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.
  • 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.
  • 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)/((1-2x)(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.
  • A100119 (program): a(n) = n-th centered n-gonal number.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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-6x^2)/((1-x)(1-x-8x^2)).
  • A100303 (program): Expansion of (1-x-4x^2)/(1-x-8x^2).
  • A100304 (program): Expansion of (1-x-6x^2)/(1-x-8x^2).
  • A100305 (program): Expansion of (1-x-4x^2)/(1-2x-7x^2+8x^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.
  • A100327 (program): Row sums of triangle A100326, in which row n equals the inverse binomial of column n of square array A100324.
  • 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.
  • A100381 (program): a(n) = 2^n*binomial(n,2).
  • A100388 (program): a(n) = Bell(n) + Fibonacci(n).
  • A100389 (program): a(n) = Bell(n) - Fibonacci(n).
  • A100394 (program): a(n) is the subscript of the greatest prime factor of (2*prime(n) + 1).
  • A100396 (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.
  • 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).
  • 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)).
  • A100455 (program): a(n) = 2^n + sin(n*Pi/2).
  • 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.
  • 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/C(n,k)^3.
  • A100519 (program): Denominator of Sum_{k=0..n} 1/C(n,k)^3.
  • A100520 (program): Numerator of Sum_{k=0..2n} (-1)^k/C(2n,k)^2.
  • A100521 (program): Denominator of Sum_{k=0..2n} (-1)^k/C(2n,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.
  • 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).
  • 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}.
  • 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.
  • 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.
  • A100672 (program): Second least-significant bit in the binary expansion of the n-th prime.
  • 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}.
  • 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.
  • 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): G.f.: (3+x+2*x^2-2*x^3)/((1-2*x)*(1+x^2)).
  • 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.
  • 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.
  • 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.
  • 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).
  • 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).
  • 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.
  • 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).
  • 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.
  • 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).
  • 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).
  • 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).
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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).
  • A101161 (program): A number triangle associated with the Chebyshev polynomials of the first kind.
  • A101162 (program): Row sums of a Chebyshev number triangle.
  • 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)))) + …
  • 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.
  • 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.
  • 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).
  • A101272 (program): a(n)=n, n <=6; a(n)=6, n > 6.
  • A101278 (program): Write n in base 3 as n = b_0 + b_1*3 + b_2*3^2 + b_3*3^3 + …; then a(n) = Product_{i >= 0} prime(i+1)^b_i.
  • 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.
  • A101297 (program): Bisection of A001622 (decimal expansion of the golden ratio).
  • 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).
  • 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”.
  • 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.
  • 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)).
  • A101418 (program): Floor of the area of a lens constructed using circular arcs of radius n.
  • 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.
  • 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).
  • 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,…
  • 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.
  • 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.
  • 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.
  • 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).
  • 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).
  • 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.
  • 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”.
  • 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.
  • 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.
  • A101705 (program): Numbers n such that n = 12*reversal(n).
  • A101711 (program): Main diagonal of A101646.
  • A101741 (program): 4th row of A101646.
  • 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).
  • A101789 (program): 8n-1 such that 4n-1 and 8n-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.
  • 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).
  • 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.
  • 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)) = cos(arccosh(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.
  • 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).
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • A102232 (program): Number of preferential arrangements of n labeled elements when at least k=three ranks 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.
  • A102261 (program): a(n) = A002144(n) - A002145(n).
  • 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.
  • 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.
  • A102341 (program): Areas of ‘close-to-equilateral’ integer triangles.
  • A102342 (program): Numbers k such that 10k + 7 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.
  • 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.
  • 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).
  • 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) = minimal number of nodes in a binary tree of height n.
  • 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.
  • 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).
  • 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).
  • 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)).
  • A102584 (program): a(n) = 1/2 times the cancellation factor in reducing Sum_{k=0 to 2n+1} 1/k! to lowest terms.
  • 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.
  • 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).
  • 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).
  • 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.
  • 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)).
  • 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.
  • 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.
  • 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.
  • 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.
  • 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, … ).
  • 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)).
  • A102881 (program): Expansion of (1+x)/sqrt(1-4x^2-8x^3-4x^4).
  • 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.
  • 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.
  • 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)+3a(n-3).
  • A103145 (program): a(n) = (1/6)*(n^3 + 21*n^2 + 74*n + 18).
  • 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.
  • 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.
  • 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.
  • 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.
  • A103271 (program): a(n) = (prime(n)+prime(n+1)) mod 4.
  • 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) ).
  • A103368 (program): Period 6: repeat [1, 1, -1, -1, 0, 0].
  • 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).
  • 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.
  • 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).
  • 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.
  • 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 without holes 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).
  • A103492 (program): Multiplicative suborder of 6 (mod 2n+1) = sord(6, 2n+1).
  • 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.
  • A103536 (program): Number of nets in a regular pyramid.
  • A103542 (program): Binary equivalents of A102370.
  • 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).
  • 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.
  • 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.
  • 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)).
  • 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).
  • 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.
  • 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.
  • 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.
  • A103779 (program): Expansion of real root of y + y^2 + y^3 = x.
  • 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).
  • 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}.
  • 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).
  • A103978 (program): Expansion of (sqrt(1-12*x^2)+12*x^2+2*x-1)/(2*x*sqrt(1-12*x^2)).
  • 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).
  • 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.
  • 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).
  • A104029 (program): Triangle, read by rows, of pairwise sums of trinomial coefficients (A027907).
  • A104039 (program): Number of primitive roots modulo prime(n)^2, where prime(n) is n-th prime.
  • 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.
  • 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).
  • A104097 (program): Denominators of coefficients in expansion of x^-2*(1-exp(-2*x))^2.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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)).
  • 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).
  • 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.
  • A104218 (program): Sum of opposite numbers on a clock, starting at 12.
  • A104220 (program): a(n) = Fibonacci[n]+1-Mod[Fibonacci[n],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.
  • 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.
  • 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.
  • 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.
  • 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).
  • A104324 (program): The Fibonacci word over the nonnegative integers; or, the number of runs of identical bits in the binary Zeckendorf representation of n.
  • A104326 (program): Dual Zeckendorf representation of n or the maximal (binary) Fibonacci representation. Also list of binary vectors not containing 00.
  • 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).
  • A104354 (program): Euler’s totient 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).
  • 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.
  • 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.
  • 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.
  • A104492 (program): Cube excess of the n-th 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)).
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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).
  • 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.
  • A104670 (program): a(n) = binomial(n+2, 2)*binomial(n+7, n).
  • A104671 (program): C(n+3,3)*C(n+8,n+0).
  • A104672 (program): C(n+4,4)*C(n+9,n+0)
  • A104673 (program): 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): n*(n+1)/2 (mod 6).
  • A104688 (program): Binomial transform of Moebius sequence.
  • 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).
  • 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.
  • 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.
  • 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.
  • 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.
  • 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).
  • 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.
  • 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.
  • A105058 (program): G.f. (1+8x-x^2)/((x+1)(x^2-6x+1)).
  • 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.
  • A105067 (program): a(n) = Sum_{j=0..11} n^j.
  • 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.
  • A105092 (program): Sum of the sides of ordered 2 prime sided prime triangles.
  • 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.
  • A105110 (program): Direct matrix (non-recursive) content of -n to n+1 symmetry matrices.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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).
  • 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).
  • 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.
  • 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.
  • 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.
  • A105476 (program): Number of compositions of n when each even part can be of two kinds.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • A105584 (program): Fixed point of the morphism 1 -> 34, 2 -> 32, 3 -> 12, 4 -> 14, starting from a(0) = 1.
  • A105604 (program): Sylvester dividends for Jacobsthal numbers.
  • A105610 (program): Numbers n such that both p1=2n+3 and p2=4n+5 are primes.
  • 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).
  • 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.
  • 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).
  • 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).
  • 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.
  • A105844 (program): Numbers n such that 37*n^2 + 37*n + 1 is a square.
  • 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.
  • 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.
  • 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): C(n+6,n)*C(n+9,6)
  • A105943 (program): a(n) = C(n+7,n) * C(n+10,7).
  • A105944 (program): C(n+8,n)*C(n+11,8)
  • A105946 (program): C(n+5,n)*C(n+3,3).
  • A105947 (program): a(n) = C(n+6,n)*C(n+4,4).
  • A105948 (program): 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 antidiagonals: a(m,n) = m!*H(n,m), where H(n,m) is a higher-order harmonic number (H(0,m) = 1/m; H(n,m) = Sum_{k=1..m} H(n-1,k)).
  • 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.
  • A105963 (program): Expansion of (1+4*x)/(1-x-3*x^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.
  • 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.
  • A106058 (program): 4th diagonal of triangle in A059317.
  • A106092 (program): Even numbers and primes.
  • 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.
  • 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.
  • 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).
  • 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.
  • 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.
  • 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.
  • 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): Anti-diagonal sums of number triangle A106270.
  • 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.
  • 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.
  • 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).
  • 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.
  • 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.
  • 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.
  • A106481 (program): An Euler phi transform of 1/(1-x^2).
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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).
  • 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.
  • 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.
  • 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.
  • 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.
  • A106865 (program): Primes of the form 2x^2 + 2xy + 3y^2.
  • 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.
  • 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).
  • A107034 (program): Expansion of f(-x) * f(-x^4) in powers of x where f() is a Ramanujan theta function.
  • 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.
  • A107061 (program): a(n) = largest number m >0 such that n*prime(n)-a(n) is a prime.
  • A107064 (program): Expansion of q^(-17/24) * (eta(q) * eta(q^6)^4) / (eta(q^2) * eta(q^3)^2) in powers of q.
  • A107066 (program): Expansion of 1/(1-2*x+x^5).
  • A107068 (program): Expansion of 1/((1+x)^3-x^4).
  • 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.
  • 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.
  • A107145 (program): Primes of the form x^2 + 40y^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.
  • 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.
  • 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).
  • 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.
  • A107283 (program): E.g.f. exp(x)*(x^2+x+2)/(1-x).
  • 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.
  • 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.
  • 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): 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).
  • 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)).
  • 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.
  • A107395 (program): 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): C(n+8,8)*C(n+10,8).
  • A107400 (program): Numbers k such that 107*k + 109 is prime.
  • 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): 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): C(n+6,6)*C(n+9,9).
  • A107422 (program): a(n) = binomial(n+7,7) * binomial(n+10,10).
  • 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.
  • 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).
  • A107490 (program): Coefficients of a certain theta series.
  • A107491 (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.).
  • 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.
  • 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.
  • A107713 (program): Convolution of 2^n*n! and n!.
  • 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.
  • A107744 (program): Smallest prime factor of 6*n+1.
  • A107745 (program): Smallest prime factor of 6*n-1.
  • 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 (+2)Sigma(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)), (+2)Sigma(1)=1.
  • A107759 (program): (+2)UnitarySigma(n): If n = Product p_i^r_i then (+2)UnitarySigma(n) = Product (2 + p_i^r_i), (+2)UnitarySigma(1) = 1.
  • 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).
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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): Numbers n whose binary representation is 1100, n times.
  • 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.
  • 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.
  • A108044 (program): Triangle read by rows: right half of Pascal’s triangle (A007318) interspersed with 0’s.
  • 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.
  • 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.
  • A108090 (program): Numbers of the form (11^i)*(13^j).
  • 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)).
  • 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.
  • 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.
  • 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.
  • 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.
  • 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).
  • 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.
  • 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.
  • 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).
  • 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.
  • 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).
  • 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).
  • 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).
  • 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).
  • 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).
  • 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.
  • 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.
  • 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.
  • 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.
  • 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).
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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 n such that n^2 + (n+1)^2 is a semiprime.
  • 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.
  • 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.
  • 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.
  • A108874 (program): Numbers n such that 41*n + 43 is prime.
  • A108882 (program): Period doubling sequence starting with ‘1 0 1’.
  • A108895 (program): Partial sums of quadruple factorial numbers n!!!! (A007662).
  • A108896 (program): Numbers such that the outer 2 digits are 9 and the inner digits are 4.
  • 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.
  • 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.
  • 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).
  • 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.
  • 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.
  • 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).
  • 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).
  • 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.
  • A109130 (program): Magic constant of smallest order-n perfect magic cube.
  • 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.
  • 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.
  • 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).
  • 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.
  • 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)).
  • 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.
  • 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.
  • 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.
  • 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)!.
  • 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).
  • 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).
  • 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.
  • 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: a(n,m) = number of closed walks of length n on the complete graph on m nodes.
  • A109506 (program): Expansion of (1 - phi(-q)^4)/ 8 in powers of q where phi() is a Ramanujan theta function.
  • 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).
  • 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.
  • 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): 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.
  • 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).
  • 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.
  • 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.
  • A109652 (program): 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.
  • 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.
  • 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.
  • 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).
  • 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).
  • 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)).
  • 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).
  • 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.
  • A109823 (program): a(n) is the minimal b >= n such that sum of consecutive integers from n to b is a semiprime.
  • A109827 (program): Numbers written in an alternating binary-then-ternary base.
  • A109834 (program): Startorial numbers: product of initial digits of integers 1 through n.
  • 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.
  • 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).
  • 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)).
  • 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.
  • 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.
  • 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.
  • 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/((2*x+1)*(1-4*x-4*x^2)).
  • 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.
  • 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)).
  • 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).
  • 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.
  • 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).
  • A110166 (program): Row sums of Riordan array A110165.
  • 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.
  • 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).
  • A110272 (program): a(n) = Pell(n)^3.
  • A110273 (program): a(n) = Pell(n)^3 + Pell(n+1)^3.
  • 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.
  • 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.
  • 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( n+k, k=0..n-1 ) = n(3n-1)/2 if n is even; a(n) = sum( n-k, k=0..n-1 ) = 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • A110444 (program): Binary expansion of A074988.
  • 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).
  • 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.
  • 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.
  • 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.
  • 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)).
  • A110520 (program): Expansion of 1/(1-2*x*c(3*x)), c(x) the g.f. of A000108.
  • A110523 (program): Expansion of (1 + x)/(1 + x + 3*x^2).
  • A110524 (program): Expansion of (1 + x)/(1 + 2*x + 2*x^3).
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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)).
  • 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.
  • 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.
  • A110812 (program): Fractalization of sqrt 2.
  • A110813 (program): A triangle of pyramidal numbers.
  • A110814 (program): Inverse of a triangle of pyramidal numbers.
  • A110831 (program): a(n) = 3*n^2 + 27*n + 1.
  • A110833 (program): a(n) = (prime(n)+1)^2.
  • 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.
  • 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).
  • 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.
  • A110962 (program): Fractalization of A025480, zero-based version of Kimberling’s paraphrases sequence.
  • A110963 (program): Fractalization of Kimberling’s paraphrases sequence beginning with 1.
  • 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).
  • 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).
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • A111166 (program): Let p < q be consecutive primes; p is in the sequence if p/(q-p) is a record.
  • 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).
  • A111192 (program): Product of the n-th sexy prime pair.
  • 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.
  • 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).
  • 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.
  • 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.
  • 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.
  • A111333 (program): Number of odd numbers <= n-th prime.
  • A111350 (program): Squares n such that 2*n + 1 is a semiprime.
  • 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.
  • 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.
  • 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).
  • 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.
  • A111505 (program): Right half of Pascal’s triangle (A007318) with zeros.
  • A111517 (program): Numbers n such that (7*n + 1)/2 is prime.
  • A111527 (program): Inverse of A111526. Row sums have general term C(n,floor(n/2))*(cos(Pi*n/2) + sin(Pi*n/2)).
  • 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)|
  • 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.
  • 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.
  • 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, …
  • 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.
  • A111706 (program): a(n) = concatenation of k times the k-th digit 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.
  • 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.
  • 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.
  • 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).
  • A111808 (program): Left half of trinomial triangle (A027907), triangle read by rows.
  • 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.
  • 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.
  • 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.
  • A111958 (program): Lucas numbers (A000032) mod 8.
  • A111959 (program): Renewal array for aerated central binomial coefficients.
  • 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).
  • 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): 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)).
  • A112132 (program): Period 4: repeat [1, 3, 1, 7].
  • A112133 (program): First differences of A112063.
  • A112141 (program): Product of the first n semiprimes.
  • 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.
  • A112242 (program): E.g.f. exp( x*(1+x)/(1-x) ).
  • A112243 (program): Expansion of exp(x(1+x)/(1-2x)).
  • 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).
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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)).
  • A112478 (program): Expansion of (1 + x + sqrt(1 + 6*x + x^2))/2.
  • A112488 (program): Third 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.
  • 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.
  • A112518 (program): Expansion of 1/(1-x+2x^3+x^4).
  • 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.
  • 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.
  • 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.
  • 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)).
  • 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.
  • 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.
  • A112677 (program): Sum of digits of the sum of the previous 4 terms.
  • 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.
  • 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.
  • 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.
  • A112745 (program): Least k such that 6*k*prime(n)^2 +1 is prime, where prime(i)=i-th prime.
  • 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.
  • 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.
  • 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.
  • 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.
  • A112821 (program): Numbers n such that lcm(1,2,3,…,n)/19 equals the denominator of the n-th harmonic number H(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)).
  • 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.
  • 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.
  • 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.
  • 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/….
  • 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.
  • 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.
  • 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.
  • A113142 (program): Expansion of x(1-3x+x^2+x^3)/(1+x)^2.
  • 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.
  • A113170 (program): Ascending descending base exponent transform of odd numbers A005408.
  • A113179 (program): Expansion of 1/sqrt((1-2x)^2-8x^3).
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • A113282 (program): Logarithmic derivative of the g.f. of A113281.
  • 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.
  • 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)).
  • 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!).
  • 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.
  • 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.
  • A113523 (program): a(n) = largest composite nonnegative integer <= n.
  • A113526 (program): Define the first two terms to be 1 and 3. All the other terms are obtained by concatenating the two previous terms.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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}].
  • 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).
  • 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.
  • 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).
  • 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): Series expansion of Farey rational polynomial based on A112627.
  • 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.
  • 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)).
  • 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).
  • A114091 (program): Number of partitions of n into parts that are distinct mod 3.
  • 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.
  • A114117 (program): Inverse of 1’s counting matrix A114116.
  • 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.
  • 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)!.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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).
  • 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.
  • 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.
  • 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.
  • A114327 (program): Table T(n,m) = n - m read by upwards antidiagonals.
  • A114334 (program): Divisors of 6^6.
  • 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.
  • A114364 (program): a(n) = n*(n+1)^2.
  • A114378 (program): Area of annuli of consecutive integer thickness.
  • 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.
  • 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.
  • A114423 (program): Multifactorial array read by ascending antidiagonals.
  • 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.
  • 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.
  • 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.
  • A114479 (program): Kekulé numbers for certain benzenoids.
  • A114480 (program): Kekulé numbers for certain benzenoids.
  • A114487 (program): Number of Dyck paths of semilength n having no UUDD’s starting at level 0.
  • 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.
  • A114540 (program): Number of correct decimal digits given by the n-th convergent to the golden ratio.
  • A114548 (program): Numbers n such that n-th heptagonal number is 3-almost prime.
  • 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.
  • 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).
  • 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): 2*A079291 (twice squares of Pell numbers).
  • A114620 (program): 2*A084158 (twice Pell triangles).
  • A114633 (program): a(n) = (n+1)*(n+2)/2 * Sum_{k=0..floor(n/2)} n!/(n-2*k)!.
  • A114637 (program): Nonnegative numbers excluding 1 and 2.
  • 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.
  • 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.
  • 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.
  • 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!.
  • 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).
  • A114913 (program): Numbers n such that A114912(n)=1. Numbers n such that A000009(n) == 2 (mod 4).
  • A114938 (program): Number of permutations of the multiset {1,1,2,2,…,n,n} with no two consecutive terms equal.
  • 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).
  • 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.
  • 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.
  • A115055 (program): Lower level digraph derived from a voltage graph.
  • A115056 (program): a(n) = n*(n^2-1)*(3*n+2).
  • 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.
  • 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.
  • 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).
  • A115107 (program): Numerator of q_n = -4*n + 2*(1+n)*HarmonicNumber(n).
  • 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).
  • 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.
  • 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).
  • 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).
  • A115256 (program): Diagonal sums of correlation triangle of central binomial coefficients.
  • A115257 (program): Partial sums of binomial(2n,n)^2.
  • 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).
  • 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.
  • 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.
  • 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].
  • 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.
  • 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.
  • 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.
  • 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).
  • 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): G.f.: (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.
  • A115525 (program): Periodic {1,1,-2,0,1,0,-1,0,0,1,-1,-1}.
  • 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).
  • 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).
  • A115634 (program): Expansion of (1-4*x^2)/(1-x^2).
  • 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.
  • 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.
  • 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).
  • 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}.
  • A115955 (program): Product of A115952 and summing matrix (1/(1-x),x).
  • 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).
  • A115964 (program): Denominator of sum_{i=1..n} 1/prime(i)^3.
  • 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.
  • 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.
  • A116000 (program): phi(n) + sigma(n) gives a semiprime (A001358).
  • 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.
  • 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)).
  • A116396 (program): Expansion of 2/((2+x)*sqrt(1-4*x)-x).
  • 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).
  • A116406 (program): Expansion of ((1 + x - 2x^2) + (1+x)*sqrt(1-4x^2))/(2(1-4x^2)).
  • 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.
  • A116413 (program): Expansion of (1+x)/(1-2x-x^2-x^3).
  • 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): Triangle, row sums = Fibonacci numbers convolved with themselves.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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,….
  • A116601 (program): a(0) = a(1) = 0; for n >= 2, a(n) = floor(sqrt(2^(n-2)-1)).
  • 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.
  • A116623 (program): a(0)=1, a(2n) = a(n)+A000079(A000523(2n)), a(2n+1) = 3*a(n) + A000079(A000523(2n+1)+1).
  • 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)).
  • 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.
  • 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.
  • A116862 (program): Row sums of triangle A116868 (called Y(1,3)).
  • A116867 (program): Convolution of generalized Catalan sequence A064063 (named C(3;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).
  • 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.
  • 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)]
  • 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.
  • 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.
  • 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.
  • 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.
  • 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].
  • 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.
  • 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(1-4x^2),xc(x^2)), c(x) the g.f. of A000108.
  • 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)}.
  • 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.
  • A117220 (program): Number of partitions of 3-smooth numbers into parts not greater than 3.
  • A117230 (program): Start with 1 and repeatedly reverse the digits and add 1 to get the next term.
  • 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.
  • A117277 (program): Number of partitions of n whose consecutive parts differ by 3.
  • 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)).
  • 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).
  • A117322 (program): a(n) = prime(n) modulo semiprime(n).
  • A117323 (program): Semiprime(n) modulo prime(n).
  • A117339 (program): a(n)=a(n-1)+a(n-2); if a(n) is not prime divide a(n) by its largest prime factor.
  • A117353 (program): Expansion of (1-x)/(1-3x+x^2+4x^3-4x^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).
  • 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).
  • 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).
  • 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.
  • 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.
  • 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)/(1-2x^2+4x^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).
  • 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}.
  • 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.
  • 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.
  • 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.
  • 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.
  • A117530 (program): Triangle read by rows: T(n,k) = k^2 - k + prime(n), 1<=k<=n.
  • 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): See Comments line.
  • 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.
  • 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.
  • 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.
  • 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).
  • 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).
  • A117681 (program): Floor of exp(n^2).
  • 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.
  • 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}.
  • 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.
  • 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.
  • 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.
  • 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).
  • 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.
  • 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).
  • 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)).
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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).
  • 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.
  • A118140 (program): Index of A005846(n) in the primes.
  • 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.
  • A118209 (program): Expansion of Sum_{k>=1} lambda(k) * k * x^k/(1 + x^k) where lambda(k) is the Liouville function, A008836.
  • 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.
  • 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.
  • A118304 (program): Start with 25 and repeatedly reverse the digits and add 1 to get the next term.
  • 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.
  • A118360 (program): Start with 1; repeatedly reverse the digits when the number is written in binary and add 2 to get the next term.
  • 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!.
  • 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.
  • A118395 (program): Expansion of e.g.f. exp(x + x^3).
  • 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): (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).
  • 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.
  • 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.
  • 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.
  • 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.
  • 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).
  • 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).
  • 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.
  • A118663 (program): Index of the least prime dividing the n-th composite number: A000720(A020639(A002808(n))).
  • A118667 (program): a(n) = a(n-1)+ ((abs(2^a(n-1)*a(n-1)) mod 10).
  • 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.
  • 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.
  • 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.
  • 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)).
  • 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.
  • 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.
  • A118885 (program): Number of binary sequences of length n containing exactly one subsequence 0011.
  • A118892 (program): Number of binary sequences of length n containing exactly one subsequence 0110.
  • A118904 (program): Perimeters of rectangles with integer sides and diagonal.
  • A118905 (program): Sum of legs of Pythagorean triangles (without multiple entries).
  • 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)).
  • 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).
  • A118934 (program): E.g.f.: exp(x + x^4/4).
  • 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.
  • 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.
  • 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.
  • 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).
  • 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) ).
  • 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).
  • 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.
  • 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).
  • A119309 (program): a(n) = binomial(2*n,n) * 6^n.
  • A119315 (program): Numbers with composite numbers as third divisors.
  • 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.
  • 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.
  • 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).
  • 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).
  • 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)).
  • 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).
  • 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.
  • 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.
  • 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).
  • 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): (n^2+n^3)*(binomial(2*n,n)).
  • A119581 (program): (2*n+n^2)*(binomial(2*n,n))/2.
  • A119582 (program): (n^2+n^3)*(binomial(2*n,n))/2.
  • A119587 (program): 2^n + 1 - 2*Fibonacci(n+1).
  • A119600 (program): a(n) = 4*Product_{i=1..n-1} (3^i+1)^2.
  • 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).
  • 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.
  • 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).
  • A119622 (program): Numbers n such that no group of order n is a Con-Cos group.
  • 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.
  • A119671 (program): a(0)=1. a(2^m +k) = a(m) + k, where 0 <= k <= 2^m -1, m >= 0.
  • A119673 (program): Triangle read by rows, 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.
  • A119674 (program): Number of states of the minimal deterministic finite automaton that accepts binary strings that represent numbers that are divisible by n.
  • 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.
  • A119688 (program): a(n) = n!! mod (n+1).
  • 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).
  • 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.
  • 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.
  • 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.
  • 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).
  • 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).
  • A119910 (program): Period 6: repeat [1, 3, 2, -1, -3, -2].
  • 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.
  • A119930 (program): Sum of the numbers of the matrix A111490 along a boustrophedon path: a11, a11+a12, a11+a12+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.
  • A119959 (program): p^2-p+1 central polygonal numbers with prime indices A002061(prime(n)).
  • 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.
  • 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.
  • A120027 (program): Triangle, generated from (3^(n-k) * 5^k) table.
  • 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): Binomial(n+3,4)*4^4.
  • 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.
  • A120088 (program): Numerators of partial sums of a series for sqrt(2).
  • A120096 (program): a(n) = (A046717(n))^2 (starting with n=1).
  • A120106 (program): a(n) = Sum_{k=0..n} lcm(1..2n+2)/lcm(1..2k+2).
  • A120109 (program): Row sums of number triangle 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.
  • A120226 (program): Numbers n such that a+n and a*n+1 are prime, case a=4.
  • 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.)
  • 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)}.
  • 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 number minus 2, or ((2n)!/(n!*(n+1)!) - 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).
  • A120353 (program): Sum of 5 consecutive powers of 3, starting with a power of 9.
  • A120354 (program): a(n) = 11*3^n.
  • 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): (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.
  • 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).
  • A120454 (program): a(n) = ceiling(GPF(n)/LPF(n)) where GPF is greatest prime factor, LPF is least prime factor.
  • A120459 (program): Row sums of A120458.
  • 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).
  • 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.
  • A120478 (program): Binomial(n+6,5)-binomial(n,5).
  • 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}].
  • 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].
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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).
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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).
  • 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.
  • 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): n + phi(n), for Euler totient function phi(n).
  • 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.
  • 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!.
  • 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.
  • A121123 (program): Unbranched a-4-catapolynonagons (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).
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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).
  • 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).
  • 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.
  • 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).
  • 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.
  • 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.
  • 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).
  • A121573 (program): Prime-gap race; difference of the cumulative sums of gaps above and below prime(2n).
  • 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.
  • 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.
  • 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.
  • 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)).
  • A121646 (program): a(n) = Fibonacci(n-1)^2 - Fibonacci(n)^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)).
  • 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.
  • 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.
  • 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.
  • 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).
  • 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.
  • 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.
  • 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.
  • 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).
  • 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).
  • 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)).
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • A122088 (program): Add 10, subtract 5, add 10, subtract 5, ad infinitum.
  • 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.
  • 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 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).
  • A122163 (program): Expansion of f(-q)^2*P(q) in powers of q.
  • A122167 (program): Expansion of x*(-1+5*x-6*x^2+x^3) / ( (2*x-1)*(x^3-3*x^2+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.
  • 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.
  • 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).