 (program): Expansion of 1/(1 - x^4 - x^5 - x^6 + x^10).
  • A147656 (program): The arithmetic mean of the n-th and (n+1)-st cubes, rounded down.
  • A147657 (program): a(1)=1, a(2)=2, thereafter (1, -2, 3, -4, 5, -6, …) interleaved with (-2, 2, -2, 2, …).
  • A147658 (program): (1, 2, -4, 6, -8, …) interleaved with (3, -3, 3, -3, 3, …).
  • A147660 (program): Coefficient expansion of toral of inverse of low ratio (1.6081283851873882) Pisot Polynomial: a(n)=Coefficient_Expansion(1/( -1 + x^2 - x^9 - x^10 + x^11)).
  • A147661 (program): a(n) = squarefree part of n^n.
  • A147662 (program): Square root of largest square dividing n^n.
  • A147666 (program): List of triples (0, 6n+1, 6n+5) for n = 0, 1, 2, …
  • A147672 (program): a(n)=a(n-2)+2^(n-1)+5 for n>3, a(0..3)=(0,1,2,7).
  • A147674 (program): Period 9:repeat 81,27,9,27,27,9,27,81,9.
  • A147675 (program): Divide by 2, multiply by 4, repeat.
  • A147676 (program): Add 10, divide by 2, repeat.
  • A147677 (program): Subtract 5, add 8, repeat.
  • A147678 (program): Double, add 0, double, add 1, double, add 2, double, add 3, etc.
  • A147683 (program): Numbers n with property that 6n-1 is in A053182.
  • A147685 (program): Squares and centered square numbers interleaved.
  • A147688 (program): a(n) = ((6 + sqrt(8))^n + (6 - sqrt(8))^n))/2.
  • A147689 (program): a(n) = ((7 + sqrt(8))^n + (7 - sqrt(8))^n)/2.
  • A147690 (program): a(0)=1; thereafter a(n+1)=F(n+3)*a(n)+F(n+3) where F_n is Fibonacci’s sequence 0,1,1,2,3,5,8, etc
  • A147703 (program): Triangle [1,1,1,0,0,0,…] DELTA [1,0,0,0,…] with Deléham DELTA defined in A084938.
  • A147704 (program): Diagonal sums of Riordan array ((1-2x)/(1 - 3x + x^2),x(1-x)/(1 - 3x + x^2)).
  • A147716 (program): Triangle of coefficients in expansion of (14 + x)^n.
  • A147719 (program): A141479(n+1)/3.
  • A147720 (program): Riordan array (1, x(1-x)/(1-3x)).
  • A147722 (program): Row sums of Riordan array ((1-3x)/(1-4x+x^2), x(1-x)/(1-4x+x^2)).
  • A147725 (program): Row sums of triangle in A147724.
  • A147746 (program): Riordan array (1, x(1-2x)/(1-3x+x^2)).
  • A147748 (program): Row sums of Riordan array ((1-3x+x^2)/(1-4x+3x^2), x(1-2x)/(1-4x+3x^2)).
  • A147753 (program): Number of maximum-size subsets of {1,2,3,…,n} whose geometric means are an integer.
  • A147754 (program): Terms of this sequence are equal to gcd between two polynomials P1(n)=(512*n^4+1024*n^3+712*n^2+194*n+15) and P2(n)=(120*n^2+151*n+47) which are used in the BBP formula
  • A147757 (program): Palindromes formed from the reflected decimal expansion of the concatenation of 1, 0 and infinite digits 1.
  • A147758 (program): Numbers whose binary representation is a palindrome formed from the reflected decimal expansion of the concatenation of 1, 0 and infinite digits 1.
  • A147759 (program): Palindromes formed from the reflected decimal expansion of the infinite concatenation of 1’s and 0’s.
  • A147760 (program): a(n) is the smallest positive integer m with exactly n ones in its binary representation and with n represented in binary as a substring of the binary representation of m.
  • A147761 (program): a(n) is the smallest positive integer m with exactly n zeros in its binary representation and with n represented in binary as a substring of the binary representation of m.
  • A147766 (program): Successive differences of A000990.
  • A147768 (program): A000012^(-2) * A027293
  • A147771 (program): a(n) = round(n^(n/2)).
  • A147772 (program): Floor[(n^n)^(1/3)].
  • A147773 (program): a(n) = round((n^n)^(1/3)).
  • A147788 (program): a(n) = floor(2*(3/2)^n).
  • A147789 (program): a(n) = round(2*(3/2)^n), using round-to-even method.
  • A147790 (program): a(1) = 3, a(n) = round(a(n-1)*3/2) for n > 1, using round-to-even method.
  • A147792 (program): A quadrisection of A061042.
  • A147795 (program): If n=A000695(k_n)+2*A000695(l_n), then a(n) is the number of nonnegative integers m<n such that k_m differs from k_n and l_m differs from l_n.
  • A147796 (program): Number of consistent sets of 3 irreflexive binary order relationships over n objects.
  • A147806 (program): Partial sums of A147809(n) = tau(n^2 + 1)/2 - 1.
  • A147807 (program): Partial sums of A147810(n) = tau(n^2 + 1)/2.
  • A147809 (program): Half the number of proper divisors (> 1) of n^2 + 1, i.e., tau(n^2 + 1)/2 - 1.
  • A147810 (program): Half the number of divisors of n^2+1.
  • A147812 (program): Primes prime(n) such that prime(n+1) - prime(n) > prime(n+2) - prime(n+1).
  • A147813 (program): Primes prime(n) such that (-prime(n) + 2*prime(n+1) - prime(n+2))/((1 - prime(n) + prime(n+1))^(3/2)) < 0.
  • A147814 (program): Number of bits in Elias omega-coded prime numbers.
  • A147816 (program): Concatenation of n digits 1 and 2(n-1) digits 0.
  • A147818 (program): Period 4: repeat [5, 9, 9, 5].
  • A147819 (program): Nearest-neighbors of odd primes.
  • A147820 (program): Nearest-neighbors of odd primes, divided by 2.
  • A147832 (program): Numbers congruent (0,2) mod 14.
  • A147833 (program): Expansion of (4*x^2+x-1)/(12*x^3+4*x^2+x-1).
  • A147834 (program): Coefficient expansion of the characteristic polynomial of the {3,4,5} simplex matrix: M = {{0, 3, 0}, {0, 0, 4}, {1, 1, 1}}; p(x)=12 + 4 x + x^2 - x^3.
  • A147835 (program): a(n) = floor(Pi * n^n).
  • A147837 (program): a(n)=7*a(n-1)-5*a(n-2), a(0)=1, a(1)=5 .
  • A147838 (program): a(n)=8*a(n-1)-6*a(n-2), a(0)=1, a(1)=6 .
  • A147839 (program): a(n)=9*a(n-1)-7*a(n-2), a(0)=1, a(1)=7 .
  • A147840 (program): a(n)=10*a(n-1)-8*a(n-2), a(0)=1, a(1)=8 .
  • A147841 (program): a(n) = 11*a(n-1) - 9*a(n-2) with a(0)=1, a(1)=9.
  • A147843 (program): a(n) = -n*A010815(n).
  • A147844 (program): Difference between the number of distinct prime divisors of (2*n)!/n!^2 and pi(2*n), where pi(x) is the prime counting function.
  • A147845 (program): Odd positive integers a(n) such that for every odd integer m>=7 there exists a unique representation of the form m=a(p)+2a(q)+4a(r)
  • A147846 (program): Triangular numbers n*(n+1)/2 with n or n+1 prime.
  • A147848 (program): Number (up to isomorphism) of groups of order 2n that have Z/nZ as a subgroup (that is, that have an element of order n).
  • A147849 (program): a(n) is the smallest triangular number > n-th prime.
  • A147855 (program): G.f.: 1 / (1 + 4*x*G(x)^2 - 7*x*G(x)^3) where G(x) = 1 + x*G(x)^4 is the g.f. of A002293.
  • A147861 (program): Triangle read by rows: T(n,k)=min(k, n/k) if k divides n, T(n,k)=0 otherwise (n >=1, 1<=k<=n).
  • A147874 (program): a(n) = (5*n-7)*(n-1).
  • A147875 (program): Second heptagonal numbers: a(n) = n*(5*n+3)/2.
  • A147882 (program): A positive integer n with k (decimal) digits is called balanced if its first ceiling (k/2) digits sum to the same value as its last ceiling (k/2) digits.
  • A147956 (program): All positive integers that are not multiples of any Fibonacci numbers >= 2.
  • A147957 (program): a(n) = ((6 + sqrt(2))^n + (6 - sqrt(2))^n)/2.
  • A147958 (program): a(n) = ((7 + sqrt(2))^n + (7 - sqrt(2))^n)/2.
  • A147959 (program): a(n) = ((8 + sqrt(2))^n + (8 - sqrt(2))^n)/2.
  • A147960 (program): a(n) = ((9 + sqrt(2))^n + (9 - sqrt(2))^n)/2.
  • A147961 (program): a(n) = ((6+sqrt(3))^n + (6-sqrt(3))^n/2.
  • A147962 (program): a(n) = ((7+sqrt(3))^n + (7-sqrt(3))^n) / 2.
  • A147965 (program): a(n) = n + 1 - A001223(n) = n - A046933(n). In words, a(n) is the difference between n+1 and the n-th gap between primes.
  • A147966 (program): a(n) = n+(A001223(n)-1) = n+A046933(n).
  • A147967 (program): a(n) = n*(A001223(n)-1) = n*A046933(n).
  • A147973 (program): a(n) = -2*n^2 + 12*n - 14.
  • A147974 (program): a(n) = n^3-((n-1)^3+(n-2)^3+(n-3)^3).
  • A147975 (program): 4^n-3^n-2^n-1.
  • A147976 (program): 5^n-4^n-3^n-2^n-1.
  • A147977 (program): a(n) = 6^n-5^n-4^n-3^n-2^n-1.
  • A147978 (program): 7^n-6^n-5^n-4^n-3^n-2^n-1.
  • A147979 (program): 8^n-7^n-6^n-5^n-4^n-3^n-2^n-1.
  • A147980 (program): Given a set of positive integers A={1,2,…,n-1,n}, n>=2. Take subsets of A of the form {1,…,n} so only subsets containing numbers 1 and n are allowed. Then a(1)=1 and a(n) is the number of subsets where arithmetic mean of the subset is an integer.
  • A147991 (program): Sequence S such that 1 is in S and if x is in S, then 3x-1 and 3x+1 are in S.
  • A147992 (program): Sequence S such that 1 is in S and if x is in S, then 4x-1 and 4x+1 are in S.
  • A147993 (program): Sequence S such that 1 is in S and if x is in S, then 6x-1 and 6x+1 are in S.
  • A147996 (program): 9^n-8^n-7^n-6^n-5^n-4^n-3^n-2^n-1.
  • A147997 (program): Number of nonnegative even integers <= Fibonacci(n).
  • A147998 (program): [r]*[2r]*[3r]*…[nr], where r=(1+sqrt(5))/2 and []=floor.
  • A148162 (program): Number of walks within N^3 (the first octant of Z^3) starting at (0,0,0) and consisting of n steps taken from {(-1, -1, 1), (-1, 1, 1), (0, 0, -1), (1, 0, 0)}.
  • A148703 (program): Number of walks within N^3 (the first octant of Z^3) starting at (0,0,0) and consisting of n steps taken from {(-1, -1, 1), (-1, 0, 1), (-1, 1, 1), (0, 0, -1), (1, 0, 0)}

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