List of integer sequences with links to LODA programs.

  • A200002 (program): G.f.: exp( Sum_{n>=1} C(2*n,n)^n/2^n * x^n/n ).
  • A200028 (program): G.f. satisfies: A(x) = 1 + x*A(x)^3 + 2*x^2*A(x)^2 + x^3*A(x).
  • A200030 (program): G.f. satisfies: A(x) = 1 + x*A(x)^3 - 2*x^2*A(x)^2 + x^3*A(x).
  • A200031 (program): G.f. satisfies: A(x) = 1 + x + 3*x*A(x) + x*A(x)^2.
  • A200039 (program): Number of -n..n arrays x(0..2) of 3 elements with sum zero and with zeroth through 2nd differences all nonzero.
  • A200047 (program): Number of compositions of n having smallest part equal to 2.
  • A200050 (program): a(2) = 1, then (p-1)*(p-4)/2, with p = prime(n), n > 2.
  • A200058 (program): Number of -n..n arrays x(0..3) of 4 elements with zero sum and elements alternately strictly increasing and strictly decreasing.
  • A200067 (program): Maximum sum of all products of absolute differences and distances between element pairs among the integer partitions of n.
  • A200069 (program): a(n) = 4*a(n-1) + 13*a(n-2) for n>2, a(1)=1, a(2)=4.
  • A200073 (program): Coefficients of a generalized Jaco-Lucas polynomial (odd indices) read by rows.
  • A200074 (program): G.f. satisfies: A(x) = (1 + x*A(x)^2)*(1 + x^2*A(x)).
  • A200075 (program): G.f. satisfies: A(x) = (1 + x*A(x)^2)*(1 + x^2*A(x)^3).
  • A200139 (program): Triangle T(n,k), read by rows, given by (1,1,0,0,0,0,0,0,0,…) DELTA (1,0,0,0,0,0,0,0,0,…) where DELTA is the operator defined in A084938.
  • A200141 (program): Upper bound by J. Rivat and J. Wu on constant arising in Piatetski-Shapiro primes.
  • A200142 (program): Number of near-matchings on the complete graph over 2n+1 vertices.
  • A200146 (program): Triangle read by rows: T(n, k) = mod(k^(n - 1), n), where 1 <= k < n.
  • A200155 (program): Number of 0..n arrays x(0..3) of 4 elements with zero 3rd differences.
  • A200166 (program): Number of -n..n arrays x(0..2) of 3 elements with nonzero sum and with zero through 2 differences all nonzero.
  • A200172 (program): Column 3 of triangle A200171.
  • A200173 (program): Column 4 of triangle A200171.
  • A200182 (program): Number of -n..n arrays x(0..3) of 4 elements with zero sum and no two consecutive declines, no adjacent equal elements, and no element more than one greater than the previous (random base sawtooth pattern).
  • A200193 (program): Number of -n..n arrays x(0..3) of 4 elements with zero sum, adjacent elements differing by more than one, and elements alternately increasing and decreasing.
  • A200213 (program): Ordered factorizations of n with 2 distinct parts, both > 1.
  • A200220 (program): Product of Fibonacci and Padovan numbers: a(n) = A000045(n+1)*A000931(n+5).
  • A200221 (program): Ordered factorizations of n with 3 parts.
  • A200243 (program): Decimal expansion of sqrt(192).
  • A200244 (program): a(n)=1 iff binary weight of n-th prime is even.
  • A200245 (program): Partial sums of A200244.
  • A200246 (program): a(n)=1 iff binary weight of n-th prime is odd.
  • A200247 (program): Partial sums of A200246.
  • A200248 (program): The number of (simultaneously) fixed and isolated points in the digraph representation of all functions f:{1,2,…,n}->{1,2,…,n}.
  • A200249 (program): Number of 0..5 arrays x(0..n-1) of n elements with each no smaller than the sum of its previous elements modulo 6.
  • A200252 (program): Number of 0..n arrays x(0..2) of 3 elements with each no smaller than the sum of its previous elements modulo (n+1).
  • A200258 (program): a(n) = Fibonacci(8n+7) mod Fibonacci(8n+1).
  • A200259 (program): Numbers n such that n-th prime has an even digit sum.
  • A200260 (program): Numbers k such that k-th prime has an odd digit sum.
  • A200261 (program): a(n) = 1 iff n-th prime has an even digit sum.
  • A200262 (program): Partial sums of A200261.
  • A200263 (program): a(n) = 1 iff n-th prime has an odd digit sum.
  • A200264 (program): Partial sums of A200263.
  • A200310 (program): a(n) = n-1 for n <= 4, otherwise if n is even then a(n) = a(n-5)+2^(n/2), and if n is odd then a(n) = a(n-1)+2^((n-3)/2).
  • A200311 (program): Number of comparisons needed for optimal merging of 2 elements with n elements.
  • A200312 (program): a(n) = A000108(n)*A006130(n), where A000108 is the Catalan numbers and A006130(n) = A006130(n-1) + 3*A006130(n-2).
  • A200316 (program): Number of permutations of [1..n] that can be drawn on a circle.
  • A200375 (program): Product of Catalan and Jacobsthal numbers: a(n) = A000108(n)*A001045(n+1).
  • A200376 (program): G.f.: 1/sqrt(1-10*x^2 + x^4/(1-8*x^2)) + x/(1-9*x^2).
  • A200380 (program): Expansion of e.g.f. exp(x+x^2-1/6*x^3).
  • A200408 (program): -4 + 5*Fibonacci(n+1)^2.
  • A200431 (program): Number of -n..n arrays x(0..3) of 4 elements with zero sum and no two or three adjacent elements summing to zero.
  • A200432 (program): Number of -n..n arrays x(0..4) of 5 elements with zero sum and no two or three adjacent elements summing to zero.
  • A200439 (program): Decimal expansion of constant arising in clubbed binomial approximation for the lightbulb process.
  • A200441 (program): Expansion of 1/(1-33*x+x^2).
  • A200442 (program): Expansion of 1/(1-31*x+x^2).
  • A200455 (program): Number of -n..n arrays x(0..2) of 3 elements with zero sum and nonzero first and second differences
  • A200511 (program): Numbers n with omega(n)=2 and bigomega(n)>2, where omega=A001221=number of distinct prime factors, bigomega=A001222=prime factors counted with multiplicity.
  • A200521 (program): Numbers n such that omega(n)=4 but bigomega(n)>4, i.e., having exactly 4 distinct prime factors, but at least one of these with multiplicity > 1.
  • A200535 (program): G.f. satisfies: A(x) = exp( Sum_{n>=1} [Sum_{k=0..2*n} C(2*n,k)^2 * x^k] / A(x)^n * x^n/n ).
  • A200536 (program): Triangle, read by rows of 2*n+1 terms, where row n lists the coefficients in (1+3*x+2*x^2)^n.
  • A200538 (program): Product of Jacobsthal and Motzkin numbers: a(n) = A001045(n+1)*A001006(n).
  • A200539 (program): Product of Fibonacci and Motzkin numbers: a(n) = A000045(n+1)*A001006(n).
  • A200540 (program): Product of Pell and Motzkin numbers: a(n) = A000129(n+1)*A001006(n).
  • A200541 (program): Product of Fibonacci and tribonacci numbers: a(n) = A000045(n+1)*A000073(n+2).
  • A200543 (program): Product of tribonacci numbers: a(n) = A000073(n+2)*A000213(n).
  • A200561 (program): Expansion of -2*x / ( (2*x-1)*(4*x^2+3*x+1) ).
  • A200562 (program): Expansion of 1 / ((1 - 2*x) * (1 + 3*x + 4*x^2)) in powers of x.
  • A200563 (program): Expansion of -2*x*(1+4*x) / ((2*x-1)*(4*x^2+3*x+1)).
  • A200564 (program): (2^(n^2)+2^((n^2+n)/2))/2.
  • A200572 (program): Number of n X 1 0..2 arrays with no average of any element and its horizontal and vertical neighbors equal to one.
  • A200580 (program): Sum of dimension exponents of supercharacter of unipotent upper triangular matrices.
  • A200613 (program): Number of quasi-abelian ideals in the affine Lie algebra sl_n^{hat}.
  • A200648 (program): Length of Stolarsky representation of n.
  • A200649 (program): Number of 1’s in the Stolarsky representation of n.
  • A200650 (program): Number of 0’s in Stolarsky representation of n.
  • A200660 (program): Sum of the number of arcs describing the set partitions of {1,2,…,n}.
  • A200661 (program): Number of 0..1 arrays x(0..n-1) of n elements with each no smaller than the sum of its three previous neighbors modulo 2.
  • A200672 (program): Partial sums of A173862.
  • A200674 (program): Eccentricity of Tower of Hanoi graph H_n^{3} (divided by 3).
  • A200675 (program): Powers of 2 repeated 4 times.
  • A200676 (program): Expansion of -(3*x^2-5*x+1)/(x^3-3*x^2+5*x-1).
  • A200677 (program): Smallest semiprime such that the sum of the two prime factors equals n, or zero if impossible.
  • A200678 (program): Partial sums of A200675.
  • A200715 (program): Expansion of (-3*x^2 + x - 1)/(x^3 - 3*x^2 + x - 1).
  • A200716 (program): G.f. satisfies: A(x) = (1 + x*A(x)^3) * (1 + x^2*A(x)).
  • A200717 (program): G.f. satisfies: A(x) = (1 + x*A(x)^3) * (1 + x^2*A(x)^2).
  • A200718 (program): G.f. satisfies: A(x) = (1 + x*A(x)^2) * (1 + x^2*A(x)^6).
  • A200719 (program): G.f. satisfies: A(x) = (1 + x*A(x)^2) * (1 + x^2*A(x)^5).
  • A200724 (program): Expansion of 1/(1-35*x+x^2).
  • A200725 (program): G.f. satisfies: A(x) = (1+x^2)*(1 + x*A(x)^3).
  • A200726 (program): Define a map f from primes to integers mod 4 by f(p) = 0,1,3,2,1 according as p == 1,2,3,4,0 mod 5; a(n) = Sum_{all primes p} v_p(n)*f(p), where v_p(n) is the exponent of the highest power of p dividing n.
  • A200728 (program): Decimal expansion of the circumradius of cyclic quadrilateral with sides 1, 2, 3, 4.
  • A200731 (program): G.f. satisfies: A(x) = (1 + x*A(x)^3) * (1 + x^2*A(x)^6).
  • A200732 (program): Primes of the form 4*n^3-5.
  • A200733 (program): Primes of the form 4*n^3-7.
  • A200734 (program): Primes of the form 4*n^3-9.
  • A200736 (program): Primes of the form 5*n^3-4.
  • A200739 (program): Expansion of (-x^2+5*x-1)/(x^3-x^2+5*x-1).
  • A200740 (program): Generating function satisfies A(x)=1-xA(x)+2x(A(x))^2-x^2(A(x))^3+x^2(A(x))^4.
  • A200746 (program): Completely multiplicative function with a(prime(k)) = prime(k)*prime(k-1), a(2) = 2.
  • A200747 (program): Number of iterations of A034968 required to reach 1.
  • A200748 (program): Smallest number requiring n terms to be expressed as a sum of factorials.
  • A200751 (program): Expansion of (1 - x) * (1 - x^2)^2 * (1 - x^3)^4 * … in powers of x.
  • A200752 (program): Expansion of (-x^2 + 3*x - 1)/(x^3 - x^2 + 3*x - 1).
  • A200753 (program): G.f. satisfies: A(x) = 1 + (x-x^2)*A(x)^3.
  • A200754 (program): G.f. satisfies: A(x) = 1 + x*A(x)^4 - x^2*A(x)^5.
  • A200755 (program): G.f. satisfies: A(x) = 1 + x*A(x)^3 - x^2*A(x)^2.
  • A200757 (program): Noncrossing forests in the regular (n+1)-polygon obtained by a grafting procedure.
  • A200768 (program): Sum of the n-th powers of the distinct prime divisors of n.
  • A200779 (program): a(n) = number of i in the range 1 <= i <= n such that b(i)=b(n), where b is the sequence A053615 taken with offset 1.
  • A200781 (program): G.f.: 1/(1-5*x+10*x^3-5*x^4).
  • A200786 (program): Number of 0..n arrays x(0..3) of 4 elements without any two consecutive increases.
  • A200793 (program): The number of forests on n nodes of rooted labeled binary trees (each node has degree <=2).
  • A200810 (program): Iterate k -> d(k) until an odd prime is reached.
  • A200814 (program): Primes of the form 6*n^3-1.
  • A200815 (program): Number of iterations of k -> d(k) until n reaches an odd prime.
  • A200833 (program): Number of 0..3 arrays x(0..n+1) of n+2 elements without any two consecutive increases or two consecutive decreases.
  • A200839 (program): Number of 0..n arrays x(0..3) of 4 elements without any two consecutive increases or two consecutive decreases.
  • A200845 (program): Primes of the form 6n^3 - 5.
  • A200846 (program): Primes of the form 3n^3-1.
  • A200847 (program): Primes of the form 3n^3-2.
  • A200849 (program): Primes of the form 3n^3-5.
  • A200850 (program): The number of forests of labeled rooted strictly binary trees (each vertex has exactly two children or none) on n nodes.
  • A200859 (program): a(n) = 2*a(n-1)+3*a(n-2)+5^n for n>1, a(0)=-2, a(1)=1.
  • A200860 (program): Multiples of 682.
  • A200862 (program): G.f.: (1-2*x^2)/(1-2*x-5*x^2+9*x^3).
  • A200864 (program): Expansion of 1/((1+x)*(1-3*x)*(1-5*x)).
  • A200865 (program): Number of 0..2 arrays x(0..n+1) of n+2 elements without any interior element greater than both neighbors or less than both neighbors.
  • A200866 (program): Number of 0..3 arrays x(0..n+1) of n+2 elements without any interior element greater than both neighbors or less than both neighbors.
  • A200872 (program): Number of 0..n arrays x(0..3) of 4 elements without any interior element greater than both neighbors or less than both neighbors.
  • A200873 (program): Number of 0..n arrays x(0..4) of 5 elements without any interior element greater than both neighbors or less than both neighbors.
  • A200880 (program): Number of 0..2 arrays x(0..n+1) of n+2 elements without any interior element greater than both neighbors.
  • A200881 (program): Number of 0..3 arrays x(0..n+1) of n+2 elements without any interior element greater than both neighbors.
  • A200887 (program): Number of 0..n arrays x(0..3) of 4 elements without any interior element greater than both neighbors.
  • A200888 (program): Number of 0..n arrays x(0..4) of 5 elements without any interior element greater than both neighbors.
  • A200903 (program): A182589(n)/8.
  • A200904 (program): E.g.f. A(x) satisfies: A(x) = x*(2*exp(A(x)) - exp(2*A(x))).
  • A200905 (program): a(n) = 3*phi(n), where phi (A000010) is the Euler totient function.
  • A200907 (program): Primes of the form 3n^3-7.
  • A200908 (program): Primes of the form 3*n^3-8.
  • A200910 (program): Primes of the form 5*n^3-1.
  • A200914 (program): Primes of the form 6n^3-7.
  • A200919 (program): Number of crossings on periodic braids with n strands such that all strands meet.
  • A200936 (program): Successive values x of solutions Mordell’s elliptic curve x^3-y^2 = d contained points {x,y} with quadratic extension sqrt(2) over rationals.
  • A200938 (program): Values d for infinite sequence x^3-y^2 = d with increasing coefficient r=sqrt(x)/|d| or family of solutions Mordell curve with extension sqrt(2).
  • A200956 (program): Primes of the form 8n^3-3.
  • A200957 (program): Primes of the form 8n^3-5.
  • A200958 (program): Primes of the form 8n^3-7.
  • A200959 (program): Primes of the form 8n^3-9.
  • A200960 (program): Primes of the form 9n^3-1.
  • A200975 (program): Numbers on the diagonals in Ulam’s spiral.
  • A200978 (program): Number of ways to arrange n books on 3 consecutive shelves leaving none of the shelves empty.
  • A200979 (program): Number of ways to arrange n books on 4 consecutive bookshelves, leaving no shelf empty.
  • A200981 (program): Numbers n such that the sum of non-divisors of n is prime.
  • A200991 (program): Decimal expansion of square root of 221/25
  • A200993 (program): Triangular numbers, T(m), that are two-thirds of another triangular number; T(m) such that 3*T(m) = 2*T(k) for some k.
  • A200994 (program): Triangular numbers, T(m), that are three-halves of another triangular number; T(m) such that 2*T(m) = 3*T(k) for some k.
  • A200998 (program): Triangular numbers, T(m), that are three-quarters of another triangular number: T(m) such that 4*T(m)=3*T(k) for some k.
  • A200999 (program): Triangular numbers, T(m), that are four-thirds of another triangular number; T(m) such that 3*T(m) = 4*T(k) for some k.
  • A201003 (program): Triangular numbers, T(m), that are four-fifths of another triangular number: T(m) such that 5*T(m) = 4*T(k) for some k.
  • A201004 (program): Triangular numbers, T(m), that are five-quarters of another triangular number; T(m) such that 4*T(m) = 5*T(k) for some k.
  • A201006 (program): The Isis problem : Array a(i,j) (by antidiagonals) of differences between area and perimeter of rectangle with sides (i,j).
  • A201008 (program): Triangular numbers, T(m), that are five-sixths of another triangular number: T(m) such that 6*T(m)=5*T(k) for some k.
  • A201015 (program): Composite numbers whose product of digits is 2.
  • A201018 (program): Composite numbers whose multiplicative digital root is 5.
  • A201020 (program): Composite numbers whose multiplicative digital root is 6.
  • A201021 (program): Composite numbers whose multiplicative digital root is 7.
  • A201023 (program): Composite numbers whose multiplicative digital root is 8.
  • A201034 (program): Primes of the form 9n^3-8.
  • A201036 (program): Primes of the form 10n^3-1.
  • A201038 (program): Primes of the form 10n^3-7.
  • A201039 (program): Primes of the form 10n^3-9.
  • A201043 (program): Number of -n..n arrays of 4 elements with adjacent element differences also in -n..n.
  • A201049 (program): Related to ranking of teams in the canonical symmetric knockout tournament of order n.
  • A201050 (program): C(n#, (n-1)#), where n# is the primorial A034386(n), the product of primes <= n.
  • A201053 (program): Nearest cube.
  • A201058 (program): Numerator of binomial(2n,n)/(2n).
  • A201059 (program): Denominator of binomial(2n,n)/(2n).
  • A201078 (program): Twice A137829.
  • A201081 (program): Number of -1..1 arrays of n elements with first and second differences also in -1..1.
  • A201106 (program): a(n) = binomial(n^2,3)/(2*n).
  • A201107 (program): Primes of the form 2k^3+1.
  • A201108 (program): Primes of the form 2n^3+3.
  • A201109 (program): Primes of the form 2n^3+5.
  • A201110 (program): Primes of the form 2n^3+7.
  • A201111 (program): Primes of the form 2n^3+9.
  • A201112 (program): Primes of the form 3n^3+1.
  • A201113 (program): Primes of the form 3n^3+2.
  • A201114 (program): Primes of the form 3n^3+4.
  • A201115 (program): Primes of the form 3n^3+5.
  • A201116 (program): Primes of the form 3n^3+7.
  • A201117 (program): Primes of the form 3n^3+8.
  • A201119 (program): Primes of the form 4n^3+5.
  • A201120 (program): Primes of the form 4n^3+7.
  • A201121 (program): Primes of the form 4n^3+9.
  • A201125 (program): Differences between odd powers of 2 and the next smaller square
  • A201146 (program): Triangle read by rows: T(n,k) = (n#)/(k#), 1 <= k <= n.
  • A201156 (program): Row sums of triangle A201146.
  • A201157 (program): y-values in the solution to 5*x^2 - 20 = y^2.
  • A201158 (program): E.g.f. exp(x)/(cos(x)-sin(x)).
  • A201163 (program): Expansion of g.f. 1+x+(1+3*x+x^2)/(1+x)^3.
  • A201171 (program): Primes of the form 5n^3+1.
  • A201174 (program): Primes of the form 5n^3+4.
  • A201177 (program): Primes of the form 5n^3+8.
  • A201179 (program): Primes of the form 6n^3+1.
  • A201180 (program): Primes of the form 6n^5+5.
  • A201181 (program): Primes of the form 6n^3+7.
  • A201196 (program): G.f. A(x) satisfies A(x) = 1+x^2/(1-x)*A(x^2/(1-x)).
  • A201202 (program): Row sums of triangle A201201: first associated monic Laguerre polynomials with parameter alpha=1 evaluated at x=1.
  • A201203 (program): Alternating row sums of triangle A201201: first associated monic Laguerre-Sonin(e) polynomials with parameter alpha=1 evaluated at x=-1.
  • A201204 (program): Half-convolution of Catalan sequence A000108 with itself.
  • A201205 (program): Bisection of half-convolution of Catalan sequence A000108; even part.
  • A201206 (program): Number of successive decreasing values of round(n^(2/3))^3 - n^2.
  • A201207 (program): Half-convolution of sequence A000032 (Lucas) with itself.
  • A201208 (program): One 1, two 2’s, three 1’s, four 2’s, five 1’s, …
  • A201219 (program): a(1) = 0; for n>1, a(n) = 1 if n is a power of 2, otherwise a(n) = 2.
  • A201225 (program): Values x for infinite sequence x^3-y^2 = d with decreasing coefficient r=sqrt(x)/d which tend to 1/(1350*sqrt(5))or infinity family of solutions Mordell curve with extension sqrt(5).
  • A201227 (program): a(n) = (A201225(n))^3 - (A201226(n))^2.
  • A201236 (program): Number of ways to place 2 non-attacking wazirs on an n X n toroidal board.
  • A201243 (program): Number of ways to place 2 non-attacking ferses on an n X n board.
  • A201259 (program): Primes of the form n^3+3.
  • A201260 (program): Primes of the form n^3 + 5.
  • A201261 (program): Primes of the form n^3 + 7.
  • A201262 (program): Primes of the form n^3 + 9.
  • A201263 (program): Primes of the form 9n^3+1.
  • A201271 (program): Number of n X 2 0..2 arrays with every row and column nondecreasing rightwards and downwards, and the number of instances of each value within one of each other.
  • A201279 (program): a(n) = 6n^2 + 10n + 5.
  • A201302 (program): Primes of the form 9n^3+8.
  • A201305 (program): Primes of the form 10n^3+7.
  • A201306 (program): Primes of the form 10n^3+9.
  • A201307 (program): Primes of the form n^3+4.
  • A201308 (program): Primes of the form n^3+6.
  • A201309 (program): Primes of the form n^3-4.
  • A201310 (program): Primes of the form n^3-6.
  • A201311 (program): Primes of the form n^3-10.
  • A201312 (program): Primes of the form n^3+10.
  • A201313 (program): Primes of the form n^2 - 10.
  • A201314 (program): Primes of the form n^2 - 17.
  • A201338 (program): E.g.f.: log((2 - exp(x))/(3 - 2*exp(x))).
  • A201339 (program): Expansion of e.g.f.: exp(x) / (3 - 2*exp(x)).
  • A201347 (program): Number of n X 2 0..1 arrays with rows and columns lexicographically nondecreasing and every element equal to at least one horizontal or vertical neighbor.
  • A201354 (program): Expansion of e.g.f.: exp(x) / (4 - 3*exp(x)).
  • A201355 (program): Expansion of e.g.f.: 3*exp(3*x) / (4 - exp(3*x)).
  • A201365 (program): Expansion of e.g.f.: exp(x) / (5 - 4*exp(x)).
  • A201366 (program): E.g.f.: 2*exp(2*x) / (5 - 3*exp(2*x)).
  • A201367 (program): E.g.f.: 3*exp(3*x) / (5 - 2*exp(3*x)).
  • A201368 (program): E.g.f.: 4*exp(4*x) / (5 - exp(4*x)).
  • A201371 (program): Number of n X 4 0..1 arrays with rows and columns lexicographically nondecreasing read forwards, and nonincreasing read backwards.
  • A201443 (program): Number of non-solvable transitive permutation groups for polynomials of degree p(n), where p(n) is n-th prime.
  • A201455 (program): a(n) = 3*a(n-1) + 4*a(n-2) for n>1, a(0)=2, a(1)=3.
  • A201461 (program): Triangle read by rows: n-th row (n>=0) gives coefficients of the polynomial ((x+1)^(2^n) + (x-1)^(2^n))/2.
  • A201462 (program): Numbers that are not coprime to their 9’s complement.
  • A201470 (program): E.g.f. satisfies: A(x) = 1/(1 - 2*x*exp(x*A(x))).
  • A201471 (program): Maximal diameter of a connected n-gamma_t-vertex-critical graph.
  • A201472 (program): The Griesmer lower bound q_4(5,n) on the length of a linear code over GF(4) of dimension 5 and minimal distance n.
  • A201473 (program): Primes of the form 2n^2 + 3.
  • A201474 (program): Primes of the form 2n^2 + 5.
  • A201475 (program): Primes of the form 2n^2 + 7.
  • A201476 (program): Primes of the form 2n^2 + 9.
  • A201477 (program): Primes of the form 3n^2 + 4.
  • A201478 (program): Primes of the form 3n^2 + 5.
  • A201479 (program): Primes of the form 3n^2 + 7.
  • A201480 (program): Primes of the form 3n^2 + 10.
  • A201481 (program): Primes of the form 5n^2 + 2.
  • A201482 (program): Primes of the form 5n^2 + 3.
  • A201483 (program): primes of the form 5n^2 + 4.
  • A201484 (program): Primes of the form 5n^2 + 6.
  • A201485 (program): Primes of the form 5n^2 + 7.
  • A201486 (program): Primes of the form 5n^2 + 8.
  • A201487 (program): Primes of the form 5n^2 + 9.
  • A201488 (program): Decimal expansion of maximal success probability of the CHSH game.
  • A201498 (program): a(n) = (prime(n) - 1)*(prime(n+1) - 1)/2 + 3.
  • A201500 (program): Number of n X 3 0..1 arrays with every row and column running average nondecreasing rightwards and downwards, and the number of instances of each value within one of each other.
  • A201504 (program): Decimal expansion of sin(1/2).
  • A201505 (program): Decimal expansion of cos(1/2).
  • A201509 (program): From abs(A028297)=A034839*A007318 to A165241 via A113402. Second row (double triangle).
  • A201541 (program): Numbers n such that 12n+5 and 12n+7 are primes.
  • A201544 (program): Odd numbers of the form a^2 + 2*b^2 with positive integers a and b.
  • A201546 (program): The number of permutations of {1,2,…,2n} that contain a cycle of length greater than n.
  • A201553 (program): Number of arrays of 6 integers in -n..n with sum zero.
  • A201555 (program): a(n) = C(2*n^2,n^2) = A000984(n^2), where A000984 is the central binomial coefficients.
  • A201556 (program): G.f.: exp( Sum_{n>=1} C(2*n^2,n^2) * x^n/n ).
  • A201560 (program): a(n) = (Sum(m^(n-1), m=1..n-1) + 1) modulo n.
  • A201595 (program): E.g.f. satisfies: A(x) = exp(x*A(x)) * cosh(x*A(x)).
  • A201600 (program): Primes of the form 6n^2 + 5.
  • A201601 (program): Primes of the form 6n^2 + 7.
  • A201602 (program): Primes of the form 7n^2 + 1.
  • A201603 (program): Primes of the form 7n^2 + 2.
  • A201604 (program): Primes of the form 7n^2 + 3.
  • A201605 (program): Primes of the form 7n^2 + 4.
  • A201606 (program): Primes of the form 7n^2 + 5.
  • A201607 (program): Primes of the form 7n^2 + 6.
  • A201608 (program): Primes of the form 7n^2 + 8.
  • A201609 (program): Primes of the form 7n^2 + 9.
  • A201610 (program): Primes of the form 7n^2 + 10.
  • A201611 (program): Primes of the form 8n^2 + 3.
  • A201612 (program): Primes of the form 8n^2 + 5.
  • A201618 (program): Number of n X 1 0..3 arrays with rows and columns lexicographically nondecreasing and every element equal to at least one horizontal or vertical neighbor.
  • A201629 (program): a(n) = n if n is even and otherwise its nearest multiple of 4.
  • A201630 (program): a(n) = a(n-1)+2*a(n-2) with n>1, a(0)=2, a(1)=7.
  • A201631 (program): Fibonacci meanders of length 2n and central angle 180 degree.
  • A201632 (program): If the sum of the squares of 4 consecutive numbers is a triangular number t(u), then a(n) is its index u.
  • A201633 (program): Numbers k such that Sum_{j=0..3} (k + j)^2 is a triangular number.
  • A201634 (program): Triangle read by rows, n>=0, k>=0, T(n,n) = 2^n, T(n,k) = sum_{j=0..k} T(n-1,j) for k=0..n-1.
  • A201635 (program): Triangle formed by T(n,n) = (-1)^n*Sum_{j=0..n} C(-n,j), T(n,k) = Sum_{j=0..k} T(n-1,j) for k=0..n-1, and n>=0, read by rows.
  • A201638 (program): Triangle read by rows, T(n,k) for 0<=k<=n, generalizes the colored Motzkin paths of A107264.
  • A201639 (program): Triangle read by rows, T(n,k) for 0<=k<=n, generalizes the Motzkin lattice paths with weights of A003645.
  • A201641 (program): Triangle read by rows, T(n,k) for 0<=k<=n, generalizes the colored Motzkin paths of A129400.
  • A201643 (program): John Leech’s example of a set of eleven distinct odd numbers the sum of whose reciprocals is 1.
  • A201684 (program): a(n) = 2*A052186(n) - n!.
  • A201685 (program): Triangular array read by rows. T(n,k) is the number of connected endofunctions on {1,2,…,n} that have exactly k nodes in the unique cycle of its digraph representation.
  • A201686 (program): a(n) = binomial(n, [n/2]) - 2.
  • A201687 (program): a(1)=0; a(n) = b(n) - Sum_{r=1..n-1} a(r)*b(n-1-r), where b(n) = A000085(n).
  • A201688 (program): Primes of the form p^2 + 18, where p is prime.
  • A201689 (program): Number of involutions avoiding the pattern 21 (with a dot over the 1).
  • A201701 (program): Riordan triangle ((1-x)/(1-2x), x^2/(1-2x)).
  • A201703 (program): Triangle read by rows: T(n,m) (0 <= m <= n) = size of smallest set of nodes whose removal from an n-dimensional hypercube leaves no subgraph isomorphic to an m-dimensional Fibonacci cube.
  • A201704 (program): Primes of the form 8n^2 + 7.
  • A201705 (program): Primes of the form 8n^2 + 9.
  • A201706 (program): Primes of the form 9n^2 + 4.
  • A201707 (program): Primes of the form 9n^2 + 7.
  • A201708 (program): Primes of the form 9n^2 + 10.
  • A201709 (program): Primes of the form 10n^2 + 1.
  • A201710 (program): Primes of the form 10n^2 + 3.
  • A201711 (program): Primes of the form 10n^2 + 9.
  • A201712 (program): Primes of the form 2n^2 - 3.
  • A201713 (program): Primes of the form 2n^2 - 5.
  • A201714 (program): Primes of the form 2n^2 - 7.
  • A201715 (program): Primes of the form 3*m^2 - 2.
  • A201716 (program): Primes of the form 3*m^2 - 4.
  • A201717 (program): Primes of the form 3*m^2 - 5.
  • A201718 (program): Primes of the form 3*m^2 - 7.
  • A201720 (program): The total number of components in (A011800) of all labeled forests on n nodes whose components are all paths.
  • A201722 (program): Number of n X 1 0..4 arrays with rows and columns lexicographically nondecreasing and no element equal to the number of horizontal and vertical neighbors equal to itself.
  • A201734 (program): Numbers n such that 90*n + 47 is prime.
  • A201739 (program): Numbers n such that 90*n + 29 is prime.
  • A201774 (program): Decimal expansion of 1/(Pi + 1).
  • A201775 (program): Decimal expansion of 1/(Pi - 1).
  • A201776 (program): Decimal expansion of 1/(e+1).
  • A201780 (program): Riordan array ((1-x)^2/(1-2x), x/(1-2x)).
  • A201781 (program): Primes of the form 3*m^2 - 8.
  • A201782 (program): Primes of the form 3n^2 - 10.
  • A201783 (program): Primes of the form 5n^2 - 1.
  • A201784 (program): Primes of the form 5n^2 - 2.
  • A201785 (program): Primes of the form 5n^2 - 3.
  • A201786 (program): Primes of the form 5*k^2 - 4.
  • A201787 (program): Primes of the form 5n^2 - 6.
  • A201788 (program): Primes of the form 5n^2 - 7.
  • A201789 (program): Primes of the form 5n^2 - 8.
  • A201790 (program): Primes of the form 5n^2 - 9.
  • A201791 (program): Primes of the form 6n^2 - 5.
  • A201792 (program): Primes of the form 6n^2 - 7.
  • A201793 (program): Primes of the form 7n^2 - 1.
  • A201795 (program): E.g.f. satisfies: A(x)+1/2*A(x)^2 = x*exp(A(x)).
  • A201804 (program): Numbers k such that 90*k + 11 is prime.
  • A201805 (program): Number of arrays of n integers in -2..2 with sum zero and equal numbers of elements greater than zero and less than zero.
  • A201812 (program): Number of arrays of 4 integers in -n..n with sum zero and equal numbers of elements greater than zero and less than zero.
  • A201813 (program): Number of arrays of 5 integers in -n..n with sum zero and equal numbers of elements greater than zero and less than zero.
  • A201816 (program): Numbers k such that 90*k + 13 is prime.
  • A201817 (program): Numbers k such that 90*k + 67 is prime.
  • A201818 (program): Numbers k such that 90*k + 49 is prime.
  • A201819 (program): Numbers n such that 90*n + 31 is prime.
  • A201820 (program): Numbers k such that 90*k + 23 is prime.
  • A201822 (program): Numbers k such that 90*k + 77 is prime.
  • A201824 (program): G.f.: Sum_{n>=0} log( 1/sqrt(1-2^n*x) )^n / n!.
  • A201825 (program): G.f.: exp( Sum_{n>=1} A119616(n)*x^n/n ) where A119616(n) = (sigma(n)^2 - sigma(n,2))/2.
  • A201837 (program): G.f.: real part of 1/(1 - i*x - i*x^2) where i=sqrt(-1).
  • A201838 (program): G.f.: imaginary part of 1/(1 - i*x - i*x^2) where i=sqrt(-1).
  • A201848 (program): Primes of the form 7n^2 - 2.
  • A201849 (program): Primes of the form 7n^2 - 3.
  • A201850 (program): Primes of the form 7n^2 - 4.
  • A201851 (program): Primes of the form 7n^2 - 5.
  • A201852 (program): Primes of the form 7n^2 - 6.
  • A201853 (program): Primes of the form 7n^2 - 8.
  • A201854 (program): Primes of the form 7n^2 - 9.
  • A201855 (program): Primes of the form 7n^2 - 10.
  • A201856 (program): Primes of the form 8n^2 - 3.
  • A201857 (program): Primes of the form 8n^2 - 5.
  • A201858 (program): Primes of the form 8n^2 - 7.
  • A201859 (program): Primes of the form 8n^2 - 9.
  • A201860 (program): Primes of the form 9n^2 - 2.
  • A201864 (program): ((F(n-1)+F(n-2))-1)/2 if F(n) is odd, otherwise ((F(n-1)+F(n-2))-2)/2, where F(n)=A000045(n) is the n-th Fibonacci number.
  • A201865 (program): Expansion of 1/((1-3*x)*(1+7*x)).
  • A201874 (program): Number of zero-sum -n..n arrays of 3 elements with first and second differences also in -n..n.
  • A201880 (program): Numbers n such that sigma_2(n) - n^2 is prime.
  • A201883 (program): The number of simple labeled graphs on n nodes such that i) all connected components have exactly one cycle, ii) all vertices have degree at most 3, iii) vertices of degree 3 are on a cycle.
  • A201908 (program): Irregular triangle of 2^k mod (2n-1).
  • A201920 (program): a(n) = 2^n mod 125.
  • A201960 (program): Primes of the form 9n^2 - 5.
  • A201961 (program): Primes of the form 9n^2 - 8.
  • A201962 (program): Primes of the form 10n^2 - 3.
  • A201963 (program): Primes of the form 10n^2 - 7.
  • A201964 (program): Primes of the form 10n^2 - 9.
  • A201967 (program): Expansion of 1/(1-2*x-3*x^2+x^4) in powers of x.
  • A201969 (program): G.f. satisfies: A(x) = 1 + x*A(x)^2 + x^2/A(x).
  • A201970 (program): G.f. satisfies: A(x) = 1 + x*A(x)^2 + x^2/A(x)^3.
  • A201971 (program): a(n) is the largest m such that n is congruent to -2, -1, 0, 1 or 2 mod k for all k from 1 to m.
  • A201975 (program): Number of n X 2 0..3 arrays with rows and columns lexicographically nondecreasing read forwards and nonincreasing read backwards.
  • A202012 (program): Expansion of (1-x+x^2)/((1-x)(1-x-x^2-x^3)).
  • A202013 (program): The number of functions f:{1,2,…,n}->{1,2,…,n} that have an odd number of odd length cycles and no even length cycles.
  • A202018 (program): a(n) = n^2 + n + 41.
  • A202022 (program): Characteristic functions of repdigit numbers in decimal representation.
  • A202023 (program): Triangle T(n,k), read by rows, given by (1, 0, 1, 0, 0, 0, 0, 0, 0, 0, …) DELTA (0, 1, -1, 0, 0, 0, 0, 0, 0, 0, …) where DELTA is the operator defined in A084938.
  • A202048 (program): Number of (n+2) X 6 binary arrays avoiding patterns 001 and 110 in rows and columns.
  • A202049 (program): Number of (n+2) X 7 binary arrays avoiding patterns 001 and 110 in rows and columns.
  • A202050 (program): Number of (n+2) X 8 binary arrays avoiding patterns 001 and 110 in rows and columns.
  • A202051 (program): Number of (n+2) X 9 binary arrays avoiding patterns 001 and 110 in rows and columns.
  • A202064 (program): Triangle T(n,k), read by rows, given by (2, -1/2, 1/2, 0, 0, 0, 0, 0, 0, 0, …) DELTA (0, 1/2, -1/2, 0, 0, 0, 0, 0, 0, 0, …) where DELTA is the operator defined in A084938.
  • A202065 (program): The number of simple labeled graphs on 2n nodes whose connected components are even length cycles.
  • A202066 (program): Mass of oriented maximal Wicks forms of genus n, multiplied by 6.
  • A202067 (program): Numerator of mass of oriented maximal Wicks forms of genus n.
  • A202068 (program): Denominator of mass of oriented maximal Wicks forms of genus n.
  • A202069 (program): Number of arrays of n+2 integers in -1..1 with sum zero and the sum of every adjacent pair being odd
  • A202083 (program): Primes of the form 16n^2 + 121.
  • A202089 (program): Numbers n such that n^2 and (n+1)^2 have same digit sum.
  • A202092 (program): Number of (n+2) X (n+2) binary arrays avoiding patterns 001 and 011 in rows and columns.
  • A202093 (program): Number of (n+2) X 3 binary arrays avoiding patterns 001 and 011 in rows and columns.
  • A202094 (program): Number of (n+2) X 4 binary arrays avoiding patterns 001 and 011 in rows and columns.
  • A202095 (program): Number of (n+2)X5 binary arrays avoiding patterns 001 and 011 in rows and columns
  • A202096 (program): Number of (n+2)X6 binary arrays avoiding patterns 001 and 011 in rows and columns
  • A202097 (program): Number of (n+2)X7 binary arrays avoiding patterns 001 and 011 in rows and columns
  • A202098 (program): Number of (n+2)X8 binary arrays avoiding patterns 001 and 011 in rows and columns
  • A202099 (program): Number of (n+2)X9 binary arrays avoiding patterns 001 and 011 in rows and columns
  • A202101 (program): Numbers n such that 90*n + 59 is prime.
  • A202103 (program): Number of points matched in largest non-crossing matching of n=w+b points in the plane (w white, b black).
  • A202104 (program): Numbers n such that 90*n + 41 is prime.
  • A202105 (program): Numbers n such that 90*n + 43 is prime.
  • A202107 (program): n^4*(n+1)^4/8.
  • A202109 (program): n^3*(n+1)^3*(n+2)^3/72.
  • A202110 (program): Numbers n such that 90*n + 7 is prime.
  • A202111 (program): a(n) = sigma(n) - p, where p is the largest prime < sigma(n).
  • A202112 (program): Numbers n such that 90n + 79 is prime.
  • A202113 (program): Numbers n such that 90n + 61 is prime.
  • A202114 (program): Numbers n such that 90n + 53 is prime.
  • A202115 (program): Numbers n such that 90n + 17 is prime.
  • A202116 (program): Numbers n such that 90n + 89 is prime.
  • A202117 (program): Number of -1..1 arrays of n elements with first, second and third differences also in -1..1.
  • A202129 (program): Numbers n such that 90n + 71 is prime.
  • A202137 (program): Numbers k such that 24k + 1 is neither square nor prime.
  • A202141 (program): a(n) = 13*n^2 - 16*n + 5.
  • A202142 (program): Decimal expansion of 4/sqrt((1+sqrt(5))/2).
  • A202143 (program): G.f. 1/[Sum_{n>=0} (2*n+1)*(-x)^(n*(n+1)/2)].
  • A202144 (program): L.g.f.: (-1/3)*log( Sum_{n>=0} (2*n+1)*(-x)^(n*(n+1)/2) ).
  • A202148 (program): Sum of rows of the triangle in A080381.
  • A202149 (program): Triangle read by rows: T(n, k) = mod(2^k, n), where 1 <= k < n.
  • A202155 (program): x-values in the solution to x^2 - 13*y^2 = -1.
  • A202156 (program): y-values in the solution to x^2 - 13*y^2 = -1.
  • A202169 (program): Size of maximal independent set in graph S_3(n).
  • A202171 (program): The covering numbers rho_3(n).
  • A202174 (program): In base 10 lunar arithmetic, a(n) is the smallest number than has exactly n different square roots (or -1 if no such number exists).
  • A202191 (program): Triangle T(n,m) = coefficient of x^n in expansion of [x/(1-x-x^3)]^m = sum(n>=m, T(n,m) x^n).
  • A202194 (program): Number of (n+2)X(n+2) binary arrays avoiding patterns 001 and 101 in rows and columns
  • A202195 (program): Number of (n+2) X 3 binary arrays avoiding patterns 001 and 101 in rows and columns.
  • A202196 (program): Number of (n+2) X 4 binary arrays avoiding patterns 001 and 101 in rows and columns.
  • A202197 (program): Number of (n+2) X 5 binary arrays avoiding patterns 001 and 101 in rows and columns.
  • A202198 (program): Number of (n+2) X 6 binary arrays avoiding patterns 001 and 101 in rows and columns.
  • A202199 (program): Number of (n+2) X 7 binary arrays avoiding patterns 001 and 101 in rows and columns.
  • A202200 (program): Number of (n+2) X 8 binary arrays avoiding patterns 001 and 101 in rows and columns.
  • A202201 (program): Number of (n+2) X 9 binary arrays avoiding patterns 001 and 101 in rows and columns.
  • A202202 (program): T(n,k)=Number of (n+2)X(k+2) binary arrays avoiding patterns 001 and 101 in rows and columns
  • A202206 (program): a(n) = 3*a(n-1)+3*a(n-2) with a(0)=1 and a(1)=2.
  • A202207 (program): a(n) = 3*a(n-1) - a(n-2) + a(n-3) with a(0)=1, a(1)=2, a(2)=5.
  • A202208 (program): Smallest square (>4n) == 1 mod 4n.
  • A202209 (program): Triangle T(n,k), read by rows, given by (2, 1/2, 1/2, 0, 0, 0, 0, 0, 0, 0, …) DELTA (0, 1/2, -1/2, 0, 0, 0, 0, 0, 0, 0, …) where DELTA is the operator defined in A084938.
  • A202237 (program): Odd numbers with the same number of prime factors of the form 4*k+1 and 4*k+3.
  • A202238 (program): Characteristic function of positive integers not prime and not a power of 2.
  • A202241 (program): Array F(n,m) read by antidiagonals: F(0,m)=1, F(n,0) = A130713(n), and column m+1 is recursively defined as the partial sums of column m.
  • A202253 (program): Number of zero-sum -n..n arrays of 3 elements with adjacent element differences also in -n..n.
  • A202254 (program): Number of zero-sum -n..n arrays of 4 elements with adjacent element differences also in -n..n.
  • A202259 (program): Right-truncatable nonprimes: every prefix is nonprime number.
  • A202267 (program): Numbers in which all digits are noncomposites (1, 2, 3, 5, 7) or 0.
  • A202269 (program): Right-truncatable triangular numbers: every prefix is triangular number.
  • A202270 (program): Largest n-digit numbers whose sum of digits is n.
  • A202276 (program): Number of integers k <= n such that sigma(x) = k has no solution, sigma = A000203.
  • A202278 (program): Right-truncatable Fibonacci numbers: every prefix is Fibonacci number.
  • A202297 (program): Product of the sum of the first n^2 primes by the sum of the first (n+1)^2 primes.
  • A202299 (program): y-values in the solution to x^2 - 18*y^2 = 1.
  • A202300 (program): Decimal expansion of the real root of x^3 + 2x^2 + 10x - 20.
  • A202301 (program): Next prime after the partial sum of the first n primes.
  • A202304 (program): a(n) = floor(sqrt(3*n)).
  • A202305 (program): Floor(sqrt(5*n)).
  • A202306 (program): Floor(sqrt(7*n)).
  • A202307 (program): Floor(sqrt(11*n)).
  • A202308 (program): Floor(sqrt(13*n)).
  • A202318 (program): Let (n)_p denote the exponent of prime p in the prime power factorization of n. Then a(n) is defined by the formulas a(1)=1; for n >= 2, (a(n))_2 = (n)_2, (a(n))_3 = (n)_3 and, for p >= 5, (a(n))_p = 1 + ((2n)/(p-1))_p if p-1|2*n, and (a(n))_p = 0 otherwise.
  • A202327 (program): Triangle read by rows, T(n, k) is the coefficient of x^n in expansion of ((-1 - x + sqrt(1 + 2*x + 5*x^2)) /2)^k.
  • A202329 (program): Number of (n+1)X(n+1) binary arrays with consecutive windows of two bits considered as a binary number nondecreasing in every row and column
  • A202330 (program): Number of (n+1) X 4 binary arrays with consecutive windows of two bits considered as a binary number nondecreasing in every row and column.
  • A202331 (program): Number of (n+1) X 5 binary arrays with consecutive windows of two bits considered as a binary number nondecreasing in every row and column.
  • A202332 (program): Number of (n+1) X 6 binary arrays with consecutive windows of two bits considered as a binary number nondecreasing in every row and column.
  • A202333 (program): Number of (n+1) X 7 binary arrays with consecutive windows of two bits considered as a binary number nondecreasing in every row and column.
  • A202334 (program): Number of (n+1) X 8 binary arrays with consecutive windows of two bits considered as a binary number nondecreasing in every row and column.
  • A202335 (program): T(n,k)=Number of (n+1)X(k+1) binary arrays with consecutive windows of two bits considered as a binary number nondecreasing in every row and column
  • A202337 (program): Range of A062723.
  • A202340 (program): Number of times n occurs in Hofstadter H-sequence A005374.
  • A202341 (program): Numbers occurring exactly once in Hofstadter H-sequence A005374.
  • A202342 (program): Numbers occurring exactly twice in Hofstadter H-sequence A005374.
  • A202349 (program): Lexicographically first sequence such that the sequence and its first and second differences share no terms, and the 3rd differences are equal to the original sequence.
  • A202363 (program): Triangular array read by rows: T(n,k) is the number of inversion pairs ( p(i) < p(j) with i>j ) that are separated by exactly k elements in all n-permutations (where the permutation is represented in one line notation); n>=2, 0<=k<=n-2.
  • A202364 (program): Number of n-permutations with at least one cycle of length >=4.
  • A202365 (program): G.f.: Sum_{n>=0} (n-x)^n * x^n / (1 + n*x - x^2)^n.
  • A202367 (program): LCM of denominators of the coefficients of polynomials Q^(2)_m(n) defined by the recursion Q^(2)_0(n)=1; for m >= 1, Q^(2)_m(n) = Sum_{i=1..n} i^2*Q^(2)_(m-1)(i).
  • A202369 (program): LCM of denominators of the coefficients of polynomials Q^(4)_m(n)defined by the recursion Q^(4)_0(n)=1; for m>=1,Q^(4)_m(n)=sum{i=1,…,n}i^4*Q^(4)_(m-1)(i).
  • A202390 (program): Triangle T(n,k), read by rows, given by (1, 0, 1, 0, 0, 0, 0, 0, 0, 0, …) DELTA (1, 1, -1, 0, 0, 0, 0, 0, 0, 0, …) where DELTA is the operator defined in A084938.
  • A202391 (program): Indices of the smallest of four consecutive triangular numbers summing up to a square.
  • A202394 (program): Expansion of f(-x)^3 + 9 * x * f(-x^9)^3 in powers of x where f() is a Ramanujan theta function.
  • A202400 (program): Number of (n+2) X 4 binary arrays avoiding patterns 000 and 010 in rows and columns.
  • A202402 (program): Number of (n+2) X 6 binary arrays avoiding patterns 000 and 010 in rows and columns.
  • A202410 (program): Inverse Lah transform of 1,2,3,…; e.g.f. exp(x/(x-1))*(2*x-1)/(x-1).
  • A202414 (program): Number of (n+2) X 3 binary arrays with no more than one of any consecutive three bits set in any row or column.
  • A202428 (program): Number of (n+2) X 3 binary arrays avoiding patterns 000 and 001 in rows, columns and nw-to-se diagonals.
  • A202429 (program): Number of (n+2)X4 binary arrays avoiding patterns 000 and 001 in rows, columns and nw-to-se diagonals
  • A202440 (program): Number of (n+2) X 3 binary arrays avoiding patterns 001 and 110 in rows, columns and nw-to-se diagonals.
  • A202451 (program): Upper triangular Fibonacci matrix, by SW antidiagonals.
  • A202452 (program): Lower triangular Fibonacci matrix, by SW antidiagonals.
  • A202455 (program): Number of (n+2) X 4 binary arrays with consecutive windows of three bits considered as a binary number nondecreasing in every row and column.
  • A202462 (program): a(n) = Sum_{j=1..n} Sum_{i=1..n} F(i,j), where F is the Fibonacci fusion array of A202453.
  • A202477 (program): The number of ways to build all endofunctions on each block of every set partition of {1,2,…,n}.
  • A202480 (program): Riordan array (1/(1-x), x(2x-1)/(1-x)^2)
  • A202481 (program): Column k = 3 of triangular array in A165241.
  • A202482 (program): Expansion of (1-(1-9*x)^(1/3))/(4-(1-9*x)^(1/3)).
  • A202486 (program): Number of (n+2)X4 binary arrays avoiding patterns 000 and 010 in rows, columns and nw-to-se diagonals
  • A202493 (program): Column k = 4 of triangular array in A165241.
  • A202502 (program): Modified lower triangular Fibonacci matrix, by antidiagonals.
  • A202516 (program): G.f.: exp( Sum_{n>=1} (2^n + 3^n)^n * x^n/n ).
  • A202520 (program): Denominator of [x^(4n+2)] in the Taylor series log(cosec(x)*sinh(x))= x^2/3 +2*x^6/2835 +2*x^10/467775 +4*x^14/127702575 +…
  • A202534 (program): Number of symmetric, reflexive, non-transitive relations on n elements.
  • A202535 (program): a(n) = n*phi(n)*abs( mobius(n) ).
  • A202541 (program): Decimal expansion of the number x satisfying e^(2x) - e^(-2x) = 1.
  • A202542 (program): Decimal expansion of the number x satisfying e^(3x)-e^(-3x)=1.
  • A202543 (program): Decimal expansion of the number x satisfying e^(x/2) - e^(-x/2) = 1.
  • A202551 (program): Triangle T(n,k), read by rows, given by (1, -1, 1, 0, 0, 0, 0, 0, 0, 0, …) DELTA (-1, 0, 0, 0, 0, 0, 0, 0, 0, 0, …) where DELTA is the operator defined in A084938.
  • A202554 (program): Number of nX2 0,1 arrays with the row and column sums nondecreasing
  • A202563 (program): Numbers which are both decagonal and pentagonal.
  • A202564 (program): Indices of pentagonal numbers which are also decagonal.
  • A202565 (program): Indices of decagonal numbers which are also pentagonal.
  • A202594 (program): Number of (n+2) X 3 binary arrays avoiding patterns 001 and 000 in rows and columns.
  • A202603 (program): Triangle T(n,k), read by rows, given by (1, 0, 0, 0, 0, 0, 0, 0, 0, 0, …) DELTA (1, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, …) where DELTA is the operator defined in A084938.
  • A202606 (program): Ceiling(((10^n - 1)^2/9 + 10^n)/18).
  • A202617 (program): E.g.f. satisfies: A(x) = exp( x*(1 + A(x)^2)/2 ).
  • A202628 (program): a(n) = (4*n+1)*(2^(4*n+1)+(-1)^n*2^(2*n+1)+1).
  • A202637 (program): x-values in the solution to x^2 - 7*y^2 = -3.
  • A202638 (program): y-values in the solution to x^2 - 7*y^2 = -3.
  • A202654 (program): Number of ways to place 3 nonattacking semi-queens on an n X n board.
  • A202670 (program): Symmetric matrix based on A000290 (the squares), by antidiagonals.
  • A202672 (program): Array: row n shows the coefficients of the characteristic polynomial of the n-th principal submatrix of the symmetric matrix A087062 based on (1,1,1,1,…); by antidiagonals.
  • A202674 (program): Symmetric matrix based on (1,3,5,7,9,…), by antidiagonals.
  • A202676 (program): Symmetric matrix based on (1,4,7,10,13,…), by antidiagonals.
  • A202688 (program): Decimal expansion of Sum_{n>=0} (-1)^(n+1) / n!!.
  • A202689 (program): a(n) = (2n)! * (n+1)! / 2^(2n).
  • A202703 (program): The third of a set of three triangles constructed by the same rule as A202692-A202694, but where the top entries in the three triangles are 0,0,1 respectively.
  • A202706 (program): Numbers n such that (sum of digits of n!) / 9 is prime.
  • A202708 (program): Sum of digits of n! divided by 9.
  • A202730 (program): Number of n X 3 nonnegative integer arrays each row and column an ascent sequence (interior element no greater than one plus up-steps preceding it) and the lower right element equal to min(n,3)-1.
  • A202736 (program): Number of n X 2 0..1 arrays with row sums equal and column sums unequal to adjacent columns.
  • A202750 (program): Triangle T(n,k) = binomial(n,k)^4 read by rows, 0<=k<=n.
  • A202752 (program): Number of n X 4 nonnegative integer arrays with each row and column increasing from zero by 0 or 1.
  • A202768 (program): Vandermonde determinant of the first n squares.
  • A202785 (program): Number of 3 X 3 0..n arrays with row and column sums equal.
  • A202789 (program): Number of n X 2 binary arrays with every one adjacent to another one horizontally, diagonally, antidiagonally or vertically.
  • A202796 (program): Number of n X 2 binary arrays with every one adjacent to another one horizontally or vertically.
  • A202803 (program): a(n) = n*(5*n+1).
  • A202804 (program): a(n) = n*(6*n+4).
  • A202807 (program): Number of n X 3 nonnegative integer arrays with each row and column increasing from zero by 0, 1 or 2.
  • A202814 (program): Moments of the quadratic coefficient of the characteristic polynomial of a random matrix in U(1) X U(1) (embedded in USp(4)).
  • A202821 (program): Position of 6^n among 3-smooth numbers A003586.
  • A202822 (program): Numbers of the form 3*(x^2 + xy + y^2 + x + y) + 1 where x and y are integers.
  • A202824 (program): Expansion of e.g.f.: exp( (1+x)^4 - 1 ).
  • A202826 (program): E.g.f.: exp( 1/(1-x)^3 - 1 ).
  • A202827 (program): Expansion of e.g.f.: exp(4*x/(1-x)) / sqrt(1-x^2).
  • A202828 (program): Expansion of e.g.f.: exp(4*x/(1-2*x)) / sqrt(1-4*x^2).
  • A202829 (program): Expansion of e.g.f.: exp(4*x/(1-3*x)) / sqrt(1-9*x^2).
  • A202830 (program): E.g.f.: exp(2*x + 3*x^2/2).
  • A202831 (program): Expansion of e.g.f.: exp(4*x/(1-5*x)) / sqrt(1-25*x^2).
  • A202832 (program): E.g.f: exp(2*x + 5*x^2/2).
  • A202833 (program): Expansion of e.g.f.: exp(9*x/(1-x)) / sqrt(1-x^2).
  • A202834 (program): E.g.f.: exp(3*x + x^2/2).
  • A202835 (program): Expansion of e.g.f.: exp(9*x/(1-2*x)) / sqrt(1-4*x^2).
  • A202836 (program): Expansion of e.g.f.: exp(9*x/(1-4*x)) / sqrt(1-16*x^2).
  • A202837 (program): E.g.f.: exp(3*x + 2*x^2).
  • A202839 (program): Number of stacks of length 1 in all 2ndary structures of size n.
  • A202846 (program): Number of stacks of odd length in all 2ndary structures of size n.
  • A202847 (program): Riordan array (f(x), x*f(x)) where f(x) is the g.f. of A126930.
  • A202856 (program): Moments of the quadratic coefficient of the characteristic polynomial of a random matrix in SU(2) X SU(2) (inside USp(4)).
  • A202865 (program): Number of 3 X 3 0..n arrays with row and column sums one greater than the previous row and column.
  • A202873 (program): Symmetric matrix based on (1,3,7,15,31,…), by antidiagonals.
  • A202874 (program): Symmetric matrix based on (1,2,3,5,8,13,…), by antidiagonals.
  • A202878 (program): Expansion of e.g.f.: exp(16*x/(1-x)) / sqrt(1-x^2).
  • A202879 (program): E.g.f.: exp(4*x + x^2/2).
  • A202882 (program): Number of nX1 0..2 arrays with every nonzero element less than or equal to some horizontal or vertical neighbor
  • A202900 (program): Number of n X 2 0..1 arrays with every one equal to some NW, E or S neighbor.
  • A202944 (program): G.f.: Sum_{n>=0} (n+1)*(n+2)/2 * 2^(n*(n-1)) * x^n.
  • A202945 (program): v(n+1)/v(n), where v=A203773.
  • A202946 (program): a(n+1) = 6*A060544(n)*a(n).
  • A202948 (program): a(n+1) = 3*A136016*a(n).
  • A202950 (program): a(n) = Sum_{k=0..n} (2*n-k)!*2^(k-n)/k!.
  • A202963 (program): Number of arrays of 3 integers in -n..n with sum zero and adjacent elements differing in absolute value
  • A202964 (program): Number of arrays of 4 integers in -n..n with sum zero and adjacent elements differing in absolute value.
  • A202973 (program): Number of n X 2 0..1 arrays with every nonzero element less than or equal to at least two horizontal and vertical neighbors.
  • A202989 (program): E.g.f: Sum_{n>=0} 3^(n^2) * exp(3^n*x) * x^n/n!.
  • A202990 (program): E.g.f: Sum_{n>=0} 3^n * 2^(n^2) * exp(-2*2^n*x) * x^n/n!.
  • A202991 (program): E.g.f: Sum_{n>=0} 3^(n^2) * exp(-2*3^n*x) * x^n/n!.
  • A202993 (program): G.f.: A(x) = exp( Sum_{n>=1} sigma(n^4)*x^n/n ), a power series in x with integer coefficients.
  • A202994 (program): a(n) = sigma(n^4).
  • A203006 (program): (n-1)-st elementary symmetric function of the first n Fibonacci numbers.
  • A203007 (program): (n-1)-st elementary symmetric function of Fibonacci numbers F(2) to F(n).
  • A203008 (program): (n-1)-st elementary symmetric function of the first n odd primes.
  • A203009 (program): (n-1)-st elementary symmetric function of first n Lucas numbers, starting with L(0)=2.
  • A203010 (program): (n-1)-st elementary symmetric function of first n Lucas numbers, starting with L(1)=1.
  • A203011 (program): (n-1)-st elementary symmetric function of {1,3,7,15,31,63,…-1+2^n}.
  • A203016 (program): Numbers congruent to {1, 2, 3, 4} mod 6, multiplied by 3.
  • A203018 (program): The n-th prime number that equals 1 (mod 4n).
  • A203019 (program): Number of elevated peakless Motzkin paths.
  • A203094 (program): Number of nX1 0..3 arrays with every nonzero element less than or equal to some horizontal or vertical neighbor.
  • A203134 (program): Decagonal hexagonal numbers
  • A203135 (program): Indices of hexagonal numbers that are also decagonal
  • A203136 (program): Indices of decagonal numbers that are also hexagonal.
  • A203147 (program): (n-1)-st elementary symmetric function of {11, 12, 13, 14, …, 10 + n}.
  • A203148 (program): (n-1)-st elementary symmetric function of {3,9,…,3^n}.
  • A203149 (program): (n-1)-st elementary symmetric function of {2,8,26,80,242,…,-1+3^n}.
  • A203150 (program): (n-1)-st elementary symmetric function of the first n terms of (1,2,1,2,1,2,1,2,1,2,…)=A000034.
  • A203151 (program): (n-1)-st elementary symmetric function of {1,1,2,2,3,3,4,4,5,5,…,Floor[(n+1)/2]}.
  • A203152 (program): (n-1)-st elementary symmetric function of {1, 2, 2, 3, 3, 4, 4, 5, 5, …, floor(1+n/2)}.
  • A203153 (program): (n-1)-st elementary symmetric function of {2, 2, 3, 3, 4, 4, 5, 5, …, floor((n+3)/2)}.
  • A203154 (program): (n-1)-st elementary symmetric function of {2, 3, 3, 4, 4, 5, 5,…,Floor[(n+4)/2]}.
  • A203155 (program): (n-1)-st elementary symmetric function of {3, 3, 4, 4, 5, 5,…, Floor[(n+5)/2]}.
  • A203156 (program): (n-1)-st elementary symmetric function of {4,9,16,25,…, (n+1)^2}.
  • A203157 (program): (n-1)-st elementary symmetric function of the first n triangular numbers.
  • A203158 (program): v(n+1)/v(n), where v=A203012.
  • A203159 (program): (n-1)-st elementary symmetric function of {2,4,6,8,…,2n}.
  • A203160 (program): (n-1)-st elementary symmetric function of the first n terms of (2,3,1,2,3,1,2,3,1,…)=A010882.
  • A203161 (program): (n-1)-st elementary symmetric function of the first n terms of (3,1,2,3,1,2,3,1,2,…).
  • A203162 (program): (n-1)-st elementary symmetric function of the first n terms of (1,2,3,1,2,3,1,2,3,…).
  • A203163 (program): (n-1)-st elementary symmetric function of the first n terms of (1,2,3,4,1,2,3,4,1,2,3,4,…) = A010883.
  • A203164 (program): (n-1)-st elementary symmetric function of the first n terms of the periodic sequence (4,1,2,3,4,1,2,3,…).
  • A203165 (program): (n-1)-st elementary symmetric function of the first n terms of the periodic sequence (3,4,1,2,3,4,1,2,…).
  • A203166 (program): (n-1)-st elementary symmetric function of the first n terms of (1,2,3,4,5,1,2,3,4,5,…)=A010884.
  • A203167 (program): (n-1)-st elementary symmetric function of the first n terms of (2,2,1,2,2,1,2,2,1,…)=(A130196 for n>0).
  • A203169 (program): Sum of the fourth powers of the first n even-indexed Fibonacci numbers.
  • A203170 (program): Sum of the fourth powers of the first n odd-indexed Fibonacci numbers.
  • A203171 (program): Alternating sum of the fourth powers of the first n even-indexed Fibonacci numbers.
  • A203172 (program): Alternating sum of the fourth powers of the first n odd-indexed Fibonacci numbers.
  • A203175 (program): Number of nX2 0..2 arrays with every 1 immediately preceded by 0 to the left or above, no 0 immediately preceded by a 0, and every 2 immediately preceded by 0 1 to the left or above.
  • A203192 (program): (n-1)-st elementary symmetric function of the first n terms of (1,2,1,4,1,6,1,8,…)=(A124625 for n>1).
  • A203193 (program): (n-1)-st elementary symmetric function of the first n terms of (1,2,1,3,1,4,1,5,…)=A133622.
  • A203194 (program): (n-1)-st elementary symmetric function of the first n terms of (1,2,6,20,70,252,…)=A000984.
  • A203195 (program): (n-1)-st elementary symmetric function of the first n Catalan numbers (A000108).
  • A203196 (program): (n-1)-st elementary symmetric function of the first n terms of (2,1,4,3,6,5,8,7,…)=A103889.
  • A203197 (program): (n-1)-st elementary symmetric function of the first n terms of (1,3,9,27,…)=A000244.
  • A203227 (program): (n-1)-st elementary symmetric function of (0!,…,(n-1)!)
  • A203228 (program): (n-1)-st elementary symmetric function of (1!,…,(n-1)!).
  • A203229 (program): (n-1)-st elementary symmetric function of (1,16,…,n^4).
  • A203230 (program): (n-1)-st elementary symmetric function of the first n terms of A010684.
  • A203231 (program): (n-1)-st elementary symmetric function of the first n terms of the periodic sequence (3,1,3,1,3,1,3,1,…).
  • A203232 (program): (n-1)-st elementary symmetric function of the first n terms of the periodic sequence (2,3,2,3,2,3,…).
  • A203233 (program): (n-1)-st elementary symmetric function of the first n terms of the periodic sequence (3,2,3,2,3,2,…).
  • A203234 (program): (n-1)-st elementary symmetric function of the first n terms of the periodic sequence (1,1,1,2,1,1,1,2,…).
  • A203235 (program): (n-1)-st elementary symmetric function of the first n terms of the periodic sequence (1,1,1,3,1,1,1,3,…).
  • A203236 (program): (n-1)-st elementary symmetric function of the first n terms of the lower Wythoff sequence, A000201.
  • A203237 (program): (n-1)-st elementary symmetric function of the first n terms of the upper Wythoff sequence, A001950.
  • A203238 (program): a(n)=(n-1)-st elementary symmetric function of the first n terms of (2, -4, 6, -8, 10, …).
  • A203239 (program): Odd numbered terms of the sequence whose n-th term is the (n-1)-st elementary symmetric function of (i, 2i, 3i, …, ni), where i=sqrt(-1).
  • A203240 (program): Real part of even numbered terms of the sequence s(n)=(n-1)-st elementary symmetric function of (i, 2i, 3i,…,ni).
  • A203241 (program): Second elementary symmetric function of the first n terms of (1,2,4,8,…).
  • A203242 (program): Second elementary symmetric function of the first n terms of (1, 3, 7, 15, 31, …).
  • A203243 (program): Second elementary symmetric function of the first n terms of (1,3,9,27,81,…).
  • A203244 (program): Second elementary symmetric function of the first n terms of (1,4,16,64,256,…).
  • A203245 (program): Second elementary symmetric function of the first n terms of (1,2,3,5,8,…).
  • A203246 (program): Second elementary symmetric function of the first n terms of (1,1,2,2,3,3,4,4,…).
  • A203264 (program): Permanent of the n-th principal submatrix of (A134446 in square format).
  • A203286 (program): Number of arrays of 2n nondecreasing integers in -3..3 with sum zero and equal numbers greater than zero and less than zero.
  • A203292 (program): Number of arrays of 4 nondecreasing integers in -n..n with sum zero and equal numbers greater than zero and less than zero.
  • A203298 (program): Second elementary symmetric function of the first n terms of (1,2,2,3,3,4,4,5,5…).
  • A203299 (program): Second elementary symmetric function of the first n terms of (2,2,3,3,4,4,5,5…).
  • A203302 (program): Cumulative sums of A201206.
  • A203303 (program): Vandermonde determinant of the first n terms of (1,2,4,8,16,…).
  • A203307 (program): v(n+1)/(2*v(n)), where v=A203305.
  • A203309 (program): Vandermonde determinant of the first n triangular numbers.
  • A203310 (program): a(n) = A203309(n+1)/A203309(n).
  • A203311 (program): Vandermonde determinant of (1,2,3,…,F(n+1)), where F=A000045 (Fibonacci numbers).
  • A203365 (program): Number of n X 2 0..2 arrays with every 1 immediately preceded by 0 to the left or above, and every 2 immediately preceded by both a 1 and a 0.
  • A203373 (program): Number of (n+1) X 4 0..1 arrays with every 2 X 2 subblock having equal diagonal elements or equal antidiagonal elements.
  • A203398 (program): T(n,k), a triangular array read by rows, is the number of classes of equivalent 2-color n-bead necklaces (turning over is not allowed) that have k necklaces.
  • A203400 (program): Partial sums of A050935.
  • A203408 (program): Numbers which are both heptagonal and decagonal.
  • A203409 (program): Indices of heptagonal numbers that are also decagonal.
  • A203410 (program): Indices of decagonal numbers that are also heptagonal.
  • A203411 (program): Discriminant of the cyclotomic binomial period polynomial for an odd prime.
  • A203421 (program): Reciprocal of Vandermonde determinant of (1,1/2,…,1/n).
  • A203422 (program): Reciprocal of Vandermonde determinant of (1/2,1/3,…,1/(n+1)).
  • A203423 (program): a(n) = w(n+1)/(2*w(n)), where w=A203422.
  • A203424 (program): Reciprocal of Vandermonde determinant of (1/2,1/4,…,1/(2n)).
  • A203425 (program): a(n) = w(n+1)/(4*w(n)), where w = A203424.
  • A203426 (program): Reciprocal of Vandermonde determinant of (1/4,1/6,…,1/(2n+2)).
  • A203427 (program): a(n) = w(n+1)/(4*w(n)), where w = A203426.
  • A203429 (program): w(n+1)/(3*w(n)), where w=A203428.
  • A203430 (program): Vandermonde determinant of the first n numbers (1,3,4,6,7,9,10,…)=(j+floor(j/2)).
  • A203431 (program): v(n+1)/v(n), where v=A203418.
  • A203433 (program): Vandermonde determinant of the first n terms of (2,3,5,6,8,9,…)=(j+floor((j+1)/2)).
  • A203444 (program): Numbers in range of Dedekind Psi function: A001615.
  • A203446 (program): Number of (n+1) X 3 0..1 arrays with column and row pair sums b(i,j)=a(i,j)+a(i,j-1) and c(i,j)=a(i,j)+a(i-1,j) such that rows of b(i,j) and columns of c(i,j) are lexicographically nondecreasing.
  • A203463 (program): Where Golay-Rudin-Shapiro sequence A020985 is positive.
  • A203464 (program): Numbers n such that 65 divides 4n^2 + 1; alternately, numbers which are 4, 9, 56, or 61 mod 65.
  • A203467 (program): a(n) = A203309(n)/A000178(n) where A000178 are superfactorials.
  • A203468 (program): Numbers that have a unique triangular proper divisor greater than 1.
  • A203469 (program): v(n)/A000178(n); v=A093883 and A000178=(superfactorials).
  • A203470 (program): a(n) = Product_{2 <= i < j <= n+1} (i + j).
  • A203471 (program): v(n)/A000178(n); v=A203470, A000178=(superfactorials).
  • A203472 (program): a(n) = Product_{3 <= i < j <= n+2} (i + j).
  • A203473 (program): v(n+1)/v(n), where v=A203472.
  • A203474 (program): a(n) = A203472(n) / A000178(n-1), where A000178 are the superfactorials.
  • A203476 (program): v(n+1)/v(n), where v=A203475.
  • A203478 (program): a(n) = v(n+1)/v(n), where v=A203477.
  • A203511 (program): a(n) = Product_{1 <= i < j <= n} (t(i) + t(j)); t = A000217 = triangular numbers.
  • A203512 (program): a(n) = v(n+1)/v(n), where v = A203511.
  • A203513 (program): a(n) = A203312(n+1)/A203312(n).
  • A203515 (program): v(n+1)/v(n), where v=A203514.
  • A203516 (program): a(n) = Product_{1 <= i < j <= n} 2*(i+j-1).
  • A203517 (program): v(n)/A000178(n); v=A203516 and A000178=(superfactorials).
  • A203536 (program): Number of nX2 0..2 arrays with every element neighboring horizontally or vertically both a 0 and a 1
  • A203551 (program): a(n) = n*(5n^2 + 3n + 4) / 6.
  • A203552 (program): a(n) = n*(5*n^2 - 3*n + 4) / 6.
  • A203553 (program): Lodumo_2 of A118175, which is n 1’s followed by n 0’s.
  • A203554 (program): Lodumo_2 of A079813, which is n 0’s followed by n 1’s..
  • A203556 (program): a(n) = sigma(n^5).
  • A203557 (program): G.f.: exp( Sum_{n>=1} sigma(n^5)*x^n/n ).
  • A203558 (program): Number of nX2 0..2 arrays with row sums equal and column sums equal
  • A203568 (program): a(n) = A026837(n) - A026838(n).
  • A203570 (program): Bisection of A201207 (half-convolution of the Lucas sequence A000032 with itself); even part.
  • A203571 (program): Period length 10: [0, 1, 2, 3, 4, 0, 4, 3, 2, 1] repeated.
  • A203572 (program): Period length 12: 0, 1, 2, 3, 4, 5, 0, 5, 4, 3, 2, 1 repeated.
  • A203573 (program): Bisection of A099924 (convolution of Lucas numbers); even arguments.
  • A203574 (program): Bisection of A099924 (Lucas convolution); one half of the terms with odd arguments.
  • A203579 (program): Exponential (or binomial) convolution of A000032 (Lucas) with itself, divided by 2.
  • A203580 (program): a(n) = Sum{d(i)*2^i: i=0,1,…,m}, where Sum{d(i)*7^i: i=0,1,…,m}=n, d(i)∈{0,1,…,6}
  • A203582 (program): v(n+1)/v(n), where v=A203581.
  • A203584 (program): v(n+1)/v(n), where v=A203583.
  • A203586 (program): v(n+1)/v(n), where v=A203585.
  • A203588 (program): a(n) = v(n+1)/v(n), where v=A203587.
  • A203590 (program): v(n+1)/v(n), where v=A203589.
  • A203601 (program): a(0)=1, a(n+1) = (a(n)*7) XOR a(n).
  • A203602 (program): Inverse permutation to A092401.
  • A203611 (program): Sum_{k=0..n} C(k-1,2*k-1-n)*C(k,2*k-n).
  • A203623 (program): Partial sums of A061395.
  • A203624 (program): Numbers which are both decagonal and octagonal.
  • A203625 (program): Indices of octagonal numbers which are also decagonal.
  • A203626 (program): Indices of decagonal numbers which are also octagonal.
  • A203628 (program): Indices of 9-gonal (nonagonal) numbers which are also 10-gonal (decagonal).
  • A203629 (program): Indices of 10-gonal (decagonal) numbers which are also 9-gonal (nonagonal).
  • A203639 (program): Multiplicative with a(p^e) = e*p^(e-1).
  • A203648 (program): a(n) = (1/4) * period of repeating sequence {S(j) mod 2n}, where S(j) is the sum of the first j squares.
  • A203678 (program): v(n+1)/v(n), where v=A203677.
  • A203719 (program): A204521(n)^2 = floor[A055812(n)/5]: Squares which written in base 5, with some digit appended, yield another square.
  • A203750 (program): Square root of v(2n)/v(2n-1), where v=A203748.
  • A203751 (program): Square root of v(2n+1)/(3v(2n), where v=A203748.
  • A203757 (program): Square root of v(2n)/v(2n-1), where v=A203755.
  • A203758 (program): Square root of v(2n+1)/(2*v(2n)), where v=A203755.
  • A203761 (program): a(n)=f(a(n-1)+1,a(n-2),a(n-3)), where f(x,y,z)=yz+zx+xy and a(1)=0, a(2)=0, a(3)=1.
  • A203762 (program): a(n)=f(a(n-1),a(n-2)+1,a(n-3)), where f(x,y,z)=yz+zx+xy and (a(1),a(2),a(3))=(0,0,1).
  • A203766 (program): Vandermonde sequence using x^2 + y^2 applied to (1,1,2,2,…,floor(n/2)).
  • A203767 (program): v(n+1)/v(n), where v=A203766.
  • A203768 (program): a(n)=f(a(n-1),a(n-2),a(n-3)+1), where f(x,y,z)=yz+zx+xy and (a(1),a(2),a(3))=(0,0,1).
  • A203769 (program): a(n) = (A203768(n+2) - 1)/2.
  • A203772 (program): a(n)=f(a(n-1),a(n-2)+1,a(n-3)+1), where f(x,y,z)=yz+zx+xy and (a(1),a(2),a(3))=(0,0,1).
  • A203773 (program): Vandermonde sequence using x^2 + y^2 applied to (0,1,1,2,2,…,floor(n/2)).
  • A203774 (program): Square root of v(2n)/v(2n-1), where v=A203773.
  • A203775 (program): Square root of v(2*n+1) / (2*v(2*n)), where v=A203773.
  • A203777 (program): Aliquot sequence starting at 220.
  • A203778 (program): a(n) = -24*A015219(n-2)*a(n-1), with a(1) = 2.
  • A203789 (program): Number of (n+1)X2 0..3 arrays with every 2X2 subblock having equal diagonal elements or equal antidiagonal elements
  • A203790 (program): Number of (n+1) X 3 0..3 arrays with every 2 X 2 subblock having equal diagonal elements or equal antidiagonal elements.
  • A203799 (program): G.f.: Sum_{n>=0} (n-2*x)^n * x^n / (1 + n*x - 2*x^2)^n.
  • A203803 (program): G.f.: exp( Sum_{n>=1} A000204(n)^3 * x^n/n ) where A000204 is the Lucas numbers.
  • A203804 (program): G.f.: exp( Sum_{n>=1} A000204(n)^4 * x^n/n ) where A000204 is the Lucas numbers.
  • A203805 (program): G.f.: exp( Sum_{n>=1} A000204(n)^5 * x^n/n ) where A000204 is the Lucas numbers.
  • A203806 (program): G.f.: exp( Sum_{n>=1} A000204(n)^6 * x^n/n ) where A000204 is the Lucas numbers.
  • A203808 (program): G.f.: exp( Sum_{n>=1} A000204(n)^8 * x^n/n ) where A000204 is the Lucas numbers.
  • A203809 (program): G.f.: exp( Sum_{n>=1} A000204(n)^9 * x^n/n ) where A000204 is the Lucas numbers.
  • A203811 (program): Denominators of s(i) = s(i-1) - (1/i)*sign(s(i-1)) with s(1) = 1.
  • A203819 (program): Number of (n+1)X2 0..3 arrays with no 2X2 subblock having equal diagonal elements or equal antidiagonal elements
  • A203820 (program): Number of (n+1)X3 0..3 arrays with no 2X2 subblock having equal diagonal elements or equal antidiagonal elements
  • A203821 (program): Number of (n+1)X4 0..3 arrays with no 2X2 subblock having equal diagonal elements or equal antidiagonal elements
  • A203829 (program): Number of (n+1) X 3 0..2 arrays with every 2 X 2 subblock having equal diagonal elements or equal antidiagonal elements.
  • A203830 (program): Number of (n+1) X 4 0..2 arrays with every 2 X 2 subblock having equal diagonal elements or equal antidiagonal elements.
  • A203838 (program): a(n) = sigma_3(n)*Fibonacci(n), where sigma_3(n) = A001158(n), the sum of cubes of divisors of n.
  • A203847 (program): a(n) = tau(n)*Fibonacci(n), where tau(n) = A000005(n), the number of divisors of n.
  • A203848 (program): a(n) = sigma(n)*Fibonacci(n), where sigma(n) = A000203(n), the sum of divisors of n.
  • A203849 (program): a(n) = sigma_2(n)*Fibonacci(n), where sigma_2(n) = A001157(n), the sum of squares of divisors of n.
  • A203850 (program): G.f.: Product_{n>=1} (1 - Lucas(n)*x^n + (-x^2)^n) / (1 + Lucas(n)*x^n + (-x^2)^n) where Lucas(n) = A000204(n).
  • A203852 (program): Expansion of e.g.f. exp( Integral -log(1-x) dx ).
  • A203860 (program): G.f.: Product_{n>=1} (1 - Lucas(n)*x^n + (-1)^n*x^(2*n)) where Lucas(n) = A000204(n).
  • A203861 (program): G.f.: Product_{n>=1} (1 - Lucas(n)*x^n + (-1)^n*x^(2*n))^3 where Lucas(n) = A000204(n).
  • A203872 (program): Number of (n+1)X3 0..3 arrays with no 2X2 subblock having equal diagonal elements or equal antidiagonal elements, and new values 0..3 introduced in row major order
  • A203873 (program): Number of (n+1)X4 0..3 arrays with no 2X2 subblock having equal diagonal elements or equal antidiagonal elements, and new values 0..3 introduced in row major order
  • A203880 (program): Number of (n+1)X2 0..6 arrays with every 2X2 subblock having equal diagonal elements or equal antidiagonal elements
  • A203881 (program): Number of (n+1) X 3 0..6 arrays with every 2 X 2 subblock having equal diagonal elements or equal antidiagonal elements.
  • A203900 (program): a(n)=f(a(n-1)+1,a(n-2),a(n-3)+1), where f(x,y,z)=yz+zx+xy and (a(1),a(2),a(3))=(0,0,1).
  • A203901 (program): a(n)=f(a(n-1)+1,a(n-2)+1,a(n-3)), where f(x,y,z)=yz+zx+xy and (a(1),a(2),a(3))=(0,0,1).
  • A203902 (program): a(n)=f(a(n-1)+1,a(n-2)+1,a(n-3)+1), where f(x,y,z)=yz+zx+xy and (a(1),a(2),a(3))=(0,0,1).
  • A203903 (program): a(n)=f(a(1),a(2),…,a(n-1)), where f=(n-2)-nd elementary symmetric function and a(1)=1, a(2)=1, a(3)=1.
  • A203905 (program): Symmetric matrix based on (1,0,1,0,1,0,1,0,…), by antidiagonals.
  • A203916 (program): Number of (n+2) X 3 0..1 arrays with every 3 X 3 subblock having equal diagonal elements or equal antidiagonal elements, and new values 0..1 introduced in row major order.
  • A203927 (program): Number of (n+1)X2 0..5 arrays with every 2X2 subblock having equal diagonal elements or equal antidiagonal elements
  • A203958 (program): Number of (n+1) X 2 0..2 arrays with column and row pair sums b(i,j)=a(i,j)+a(i,j-1) and c(i,j)=a(i,j)+a(i-1,j) such that rows of b(i,j) and columns of c(i,j) are lexicographically nondecreasing.
  • A203967 (program): The number of positive integers <= n that have a prime number of divisors.
  • A203976 (program): a(n) = 3*a(n-2) - a(n-4), a(0)=0, a(1)=1, a(2)=5, a(3)=4.
  • A203979 (program): Number of (n+1)X4 0..2 arrays with no 2X2 subblock having equal diagonal elements or equal antidiagonal elements, and new values 0..2 introduced in row major order
  • A203980 (program): Number of (n+1) X 5 0..2 arrays with no 2 X 2 subblock having equal diagonal elements or equal antidiagonal elements, and new values 0..2 introduced in row major order.
  • A203981 (program): Number of (n+1) X 6 0..2 arrays with no 2 X 2 subblock having equal diagonal elements or equal antidiagonal elements, and new values 0..2 introduced in row major order.
  • A203990 (program): Symmetric matrix based on f(i,j) = (i+j)*min(i,j), by antidiagonals.
  • A203994 (program): Symmetric matrix based on f(i,j) = (i+j)*min{i,j}, by antidiagonals.
  • A203996 (program): Symmetric matrix based on f(i,j)=min{i(j+1),j(i+1)}, by antidiagonals.
  • A203998 (program): Symmetric matrix based on f(i,j)=max{i(j+1)-1,j(i+1)-1}, by antidiagonals.
  • A204000 (program): Symmetric matrix based on f(i,j)=min{i(j+1)-1,j(i+1)-1}, by antidiagonals.
  • A204002 (program): Symmetric matrix based on f(i,j)=min{2i+j,i+2j}, by antidiagonals.
  • A204004 (program): Symmetric matrix based on f(i,j) = max{2i+j-2,i+2j-2}, by antidiagonals.
  • A204006 (program): Symmetric matrix based on f(i,j)=min{2i+j-2,i+2j-2}, by antidiagonals.
  • A204008 (program): Symmetric matrix based on f(i,j) = max{3i+j-3,i+3j-3}, by antidiagonals.
  • A204009 (program): a(n) is a binary vector for selecting distinct terms from A000124 that when summed give n; it uses the greedy algorithm.
  • A204010 (program): Expansion of f(-x^12) * phi(-x) in powers of x where f(), phi() are Ramanujan theta functions.
  • A204012 (program): Symmetric matrix based on f(i,j)=min{3i+j-3,i+3j-3}, by antidiagonals.
  • A204014 (program): Symmetric matrix based by antidiagonals, based on f(i,j)=min{1+(j mod i), 1+( i mod j)}.
  • A204016 (program): Symmetric matrix based on f(i,j) = max{j mod i, i mod j), by antidiagonals.
  • A204018 (program): Symmetric matrix based on f(i,j)=1+max{j mod i, i mod j), by antidiagonals.
  • A204021 (program): Triangle read by rows: row n shows the coefficients of the characteristic polynomial of the n-th principal submatrix of min(2i-1,2j-1) (A157454).
  • A204022 (program): Symmetric matrix based on f(i,j) = max(2i-1, 2j-1), by antidiagonals.
  • A204026 (program): Symmetric matrix based on f(i,j)=min(F(i+1),F(j+1)), where F=A000045 (Fibonacci numbers), by antidiagonals.
  • A204028 (program): Symmetric matrix based on f(i,j)=min(3i-2,3j-2), by antidiagonals.
  • A204030 (program): Symmetric matrix based on f(i,j) = gcd(i+1, j+1), by antidiagonals.
  • A204032 (program): Number of (n+1) X 2 0..1 arrays with the sums of 2 X 2 subblocks nondecreasing rightwards and downwards.
  • A204040 (program): Triangle T(n,k), read by rows, given by (0, 2, -2, 1, 0, 0, 0, 0, 0, 0, 0, …) DELTA (1, 0, 0, 0, 0, 0, 0, 0, …) where DELTA is the operator defined in A084938.
  • A204042 (program): The number of functions f:{1,2,…,n}->{1,2,…,n} (endofunctions) such that all of the fixed points in f are isolated.
  • A204057 (program): Triangle derived from an array of f(x), Narayana polynomials.
  • A204060 (program): G.f.: Sum_{n>=1} Fibonacci(n^2)*x^(n^2).
  • A204061 (program): G.f.: exp( Sum_{n>=1} A001333(n)^2 * x^n/n ) where A001333(n) = A002203(n)/2, one-half the companion Pell numbers.
  • A204062 (program): Expansion of g.f.: exp( Sum_{n>=1} A002203(n)^2 * x^n/n ) where A002203 are the companion Pell numbers.
  • A204064 (program): G.f.: Sum_{n>=0} x^n * Product_{k=1..n} (k + n*x) / (1 + k*x + n*x^2).
  • A204070 (program): Number of (n+1) X 3 0..2 arrays with every 2 X 2 subblock having equal diagonal elements or equal antidiagonal elements, and new values 0..2 introduced in row major order.
  • A204071 (program): Number of (n+1) X 4 0..2 arrays with every 2 X 2 subblock having equal diagonal elements or equal antidiagonal elements, and new values 0..2 introduced in row major order.
  • A204078 (program): Number of nX2 0..3 arrays with every element neighboring horizontally or vertically both a 0 and a 1.
  • A204089 (program): The number of 1 by n Haunted Mirror Maze puzzles with a unique solution ending with a mirror, where mirror orientation is fixed.
  • A204090 (program): The number of 1 X n Haunted Mirror Maze puzzles with a unique solution where mirror orientation is fixed.
  • A204091 (program): The number of 1 X n Haunted Mirror Maze puzzles with a unique solution ending with a mirror.
  • A204092 (program): The number of 1 by n Haunted Mirror Maze puzzles with a unique solution.
  • A204093 (program): Numbers whose set of base-10 digits is {0,6}.
  • A204094 (program): Numbers whose set of base 10 digits is {0,7}.
  • A204095 (program): Numbers whose base 10 digits are a subset of {0, 8}.
  • A204099 (program): Number of integers between successive twin prime pairs.
  • A204100 (program): Number of integers between successive twin primes, divided by 3.
  • A204102 (program): Number of (n+1) X 5 0..2 arrays with column and row pair sums b(i,j)=a(i,j)+a(i,j-1) and c(i,j)=a(i,j)+a(i-1,j) such that b(i,j)*b(i-1,j)-c(i,j)*c(i,j-1) is nonzero.
  • A204103 (program): Number of (n+1) X 6 0..2 arrays with column and row pair sums b(i,j)=a(i,j)+a(i,j-1) and c(i,j)=a(i,j)+a(i-1,j) such that b(i,j)*b(i-1,j)-c(i,j)*c(i,j-1) is nonzero.
  • A204112 (program): Symmetric matrix based on f(i,j) = gcd(F(i+1), F(j+1)), where F=A000045 (Fibonacci numbers), by antidiagonals.
  • A204114 (program): Symmetric matrix based on f(i,j) = gcd(L(i), L(j)), where L=A000032 (Lucas numbers), by antidiagonals.
  • A204116 (program): Symmetric matrix based on f(i,j) = gcd(2^i-1, 2^j-1), by antidiagonals.
  • A204118 (program): Symmetric matrix based on f(i,j) = gcd(prime(i), prime(j)), by antidiagonals.
  • A204120 (program): Symmetric matrix based on f(i,j) = gcd(prime(i+1),prime(j+1)), by antidiagonals.
  • A204123 (program): Symmetric matrix based on f(i,j)=max([i/j],[j/i]), where [ ]=floor, by antidiagonals.
  • A204125 (program): Symmetric matrix based on f(i,j)=(i if i=j and 1 otherwise), by antidiagonals.
  • A204127 (program): Symmetric matrix based on f(i,j)=(F(i+1) if i=j and 1 otherwise), where F=A000045 (Fibonacci numbers), by antidiagonals.
  • A204129 (program): Symmetric matrix based on f(i,j)=(L(i) if i=j and 1 otherwise), where L=A000032 (Lucas numbers), by antidiagonals.
  • A204131 (program): Symmetric matrix based on f(i,j)=(2i-1 if i=j and 1 otherwise), by antidiagonals.
  • A204133 (program): Symmetric matrix based on f(i,j)=(2^(i-1) if i=j and 1 otherwise), by antidiagonals.
  • A204136 (program): Number of composites between successive twin prime pairs.
  • A204143 (program): Symmetric matrix based on f(i,j)=max(ceiling(i/j),ceiling(j/i)), by antidiagonals.
  • A204146 (program): Number of (n+2) X 3 0..2 arrays with every 3 X 3 subblock having equal diagonal elements or equal antidiagonal elements, and new values 0..2 introduced in row major order.
  • A204154 (program): Symmetric matrix based on f(i,j) = max(2i-j, 2j-i), by antidiagonals.
  • A204156 (program): Symmetric matrix based on f(i,j)=max(3i-j, 3j-i), by antidiagonals.
  • A204158 (program): Symmetric matrix based on f(i,j)=max(3i-2j, 3j-2i), by antidiagonals.
  • A204160 (program): Symmetric matrix based on f(i,j)=(3i-2 if i=j and = 0 otherwise), by antidiagonals.
  • A204162 (program): Symmetric matrix based on f(i,j) = (floor((i+1)/2) if i=j and = 1 otherwise), by antidiagonals.
  • A204164 (program): Symmetric matrix based on f(i,j)=floor[(i+j)/2], by antidiagonals.
  • A204166 (program): Symmetric matrix based on f(i,j)=ceiling[(i+j)/2], by antidiagonals.
  • A204171 (program): Symmetric matrix based on f(i,j)=(1 if max(i,j) is odd, and 0 otherwise), by antidiagonals.
  • A204173 (program): Symmetric matrix based on f(i,j)=(2i-1 if max(i,j) is odd, and 0 otherwise), by antidiagonals.
  • A204175 (program): Symmetric matrix based on f(i,j)=(1 if max(i,j) is even, and 0 otherwise), by antidiagonals.
  • A204177 (program): Symmetric matrix based on f(i,j)=(1 if i=1 or j=1 or i=j, and 0 otherwise), by antidiagonals.
  • A204178 (program): Array: row n shows the coefficients of the characteristic polynomial of the n-th principal submatrix of (f(i,j)), where f(i,j)=(1 if i=1 or j=1 or i=j, and 0 otherwise) as in A204177.
  • A204179 (program): Symmetric matrix based on f(i,j) defined by f(i,1)=f(1,j)=1; f(i,i)= i; f(i,j)=0 otherwise; by antidiagonals.
  • A204181 (program): Symmetric matrix based on f(i,j) defined by f(i,1)=f(1,j)=1; f(i,i)= 2i-1; f(i,j)=0 otherwise; by antidiagonals.
  • A204183 (program): Symmetric matrix based on f(i,j) defined by f(i,1)=f(1,j)=1; f(i,i)= (-1)^(i-1); f(i,j)=0 otherwise; by antidiagonals.
  • A204185 (program): Number of quadrilaterals in a triangular matchstick arrangement of side n.
  • A204187 (program): a(n) = Sum_{m=1..n-1} m^(n-1) modulo n.
  • A204188 (program): Decimal expansion of sqrt(5)/4.
  • A204189 (program): Benoît Perichon’s 26 primes in arithmetic progression.
  • A204200 (program): INVERT transform of [1, 0, 1, 3, 9, 27, 81, …].
  • A204201 (program): Triangle based on (0,1/3,1) averaging array.
  • A204202 (program): Triangle based on (0,2/3,1) averaging array.
  • A204203 (program): Triangle based on (0,1/4,1) averaging array.
  • A204204 (program): Triangle based on (0,3/4,1) averaging array.
  • A204205 (program): Triangle based on (0,1/5,1) averaging array.
  • A204206 (program): Triangle based on (1,3/2,2) averaging array.
  • A204207 (program): Triangle based on (1,2,3) averaging array.
  • A204214 (program): Number of length 6 nonnegative integer arrays starting and ending with 0 with adjacent elements differing by no more than n.
  • A204217 (program): G.f.: Sum_{n>=1} n * x^(n*(n+1)/2) / (1 - x^n).
  • A204221 (program): Integers of the form (n^2 - 1) / 15.
  • A204223 (program): Number of (n+1)X2 0..2 arrays with the sums of 2X2 subblocks nondecreasing rightwards and downwards
  • A204232 (program): Numbers whose binary reversal is prime.
  • A204237 (program): Symmetric matrix given by f(i,j)=max(3i-j,3j-i).
  • A204238 (program): Determinant of the n-th principal submatrix of A204237.
  • A204240 (program): Determinant of the n-th principal submatrix of A204158.
  • A204242 (program): Infinite symmetric matrix given by f(i,1)=1, f(1,j)=1, f(i,i)=2^i-1 and f(i,j)=0 otherwise, read by antidiagonals.
  • A204243 (program): Determinant of the n-th principal submatrix of A204242.
  • A204244 (program): Symmetric matrix given by f(i,1)=1, f(1,j)=1, f(i,i)=i! and f(i,j)=0 otherwise.
  • A204245 (program): Determinant of the n-th principal submatrix of A204244.
  • A204246 (program): Array given by f(i,1)=1, f(1,j)=1, f(i,i)=(i-1)!, and f(i,j)=0 otherwise, read by antidiagonals.
  • A204247 (program): Determinant of the n-th principal submatrix of A204246.
  • A204250 (program): Symmetric matrix read by antidiagonals given by T(i,j)=i*j+i+j-2.
  • A204253 (program): Symmetric matrix given by f(i,j)=1+[(i+j) mod 3].
  • A204255 (program): Symmetric matrix given by f(i,j)=1+[(i+j) mod 4].
  • A204257 (program): Matrix given by f(i,j)=1+[(i+2j) mod 3], by antidiagonals.
  • A204259 (program): Matrix given by f(i,j) = 1 + [(2i+j) mod 3], by antidiagonals.
  • A204260 (program): Symmetric matrix given by f(i,j)=ceiling(i*j/(i+j)) .
  • A204263 (program): Symmetric matrix: f(i,j)=(i+j mod 3), by antidiagonals.
  • A204267 (program): Symmetric matrix: f(i,j)=(i+j+1 mod 3), by antidiagonals.
  • A204269 (program): Symmetric matrix: f(i,j)=floor[(i+j+2)/4]-floor[(i+j)/4], by (constant) antidiagonals.
  • A204270 (program): a(n) = tau(n)*Pell(n), where tau(n) = A000005(n), the number of divisors of n.
  • A204271 (program): a(n) = sigma(n)*Pell(n), where sigma(n) = A000203(n), the sum of divisors of n.
  • A204272 (program): a(n) = sigma_2(n)*Pell(n), where sigma_2(n) = A001157(n), the sum of squares of divisors of n.
  • A204273 (program): a(n) = sigma_3(n)*Pell(n), where sigma_3(n) = A001158(n), the sum of cubes of divisors of n.
  • A204274 (program): G.f.: Sum_{n>=1} Pell(n^2)*x^(n^2).
  • A204292 (program): Binomial(n, d(n)), where d(n) = A000005(n) is the number of divisors of n.
  • A204293 (program): Pascal’s triangle interspersed with rows of zeros, and the rows of Pascal’s triangle are interspersed with zeros.
  • A204327 (program): a(n) = Pell(n^2).
  • A204330 (program): a(n) is the number of k satisfying 1 <= k <= n and such that floor(sqrt(k)) divides k.
  • A204342 (program): a(n) = (-1)^n * Sum_{2*m + 1 | 2*n + 1} (-1)^m (2*m + 1)^4.
  • A204372 (program): Expansion of phi(x)^2 * (5 * phi(-x)^8 + 64 * x * psi(-x)^8) in powers of x where phi(), psi() are Ramanujan theta functions.
  • A204386 (program): Expansion of (theta_2(q)^8 + 4 * theta_2(q^2)^8) / 256 in powers of q^2.
  • A204391 (program): Number of (n+2) X 3 0..1 arrays with no 3 X 3 subblock having three equal diagonal elements or three equal antidiagonal elements, and new values 0..1 introduced in row major order.
  • A204399 (program): Numbers k such that floor(2^k / 3^n) = 1.
  • A204418 (program): Periodic sequence 1,0,1,…, arranged in a triangle.
  • A204421 (program): Symmetric matrix: f(i,j)=(i+j+2 mod 3), by antidiagonals.
  • A204423 (program): Infinite matrix: f(i,j)=(2i+j mod 3), by antidiagonals.
  • A204425 (program): Infinite matrix: f(i,j)=(2i+j+1 mod 3), by antidiagonals.
  • A204427 (program): Infinite matrix: f(i,j)=(2i+j+2 mod 3), read by antidiagonals.
  • A204429 (program): Symmetric matrix: f(i,j)=(2*i + 2*j) mod 3, by antidiagonals.
  • A204431 (program): Symmetric matrix: f(i,j)=(2i+j+1 mod 3), by antidiagonals.
  • A204433 (program): Symmetric matrix: f(i,j) = (2*i + 2*j + 2) mod 3, by antidiagonals.
  • A204435 (program): Symmetric matrix: f(i,j)=((i+j)^2 mod 3), read by (constant) antidiagonals.
  • A204437 (program): Symmetric matrix: f(i,j)=((i+j+1)^2 mod 3), by (constant) antidiagonals.
  • A204439 (program): Symmetric matrix: f(i,j)=((i+j+2)^2 mod 3), by (constant) antidiagonals.
  • A204441 (program): Symmetric matrix: f(i,j)=floor[(i+j+2)/4]-floor[(i+j-1)/4], by (constant) antidiagonals.
  • A204443 (program): Symmetric matrix: f(i,j)=floor[(i+j+3)/4]-floor[(i+j)/4], by (constant) antidiagonals.
  • A204445 (program): Symmetric matrix: f(i,j)=floor[(i+j+4)/4]-floor[(i+j+1)/4], by (constant) antidiagonals.
  • A204447 (program): Symmetric matrix: f(i,j)=floor[(i+j+5)/4]-floor[(i+j+2)/4], by (constant) antidiagonals.
  • A204453 (program): Period length 14: [0, 1, 2, 3, 4, 5, 6, 0, 6, 5, 4, 3, 2, 1] repeated.
  • A204454 (program): Odd numbers not divisible by 11.
  • A204455 (program): Squarefree product of all odd primes dividing n, and 1 if n is a power of 2: A099985/2.
  • A204457 (program): Odd numbers not divisible by 13.
  • A204458 (program): Odd numbers not divisible by 17.
  • A204467 (program): Number of 3-element subsets that can be chosen from {1,2,…,6*n+3} having element sum 9*n+6.
  • A204468 (program): Number of 4-element subsets that can be chosen from {1,2,…,4*n} having element sum 8*n+2.
  • A204502 (program): Numbers such that floor[a(n)^2 / 9] is a square.
  • A204503 (program): Squares n^2 such that floor(n^2/9) is again a square.
  • A204504 (program): A204512(n)^2 = floor[A055872(n)/8]: Squares such that appending some digit in base 8 yields another square.
  • A204512 (program): Square roots of [A055872/8]: Their square written in base 8, with some digit appended, is again a square.
  • A204514 (program): Numbers such that floor(a(n)^2 / 8) is again a square.
  • A204515 (program): a(n) = (2*n)! * (2*n+1)! / ((n+1)^2 * n!^3).
  • A204520 (program): Numbers such that floor(a(n)^2 / 5) is a square.
  • A204521 (program): Square root of floor(A055812(n) / 5).
  • A204532 (program): Largest prime factors of zerofull restricted pandigital numbers A050278.
  • A204533 (program): Triangle T(n,k), read by rows, given by (0, 1, 2, -1/2, 1/2, 0, 0, 0, 0, 0, 0, 0, …) DELTA (1, 0, 0, 0, 0, 0, 0, 0, 0, 0, …) where DELTA is the operator defined in A084938.
  • A204539 (program): a(n) is the number of integers N=4k whose “basin” sequence (cf. comment) ends in n^2.
  • A204542 (program): Numbers that are congruent to {1, 4, 11, 14} mod 15.
  • A204544 (program): Fractional part of (3/2)^n without the decimal point.
  • A204545 (program): Symmetric matrix: f(i,j)=floor[(i+j+3)/4]-floor[(i+j+1)/4], by (constant) antidiagonals.
  • A204547 (program): Symmetric matrix: f(i,j)=floor[(i+j+4)/4]-floor[(i+j+2)/4], by (constant) antidiagonals.
  • A204549 (program): Symmetric matrix: f(i,j)=floor[(i+j+5)/4]-floor[(i+j+3)/4], by (constant) antidiagonals.
  • A204551 (program): Symmetric matrix: f(i,j)=floor[(2i+2j+1)/4]-floor[(i+j)/4], by (constant) antidiagonals.
  • A204553 (program): Symmetric matrix: f(i,j)=floor[(2i+2j+2)/4]-floor[(i+j+1)/4], by (constant) antidiagonals.
  • A204555 (program): The number of subsets of the numbers {1,2,3…,n} consisting of at most 3 elements and at most two of those are even.
  • A204556 (program): Left edge of the triangle A045975.
  • A204557 (program): Right edge of the triangle A045975.
  • A204558 (program): Row sums of the triangle A045975.
  • A204560 (program): Symmetric matrix: f(i,j)=floor[(2i+2j+4)/4]-floor[(i+j+2)/4], by (constant) antidiagonals.
  • A204562 (program): Symmetric matrix: f(i,j) = floor((2i+2j+6)/4)-floor((i+j+3)/4), by (constant) antidiagonals.
  • A204565 (program): Number of (n+1) X 2 0..3 arrays with every 2 X 2 subblock having equal diagonal elements or equal antidiagonal elements, and new values 0..3 introduced in row major order.
  • A204574 (program): Numbers such that floor[a(n)^2/2] is a square (A001541), written in binary.
  • A204575 (program): Squares such that [a(n)/2] is again a square (A055792), written in binary.
  • A204576 (program): Floor[A055792(n-1)/2]=A084703(n-2) (truncated squares), written in binary.
  • A204577 (program): Sqrt(floor[A204575(n)/2]), written in binary.
  • A204590 (program): Nearest integer to 100*1.1^n.
  • A204591 (program): Nearest integer to 1.1^n.
  • A204595 (program): a(n) = maximal i such that there is a quasigroup q of order n such that q, q^2, …, q^i are quasigroups of order n.
  • A204597 (program): Number of connected non-isomorphic well-covered circulant graphs on n nodes (including the complete graph).
  • A204609 (program): Number of (n+1) X 2 0..1 arrays with the determinants of 2 X 2 subblocks nondecreasing rightwards and downwards.
  • A204617 (program): Multiplicative with a(p^e) = p^(e-1)*H(p). H(2)=1, H(p) = p-1 if p=1 (mod 4) and H(p) = p+1 if p=3 (mod 4).
  • A204618 (program): a(n) = n^2 * B(n) where B(n) are the Bell numbers, A000110.
  • A204621 (program): Triangle read by rows: coordinator triangle for lattice A*_n.
  • A204623 (program): Number of (n+1)X2 0..2 arrays with every 2X2 subblock having unequal diagonal elements or unequal antidiagonal elements, and new values 0..2 introduced in row major order
  • A204624 (program): Number of (n+1) X 3 0..2 arrays with every 2 X 2 subblock having unequal diagonal elements or unequal antidiagonal elements, and new values 0..2 introduced in row major order.
  • A204631 (program): Expansion of 1/(1 - x - x^2 + x^5 - x^7).
  • A204644 (program): Number of (n+1) X 2 0..1 arrays with column and row pair sums b(i,j)=a(i,j)+a(i,j-1) and c(i,j)=a(i,j)+a(i-1,j) nondecreasing in column and row directions, respectively.
  • A204645 (program): Number of (n+1) X 3 0..1 arrays with column and row pair sums b(i,j)=a(i,j)+a(i,j-1) and c(i,j)=a(i,j)+a(i-1,j) nondecreasing in column and row directions, respectively.
  • A204665 (program): Primes p such that q-p = 52, where q is the next prime after p.
  • A204671 (program): a(n) = n^n (mod 6).
  • A204674 (program): a(n) = 4*n^3 + 5*n^2 + 2*n + 1.
  • A204675 (program): a(n) = 16*n^2 + 2*n + 1.
  • A204678 (program): Number of n X 1 0..3 arrays with no occurrence of three equal elements in a row horizontally, vertically, diagonally or antidiagonally, and new values 0..3 introduced in row major order.
  • A204688 (program): a(n) = n^n (mod 3).
  • A204689 (program): a(n) = n^n (mod 4).
  • A204690 (program): n^n (mod 5).
  • A204693 (program): a(n) = n^n (mod 7).
  • A204694 (program): a(n) = n^n (mod 8).
  • A204695 (program): a(n) = n^n (mod 9).
  • A204696 (program): G.f.: (32*x^7/(1-2*x) + 16*x^5 + 24*x^6)/(1-2*x^2).
  • A204697 (program): Final nonzero digit of n^n in base 3.
  • A204699 (program): Number of n X 2 0..2 arrays with no occurrence of three equal elements in a row horizontally, vertically or nw-to-se diagonally, and new values 0..2 introduced in row major order.
  • A204707 (program): Number of (n+1) X 3 0..1 arrays with the permanents of all 2 X 2 subblocks equal and nonzero.
  • A204708 (program): Number of (n+1) X 4 0..1 arrays with the permanents of all 2 X 2 subblocks equal and nonzero.
  • A204716 (program): Number of (n+1) X 2 0..1 arrays with the permanents of 2 X 2 subblocks nondecreasing rightwards and downwards.
  • A204734 (program): Number of (n+1)X3 0..1 arrays with rows and columns of permanents of all 2X2 subblocks lexicographically nondecreasing, and all 2X2 permanents nonzero
  • A204746 (program): Number of (n+2)X(n+2) 0..1 arrays with every 3X3 subblock having three equal elements in a row horizontally, vertically, diagonally or antidiagonally exactly three ways, and new values 0..1 introduced in row major order
  • A204750 (program): Number of (n+2) X 6 0..1 arrays with every 3 X 3 subblock having three equal elements in a row horizontally, vertically, diagonally or antidiagonally exactly three ways, and new values 0..1 introduced in row major order.
  • A204766 (program): a(n) = 167*(n-1)-a(n-1) with n>1, a(1)=13.
  • A204768 (program): 7^p - 6^p - 1, with p = prime(n).
  • A204769 (program): a(n) = 151*(n-1) - a(n-1) with n>1, a(1)=46.
  • A204770 (program): Expansion of psi(x^3) * f(-x) in powers of x where psi(), f() are Ramanujan theta functions.
  • A204809 (program): Number of skew-symmetric n X n matrices A = (a_ij) with entries from {-1,0,+1} such that a_wx a_yz + a_wy a_xz + a_wz a_xy = a_wx a_wy a_wz a_xy a_xz a_yz for all distinct w,x,y,z in {1..n}.
  • A204815 (program): Final nonzero digit of n^n in base 5.
  • A204816 (program): Final nonzero digit of n^n in base 6.
  • A204817 (program): Final nonzero digit of n^n in base 7.
  • A204818 (program): Final nonzero digit of n^n in base 8.
  • A204819 (program): Final nonzero digit of n^n in base 9.
  • A204820 (program): a(n) = -4*a(n-1)*A001505(n-2), with a(1)=8.
  • A204822 (program): Sum of divisors (A000203) of abundant numbers (A005101).
  • A204823 (program): Sum of divisors (A000203) of deficient numbers (A005100).
  • A204825 (program): Abundant numbers with even sum of divisors.
  • A204827 (program): Deficient numbers with even sum of divisors.
  • A204829 (program): Numbers with abundancy 2 <= a < 3.
  • A204841 (program): (2n)! - 2^n*n!.
  • A204842 (program): Triangle by rows relating to A081696
  • A204847 (program): Primitive cofactor of n-th repunit A002275(n).
  • A204848 (program): Algebraic cofactor of n-th repunit A002275(n).
  • A204849 (program): A Motzkin triangle by rows.
  • A204850 (program): Expansion of f(x)^3 - 9 * x * f(x^9)^3 in powers of x where f() is a Ramanujan theta function.
  • A204851 (program): Triangle by rows relating to A005773
  • A204854 (program): G.f.: Sum_{n>=0} x^n * Product_{k=1..n} (1 - x^k) / (1 + x^k).
  • A204877 (program): Continued fraction expansion of 3*tanh(1/3).
  • A204878 (program): Numbers that cannot be written as sum of perfect numbers.
  • A204879 (program): Numbers that can be written as sum of perfect numbers.
  • A204890 (program): Ordered differences of primes.
  • A204893 (program): The index j<k such that n divides s(k)-s(j), where k is the least index (A204892) for which such j exists, and s(k)=prime(k).
  • A204895 (program): The prime q such that n divides p-q, where p>q is the least prime for which such a prime q exists.
  • A204896 (program): p(n)-q(n), where (p(n), q(n)) is the least pair of primes (ordered as in A204890) for which n divides p(n)-q(n).
  • A204897 (program): a(n) = (p(n)-q(n))/n, where (p(n), q(n)) is the least pair of primes for which n divides p(n)-q(n).
  • A204898 (program): Ordered differences of odd primes.
  • A204904 (program): p(n)-q(n), where (p(n), q(n)) is the least pair of odd primes for which n divides p(n)-q(n).
  • A204906 (program): Ordered differences of primes >=5.
  • A204912 (program): Ordered differences of double factorials.
  • A204914 (program): Ordered differences of squared primes.
  • A204922 (program): Ordered differences of Fibonacci numbers.
  • A204930 (program): Ordered differences of factorials.
  • A204979 (program): Least k such that n divides 2^(k-1)-2^(j-1) for some j satisfying 1<=j<k.
  • A204980 (program): Ordered differences of distinct averages of two consecutive odd primes.
  • A204981 (program): Least 2^(k-1) such that n divides 2^(k-1)-2^(j-1) for some j<k.
  • A204983 (program): 2^(k-1)-2^(j-1), where (2^(k-1),2^(j-1)) is the least pair of distinct positive powers of 2 for which n divides 2^(k-1)-2^(j-1).
  • A204984 (program): (1/n)*A204983(n).
  • A204985 (program): Ordered differences of numbers 2^k for k>=1.
  • A204987 (program): Least k such that n divides 2^k - 2^j for some j satisfying 1 <= j < k.
  • A204988 (program): The index j < k such that n divides 2^k - 2^j, where k is the least index (A204987) for which such j exists.
  • A204989 (program): Least 2^k such that n divides 2^k-2^j for some j<k.
  • A204990 (program): (1/2)*(A204991).
  • A204991 (program): 2^k-2^j, where (2^k,2^j) is the least pair of distinct positive powers of 2 for which n divides 2^k-2^j.
  • A204992 (program): (1/n)*A204991(n).
  • A204993 (program): Negative of the discriminant of quadratic field Q(sqrt(-n)).
  • A205002 (program): Least k such that n divides s(k)-s(j) for some j satisfying 1<=j<k, where s(j)=j(j+1)/2.
  • A205003 (program): The index j<k such that n divides s(k)-s(j), where k is the least index (A205002) for which such j exists, and s(k)=k(k+1)/2.
  • A205004 (program): Least k(k+1)/2 such that n divides k(k+1)/2-j(j+1)/2 for some j<k.
  • A205005 (program): The triangular number T(j) such that n divides T(k)-T(j)>0, where k is the least positive integer for which such a j exists.
  • A205006 (program): a(n) = s(k)-s(j), where (s(k),s(j)) is the least pair of distinct triangular numbers for which n divides their difference.
  • A205007 (program): a(n) = (1/n)*A205006(n), where A205006(n) = s(k)-s(j), with (s(k),s(j)) the least pair of distinct triangular numbers for which n divides their difference.
  • A205008 (program): Ordered differences of central binomial coefficients.
  • A205016 (program): Ordered differences of oblong numbers.
  • A205018 (program): Least k such that n divides s(k)-s(j) for some j satisfying 1<=j<k, where s(j)=j*(j+1).
  • A205028 (program): The index j<k such that n divides s(k)-s(j), where k is the least index (A205018) for which such j exists, and s(k)=k*(k+1).
  • A205029 (program): Least s(k) such that n divides s(k)-s(j) for some j<k, where s(j)=j*(j+1).
  • A205030 (program): The number s(j)=j*(j+1) such that n divides s(k)-s(j)>0, where k is the least positive integer for which such a j exists.
  • A205031 (program): s(k)-s(j), where (s(k),s(j)) is the least pair of oblong numbers for which n divides their difference.
  • A205032 (program): a(n) = (s(k)-s(j))/n, where (s(k),s(j)) is the least pair of oblong numbers (A002378) for which n divides their difference; a(n) = (1/n)*A205031(n).
  • A205083 (program): Parity of A070885.
  • A205084 (program): a(n)=n 4’s sandwiched between two 1’s.
  • A205085 (program): a(n) = n 5’s sandwiched between two 1’s.
  • A205086 (program): a(n) = n 6’s sandwiched between two 1’s.
  • A205087 (program): a(n)=n 7’s sandwiched between two 1’s.
  • A205088 (program): a(n)=n 8’s sandwiched between two 1’s.
  • A205098 (program): Sum of proper divisors (A001065) of abundant numbers (A005101).
  • A205099 (program): Sum of proper divisors (A001065) of deficient numbers (A005100).
  • A205105 (program): Ordered differences of numbers 3^j-2^j, as in A001047.
  • A205112 (program): Ordered differences of Lucas numbers.
  • A205120 (program): Ordered differences of distinct numbers k*(2^(k-1)).
  • A205128 (program): Ordered differences of distinct hexagonal numbers.
  • A205136 (program): Ordered differences of distinct pentagonal numbers.
  • A205144 (program): Ordered differences of distinct binary products of consecutive primes.
  • A205163 (program): Number of (n+1) X 2 0..3 arrays with every 2 X 2 subblock having unequal diagonal elements or unequal antidiagonal elements, and new values 0..3 introduced in row major order.
  • A205171 (program): The lesser of twin primes == 1 (mod 8).
  • A205172 (program): Primes p == 5 (mod 8) such that p + 2 is also prime.
  • A205184 (program): Period 12: repeat (1, 8, 4, 9, 7, 8, 7, 9, 4, 8, 1, 9).
  • A205185 (program): Period 6: repeat [1, 8, 9, 8, 1, 0].
  • A205186 (program): Number of (n+1) X (n+1) 0..1 arrays with the number of clockwise edge increases in every 2 X 2 subblock differing from each horizontal or vertical neighbor.
  • A205187 (program): Number of (n+1)X2 0..1 arrays with the number of clockwise edge increases in every 2X2 subblock differing from each horizontal or vertical neighbor
  • A205189 (program): Number of (n+1) X 5 0..1 arrays with the number of clockwise edge increases in every 2 X 2 subblock differing from each horizontal or vertical neighbor.
  • A205219 (program): Number of (n+1)X2 0..1 arrays with the number of equal 2X2 subblock diagonal pairs and equal antidiagonal pairs differing from each horizontal or vertical neighbor, and new values 0..1 introduced in row major order
  • A205220 (program): Number of (n+1) X 3 0..1 arrays with the number of equal 2 X 2 subblock diagonal pairs and equal antidiagonal pairs differing from each horizontal or vertical neighbor, and new values 0..1 introduced in row major order.
  • A205248 (program): Number of (n+1) X 2 0..1 arrays with the number of clockwise edge increases in every 2 X 2 subblock the same.
  • A205249 (program): Number of (n+1) X 3 0..1 arrays with the number of clockwise edge increases in every 2 X 2 subblock the same.
  • A205250 (program): Number of (n+1) X 4 0..1 arrays with the number of clockwise edge increases in every 2 X 2 subblock the same.
  • A205295 (program): Number of connected 5-regular simple graphs on 2n vertices with girth at least 5.
  • A205312 (program): Number of (n+1) X 3 0..1 arrays with every 2 X 2 subblock having the same number of equal edges, and new values 0..1 introduced in row major order.
  • A205313 (program): Number of (n+1) X 4 0..1 arrays with every 2 X 2 subblock having the same number of equal edges, and new values 0..1 introduced in row major order.
  • A205328 (program): Number of (n+1) X 2 0..2 arrays with the number of equal 2 X 2 subblock diagonal pairs and equal antidiagonal pairs differing from each horizontal or vertical neighbor, and new values 0..2 introduced in row major order.
  • A205329 (program): Number of (n+1) X 3 0..2 arrays with the number of equal 2 X 2 subblock diagonal pairs and equal antidiagonal pairs differing from each horizontal or vertical neighbor, and new values 0..2 introduced in row major order.
  • A205342 (program): Number of length 5 nonnegative integer arrays starting and ending with 0 with adjacent elements unequal but differing by no more than n.
  • A205343 (program): Number of length 6 nonnegative integer arrays starting and ending with 0 with adjacent elements unequal but differing by no more than n.
  • A205354 (program): Number of (n+1) X 2 0..2 arrays with every 2 X 2 subblock having the same number of equal diagonal or antidiagonal elements, and new values 0..2 introduced in row major order.
  • A205371 (program): Ordered differences of odd-indexed Fibonacci numbers.
  • A205376 (program): Ordered differences of distinct odd squares, stored in triangle.
  • A205378 (program): Least k such that n divides s(k)-s(j) for some j<k, where s(j)=(2j-1)^2.
  • A205379 (program): The index j<k such that n divides s(k)-s(j) for some j, where s(j)=(2j-1)^2.
  • A205380 (program): Least s(k) such that n divides s(k)-s(j) for some j<k, where s(j)=(2j-1)^2.
  • A205381 (program): s(A205379), where s(j)=(2j-1)^2.
  • A205382 (program): s(k)-s(j), where (s(k),s(j)) is the least such pair for which n divides their difference, and s(j)=(2j-1)^2.
  • A205383 (program): a(n) = (1/n)*A205382(n).
  • A205384 (program): Ordered differences of numbers s(j)=(1/2)C(2j,j)).
  • A205392 (program): Ordered differences of numbers s(j)=ceiling(j^2/2).
  • A205400 (program): Ordered differences of quarter-squares.
  • A205448 (program): Ordered differences of even-indexed Fibonacci numbers.
  • A205456 (program): Symmetric matrix by antidiagonals: C(max(i,j),min(i,j)), i>=1, j>=1.
  • A205457 (program): Symmetric matrix, by antidiagonals: C(max(2i,2j),min(2i,2j)), i>=0, j>=0.
  • A205505 (program): Fibonacci(n*(n+1)) / Fibonacci(n).
  • A205507 (program): a(n) = Fibonacci(n) * A004018(n) for n>=1 with a(0)=1, where A004018(n) is the number of ways of writing n as a sum of 2 squares.
  • A205508 (program): a(n) = Pell(n) * A004018(n) for n>=1 with a(0)=1, where A004018(n) is the number of ways of writing n as a sum of 2 squares.
  • A205510 (program): Binary Hamming distance between prime(n) and prime(n+1).
  • A205523 (program): Numbers n such that gcd(n, sigma(n)) = sigma(n) (mod n).
  • A205524 (program): Numbers n such that gcd(n, sigma(n)) is not equal to sigma(n) mod n.
  • A205534 (program): Record values of A205531 and A205535.
  • A205543 (program): Logarithmic derivative of the Bell numbers (A000110).
  • A205545 (program): Symmetric matrix by antidiagonals: C(max(3i,3j),min(3i,3j)), i>=0, j>=0.
  • A205548 (program): Symmetric matrix by antidiagonals: C(max(i+1,j+1),min(i+1,j+1)), i>=1, j>=1.
  • A205549 (program): Symmetric matrix by antidiagonals: C(max(i+2,j+2),min(i+2,j+2)), i>=1, j>=1.
  • A205550 (program): Symmetric matrix by antidiagonals: C(max(g(i),g(j)),min(g(i),g(j)), where g(k)=2k-1.
  • A205552 (program): Square array: C(max(2i-2,j-1),min(2i-2,j-1)), i>=1, j>=1; by antidiagonals.
  • A205553 (program): Square array by antidiagonals: C(max(i-1,2j-2),min(i-1,2j-2)), i>=1, j>=1.
  • A205556 (program): Positions of multiples of 2 in A204922 (differences of Fibonacci numbers).
  • A205558 (program): (A204898)/2 = (prime(k)-prime(j))/2; A086802 without its zeros.
  • A205565 (program): Number of ways of writing n = u + v with u <= v, and u,v having in ternary representation no 3.
  • A205568 (program): Number of 9-chromatic (i.e., chromatic number equals 9) simple graphs on n nodes.
  • A205571 (program): E.g.f.: 1/(1 - x*cosh(x)).
  • A205579 (program): a(n) = round(r^n) where r is the smallest Pisot number (real root r=1.3247179.. of x^3-x-1).
  • A205591 (program): a(1) = 1, a(n) = a(floor((2n-1)/3)) + a(floor(2n/3)) for n > 1.
  • A205592 (program): a(2) = 1, a(3k) = a(3k+1) = a(2k), a(3k+2) = 2a(2k+1) for k >= 1.
  • A205593 (program): a(2) = 0, a(3k) = a(3k+1) = a(2k), a(3k+2) = a(2k+1) + 1 for k >= 1.
  • A205633 (program): Expansion of f(x^3, x^7) in powers of x where f() is Ramanujan’s two-variable theta function.
  • A205646 (program): Number of empty faces in Freij’s family of Hansen polytopes.
  • A205649 (program): Hamming distance between twin primes.
  • A205650 (program): Period 12: repeat (1, 6, 8, 6, 1, 9, 8, 3, 1, 3, 8, 9).
  • A205651 (program): Period 6: repeat [1, 6, 5, 4, 9, 0].
  • A205676 (program): Positions of multiples of 4 in A204890 (differences of primes).
  • A205677 (program): Numbers k for which 4 divides prime(k)-prime(j) for some j<k; each k occurs once for each such j.
  • A205678 (program): The number j such that 4 divides prime(k)-prime(j), where k(n)=A205677(n).
  • A205679 (program): Prime(A205677(n)), the n-th number s(k) such that 4 divides s(k)-s(j) for some j<k, where s(j)=prime(j).
  • A205680 (program): Prime(A205678(n)), the n-th number s(j) such that 4 divides s(k)-s(j), where the pairs (k,j) are given by A205677 and A205678.
  • A205681 (program): Prime(k)-prime(j), where the pairs (k,j) are given by A205677 and A205678.
  • A205682 (program): (prime(k)-prime(j))/4, where the pairs (k,j) are given by A205677 and A205678.
  • A205726 (program): Number of semiprimes <= n^2.
  • A205745 (program): a(n) = card { d | d*p = n, d odd, p prime }
  • A205769 (program): Given an equilateral triangle T, partition each side (with the same orientation) into segments exhibiting the Golden Ratio. Let t be the resulting internal equilateral triangle t. Sequence gives decimal expansion of ratio of areas T/t.
  • A205794 (program): Least positive integer j such that n divides C(k)-C(j) , where k, as in A205793, is the least number for which there is such a j, and C=A002808 (composite numbers).
  • A205795 (program): Sums of coefficients of polynomials from 5n-th moments of X ~ Hypergeometric(4m, 5m, m).
  • A205797 (program): G.f.: A(x) = exp( Sum_{n>=1} sigma(n)^4 * x^n/n ).
  • A205800 (program): Expansion of e.g.f. exp( Sum_{n>=1} x^(n^2) ).
  • A205801 (program): Expansion of e.g.f. exp( Sum_{n>=1} x^(n^2) / (n^2) ).
  • A205805 (program): Zarankiewicz number z(n; C_4).
  • A205808 (program): G.f.: Sum_{n=-oo..oo} q^(9*n^2 + 2*n).
  • A205809 (program): G.f.: Sum_{n=-oo..oo} q^(9n^2+4n).
  • A205811 (program): G.f.: Product_{n>=1} [ (1 - x^n) / (1 - (n+1)^n*x^n) ]^(1/n).
  • A205812 (program): a(n) = Sum_{k=1..n} binomial(n,k) * sigma(n,k).
  • A205813 (program): Triangle T(n,k), read by rows, given by (0, 2, 1, 1, 1, 1, 1, 1, 1, …) DELTA (1, 0, 0, 0, 0, 0, 0, 0, …) where DELTA is the operator defined in A084938.
  • A205817 (program): Number of (n+1) X 3 0..2 arrays with the number of clockwise edge increases in every 2 X 2 subblock unequal to the number of counterclockwise edge increases.
  • A205824 (program): (3n)!/[3n*n!*(n+1)!]
  • A205825 (program): a(n) = n!/ceiling(n/2)!.
  • A205829 (program): Number of (n+1) X 2 0..2 arrays with the number of clockwise edge increases in every 2 X 2 subblock equal to two.
  • A205837 (program): Numbers k for which 2 divides s(k)-s(j) for some j<k; each k occurs once for each such j; s(k) denotes the (k+1)-st Fibonacci number.
  • A205838 (program): The least number j such that 2 divides s(k)-s(j), where k(n)=A205720(n).
  • A205839 (program): s(k)-s(j), where the pairs (k,j) are given by A205837 and A205838.
  • A205840 (program): [s(k)-s(j)]/2, where the pairs (k,j) are given by A205837 and A205838.
  • A205841 (program): Positions of multiples of 3 in A204922 (differences of Fibonacci numbers).
  • A205842 (program): Numbers k for which 3 divides s(k)-s(j) for some j<k; each k occurs once for each such j; s(k) denotes the (k+1)-st Fibonacci number.
  • A205843 (program): The least number j such that 3 divides s(k)-s(j), where k(n)=A205842(n) and s(k) denotes the (k+1)-st Fibonacci number.
  • A205844 (program): s(k)-s(j), where the pairs (k,j) are given by A205842 and A205843, and s(k) denotes the (k+1)-st Fibonacci number.
  • A205845 (program): [s(k)-s(j)]/3, where the pairs (k,j) are given by A205842 and A205843, and s(k) denotes the (k+1)-st Fibonacci number.
  • A205846 (program): Positions of multiples of 4 in A204922 (differences of Fibonacci numbers).
  • A205847 (program): Numbers k for which 4 divides s(k)-s(j) for some j<k; each k occurs once for each such j; s(k) denotes the (k+1)-st Fibonacci number.
  • A205848 (program): The least number j such that 4 divides s(k)-s(j), where k(n)=A205847(n) and s(k) denotes the (k+1)-st Fibonacci number.
  • A205849 (program): s(k)-s(j), where the pairs (k,j) are given by A205847 and A205848, and s(k) denotes the (k+1)-st Fibonacci number.
  • A205850 (program): [s(k)-s(j)]/4, where the pairs (k,j) are given by A205847 and A205848, and s(k) denotes the (k+1)-st Fibonacci number.
  • A205851 (program): Positions of multiples of 5 in A204922 (differences of Fibonacci numbers).
  • A205852 (program): Numbers k for which 5 divides s(k)-s(j) for some j<k; each k occurs once for each such j; s(k) denotes the (k+1)-st Fibonacci number.
  • A205853 (program): The least number j such that 5 divides s(k)-s(j), where k(n)=A205852(n) and s(k) denotes the (k+1)-st Fibonacci number.
  • A205854 (program): s(k)-s(j), where the pairs (k,j) are given by A205852 and A205853, and s(k) denotes the (k+1)-st Fibonacci number.
  • A205855 (program): [s(k)-s(j)]/5, where the pairs (k,j) are given by A205852 and A205853, and s(k) denotes the (k+1)-st Fibonacci number.
  • A205856 (program): Positions of multiples of 6 in A204922 (differences of Fibonacci numbers).
  • A205857 (program): Numbers k for which 6 divides s(k)-s(j) for some j<k; each k occurs once for each such j; s(k) denotes the (k+1)-st Fibonacci number.
  • A205858 (program): The least number j such that 6 divides s(k)-s(j), where k(n)=A205857(n) and s(k) denotes the (k+1)-st Fibonacci number.
  • A205859 (program): s(k)-s(j), where the pairs (k,j) are given by A205857 and A205858, and s(k) denotes the (k+1)-st Fibonacci number.
  • A205860 (program): [s(k)-s(j)]/6, where the pairs (k,j) are given by A205857 and A205858, and s(k) denotes the (k+1)-st Fibonacci number.
  • A205861 (program): Positions of multiples of 7 in A204922 (differences of Fibonacci numbers).
  • A205862 (program): Numbers k for which 7 divides s(k)-s(j) for some j<k; each k occurs once for each such j; s(k) denotes the (k+1)-st Fibonacci number.
  • A205863 (program): The least number j such that 7 divides s(k)-s(j), where k(n)=A205862(n) and s(k) denotes the (k+1)-st Fibonacci number.
  • A205864 (program): s(k)-s(j), where the pairs (k,j) are given by A205862 and A205863, and s(k) denotes the (k+1)-st Fibonacci number.
  • A205865 (program): [s(k)-s(j)]/7, where the pairs (k,j) are given by A205862 and A205863, and s(k) denotes the (k+1)-st Fibonacci number.
  • A205866 (program): Positions of multiples of 8 in A204922 (differences of Fibonacci numbers).
  • A205867 (program): Numbers k for which 8 divides s(k)-s(j) for some j<k; each k occurs once for each such j; s(k) denotes the (k+1)-st Fibonacci number.
  • A205868 (program): The least number j such that 8 divides s(k)-s(j), where k(n)=A205867(n) and s(k) denotes the (k+1)-st Fibonacci number.
  • A205869 (program): s(k)-s(j), where the pairs (k,j) are given by A205867 and A205868, and s(k) denotes the (k+1)-st Fibonacci number.
  • A205870 (program): [s(k)-s(j)]/8, where the pairs (k,j) are given by A205867 and A205868, and s(k) denotes the (k+1)-st Fibonacci number.
  • A205871 (program): Positions of multiples of 9 in A204922 (differences of Fibonacci numbers).
  • A205872 (program): Numbers k for which 9 divides s(k)-s(j) for some j<k; each k occurs once for each such j; s(k) denotes the (k+1)-st Fibonacci number.
  • A205873 (program): The least number j such that 9 divides s(k)-s(j), where k(n)=A205872(n) and s(k) denotes the (k+1)-st Fibonacci number.
  • A205874 (program): s(k)-s(j), where the pairs (k,j) are given by A205872 and A205873, and s(k) denotes the (k+1)-st Fibonacci number.
  • A205875 (program): [s(k)-s(j)]/9, where the pairs (k,j) are given by A205872 and A205873, and s(k) denotes the (k+1)-st Fibonacci number.
  • A205876 (program): Positions of multiples of 10 in A204922 (differences of Fibonacci numbers).
  • A205877 (program): Numbers k for which 10 divides s(k)-s(j) for some j<k; each k occurs once for each such j; s(k) denotes the (k+1)-st Fibonacci number.
  • A205878 (program): The least number j such that 10 divides s(k)-s(j), where k(n)=A205877(n) and s(k) denotes the (k+1)-st Fibonacci number.
  • A205879 (program): s(k)-s(j), where the pairs (k,j) are given by A205877 and A205878, and s(k) denotes the (k+1)-st Fibonacci number.
  • A205880 (program): [s(k)-s(j)]/10, where the pairs (k,j) are given by A205877 and A205878, and s(k) denotes the (k+1)-st Fibonacci number.
  • A205882 (program): a(n) = Fibonacci(n)*A109064(n) for n>=1 with a(0)=1.
  • A205884 (program): a(n) = Pell(n)*A109064(n) for n >= 1 with a(0)=1.
  • A205955 (program): a(n) = prime(n) * (prime(n+2) - prime(n+1)).
  • A205957 (program): a(n) = exp(-Sum_{k=1..n} Sum_{d|k, d prime} moebius(d)*log(k/d)).
  • A205959 (program): a(n) = n^omega(n)/rad(n).
  • A205960 (program): Smallest odd number with digit sum equal to n.
  • A205963 (program): a(n) = Fibonacci(n)*A000118(n) for n>=1 with a(0)=1, where A000118(n) is the number of ways of writing n as a sum of 4 squares.
  • A205964 (program): a(n) = Fibonacci(n)*A000143(n) for n>=1 with a(0)=1, where A000143(n) is the number of ways of writing n as a sum of 8 squares.
  • A205965 (program): a(n) = Fibonacci(n)*A001227(n) for n>=1, where A001227(n) is the number of odd divisors of n.
  • A205966 (program): a(n) = Fibonacci(n)*A004016(n) for n>=1, with a(0)=1, where A004016(n) is the number of integer solutions (x,y) to x^2 + x*y + y^2 = n.
  • A205967 (program): a(n) = Fibonacci(n)*A008653(n) for n>=1, with a(0)=1, where A008653 is the theta series of direct sum of 2 copies of hexagonal lattice.
  • A205969 (program): a(n) = Fibonacci(n)*A113973(n) for n>=1, with a(0)=1, where A113973 lists the coefficients in phi(x^3)^3/phi(x) and phi() is a Ramanujan theta function.
  • A205970 (program): a(n) = Fibonacci(n)*A132973(n) for n>=1, with a(0)=1, where A132973 lists the coefficients in psi(-q)^3/psi(-q^3) and where psi() is a Ramanujan theta function.
  • A205971 (program): a(n) = Fibonacci(n)*A034896(n) for n >= 1, with a(0)=1, where A034896 lists the number of solutions to a^2 + b^2 + 3*c^2 + 3*d^2 = n.
  • A205972 (program): a(n) = Fibonacci(n)*A122859(n) for n>=1, with a(0)=1, where A122859 lists the coefficients in phi(-q)^3/phi(-q^3) and phi() is a Ramanujan theta function.
  • A205973 (program): a(n) = Fibonacci(n)*A109041(n) for n>=1, with a(0)=1, where A109041 lists the coefficients in eta(q)^9/eta(q^3)^3.
  • A205974 (program): a(n) = Fibonacci(n)*A033719(n) for n>=1, with a(0)=1, where A033719 lists the coefficients in theta_3(q)*theta_3(q^7).
  • A205975 (program): a(n) = Fibonacci(n)*A002652(n) for n>=1, with a(0)=1, where A002652 lists the coefficients in theta series of Kleinian lattice Z[(-1+sqrt(-7))/2].
  • A205976 (program): a(n) = Fibonacci(n)*A028594(n) for n>=1, with a(0)=1, where A028594 lists the coefficients in (theta_3(x)*theta_3(7*x)+theta_2(x)*theta_2(7*x))^2.
  • A205987 (program): G.f.: Sum_{n=-oo..oo} q^(9n^2+8n).
  • A205988 (program): Expansion of f(x^1, x^9) in powers of x where f(, ) is Ramanujan’s general theta function.
  • A206011 (program): The n-th semiprime minus its sum of digits.
  • A206014 (program): Number of (n+1) X 2 0..3 arrays with the number of clockwise edge increases in every 2 X 2 subblock unequal to the number of counterclockwise edge increases.
  • A206022 (program): Riordan array (1, x*exp(arcsinh(-2*x)).
  • A206029 (program): a(n) = sum of numbers k <= sigma(n) such that k is not equal to sigma(d) for any divisor d of n where sigma = A000203.
  • A206032 (program): a(n) = Product_{d|n} sigma(d) where sigma = A000203.
  • A206033 (program): a(1) =1; for n>=1: a(n) = product of numbers k <= sigma(n) such that k is not equal to sigma(d) for any divisor d of n where sigma = A000203.
  • A206037 (program): Values of the difference d for 3 primes in arithmetic progression with the minimal start sequence {3 + j*d}, j = 0 to 2.
  • A206038 (program): Values of the difference d for 4 primes in arithmetic progression with the minimal start sequence {5 + j*d}, j = 0 to 3.
  • A206039 (program): Values of the difference d for 5 primes in arithmetic progression with the minimal start sequence {5 + j*d}, j = 0 to 4.
  • A206047 (program): Number of (n+1) X 2 0..2 arrays with the number of clockwise edge increases in every 2 X 2 subblock equal to one.
  • A206076 (program): Numerator of p(n,-1/2), where p(n,x) is the polynomial given by A205073.
  • A206143 (program): Number of (n+1) X 2 0..2 arrays with every 2 X 3 or 3 X 2 subblock having exactly three counterclockwise and three clockwise edge increases.
  • A206144 (program): Number of (n+1) X 3 0..2 arrays with every 2 X 3 or 3 X 2 subblock having exactly three counterclockwise and three clockwise edge increases.
  • A206145 (program): Number of (n+1) X 4 0..2 arrays with every 2 X 3 or 3 X 2 subblock having exactly three counterclockwise and three clockwise edge increases.
  • A206151 (program): G.f.: exp( Sum_{n>=1} A206152(n)*x^n/n ), where A206152(n) = Sum_{k=0..n} binomial(n,k)^(n+k).
  • A206152 (program): a(n) = Sum_{k=0..n} binomial(n,k)^(n+k).
  • A206153 (program): G.f.: exp( Sum_{n>=1} A206154(n)*x^n/n ), where A206154(n) = Sum_{k=0..n} binomial(n,k)^(k+2).
  • A206154 (program): a(n) = Sum_{k=0..n} binomial(n,k)^(k+2).
  • A206155 (program): G.f.: exp( Sum_{n>=1} A206156(n)*x^n/n ), where A206156(n) = Sum_{k=0..n} binomial(n,k)^(2*k).
  • A206156 (program): a(n) = Sum_{k=0..n} binomial(n,k)^(2*k).
  • A206157 (program): G.f.: exp( Sum_{n>=1} A206158(n)*x^n/n ), where A206158(n) = Sum_{k=0..n} binomial(n,k)^(2*k+1).
  • A206158 (program): a(n) = Sum_{k=0..n} binomial(n,k)^(2*k+1).
  • A206170 (program): Number of 2 X (n+1) 0..3 arrays with every 2 X 2 subblock in a row having an equal number of equal diagonal or equal antidiagonal elements, adjacent rows differing in this number, and new values 0..3 introduced in row major order.
  • A206177 (program): G.f.: exp( Sum_{n>=1} x^n/n * Sum_{k=0..n} binomial(n,k)^3 * 2^k ).
  • A206178 (program): a(n) = Sum_{k=0..n} binomial(n,k)^3 * 2^k.
  • A206179 (program): G.f.: exp( Sum_{n>=1} x^n/n * Sum_{k=0..n} binomial(n,k)^3 * 3^k ).
  • A206180 (program): a(n) = Sum_{k=0..n} binomial(n,k)^3 * 3^k.
  • A206224 (program): Floor(n^2/4) appears 1+floor(n/2) times.
  • A206248 (program): Number of (n+1) X 2 0..3 arrays with every 2 X 2 subblock having zero permanent.
  • A206250 (program): Number of (n+1) X 4 0..3 arrays with every 2 X 2 subblock having zero permanent.
  • A206258 (program): 1/8 the number of 2 X 2 -n..n arrays with a 2 X 2 -n..n inverse, i.e., with determinant +-1.
  • A206259 (program): Number of (n+1) X (n+1) 0..1 arrays with the number of rightwards and downwards edge increases in each 2 X 2 subblock equal to the number in all its horizontal and vertical neighbors.
  • A206260 (program): Number of (n+1) X 2 0..1 arrays with the number of rightwards and downwards edge increases in each 2 X 2 subblock equal to the number in all its horizontal and vertical neighbors.
  • A206261 (program): Number of (n+1) X 3 0..1 arrays with the number of rightwards and downwards edge increases in each 2 X 2 subblock equal to the number in all its horizontal and vertical neighbors.
  • A206262 (program): Number of (n+1) X 4 0..1 arrays with the number of rightwards and downwards edge increases in each 2 X 2 subblock equal to the number in all its horizontal and vertical neighbors.
  • A206263 (program): Number of (n+1) X 5 0..1 arrays with the number of rightwards and downwards edge increases in each 2 X 2 subblock equal to the number in all its horizontal and vertical neighbors.
  • A206264 (program): Number of (n+1) X 6 0..1 arrays with the number of rightwards and downwards edge increases in each 2 X 2 subblock equal to the number in all its horizontal and vertical neighbors.
  • A206265 (program): Number of (n+1) X 7 0..1 arrays with the number of rightwards and downwards edge increases in each 2 X 2 subblock equal to the number in all its horizontal and vertical neighbors.
  • A206266 (program): Number of (n+1) X 8 0..1 arrays with the number of rightwards and downwards edge increases in each 2 X 2 subblock equal to the number in all its horizontal and vertical neighbors.
  • A206268 (program): Number of compositions of n with at most one 1.
  • A206282 (program): a(n) = ( a(n-1) * a(n-3) + a(n-2) ) / a(n-4), a(1) = a(2) = 1, a(3) = -1, a(4) = -4.
  • A206286 (program): Nonprime numbers starting with a digit 1.
  • A206294 (program): Riordan array (1, x/(1-x)^3).
  • A206297 (program): Position of n in the canonical bijection from the positive integers to the positive rational numbers.
  • A206300 (program): Expand the real root of y^3 - y + x in powers of x, then multiply coefficient of x^n by -4^n to get integers.
  • A206303 (program): E.g.f.: Product_{n>=1} (1 - x^(2*n-1))^(-1/(2*n-1)).
  • A206306 (program): Riordan array (1, x/(1-3*x+2*x^2)).
  • A206307 (program): a(n) = ((2n+2)(2n+3)-1) * a(n-1) + 2n(2n+1) * a(n-2), a(0)=0, a(1)=6.
  • A206308 (program): a(n) = ((2n+2)(2n+3)-1)*a(n-1) + 2n(2n+1)*a(n-2), a(0)=1, a(1)=19.
  • A206332 (program): Complement of A092754.
  • A206344 (program): Floor(n/2)^n.
  • A206350 (program): Position of 1/n in the canonical bijection from the positive integers to the positive rational numbers.
  • A206351 (program): a(n) = 7*a(n-1) - a(n-2) - 4 with a(1)=1, a(2)=3.
  • A206369 (program): a(p^k) = p^k - p^(k-1) + p^(k-2) - … +- 1, and then extend by multiplicativity.
  • A206371 (program): 31*2^n + 1.
  • A206372 (program): 14*4^n - 1.
  • A206373 (program): (14*4^n + 1)/3.
  • A206374 (program): a(n) = (7*4^n - 1)/3.
  • A206399 (program): a(0) = 1; for n>0, a(n) = 41*n^2 + 2.
  • A206400 (program): Number of composites of the form n^2 + 1 between two successive primes of this form.
  • A206417 (program): (5*F(n)+3*L(n)-8)/2.
  • A206419 (program): Fibonacci sequence beginning 11, 7.
  • A206420 (program): Fibonacci sequence beginning 11, 8.
  • A206422 (program): Fibonacci sequence beginning 11, 9.
  • A206423 (program): Fibonacci sequence beginning 12, 7.
  • A206424 (program): The number of 1’s in row n of Pascal’s Triangle (mod 3)
  • A206427 (program): Square array 2^(m-1)*(3^n+1), read by antidiagonals.
  • A206428 (program): Rectangular array, a(m,n) = 2^(m-1)*(3^n-1), read by antidiagonals.
  • A206429 (program): Triangular array read by rows. T(n,k) is the number of rooted labeled trees on n nodes such that the root node has degree k. n>=2, 1<=k<=n-1.
  • A206444 (program): Least n such that L(n)<-1 and L(n)<L(n-1), where L(k) means the least root of the polynomial p(k,x) defined at A206284, and a(1)=13.
  • A206450 (program): Number of 0..3 arrays of length n avoiding the consecutive pattern 0..3.
  • A206451 (program): Number of 0..4 arrays of length n avoiding the consecutive pattern 0..4
  • A206452 (program): Number of 0..5 arrays of length n avoiding the consecutive pattern 0..5.
  • A206453 (program): Number of 0..6 arrays of length n avoiding the consecutive pattern 0..6.
  • A206454 (program): Number of 0..7 arrays of length n avoiding the consecutive pattern 0..7.
  • A206456 (program): Number of 0..n arrays of length n+2 avoiding the consecutive pattern 0..n
  • A206467 (program): Number of (n+1) X 4 0..2 arrays with every 2 X 2 subblock having zero permanent.
  • A206474 (program): Riordan array ((1+x-x^2)/(1-x^2), x/(1-x^2)).
  • A206475 (program): First differences of A206369.
  • A206479 (program): Number of terms common to the binary expansions of m and n; a matrix by antidiagonals.
  • A206481 (program): a(n) + a(n+2) = n^3.
  • A206492 (program): Sums of rows of the sequence of triangles with nonnegative integers and row widths defined by A004738.
  • A206525 (program): a(n) = 113*(n-1) - a(n-1) with n>1, a(1)=51.
  • A206526 (program): a(n) = 137*(n-1) - a(n-1) with n>1, a(1)=31.
  • A206527 (program): 3^n concatenated with itself.
  • A206528 (program): 5^n concatenated with itself.
  • A206529 (program): 7^n concatenated with itself.
  • A206531 (program): a(n) = (2(n+1)(2n+1)-1) * a(n-1) + 2n(2n-1) * a(n-2), a(0)=0, a(1)=2.
  • A206532 (program): a(n) = (2(n+1)(2n+1)-1) * a(n-1) + 2n(2n-1) * a(n-2), a(0) = 1, a(1) = 11.
  • A206533 (program): Decimal expansion of 1/(1-cos(1)).
  • A206543 (program): Period 10: repeat 1, 3, 5, 7, 9, 9, 7, 5, 3, 1.
  • A206544 (program): Period 12: repeat 1, 3, 5, 7, 9, 11, 11, 9, 7, 5, 3, 1.
  • A206545 (program): Period length 16: repeat 1, 3, 5, 7, 9, 11, 13, 15, 15, 13, 11, 9, 7, 5, 3, 1.
  • A206546 (program): Period 8: repeat [1, 7, 11, 13, 13, 11, 7, 1].
  • A206547 (program): Positive odd numbers relatively prime to 21.
  • A206548 (program): Period 12: repeat 1, 5, 11, 13, 17, 19, 19, 17, 13, 11, 5, 1.
  • A206555 (program): Number of 5’s in the last section of the set of partitions of n.
  • A206556 (program): Number of 6’s in the last section of the set of partitions of n.
  • A206557 (program): Number of 7’s in the last section of the set of partitions of n.
  • A206558 (program): Number of 8’s in the last section of the set of partitions of n.
  • A206559 (program): Number of 9’s in the last section of the set of partitions of n.
  • A206560 (program): Number of 10’s in the last section of the set of partitions of n.
  • A206564 (program): Fibonacci sequence beginning 14, 13.
  • A206565 (program): Expansion of 1/(1 - 37*x + x^2).
  • A206566 (program): Triangular array: T(i,j) = number of terms common to the binary expansions of i+1 and j, for j=1,2,3,…,i; i=1,2,3,…
  • A206570 (program): Number of n X 1 0..3 arrays avoiding the pattern z-1 z-1 z in any row, column or nw-to-se diagonal.
  • A206571 (program): Number of nX2 0..3 arrays avoiding the pattern z-1 z-1 z in any row, column or nw-to-se diagonal
  • A206581 (program): Odd primes p such that p+1 is a prime times a power of two.
  • A206590 (program): Number of solutions (n,k) of k^3=n^3 (mod n), where 1<=k<n.
  • A206601 (program): 3^(n(n+1)/2) - 1.
  • A206603 (program): Maximal apex value of an addition triangle whose base is a permutation of {k-n/2, k=0..n}.
  • A206604 (program): Number of integers in the smallest interval containing both minimal and maximal possible apex values of an addition triangle whose base is a permutation of n+1 consecutive integers.
  • A206605 (program): Fibonacci sequence beginning 14, 11.
  • A206607 (program): Fibonacci sequence beginning 13, 11.
  • A206608 (program): Fibonacci sequence beginning 13, 10.
  • A206609 (program): Fibonacci sequence beginning 13, 9.
  • A206610 (program): Fibonacci sequence beginning 13, 8.
  • A206611 (program): Fibonacci sequence beginning 13, 7.
  • A206612 (program): Fibonacci sequence beginning 13, 6.
  • A206624 (program): G.f.: Product_{n>0} ( (1+x^n)/(1-x^n) )^(n^4).
  • A206625 (program): Expansion of x * (1 + x) * (1 - x^2) * (1 + x^3) / (1 - 2*x^2 - 2*x^4 - 2*x^6 + x^8) in powers of x.
  • A206641 (program): Fibonacci sequence beginning 14, 9.
  • A206643 (program): Number of halving and tripling steps to reach 1 in 3x+1 problem applied the Fibonacci numbers.
  • A206687 (program): Number of n X 2 0..3 arrays with no element equal to another within two positions in the same row or column, and new values 0..3 introduced in row major order.
  • A206694 (program): Number of n X 2 0..2 arrays avoiding the pattern z-2 z-1 z in any row or column.
  • A206703 (program): Triangular array read by rows. T(n,k) is the number of partial permutations (injective partial functions) of {1,2,…,n} that have exactly k elements in a cycle. The k elements are not necessarily in the same cycle. A fixed point is considered to be in a cycle.
  • A206715 (program): Numbers matched to polynomials divisible by x^2+1.
  • A206716 (program): (1/5)A206715.
  • A206717 (program): Numbers matched to polynomials divisible by x^2+x+1.
  • A206718 (program): (1/7)*A206717.
  • A206723 (program): a(n) = 7*( ((3 + sqrt(5))/2)^n + ((3 - sqrt(5))/2)^n - 2 ).
  • A206727 (program): Number of nX1 0..2 arrays avoiding the pattern z-1 z-1 z in any row, column or nw-to-se diagonal
  • A206728 (program): Number of n X 2 0..2 arrays avoiding the pattern z-1 z-1 z in any row, column or nw-to-se diagonal.
  • A206735 (program): Triangle T(n,k), read by rows, given by (0, 2, -1/2, 1/2, 0, 0, 0, 0, 0, 0, 0, …) DELTA (1, 0, -1/2, 1/2, 0, 0, 0, 0, 0, 0, 0, …) where DELTA is the operator defined in A084938.
  • A206771 (program): 0 followed by the numerators of the reduced (A001803(n) + A001790(n)) / (2*A046161(n)).
  • A206772 (program): Table T(n,k)=max{4*n+k-4,n+4*k-4} n, k > 0, read by antidiagonals.
  • A206773 (program): Sum of nonprime proper divisors (or nonprime aliquot parts) of n.
  • A206774 (program): First differences of A033922.
  • A206776 (program): a(n) = 3*a(n-1) + 2*a(n-2) for n>1, a(0)=2, a(1)=3.
  • A206786 (program): Remainder of n^340 divided by 341.
  • A206787 (program): Sum of the odd squarefree divisors of n.
  • A206790 (program): Number of nX1 0..3 arrays avoiding the pattern z z+1 z in any row, column, diagonal or antidiagonal
  • A206791 (program): Number of n X 2 0..3 arrays avoiding the pattern z z+1 z in any row, column, diagonal or antidiagonal.
  • A206800 (program): Riordan array (1/(1-3*x+x^2), x*(1-x)/(1-3*x+x^2)).
  • A206802 (program): a(n) = (1/2)*A185382(n).
  • A206803 (program): Sum_{0<j<k<=n} P(k)-P(j), where P(j)=A065091(j) is the j-th odd prime.
  • A206804 (program): (1/2)*A206803.
  • A206805 (program): Position of 2^n when {2^j} and {3^k} are jointly ranked; complement of A206807.
  • A206806 (program): Sum_{0<j<k<=n} s(k)-s(j), where s(j)=A002620(j) is the j-th quarter-square.
  • A206807 (program): Position of 3^n when {2^j} and {3^k} are jointly ranked; complement of A206805.
  • A206808 (program): Sum_{0<j<n} n^3-j^3.
  • A206809 (program): Sum_{0<j<k<=n} k^3-j^3.
  • A206810 (program): Sum_{0<j<n} (n^4-j^4).
  • A206811 (program): Sum_{0<j<k<=n} (k^4-j^4).
  • A206812 (program): Position of 2^n in joint ranking of {2^i}, {3^j}, {5^k}.
  • A206816 (program): Sum_{0<j<n} (n!-j!).
  • A206817 (program): Sum_{0<j<k<=n} (k!-j!).
  • A206819 (program): Riordan array (1/(1-10*x-10*x^2), x/(1-10*x-10*x^2)).
  • A206824 (program): Number of solutions (n,k) of s(k) = s(n) (mod n), where 1 <= k < n and s(k) = k(k+1)/2.
  • A206825 (program): Number of solutions (n,k) of k^4=n^4 (mod n), where 1<=k<n.
  • A206827 (program): Number of solutions (n,k) of s(k)=s(n) (mod n), where 1<=k<n and s(k)=k(k+1)(2k+1)/6.
  • A206831 (program): Triangle T(n,k), read by rows, given by (1, -2, 1, 0, 0, 0, 0, 0, 0, 0, …) DELTA (1, 0, 0, 0, 0, 0, 0, 0, 0, 0, …) where DELTA is the operator defined in A084938.
  • A206839 (program): Number of 1 X n 0..3 arrays avoiding the pattern z-2 z-1 z in any row, column, nw-to-se diagonal or ne-to-sw antidiagonal.
  • A206840 (program): Number of 2 X n 0..3 arrays avoiding the pattern z-2 z-1 z in any row, column, nw-to-se diagonal or ne-to-sw antidiagonal.
  • A206848 (program): G.f.: exp( Sum_{n>=1} x^n/n * Sum_{k=0..n} binomial(n^2, k^2) ).
  • A206849 (program): a(n) = Sum_{k=0..n} binomial(n^2, k^2).
  • A206853 (program): a(1)=1, for n>1, a(n) is the least number > a(n-1) such that the Hamming distance D(a(n-1), a(n)) = 2.
  • A206857 (program): Number of n X 2 0..2 arrays avoiding the pattern z z+1 z in any row, column, diagonal or antidiagonal.
  • A206901 (program): Number of nonisomorphic graded posets with 0 of rank n with no 3-element antichain.
  • A206902 (program): Number of nonisomorphic graded posets with 0 and uniform Hasse diagram of rank n with no 3-element antichain.
  • A206903 (program): n+[ns/r]+[nt/r], where []=floor, r=3, s=sqrt(3), t=1/s.
  • A206904 (program): n+[nr/s]+[nt/s], where []=floor, r=3, s=sqrt(3), t=1/s.
  • A206905 (program): n+[nr/t]+[ns/t], where []=floor, r=3, s=sqrt(3), t=1/s.
  • A206906 (program): n+[ns/r]+[nt/r], where []=floor, r=1/3, s=sqrt(3), t=1/s.
  • A206907 (program): n+[nr/s]+[nt/s], where []=floor, r=1/3, s=sqrt(3), t=1/s.
  • A206908 (program): a(n) = 4*n + floor(n/sqrt(3)).
  • A206909 (program): Position of 2n+cos(n) when the sets {2k+cos(k)} and {2k+sin(k)} are jointly ranked.
  • A206910 (program): Position of 2n+sin(n) when the sets {2k+cos(k)} and {2k+sin(k)} are jointly ranked.
  • A206912 (program): Position of log(n+1) when the partial sums of the harmonic series are jointly ranked with the set {log(k+1)}; complement of A206911.
  • A206913 (program): Greatest binary palindrome <= n; the binary palindrome floor function.
  • A206914 (program): Least binary palindrome >= n; the binary palindrome ceiling function.
  • A206915 (program): The index (in A006995) of the greatest binary palindrome <= n; also the ‘lower inverse’ of A006995.
  • A206916 (program): Index of the least binary palindrome >=n; also the “upper inverse” of A006995.
  • A206917 (program): Sum of binary palindromes in the half-open interval [2^(n-1), 2^n).
  • A206918 (program): Sum of binary palindromes p < 2^n.
  • A206919 (program): Sum of binary palindromes <= n.
  • A206920 (program): Sum of the first n binary palindromes; a(n) = Sum_{k=1..n} A006995(k).
  • A206927 (program): Minimal numbers of binary length n+1 such that the number of contiguous palindromic bit patterns in the binary representation is minimal.
  • A206947 (program): Number of nonisomorphic graded posets with 0 and non-uniform Hasse graph of rank n, with exactly 2 elements of each rank above 0.
  • A206949 (program): Number of nonisomorphic graded posets with 0 and non-uniform Hasse graph of rank n, with no 3-element antichain.
  • A206958 (program): Expansion of f(x^5, -x^7) - x * f(-x, x^11) in powers of x where f() is Ramanujan’s two-variable theta function.
  • A206959 (program): Expansion of f(-x^5, x^7) + x * f(x, -x^11) in powers of x where f() is Ramanujan’s two-variable theta function.
  • A206981 (program): Number of nX2 0..1 arrays avoiding the patterns 0 1 0 or 1 0 1 in any row, column, diagonal or antidiagonal
  • A207008 (program): Number of n X 1 0..2 arrays avoiding the patterns z z+1 z or z z-1 z in any row or column.
  • A207009 (program): Number of n X 2 0..2 arrays avoiding the patterns z z+1 z or z z-1 z in any row or column.
  • A207020 (program): Number of n X 4 0..1 arrays avoiding 0 0 0 and 0 1 1 horizontally and 0 0 1 and 1 0 1 vertically.
  • A207021 (program): Number of nX5 0..1 arrays avoiding 0 0 0 and 0 1 1 horizontally and 0 0 1 and 1 0 1 vertically
  • A207022 (program): Number of nX6 0..1 arrays avoiding 0 0 0 and 0 1 1 horizontally and 0 0 1 and 1 0 1 vertically
  • A207025 (program): Number of 2 X n 0..1 arrays avoiding 0 0 0 and 0 1 1 horizontally and 0 0 1 and 1 0 1 vertically.
  • A207038 (program): Partial sums of A207034.
  • A207039 (program): Primes whose binary expansion is not palindromic.
  • A207063 (program): a(n) is the smallest number larger than a(n-1) with mutual Hamming distance 2 and a(1)=0.
  • A207064 (program): Number of n X 4 0..1 arrays avoiding 0 0 1 and 0 1 0 horizontally and 0 0 1 and 1 0 1 vertically.
  • A207065 (program): Number of n X 5 0..1 arrays avoiding 0 0 1 and 0 1 0 horizontally and 0 0 1 and 1 0 1 vertically.
  • A207069 (program): Number of 2 X n 0..1 arrays avoiding 0 0 1 and 0 1 0 horizontally and 0 0 1 and 1 0 1 vertically.
  • A207094 (program): Number of 0..2 arrays x(0..n-1) of n elements with each no smaller than the sum of its two previous neighbors modulo 3.
  • A207106 (program): Number of n X 3 0..1 arrays avoiding 0 0 0 and 0 1 1 horizontally and 0 0 1 and 1 1 0 vertically.
  • A207107 (program): Number of n X 4 0..1 arrays avoiding 0 0 0 and 0 1 1 horizontally and 0 0 1 and 1 1 0 vertically.
  • A207118 (program): Number of n X 3 0..1 arrays avoiding 0 0 1 and 0 1 0 horizontally and 0 0 1 and 0 1 1 vertically.
  • A207119 (program): Number of nX4 0..1 arrays avoiding 0 0 1 and 0 1 0 horizontally and 0 0 1 and 0 1 1 vertically
  • A207120 (program): Number of nX5 0..1 arrays avoiding 0 0 1 and 0 1 0 horizontally and 0 0 1 and 0 1 1 vertically
  • A207135 (program): G.f.: exp( Sum_{n>=1} x^n/n * Sum_{k=0..n} binomial(n^2, k*(n-k)) ).
  • A207136 (program): a(n) = Sum_{k=0..n} binomial(n^2, k*(n-k)).
  • A207139 (program): G.f.: exp( Sum_{n>=1} x^n/n * Sum_{k=0..n} binomial(n,k) * binomial(n^2,k^2) ).
  • A207140 (program): a(n) = Sum_{k=0..n} binomial(n,k) * binomial(n^2,k^2).
  • A207165 (program): Number of n X 4 0..1 arrays avoiding 0 0 0 and 1 0 1 horizontally and 0 0 1 and 1 0 1 vertically.
  • A207166 (program): Number of n X 5 0..1 arrays avoiding 0 0 0 and 1 0 1 horizontally and 0 0 1 and 1 0 1 vertically.
  • A207167 (program): Number of n X 6 0..1 arrays avoiding 0 0 0 and 1 0 1 horizontally and 0 0 1 and 1 0 1 vertically.
  • A207168 (program): Number of n X 7 0..1 arrays avoiding 0 0 0 and 1 0 1 horizontally and 0 0 1 and 1 0 1 vertically
  • A207170 (program): Number of 2Xn 0..1 arrays avoiding 0 0 0 and 1 0 1 horizontally and 0 0 1 and 1 0 1 vertically
  • A207188 (program): Numbers matching polynomials y(k,x) that have x as a factor; see Comments.
  • A207189 (program): Numbers matching polynomials y(k,x) that have x-1 as a factor; see Comments.
  • A207255 (program): Number of 4 X n 0..1 arrays avoiding 0 0 1 and 1 0 1 horizontally and 0 1 0 and 1 0 1 vertically.
  • A207256 (program): Number of 5 X n 0..1 arrays avoiding 0 0 1 and 1 0 1 horizontally and 0 1 0 and 1 0 1 vertically.
  • A207260 (program): Triangle T(n,k) with T(n,k) = k^2 + (1-(-1)^(n-k))/2.
  • A207262 (program): a(n) = 2^(4n - 2) + 1.
  • A207302 (program): Number of n X 5 0..1 arrays avoiding 0 0 0 and 1 0 1 horizontally and 0 0 1 and 1 1 0 vertically.
  • A207321 (program): Partial sums of A002893.
  • A207322 (program): a(n) = Sum{k=0..n} (-1)^k*A002893(k)).
  • A207323 (program): a(n) = Sum_{k=0..n} k*A002893(k).
  • A207327 (program): Riordan array (1, x*(1+x)^2/(1-x)).
  • A207332 (program): Double factorials (prime(n)-2)!!.
  • A207336 (program): One half of smallest positive nontrivial even solution of the congruence x^2 == 1 (mod A001748(n+2)), n>=1.
  • A207337 (program): Primes of the form (m^2+1)/10.
  • A207339 (program): Triangular numbers T from A000217 such that (4*T+1)/5 is prime.
  • A207361 (program): Displacement under constant discrete unit surge.
  • A207363 (program): Number of n X 3 0..1 arrays avoiding 0 0 0 and 0 1 1 horizontally and 0 0 1 and 0 1 1 vertically.
  • A207364 (program): Number of n X 4 0..1 arrays avoiding 0 0 0 and 0 1 1 horizontally and 0 0 1 and 0 1 1 vertically.
  • A207365 (program): Number of nX5 0..1 arrays avoiding 0 0 0 and 0 1 1 horizontally and 0 0 1 and 0 1 1 vertically
  • A207366 (program): Number of nX6 0..1 arrays avoiding 0 0 0 and 0 1 1 horizontally and 0 0 1 and 0 1 1 vertically
  • A207374 (program): Composites of the form 24n - 1.
  • A207376 (program): Sum of central divisors of n.
  • A207399 (program): Number of n X 4 0..1 arrays avoiding 0 0 1 and 0 1 1 horizontally and 0 0 1 and 1 1 0 vertically.
  • A207400 (program): Number of n X 5 0..1 arrays avoiding 0 0 1 and 0 1 1 horizontally and 0 0 1 and 1 1 0 vertically.
  • A207401 (program): Number of n X 6 0..1 arrays avoiding 0 0 1 and 0 1 1 horizontally and 0 0 1 and 1 1 0 vertically.
  • A207402 (program): Number of n X 7 0..1 arrays avoiding 0 0 1 and 0 1 1 horizontally and 0 0 1 and 1 1 0 vertically.
  • A207404 (program): Number of 4Xn 0..1 arrays avoiding 0 0 1 and 0 1 1 horizontally and 0 0 1 and 1 1 0 vertically
  • A207405 (program): Number of 5Xn 0..1 arrays avoiding 0 0 1 and 0 1 1 horizontally and 0 0 1 and 1 1 0 vertically
  • A207406 (program): Number of 6Xn 0..1 arrays avoiding 0 0 1 and 0 1 1 horizontally and 0 0 1 and 1 1 0 vertically
  • A207407 (program): Number of 7Xn 0..1 arrays avoiding 0 0 1 and 0 1 1 horizontally and 0 0 1 and 1 1 0 vertically
  • A207409 (program): Triangular array: T(k,j)=prime(k)(mod prime(j)), 1<=j<k.
  • A207422 (program): Number of nX4 0..1 arrays avoiding 0 0 0 and 0 1 0 horizontally and 0 0 1 and 0 1 0 vertically
  • A207427 (program): Number of 3Xn 0..1 arrays avoiding 0 0 0 and 0 1 0 horizontally and 0 0 1 and 0 1 0 vertically
  • A207436 (program): Number of n X 2 0..1 arrays avoiding 0 0 1 and 0 1 0 horizontally and 0 0 1 and 1 0 0 vertically.
  • A207449 (program): Number of n X 4 0..1 arrays avoiding 0 0 0 and 0 0 1 horizontally and 0 0 1 and 1 0 1 vertically.
  • A207450 (program): Number of n X 5 0..1 arrays avoiding 0 0 0 and 0 0 1 horizontally and 0 0 1 and 1 0 1 vertically.
  • A207451 (program): Number of n X 6 0..1 arrays avoiding 0 0 0 and 0 0 1 horizontally and 0 0 1 and 1 0 1 vertically.
  • A207452 (program): Number of n X 7 0..1 arrays avoiding 0 0 0 and 0 0 1 horizontally and 0 0 1 and 1 0 1 vertically.
  • A207454 (program): Number of 3 X n 0..1 arrays avoiding 0 0 0 and 0 0 1 horizontally and 0 0 1 and 1 0 1 vertically.
  • A207455 (program): Number of 4 X n 0..1 arrays avoiding 0 0 0 and 0 0 1 horizontally and 0 0 1 and 1 0 1 vertically.
  • A207456 (program): Number of 5 X n 0..1 arrays avoiding 0 0 0 and 0 0 1 horizontally and 0 0 1 and 1 0 1 vertically.
  • A207457 (program): Number of 6 X n 0..1 arrays avoiding 0 0 0 and 0 0 1 horizontally and 0 0 1 and 1 0 1 vertically.
  • A207458 (program): Number of 7 X n 0..1 arrays avoiding 0 0 0 and 0 0 1 horizontally and 0 0 1 and 1 0 1 vertically.
  • A207480 (program): a(n) = (3/2)*(1+prime(n)) - prime(n+1).
  • A207481 (program): Numbers such that e <= p for all p^e in their prime factorization, p prime.
  • A207524 (program): Number of rational numbers p/q such that 0<p<q<=n and p/q<=(greatest quotient of consecutive Fibonacci numbers having denominator <= n).
  • A207536 (program): Triangle of coefficients of polynomials u(n,x) jointly generated with A105070; see Formula section.
  • A207537 (program): Triangle of coefficients of polynomials u(n,x) jointly generated with A207538; see Formula section.
  • A207538 (program): Triangle of coefficients of polynomials v(n,x) jointly generated with A207537; see Formula section.
  • A207543 (program): Triangle read by rows, expansion of (1+y*x)/(1-2*y*x+y*(y-1)*x^2).
  • A207590 (program): Number of 3 X n 0..1 arrays avoiding 0 0 0 and 0 0 1 horizontally and 0 0 1 and 1 1 1 vertically.
  • A207596 (program): Number of n X 5 0..1 arrays avoiding 0 0 0 and 0 1 0 horizontally and 0 0 1 and 1 0 1 vertically.
  • A207597 (program): Number of n X 6 0..1 arrays avoiding 0 0 0 and 0 1 0 horizontally and 0 0 1 and 1 0 1 vertically.
  • A207598 (program): Number of n X 7 0..1 arrays avoiding 0 0 0 and 0 1 0 horizontally and 0 0 1 and 1 0 1 vertically.
  • A207600 (program): Number of 3Xn 0..1 arrays avoiding 0 0 0 and 0 1 0 horizontally and 0 0 1 and 1 0 1 vertically
  • A207601 (program): Number of 4Xn 0..1 arrays avoiding 0 0 0 and 0 1 0 horizontally and 0 0 1 and 1 0 1 vertically
  • A207602 (program): Number of 5Xn 0..1 arrays avoiding 0 0 0 and 0 1 0 horizontally and 0 0 1 and 1 0 1 vertically
  • A207603 (program): Number of 6Xn 0..1 arrays avoiding 0 0 0 and 0 1 0 horizontally and 0 0 1 and 1 0 1 vertically
  • A207604 (program): Number of 7Xn 0..1 arrays avoiding 0 0 0 and 0 1 0 horizontally and 0 0 1 and 1 0 1 vertically
  • A207605 (program): Triangle of coefficients of polynomials u(n,x) jointly generated with A106195; see the Formula section.
  • A207606 (program): Triangle of coefficients of polynomials u(n,x) jointly generated with A207607; see the Formula section.
  • A207607 (program): Triangle of coefficients of polynomials v(n,x) jointly generated with A207606; see Formula section.
  • A207611 (program): Triangle of coefficients of polynomials v(n,x) jointly generated with A207610; see Formula section.
  • A207613 (program): Triangle of coefficients of polynomials v(n,x) jointly generated with A207612; see Formula section.
  • A207615 (program): Triangle of coefficients of polynomials v(n,x) jointly generated with A207614; the see Formula section.
  • A207616 (program): Triangle of coefficients of polynomials u(n,x) jointly generated with A207617; see the Formula section.
  • A207617 (program): Triangle of coefficients of polynomials v(n,x) jointly generated with A207616; the see Formula section.
  • A207619 (program): Triangle of coefficients of polynomials v(n,x) jointly generated with A207618; the see Formula section.
  • A207620 (program): Triangle of coefficients of polynomials u(n,x) jointly generated with A207621; see the Formula section.
  • A207621 (program): Triangle of coefficients of polynomials v(n,x) jointly generated with A207620; the see Formula section.
  • A207627 (program): Triangle of coefficients of polynomials u(n,x) jointly generated with A207628; see the Formula section.
  • A207628 (program): Triangle of coefficients of polynomials v(n,x) jointly generated with A207627; see the Formula section.
  • A207635 (program): Triangle of coefficients of polynomials u(n,x) jointly generated with A207636; see the Formula section.
  • A207636 (program): Triangle of coefficients of polynomials v(n,x) jointly generated with A207635; see Formula section.
  • A207641 (program): G.f.: Sum_{n>=0} x^n * Product_{k=1..n} (1+x^k)/(1-x^k).
  • A207643 (program): a(n) = 1 + (n-1) + (n-1)*[n/2-1] + (n-1)*[n/2-1]*[n/3-1] + (n-1)*[n/2-1]*[n/3-1]*[n/4-1] +… for n>0 with a(0)=1, where [x] = floor(x).
  • A207646 (program): Product_{k=1..n} floor(2*n/k - 1).
  • A207647 (program): a(n) = Product_{k=1..n} floor((2*n+1)/k - 1).
  • A207656 (program): Number of n X 3 0..1 arrays avoiding 0 0 0 and 1 1 1 horizontally and 0 0 1 and 1 0 0 vertically.
  • A207673 (program): n+[nr/s]+[nt/s], where []=floor, r=5, s=(1+sqrt(5))/2, t=1/s.
  • A207694 (program): Number of 3 X n 0..1 arrays avoiding 0 0 0 and 0 1 0 horizontally and 0 0 1 and 1 1 1 vertically.
  • A207701 (program): Number of n X 6 0..1 arrays avoiding 0 0 0 and 0 1 0 horizontally and 0 0 1 and 1 1 0 vertically.
  • A207704 (program): Number of 3Xn 0..1 arrays avoiding 0 0 0 and 0 1 0 horizontally and 0 0 1 and 1 1 0 vertically
  • A207705 (program): Number of 4Xn 0..1 arrays avoiding 0 0 0 and 0 1 0 horizontally and 0 0 1 and 1 1 0 vertically
  • A207706 (program): Number of 5Xn 0..1 arrays avoiding 0 0 0 and 0 1 0 horizontally and 0 0 1 and 1 1 0 vertically
  • A207718 (program): Number of 3 X n 0..1 arrays avoiding 0 0 0 and 0 0 1 horizontally and 0 0 1 and 1 0 0 vertically.
  • A207725 (program): Number of n X 4 0..1 arrays avoiding 0 0 0 and 0 1 0 horizontally and 0 1 1 and 1 0 1 vertically.
  • A207730 (program): Number of 3 X n 0..1 arrays avoiding 0 0 0 and 0 1 0 horizontally and 0 1 1 and 1 0 1 vertically.
  • A207732 (program): Number of 5Xn 0..1 arrays avoiding 0 0 0 and 0 1 0 horizontally and 0 1 1 and 1 0 1 vertically
  • A207733 (program): Number of 6Xn 0..1 arrays avoiding 0 0 0 and 0 1 0 horizontally and 0 1 1 and 1 0 1 vertically
  • A207735 (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.
  • A207737 (program): Number of n X 4 0..1 arrays avoiding 0 0 0 and 0 1 0 horizontally and 0 0 1 and 1 0 0 vertically.
  • A207753 (program): Number of 4 X n 0..1 arrays avoiding 0 0 1 and 0 1 1 horizontally and 0 0 1 and 1 0 0 vertically.
  • A207754 (program): Number of 5Xn 0..1 arrays avoiding 0 0 1 and 0 1 1 horizontally and 0 0 1 and 1 0 0 vertically
  • A207755 (program): Number of 6Xn 0..1 arrays avoiding 0 0 1 and 0 1 1 horizontally and 0 0 1 and 1 0 0 vertically
  • A207756 (program): Number of 7Xn 0..1 arrays avoiding 0 0 1 and 0 1 1 horizontally and 0 0 1 and 1 0 0 vertically
  • A207814 (program): Series expansion of the reciprocal of the generating function of A068432.
  • A207815 (program): Triangle of coefficients of Chebyshev’s S(n,x-3) polynomials (exponents of x in increasing order).
  • A207817 (program): a(n) = (4*n)! / (n!^4 * (n+1)).
  • A207823 (program): Triangle of coefficients of Chebyshev’s S(n,x+4) polynomials (exponents of x in increasing order).
  • A207824 (program): Triangle of coefficients of Chebyshev’s S(n,x+5) polynomials (exponents of x in increasing order).
  • A207830 (program): Positive multiples of 3 that contain the decimal digit 1.
  • A207832 (program): Numbers x such that 20*x^2 + 1 is a perfect square.
  • A207833 (program): E.g.f.: T(T(x)), where T(x) is the e.g.f. for labeled rooted trees, A000169.
  • A207836 (program): a(n) = n*A052530(n)/2.
  • A207846 (program): Number of 3 X n 0..1 arrays avoiding 0 0 0 and 0 0 1 horizontally and 0 0 0 and 1 1 1 vertically.
  • A207847 (program): Number of 4 X n 0..1 arrays avoiding 0 0 0 and 0 0 1 horizontally and 0 0 0 and 1 1 1 vertically.
  • A207854 (program): Number of nX4 0..1 arrays avoiding 0 0 0 and 0 1 0 horizontally and 0 1 0 and 1 0 1 vertically
  • A207864 (program): Number of n X 2 nonnegative integer arrays with new values 0 upwards introduced in row major order and no element equal to any horizontal or vertical neighbor (colorings ignoring permutations of colors).
  • A207872 (program): Denominator of Z(n,1/2), where Z(n,x) is the n-th Zeckendorf polynomial.
  • A207873 (program): Numerator of Z(n,1/2), where Z(n,x) is the n-th Zeckendorf polynomial.
  • A207896 (program): Number of 3 X n 0..1 arrays avoiding 0 0 0 and 1 0 1 horizontally and 0 0 0 and 1 1 1 vertically.
  • A207904 (program): Number of nX4 0..1 arrays avoiding 0 0 0 and 0 1 0 horizontally and 0 0 0 and 0 1 1 vertically
  • A207909 (program): Number of 4Xn 0..1 arrays avoiding 0 0 0 and 0 1 0 horizontally and 0 0 0 and 0 1 1 vertically
  • A207929 (program): Number of 3 X n 0..1 arrays avoiding 0 0 0 and 0 1 0 horizontally and 0 0 0 and 1 1 1 vertically.
  • A207930 (program): Number of 4Xn 0..1 arrays avoiding 0 0 0 and 0 1 0 horizontally and 0 0 0 and 1 1 1 vertically
  • A207947 (program): Number of nX6 0..1 arrays avoiding 0 0 1 and 0 1 1 horizontally and 0 1 0 and 1 0 1 vertically
  • A207950 (program): Number of 4 X n 0..1 arrays avoiding 0 0 1 and 0 1 1 horizontally and 0 1 0 and 1 0 1 vertically.
  • A207951 (program): Number of 5Xn 0..1 arrays avoiding 0 0 1 and 0 1 1 horizontally and 0 1 0 and 1 0 1 vertically
  • A207974 (program): Triangle related to A152198.
  • A207977 (program): Infinite sequence of integers arising in the Quantum Walk of F. Riesz.
  • A207978 (program): Number of n X 2 nonnegative integer arrays with new values 0 upwards introduced in row major order and no element equal to any diagonal or antidiagonal neighbor (colorings ignoring permutations of colors).
  • A207990 (program): Primes of the form prime(n) + prime(n+1) - 5.
  • A207991 (program): Primes of the form prime(n) + prime(n+1) + 5.
  • A207998 (program): Number of nX2 nonnegative integer arrays with new values 0 upwards introduced in row major order and no element equal to any knight-move neighbor (colorings ignoring permutations of colors).
  • A208009 (program): Number of n X 4 0..1 arrays avoiding 0 0 0 and 1 0 1 horizontally and 0 0 1 and 0 1 1 vertically.
  • A208010 (program): Number of nX5 0..1 arrays avoiding 0 0 0 and 1 0 1 horizontally and 0 0 1 and 0 1 1 vertically
  • A208011 (program): Number of nX6 0..1 arrays avoiding 0 0 0 and 1 0 1 horizontally and 0 0 1 and 0 1 1 vertically
  • A208012 (program): Number of nX7 0..1 arrays avoiding 0 0 0 and 1 0 1 horizontally and 0 0 1 and 0 1 1 vertically
  • A208034 (program): G.f.: exp( Sum_{n>=1} 2*Pell(n)^2 * x^n/n ), where Pell(n) = A000129(n).
  • A208035 (program): Number of n X 4 0..1 arrays avoiding 0 0 0 and 0 1 0 horizontally and 0 0 0 and 1 0 1 vertically.
  • A208044 (program): Number of n X 3 0..3 arrays with new values 0..3 introduced in row major order and no element equal to any horizontal, vertical or antidiagonal neighbor (colorings ignoring permutations of colors).
  • A208057 (program): Triangle by rows, generated from the odd integers and related to A000165.
  • A208058 (program): Triangle by rows relating to the factorials, generated from A002260.
  • A208060 (program): a(n) = 1 + 2*n + 2^2*n*[n/2] + 2^3*n*[n/2]*[n/3] + 2^4*n*[n/2]*[n/3]*[n/4] + … where [x]=floor(x).
  • A208061 (program): G.f. 1/sum(k>=0, (-1)^k * x^(k*(k+1)/2)).
  • A208064 (program): Number of n X 3 0..1 arrays avoiding 0 0 0 and 1 1 1 horizontally and 0 0 1 and 0 1 1 vertically.
  • A208065 (program): Number of n X 4 0..1 arrays avoiding 0 0 0 and 1 1 1 horizontally and 0 0 1 and 0 1 1 vertically.
  • A208066 (program): Number of n X 5 0..1 arrays avoiding 0 0 0 and 1 1 1 horizontally and 0 0 1 and 0 1 1 vertically.
  • A208067 (program): Number of n X 6 0..1 arrays avoiding 0 0 0 and 1 1 1 horizontally and 0 0 1 and 0 1 1 vertically.
  • A208068 (program): Number of n X 7 0..1 arrays avoiding 0 0 0 and 1 1 1 horizontally and 0 0 1 and 0 1 1 vertically.
  • A208071 (program): Number of 6 X n 0..1 arrays avoiding 0 0 0 and 1 1 1 horizontally and 0 0 1 and 0 1 1 vertically.
  • A208079 (program): Number of 4 X n 0..1 arrays avoiding 0 0 0 and 0 0 1 horizontally and 0 0 0 and 0 1 0 vertically.
  • A208081 (program): Number of 6 X n 0..1 arrays avoiding 0 0 0 and 0 0 1 horizontally and 0 0 0 and 0 1 0 vertically.
  • A208086 (program): Number of 4 X (n+1) 0..1 arrays with every 2 X 2 subblock having the same number of equal edges as its horizontal neighbors and a different number from its vertical neighbors, and new values 0..1 introduced in row major order.
  • A208087 (program): Number of 6 X (n+1) 0..1 arrays with every 2 X 2 subblock having the same number of equal edges as its horizontal neighbors and a different number from its vertical neighbors, and new values 0..1 introduced in row major order.
  • A208088 (program): Number of 7 X (n+1) 0..1 arrays with every 2 X 2 subblock having the same number of equal edges as its horizontal neighbors and a different number from its vertical neighbors, and new values 0..1 introduced in row major order.
  • A208089 (program): Number of 8 X (n+1) 0..1 arrays with every 2 X 2 subblock having the same number of equal edges as its horizontal neighbors and a different number from its vertical neighbors, and new values 0..1 introduced in row major order.
  • A208101 (program): Triangle read by rows: T(n,0) = 1; for n > 0: T(n,1) = n, for n>1: T(n,n) = T(n-1,n-2); T(n,k) = T(n-2,k-1) + T(n-1,k) for k: 1 < k < n.
  • A208103 (program): Number of n X 3 0..1 arrays avoiding 0 0 0 and 0 1 0 horizontally and 0 1 1 and 1 1 0 vertically.
  • A208104 (program): Number of n X 4 0..1 arrays avoiding 0 0 0 and 0 1 0 horizontally and 0 1 1 and 1 1 0 vertically.
  • A208109 (program): Number of 4 X n 0..1 arrays avoiding 0 0 0 and 0 1 0 horizontally and 0 1 1 and 1 1 0 vertically.
  • A208110 (program): Number of 5 X n 0..1 arrays avoiding 0 0 0 and 0 1 0 horizontally and 0 1 1 and 1 1 0 vertically.
  • A208111 (program): Number of 6 X n 0..1 arrays avoiding 0 0 0 and 0 1 0 horizontally and 0 1 1 and 1 1 0 vertically.
  • A208112 (program): Number of 7Xn 0..1 arrays avoiding 0 0 0 and 0 1 0 horizontally and 0 1 1 and 1 1 0 vertically
  • A208114 (program): Number of n X 4 0..1 arrays avoiding 0 0 0 and 0 1 0 horizontally and 0 0 1 and 0 1 1 vertically.
  • A208115 (program): Number of n X 5 0..1 arrays avoiding 0 0 0 and 0 1 0 horizontally and 0 0 1 and 0 1 1 vertically.
  • A208116 (program): Number of nX6 0..1 arrays avoiding 0 0 0 and 0 1 0 horizontally and 0 0 1 and 0 1 1 vertically
  • A208117 (program): Number of nX7 0..1 arrays avoiding 0 0 0 and 0 1 0 horizontally and 0 0 1 and 0 1 1 vertically
  • A208119 (program): Number of 4 X n 0..1 arrays avoiding 0 0 0 and 0 1 0 horizontally and 0 0 1 and 0 1 1 vertically.
  • A208120 (program): Number of 5Xn 0..1 arrays avoiding 0 0 0 and 0 1 0 horizontally and 0 0 1 and 0 1 1 vertically
  • A208121 (program): Number of 6 X n 0..1 arrays avoiding 0 0 0 and 0 1 0 horizontally and 0 0 1 and 0 1 1 vertically.
  • A208122 (program): Number of 7Xn 0..1 arrays avoiding 0 0 0 and 0 1 0 horizontally and 0 0 1 and 0 1 1 vertically
  • A208124 (program): a(1)=2, a(n) = (4n/3)*(2n-1)!! (see A001147) for n>1.
  • A208131 (program): Partial products of A052901.
  • A208134 (program): Number of zeros in n-th row of Pascal’s triangle mod 10 (A008975).
  • A208138 (program): Number of n X 4 0..1 arrays avoiding 0 0 1 and 0 1 1 horizontally and 0 0 1 and 1 0 1 vertically.
  • A208139 (program): Number of n X 5 0..1 arrays avoiding 0 0 1 and 0 1 1 horizontally and 0 0 1 and 1 0 1 vertically.
  • A208140 (program): Number of n X 6 0..1 arrays avoiding 0 0 1 and 0 1 1 horizontally and 0 0 1 and 1 0 1 vertically.
  • A208141 (program): Number of n X 7 0..1 arrays avoiding 0 0 1 and 0 1 1 horizontally and 0 0 1 and 1 0 1 vertically.
  • A208143 (program): Number of 4Xn 0..1 arrays avoiding 0 0 1 and 0 1 1 horizontally and 0 0 1 and 1 0 1 vertically
  • A208144 (program): Number of 5Xn 0..1 arrays avoiding 0 0 1 and 0 1 1 horizontally and 0 0 1 and 1 0 1 vertically
  • A208145 (program): Number of 6Xn 0..1 arrays avoiding 0 0 1 and 0 1 1 horizontally and 0 0 1 and 1 0 1 vertically
  • A208146 (program): Number of 7Xn 0..1 arrays avoiding 0 0 1 and 0 1 1 horizontally and 0 0 1 and 1 0 1 vertically
  • A208147 (program): Sequence generated from A089080.
  • A208148 (program): Number of n state 1 dimensional radius-1 totalistic cellular automata.
  • A208176 (program): a(n) = F(n+1)^2, if n>=0 is even (F=A000045) and a(n) = (L(2n+2)+8)/5, if n is odd (L=A000204).
  • A208177 (program): Primes of the form 128*k + 1.
  • A208178 (program): Primes of the form 256*k + 1.
  • A208202 (program): a(n) = (a(n-1)*a(n-2)^2+1)/a(n-3) with a(0)=a(1)=a(2)=1.
  • A208203 (program): a(n) = (a(n-1)*a(n-2)^3+1)/a(n-3) with a(0)=a(1)=a(2)=1.
  • A208204 (program): a(n) = (a(n-1)*a(n-2)^4+1)/a(n-3) with a(0)=a(1)=a(2)=1.
  • A208206 (program): a(n)=(a(n-1)^2*a(n-2)+1)/a(n-3) with a(0)=a(1)=a(2)=1.
  • A208218 (program): a(n)=(a(n-1)^2*a(n-3)+a(n-2))/a(n-4) with a(0)=a(1)=a(2)=a(3)=1.
  • A208219 (program): a(n)=(a(n-1)^3*a(n-3)+a(n-2))/a(n-4) with a(0)=a(1)=a(2)=a(3)=1.
  • A208220 (program): a(n)=(a(n-1)*a(n-3)^2+a(n-2))/a(n-4) with a(0)=a(1)=a(2)=a(3)=1.
  • A208221 (program): a(n)=(a(n-1)^2*a(n-3)^2+a(n-2))/a(n-4) with a(0)=a(1)=a(2)=a(3)=1.
  • A208223 (program): a(n)=(a(n-1)*a(n-3)^3+a(n-2))/a(n-4) with a(0)=a(1)=a(2)=a(3)=1.
  • A208224 (program): a(n)=(a(n-1)^2*a(n-3)^3+a(n-2))/a(n-4) with a(0)=a(1)=a(2)=a(3)=1.
  • A208226 (program): a(n)=(a(n-1)*a(n-3)^4+a(n-2))/a(n-4) with a(0)=a(1)=a(2)=a(3)=1.
  • A208227 (program): a(n) = (a(n-1)^2*a(n-3)^4+a(n-2))/a(n-4) with a(0)=a(1)=a(2)=a(3)=1.
  • A208230 (program): Number of functions f:{1,2,…,n}->{1,2,…,n} with all cycles of length >= 4.
  • A208233 (program): First inverse function (numbers of rows) for pairing function A188568.
  • A208234 (program): Second inverse function (numbers of columns) for pairing function A188568.
  • A208240 (program): Number of functions f:{1,2,…,n}->{1,2,…,n} with at least one cycle of length >= 3.
  • A208244 (program): Number of ways to write n as the sum of a practical number (A005153) and a triangular number (A000217).
  • A208245 (program): Triangle read by rows: a(n,k) = a(n-2,k) + a(n-2,k-1).
  • A208251 (program): Number of refactorable numbers less than or equal to n.
  • A208253 (program): Number of n X 3 0..2 arrays with new values 0..2 introduced in row major order and no element equal to more than one of its immediate leftward or upward neighbors.
  • A208259 (program): Numbers starting and ending with digit 1.
  • A208260 (program): Nonprime numbers starting and ending with digit 1.
  • A208264 (program): Number of n X 3 0..1 arrays with new values 0..1 introduced in row major order and no element equal to more than two of its immediate leftward or upward or left-upward diagonal neighbors.
  • A208270 (program): Primes containing a digit 1.
  • A208271 (program): Nonprime numbers containing a digit 1.
  • A208273 (program): Composite numbers containing a digit 2.
  • A208274 (program): Expansion of phi(q) / phi(q^4) in powers of q where phi() is a Ramanujan theta function.
  • A208278 (program): Row sums of Pascal’s triangle mod 10 (A008975).
  • A208279 (program): Central terms of Pascal’s triangle mod 10 (A008975).
  • A208283 (program): Number of n X 4 0..1 arrays avoiding 0 0 0 and 0 0 1 horizontally and 0 0 1 and 1 1 0 vertically.
  • A208288 (program): Number of 4 X n 0..1 arrays avoiding 0 0 0 and 0 0 1 horizontally and 0 0 1 and 1 1 0 vertically.
  • A208289 (program): Number of 5 X n 0..1 arrays avoiding 0 0 0 and 0 0 1 horizontally and 0 0 1 and 1 1 0 vertically.
  • A208296 (program): Smallest positive nontrivial odd solution of the congruence x^2 == 1 (mod A001748(n+2)), n >= 1.
  • A208309 (program): Number of n X 3 0..1 arrays with new values 0..1 introduced in row major order and no element equal to more than one of its immediate leftward or upward neighbors.
  • A208316 (program): Number of n X 2 0..2 arrays with new values 0..2 introduced in row major order and no element equal to more than two of its immediate leftward or upward or left-upward diagonal neighbors.
  • A208324 (program): Triangle T(n,k), read by rows, given by (2, -1/2, 1/2, 0, 0, 0, 0, 0, 0, 0, …) DELTA (4, -2, 0, 0, 0, 0, 0, 0, 0, 0, …) where DELTA is the operator defined in A084938.
  • A208326 (program): n + [nr/t] + [ns/t], where []=floor, r=5, s=(1+sqrt(5))/2, t=1/s.
  • A208327 (program): Position of f(n) when the numbers f(j) and g(k) are jointly ranked, where f(j)=j + |cos j | and g(k)=k + |sin k|.
  • A208328 (program): Triangle of coefficients of polynomials u(n,x) jointly generated with A208329; see the Formula section.
  • A208330 (program): Triangle of coefficients of polynomials u(n,x) jointly generated with A208331; see the Formula section.
  • A208331 (program): Triangle of coefficients of polynomials v(n,x) jointly generated with A208330; see the Formula section.
  • A208332 (program): Triangle of coefficients of polynomials u(n,x) jointly generated with A208333; see the Formula section.
  • A208334 (program): Triangle of coefficients of polynomials u(n,x) jointly generated with A208335; see the Formula section.
  • A208335 (program): Triangle of coefficients of polynomials v(n,x) jointly generated with A208834; see the Formula section.
  • A208336 (program): Triangle of coefficients of polynomials u(n,x) jointly generated with A208337; see the Formula section.
  • A208337 (program): Triangle of coefficients of polynomials v(n,x) jointly generated with A208836; see the Formula section.
  • A208338 (program): Triangle of coefficients of polynomials u(n,x) jointly generated with A208339; see the Formula section.
  • A208339 (program): Triangle of coefficients of polynomials v(n,x) jointly generated with A208838; see the Formula section.
  • A208340 (program): Triangle of coefficients of polynomials v(n,x) jointly generated with A202390; see the Formula section.
  • A208341 (program): Triangle read by rows, T(n,k) = hypergeometric_2F1([n-k+1, -k], [1], -1) for n>=0 and k>=0.
  • A208342 (program): Triangle of coefficients of polynomials u(n,x) jointly generated with A208343; see the Formula section.
  • A208344 (program): Triangle of coefficients of polynomials u(n,x) jointly generated with A208345; see the Formula section.
  • A208347 (program): Number of nX2 0..3 arrays with new values 0..3 introduced in row major order and no element equal to any knight-move neighbor (colorings ignoring permutations of colors)
  • A208354 (program): Number of compositions of n with at most one even part.
  • A208355 (program): Right edge of the triangle in A208101.
  • A208375 (program): Number of n X 4 0..1 arrays avoiding 0 0 0 and 1 1 1 horizontally and 0 0 1 and 1 0 1 vertically.
  • A208376 (program): Number of n X 5 0..1 arrays avoiding 0 0 0 and 1 1 1 horizontally and 0 0 1 and 1 0 1 vertically.
  • A208377 (program): Number of n X 6 0..1 arrays avoiding 0 0 0 and 1 1 1 horizontally and 0 0 1 and 1 0 1 vertically.
  • A208378 (program): Number of n X 7 0..1 arrays avoiding 0 0 0 and 1 1 1 horizontally and 0 0 1 and 1 0 1 vertically.
  • A208387 (program): Number of nX3 0..2 arrays with new values 0..2 introduced in row major order and no element equal to more than two of its immediate leftward or upward or right-upward antidiagonal neighbors
  • A208388 (program): Number of n X 4 0..2 arrays with new values 0..2 introduced in row major order and no element equal to more than two of its immediate leftward or upward or right-upward antidiagonal neighbors.
  • A208393 (program): Number of 2 X n 0..2 arrays with new values 0..2 introduced in row major order and no element equal to more than two of its immediate leftward or upward or right-upward antidiagonal neighbors.
  • A208402 (program): Number of n X 2 0..3 arrays with new values 0..3 introduced in row major order and no element equal to more than two of its immediate leftward or upward or right-upward antidiagonal neighbors.
  • A208421 (program): Number of 4 X n 0..1 arrays avoiding 0 0 0 and 0 0 1 horizontally and 0 0 0 and 0 1 1 vertically.
  • A208425 (program): G.f.: Sum_{n>=0} (3*n)!/n!^3 * x^(2*n)/(1-x)^(3*n+1).
  • A208426 (program): G.f.: Sum_{n>=0} (3*n)!/n!^3 * x^(2*n)/(1-3*x)^(3*n+1).
  • A208428 (program): Number of n X 2 0..2 arrays with new values 0..2 introduced in row major order and no element equal to any knight-move neighbor (colorings ignoring permutations of colors).
  • A208448 (program): Greatest common divisors of consecutive floor-factorial numbers (A010786).
  • A208449 (program): Numerator of A010786(n+1) / A010786(n).
  • A208450 (program): Denominator of A010786(n+1) / A010786(n).
  • A208458 (program): Digits of the Golden Ratio (1+(Sqrt[5]-1)/2) read in decimal as if written in hexadecimal.
  • A208462 (program): Number of nX3 nonnegative integer arrays with new values 0 upwards introduced in row major order and no element equal to more than two of its immediate leftward or upward or right-upward antidiagonal neighbors
  • A208473 (program): Central coefficients of triangle A185384.
  • A208481 (program): Diagonal sums of triangle A185384.
  • A208485 (program): Number of (n+1) X 2 0..3 arrays with the number of clockwise edge increases in every 2 X 2 subblock equal to the number of counterclockwise edge increases.
  • A208502 (program): Number of 4 X n 0..1 arrays avoiding 0 0 0 and 0 0 1 horizontally and 0 1 0 and 1 1 1 vertically.
  • A208506 (program): p^(p+1) + (p+1)^p, where p = prime(n).
  • A208508 (program): Triangle of coefficients of polynomials u(n,x) jointly generated with A208509; see the Formula section.
  • A208509 (program): Triangle of coefficients of polynomials v(n,x) jointly generated with A208508; see the Formula section.
  • A208510 (program): Triangle of coefficients of polynomials u(n,x) jointly generated with A029653; see the Formula section.
  • A208511 (program): Triangle of coefficients of polynomials u(n,x) jointly generated with A208512; see the Formula section.
  • A208513 (program): Triangle of coefficients of polynomials u(n,x) jointly generated with A111125; see the Formula section.
  • A208514 (program): Triangle of coefficients of polynomials u(n,x) jointly generated with A208515; see the Formula section.
  • A208515 (program): Triangle of coefficients of polynomials v(n,x) jointly generated with A208514; see the Formula section.
  • A208516 (program): Triangle of coefficients of polynomials u(n,x) jointly generated with A208517; see the Formula section.
  • A208517 (program): Triangle of coefficients of polynomials v(n,x) jointly generated with A208516; see the Formula section.
  • A208518 (program): Triangle of coefficients of polynomials u(n,x) jointly generated with A208519; see the Formula section.
  • A208519 (program): Triangle of coefficients of polynomials v(n,x) jointly generated with A208518; see the Formula section.
  • A208520 (program): Triangle of coefficients of polynomials u(n,x) jointly generated with A208521; see the Formula section.
  • A208521 (program): Triangle of coefficients of polynomials v(n,x) jointly generated with A208520; see the Formula section.
  • A208522 (program): Triangle of coefficients of polynomials u(n,x) jointly generated with A208522; see the Formula section.
  • A208523 (program): Triangle of coefficients of polynomials v(n,x) jointly generated with A208522; see the Formula section.
  • A208524 (program): Triangle of coefficients of polynomials u(n,x) jointly generated with A208525; see the Formula section.
  • A208525 (program): Triangle of coefficients of polynomials v(n,x) jointly generated with A208524; see the Formula section.
  • A208526 (program): Triangle of coefficients of polynomials u(n,x) jointly generated with A208527; see the Formula section.
  • A208527 (program): Triangle of coefficients of polynomials v(n,x) jointly generated with A208526; see the Formula section.
  • A208528 (program): Number of permutations of n>1 having exactly 3 points P on the boundary of their bounding square.
  • A208529 (program): Number of permutations of n > 1 having exactly 2 points on the boundary of their bounding square.
  • A208532 (program): Mirror image of triangle in A125185; unsigned version of A120058.
  • A208536 (program): Number of 5-bead necklaces of n colors not allowing reversal, with no adjacent beads having the same color.
  • A208537 (program): Number of 7-bead necklaces of n colors not allowing reversal, with no adjacent beads having the same color.
  • A208545 (program): Number of 7-bead necklaces of n colors allowing reversal, with no adjacent beads having the same color.
  • A208551 (program): Number of n X 4 0..1 arrays avoiding 0 0 0 and 0 0 1 horizontally and 0 0 1 and 0 1 1 vertically.
  • A208552 (program): Number of n X 5 0..1 arrays avoiding 0 0 0 and 0 0 1 horizontally and 0 0 1 and 0 1 1 vertically.
  • A208553 (program): Number of nX6 0..1 arrays avoiding 0 0 0 and 0 0 1 horizontally and 0 0 1 and 0 1 1 vertically
  • A208554 (program): Number of nX7 0..1 arrays avoiding 0 0 0 and 0 0 1 horizontally and 0 0 1 and 0 1 1 vertically
  • A208556 (program): Number of 4 X n 0..1 arrays avoiding 0 0 0 and 0 0 1 horizontally and 0 0 1 and 0 1 1 vertically.
  • A208557 (program): Number of 5 X n 0..1 arrays avoiding 0 0 0 and 0 0 1 horizontally and 0 0 1 and 0 1 1 vertically.
  • A208558 (program): Number of 6 X n 0..1 arrays avoiding 0 0 0 and 0 0 1 horizontally and 0 0 1 and 0 1 1 vertically.
  • A208559 (program): Number of 7 X n 0..1 arrays avoiding 0 0 0 and 0 0 1 horizontally and 0 0 1 and 0 1 1 vertically.
  • A208561 (program): Number of n X 2 0..2 arrays with new values 0..2 introduced in row major order and no element equal to more than one of its immediate leftward or upward or left-upward diagonal neighbors.
  • A208569 (program): Triangular array T(n,k), n>=1, k=1..2^(n-1), read by rows in bracketed pairs such that highest ranked element is bracketed with lowest ranked.
  • A208570 (program): LCM of n and smallest nondivisor of n.
  • A208575 (program): Product of digits of n in factorial base.
  • A208576 (program): Multiplicative persistence of n in factorial base.
  • A208577 (program): Number of nX2 nonnegative integer arrays with new values 0 upwards introduced in row major order and no element equal to more than one of its immediate leftward or upward or right-upward antidiagonal neighbors
  • A208588 (program): Row square-sums of triangle A185384.
  • A208589 (program): Expansion of phi(x) / psi(x^4) in powers of x where phi(), psi() are Ramanujan theta functions.
  • A208591 (program): Number of n-bead necklaces labeled with numbers -2..2 not allowing reversal, with sum zero.
  • A208592 (program): Number of n-bead necklaces labeled with numbers -3..3 not allowing reversal, with sum zero.
  • A208598 (program): Number of 4-bead necklaces labeled with numbers -n..n not allowing reversal, with sum zero.
  • A208599 (program): Number of 5-bead necklaces labeled with numbers -n..n not allowing reversal, with sum zero.
  • A208602 (program): Number of n-bead necklaces labeled with numbers -1..1 not allowing reversal, with sum zero.
  • A208603 (program): McKay-Thompson series of class 16B for the Monster group with a(0) = 2.
  • A208604 (program): Expansion of phi(-q) / phi(q^4) in powers of q where phi() is a Ramanujan theta function.
  • A208605 (program): Expansion of q * psi(q^8) / phi(q) in powers of q where phi(), psi() are Ramanujan theta functions.
  • A208624 (program): Number of Young tableaux with n 4-length rows, increasing entries down the columns and monotonic entries along the rows (first row increasing).
  • A208633 (program): Number of n X 4 0..1 arrays with new values 0..1 introduced in row major order and no element equal to more than one of its immediate leftward or upward or right-upward antidiagonal neighbors.
  • A208634 (program): Number of n X 5 0..1 arrays with new values 0..1 introduced in row major order and no element equal to more than one of its immediate leftward or upward or right-upward antidiagonal neighbors.
  • A208635 (program): Number of n X 6 0..1 arrays with new values 0..1 introduced in row major order and no element equal to more than one of its immediate leftward or upward or right-upward antidiagonal neighbors.
  • A208638 (program): Number of 3 X n 0..1 arrays with new values 0..1 introduced in row major order and no element equal to more than one of its immediate leftward or upward or right-upward antidiagonal neighbors.
  • A208639 (program): Number of 4 X n 0..1 arrays with new values 0..1 introduced in row major order and no element equal to more than one of its immediate leftward or upward or right-upward antidiagonal neighbors.
  • A208643 (program): Least positive integer m such that those k*(k-1) mod m with k=1,…,n are pairwise distinct.
  • A208645 (program): Least x>0 such that x^2+x+n is not prime.
  • A208647 (program): Numerators of Pokrovskiy’s lower bound on the ratio of e(G^n) the number of edges in the n-th power of a graph G, to E(G) the number of edges of G.
  • A208648 (program): Denominators of Pokrovskiy’s lower bound on the ratio of e(G^n) the number of edges in the n-th power of a graph G, to E(G) the number of edges of G.
  • A208649 (program): (1/n)*A073617(n+1).
  • A208650 (program): Number of constant paths through the subset array of {1,2,…,n}; see Comments.
  • A208651 (program): Number of paths through the subset array whose trace is a permutation of (1,2,…,n); see Comments.
  • A208652 (program): Product{i*C(n,i) : 1<=i<=floor[(n+1)/2]}.
  • A208653 (program): a(n) = Product_{i=floor((n + 1)/2)..n-1} binomial(n-1, i).
  • A208656 (program): Triangle T(n, k) = n*C(n,k) - C(n-1,k-1), 1 <= k <= n, read by rows.
  • A208657 (program): Triangular array read by rows: n*binomial(n,n-k+1)-binomial(n-1,n-k) with k = 1..n, n >= 1.
  • A208658 (program): Row sums of A208657.
  • A208659 (program): Triangle of coefficients of polynomials v(n,x) jointly generated with A185045; see the Formula section.
  • A208660 (program): Triangle of coefficients of polynomials u(n,x) jointly generated with A208904; see the Formula section.
  • A208661 (program): Number of paths through the subset array of {1,2,…,n} that have range a subset of {1,2}; see Comments at A208650.
  • A208665 (program): Numbers that match odd ternary polynomials; see Comments.
  • A208667 (program): Number of 2n-bead necklaces labeled with numbers 1..4 allowing reversal, with neighbors differing by exactly 1.
  • A208674 (program): Number of words, either empty or beginning with the first letter of the n-ary alphabet, where each letter of the alphabet occurs 3 times and letters of neighboring word positions are equal or neighbors in the alphabet.
  • A208675 (program): Number of words, either empty or beginning with the first letter of the ternary alphabet, where each letter of the alphabet occurs n times and letters of neighboring word positions are equal or neighbors in the alphabet.
  • A208689 (program): Number of 3 X n 0..1 arrays avoiding 0 0 0 and 0 0 1 horizontally and 0 1 1 and 1 0 1 vertically.
  • A208691 (program): Number of 5 X n 0..1 arrays avoiding 0 0 0 and 0 0 1 horizontally and 0 1 1 and 1 0 1 vertically.
  • A208692 (program): Number of 6 X n 0..1 arrays avoiding 0 0 0 and 0 0 1 horizontally and 0 1 1 and 1 0 1 vertically.
  • A208704 (program): Number of nX3 0..1 arrays with new values 0..1 introduced in row major order and no element equal to more than two of its immediate leftward or upward or right-upward antidiagonal neighbors.
  • A208705 (program): Number of n X 4 0..1 arrays with new values 0..1 introduced in row major order and no element equal to more than two of its immediate leftward or upward or right-upward antidiagonal neighbors.
  • A208710 (program): Number of 3 X n 0..1 arrays with new values 0..1 introduced in row major order and no element equal to more than two of its immediate leftward or upward or right-upward antidiagonal neighbors.
  • A208723 (program): Number of 2n-bead necklaces labeled with numbers 1..4 not allowing reversal, with neighbors differing by exactly 1.
  • A208724 (program): Number of 2n-bead necklaces labeled with numbers 1..5 not allowing reversal, with neighbors differing by exactly 1.
  • A208725 (program): Number of 2n-bead necklaces labeled with numbers 1..6 not allowing reversal, with neighbors differing by exactly 1.
  • A208736 (program): Number of nonisomorphic graded posets with 0 and 1 and non-uniform Hasse graph of rank n, with exactly 2 elements of each rank level between 0 and 1.
  • A208737 (program): Number of nonisomorphic graded posets with 0 and 1 and non-uniform Hasse graph of rank n, with no 3-element antichain.
  • A208738 (program): Number of multisets occurring as the peak heights multiset of a Dyck n-path.
  • A208739 (program): 2^n minus the number of partitions of n
  • A208740 (program): Number of multisets that occurring as the peak heights multiset of a Dyck n-path that are the also the peak heights multiset of a smaller Dyck path.
  • A208743 (program): Number of subsets of the set {1,2,…,n} which do not contain two elements whose difference is 6.
  • A208744 (program): Triangle relating to ordered Bell numbers, A000670.
  • A208745 (program): Decimal expansion of the gravitoid constant.
  • A208747 (program): Triangle of coefficients of polynomials u(n,x) jointly generated with A208748; see the Formula section.
  • A208752 (program): Triangle of coefficients of polynomials v(n,x) jointly generated with A208751; see the Formula section.
  • A208755 (program): Triangle of coefficients of polynomials u(n,x) jointly generated with A208756; see the Formula section.
  • A208757 (program): Triangle of coefficients of polynomials u(n,x) jointly generated with A208758; see the Formula section.
  • A208759 (program): Triangle of coefficients of polynomials u(n,x) jointly generated with A208760; see the Formula section.
  • A208760 (program): Triangle of coefficients of polynomials v(n,x) jointly generated with A208759; see the Formula section.
  • A208763 (program): Triangle of coefficients of polynomials u(n,x) jointly generated with A208764; see the Formula section.
  • A208765 (program): Triangle of coefficients of polynomials u(n,x) jointly generated with A208766; see the Formula section.
  • A208766 (program): Triangle of coefficients of polynomials v(n,x) jointly generated with A208765; see the Formula section.
  • A208768 (program): The distinct values of A070198.
  • A208772 (program): Number of n-bead necklaces labeled with numbers 1..3 not allowing reversal, with no adjacent beads differing by more than 1.
  • A208773 (program): Number of n-bead necklaces labeled with numbers 1..4 not allowing reversal, with no adjacent beads differing by more than 1.
  • A208774 (program): Number of n-bead necklaces labeled with numbers 1..5 not allowing reversal, with no adjacent beads differing by more than 1.
  • A208778 (program): Number of n X 6 0..1 arrays avoiding 0 0 0 and 0 0 1 horizontally and 0 1 1 and 1 1 1 vertically.
  • A208779 (program): Number of n X 7 0..1 arrays avoiding 0 0 0 and 0 0 1 horizontally and 0 1 1 and 1 1 1 vertically.
  • A208782 (program): Number of nX2 nonnegative integer arrays with new values 0 upwards introduced in row major order and no element equal to any antidiagonal neighbor (colorings ignoring permutations of colors)
  • A208783 (program): Number of nX3 nonnegative integer arrays with new values 0 upwards introduced in row major order and no element equal to any antidiagonal neighbor (colorings ignoring permutations of colors)
  • A208841 (program): Number of 4 X n 0..1 arrays avoiding 0 0 0 and 0 0 1 horizontally and 0 1 1 and 1 1 0 vertically.
  • A208842 (program): Number of 5 X n 0..1 arrays avoiding 0 0 0 and 0 0 1 horizontally and 0 1 1 and 1 1 0 vertically.
  • A208843 (program): Number of 6 X n 0..1 arrays avoiding 0 0 0 and 0 0 1 horizontally and 0 1 1 and 1 1 0 vertically.
  • A208844 (program): Number of 7 X n 0..1 arrays avoiding 0 0 0 and 0 0 1 horizontally and 0 1 1 and 1 1 0 vertically.
  • A208845 (program): Expansion of f(x)^2 in powers of x where f() is a Ramanujan theta function.
  • A208850 (program): Expansion of phi(q^2) / phi(-q) in powers of q where phi() is a Ramanujan theta function.
  • A208851 (program): Partitions of 2*n + 1 into parts not congruent to 0, +-4, +-6, +-10, 16 (mod 32).
  • A208855 (program): Array of even catheti of primitive Pythagorean triangles when read by SW-NE diagonals.
  • A208856 (program): Partitions of n into parts not congruent to 0, +-4, +-6, +-10, 16 (mod 32).
  • A208866 (program): Number of n X 2 0..3 arrays with new values 0..3 introduced in row major order and no element equal to more than one of its immediate leftward or upward or right-upward antidiagonal neighbors.
  • A208881 (program): Number of words either empty or beginning with the first letter of the ternary alphabet, where each letter of the alphabet occurs n times.
  • A208882 (program): Number of representations of square of prime(n) as a^2 + b^2 + c^2 with 0 < a <= b <= c.
  • A208884 (program): a(n) = (a(n-1) + n)/2^k where 2^k is the largest power of 2 dividing a(n-1) + n, for n>1 with a(1)=1.
  • A208890 (program): a(n) = A000984(n)*A004981(n), the term-wise product of the coefficients in (1-4*x)^(-1/2) and (1-8*x)^(-1/4).
  • A208891 (program): Pascal’s triangle matrix augmented with a right border of 1’s.
  • A208895 (program): Number of non-congruent solutions to x^2 + y^2 + z^2 + t^2 == 1 (mod n).
  • A208899 (program): Decimal expansion of sqrt(5)/3 .
  • A208900 (program): Number of bitstrings of length n which (if having two or more runs) the last two runs have different lengths.
  • A208901 (program): Number of bitstrings of length n (with at least two runs) where the last two runs have different lengths.
  • A208902 (program): The sum over all bitstrings b of length n of the number of runs in b not immediately followed by a longer run.
  • A208903 (program): The sum over all bitstrings b of length n with at least two runs of the number of runs in b not immediately followed by a longer run.
  • A208904 (program): Triangle of coefficients of polynomials v(n,x) jointly generated with A208660; see the Formula section.
  • A208905 (program): Triangle of coefficients of polynomials u(n,x) jointly generated with A208906; see the Formula section.
  • A208906 (program): Triangle of coefficients of polynomials v(n,x) jointly generated with A208905; see the Formula section.
  • A208907 (program): Triangle of coefficients of polynomials u(n,x) jointly generated with A208756; see the Formula section.
  • A208908 (program): Triangle of coefficients of polynomials v(n,x) jointly generated with A208923; see the Formula section.
  • A208910 (program): Triangle of coefficients of polynomials v(n,x) jointly generated with A208755; see the Formula section.
  • A208911 (program): Triangle of coefficients of polynomials u(n,x) jointly generated with A208912; see the Formula section.
  • A208912 (program): Triangle of coefficients of polynomials v(n,x) jointly generated with A208911; see the Formula section.
  • A208913 (program): Triangle of coefficients of polynomials u(n,x) jointly generated with A208914; see the Formula section.
  • A208914 (program): Triangle of coefficients of polynomials v(n,x) jointly generated with A208913; see the Formula section.
  • A208915 (program): Triangle of coefficients of polynomials u(n,x) jointly generated with A208916; see the Formula section.
  • A208916 (program): Triangle of coefficients of polynomials v(n,x) jointly generated with A208915; see the Formula section.
  • A208917 (program): Triangle of coefficients of polynomials u(n,x) jointly generated with A208918; see the Formula section.
  • A208918 (program): Triangle of coefficients of polynomials v(n,x) jointly generated with A208917; see the Formula section.
  • A208919 (program): Triangle of coefficients of polynomials u(n,x) jointly generated with A208920; see the Formula section.
  • A208920 (program): Triangle of coefficients of polynomials v(n,x) jointly generated with A208919; see the Formula section.
  • A208923 (program): Triangle of coefficients of polynomials u(n,x) jointly generated with A208908; see the Formula section.
  • A208933 (program): Expansion of phi(q^4) / phi(-q) in powers of q where phi() is a Ramanujan theta function.
  • A208935 (program): Digits of Pi read in decimal as if written in hexadecimal.
  • A208936 (program): Prime production length of the polynomial P = x^2 + x + prime(n): max { k>0 | P(x) is prime for all x=0,…,k-1 }.
  • A208946 (program): Number of 4-bead necklaces labeled with numbers -n..n not allowing reversal, with sum zero with no three beads in a row equal.
  • A208950 (program): a(4*n) = n*(16*n^2-1)/3, a(2*n+1) = n*(n+1)*(2*n+1)/6, a(4*n+2) = (4*n+1)*(4*n+2)*(4*n+3)/6.
  • A208954 (program): a(n) = n^4*(n-1)*(n+1)/12.
  • A208955 (program): Expansion of phi(x) * phi(x^9) / chi(x^3)^2 in powers of x where phi(), chi() are Ramanujan theta functions.
  • A208956 (program): Triangular array read by rows. T(n,k) is the number of n-permutations that have at least k fixed points with n >= 1 and 1 <= k <= n.
  • A208971 (program): Number of 4-bead necklaces labeled with numbers -n..n allowing reversal, with sum zero and first and second differences in -n..n.
  • A208976 (program): Row sums of the triangle in A208101.
  • A208978 (program): Expansion of f(x) * f(x^3) where f() is a Ramanujan theta function.
  • A208981 (program): Number of iterations required to reach a power of 2 in the 3x+1 sequence starting at n.
  • A208982 (program): Numbers n such that the next larger number with mutual Hamming distance 1 is prime.
  • A208983 (program): Central terms of the triangle in A208101.
  • A208994 (program): Number of 3-bead necklaces labeled with numbers -n..n not allowing reversal, with sum zero and first differences in -n..n.
  • A208995 (program): Number of 4-bead necklaces labeled with numbers -n..n not allowing reversal, with sum zero and first differences in -n..n.
  • A209008 (program): Number of 4-bead necklaces labeled with numbers -n..n not allowing reversal, with sum zero and first and second differences in -n..n.
  • A209036 (program): Number of permutations of the multiset {1,1,2,2,….,n,n} with exactly two consecutive equal terms.
  • A209041 (program): Number of n X 2 0..3 arrays with no element equal the average of immediate neighbors vertically above and horizontally left of it.
  • A209081 (program): Floor(A152170(n)/n^n). Floor of the expected value of the cardinality of the image of a function from [n] to [n].
  • A209084 (program): a(n) = 2*a(n-1) + 4*a(n-2) with n>1, a(0)=0, a(1)=4.
  • A209085 (program): a(n) is the next larger than A208982(n) number with mutual Hamming distance 1.
  • A209094 (program): Number of n X 2 0..2 arrays with new values 0..2 introduced in row major order and no element equal to more than one of its immediate leftward or upward or right-upward antidiagonal neighbors.
  • A209101 (program): Number of 2 X n 0..2 arrays with new values 0..2 introduced in row major order and no element equal to more than one of its immediate leftward or upward or right-upward antidiagonal neighbors.
  • A209116 (program): Number of 4-bead necklaces labeled with numbers -n..n not allowing reversal, with sum zero and avoiding the patterns z z+1 z+2 and z z-1 z-2.
  • A209122 (program): Numbers a(n) for which there exists k>1 such that the number of partitions of a(n) into k parts is k.
  • A209131 (program): Triangle of coefficients of polynomials u(n,x) jointly generated with A209132; see the Formula section.
  • A209132 (program): Triangle of coefficients of polynomials v(n,x) jointly generated with A209131; see the Formula section.
  • A209144 (program): Triangle of coefficients of polynomials v(n,x) jointly generated with A209143; see the Formula section.
  • A209145 (program): Triangle of coefficients of polynomials u(n,x) jointly generated with A122075; see the Formula section.
  • A209148 (program): Triangle of coefficients of polynomials u(n,x) jointly generated with A209149; see the Formula section.
  • A209149 (program): Triangle of coefficients of polynomials v(n,x) jointly generated with A209146; see the Formula section.
  • A209150 (program): Triangle of coefficients of polynomials u(n,x) jointly generated with A208335; see the Formula section.
  • A209151 (program): Triangle of coefficients of polynomials u(n,x) jointly generated with A208337; see the Formula section.
  • A209158 (program): Triangle of coefficients of polynomials u(n,x) jointly generated with A209159; see the Formula section.
  • A209159 (program): Triangle of coefficients of polynomials v(n,x) jointly generated with A209158; see the Formula section.
  • A209160 (program): Triangle of coefficients of polynomials u(n,x) jointly generated with A209161; see the Formula section.
  • A209161 (program): Triangle of coefficients of polynomials v(n,x) jointly generated with A209160; see the Formula section.
  • A209164 (program): Triangle of coefficients of polynomials u(n,x) jointly generated with A209165; see the Formula section.
  • A209165 (program): Triangle of coefficients of polynomials v(n,x) jointly generated with A209164; see the Formula section.
  • A209172 (program): Triangle of coefficients of polynomials u(n,x) jointly generated with A209413; see the Formula section.
  • A209187 (program): Sum of divisors of n minus cototient of n.
  • A209188 (program): Smallest prime factor of n^2 + n - 1.
  • A209189 (program): Smallest prime factor of n^2 + n + 1.
  • A209190 (program): Least prime factor of reversal of digits of n.
  • A209197 (program): Column 1 of triangle A209196.
  • A209200 (program): G.f.: (1-4*x)^(-1/2) * (1-8*x)^(-1/4).
  • A209202 (program): Values of the difference d for 3 primes in geometric-arithmetic progression with the minimal sequence {3*3^j + j*d}, j = 0 to 2.
  • A209211 (program): Numbers n such that n-1 and phi(n) are relatively prime.
  • A209225 (program): Number of 4 X n 0..1 arrays avoiding 0 0 0 and 0 1 0 horizontally and 0 1 0 and 1 1 1 vertically.
  • A209229 (program): Characteristic function of powers of 2, cf. A000079.
  • A209230 (program): Number of set partitions of [n] that avoid 1231 and 1121.
  • A209231 (program): Number of binary words of length n such that there is at least one 0 and every run of consecutive 0’s is of length >= 4.
  • A209239 (program): Number of length n words on {0,1,2} with no four consecutive 0’s.
  • A209245 (program): Main diagonal of the triple recurrence x(i,j,k) = x(i-1,j,k) + x(i,j-1,k) + x(i,j,k-1) with x(i,j,k) = 1 if 0 in {i,j,k}.
  • A209246 (program): Row sums of triangle A196020.
  • A209262 (program): a(n) = 1 + 2*n^2 + 3*n^3 + 4*n^4.
  • A209263 (program): a(n) = 1 + 2*n^2 + 3*n^3 + 4*n^4 + 5*n^5.
  • A209264 (program): a(n) = 1 + 2*n^2 + 3*n^3 + 4*n^4 +5*n^5 + 6*n^6.
  • A209265 (program): a(n) = 1 + 2*n^2 + 3*n^3 + 4*n^4 +5*n^5 + 6*n^6 + 7*n^7.
  • A209267 (program): 1 + 2*n^2 + 3*n^3 + 4*n^4 + 5*n^5 + 6*n^6 + 7*n^7 + 8*n^8.
  • A209268 (program): Inverse permutation A054582.
  • A209274 (program): Table T(n,k) = n*(n+2^k-1)/2, n, k > 0 read by antidiagonals.
  • A209275 (program): a(n) = 1 + 2*n^2 + 3*n^3 + 4*n^4 + 5*n^5 + 6*n^6 + 7*n^7 + 8*n^8 + 9*n^9.
  • A209278 (program): Second inverse function (numbers of rows) for pairing function A185180.
  • A209279 (program): First inverse function (numbers of rows) for pairing function A185180.
  • A209280 (program): First difference of A050289 = numbers whose digits are a permutation of (1,…,9).
  • A209281 (program): Start with first run [0,1] then, for n >= 2, the n-th run has length 2^n and is the concatenation of [a(1),a(2),…,a(2^n/2)] and [n-a(1),n-a(2),…,n-a(2^n/2)].
  • A209286 (program): a(n) = a(n-1) + (1+a(n-2))*a(n-3) for n>1, a(1) = 1, a(n) = 0 for n<1.
  • A209289 (program): Number of functions f:{1,2,…,2n}->{1,2,…,2n} such that every preimage has an even cardinality.
  • A209290 (program): Number of elements whose preimage is the empty set summed over all functions f:{1,2,…,n}->{1,2,…,n}.
  • A209291 (program): Sum of the refactorable numbers less than or equal to n.
  • A209292 (program): Non-semiprimes n such that 2n+1 are non-semiprimes.
  • A209293 (program): Inverse permutation of A185180.
  • A209294 (program): a(n) = (7*n^2 - 7*n + 4)/2.
  • A209295 (program): Antidiagonal sums of the gcd(.,.) array A109004.
  • A209297 (program): Triangle read by rows: T(n,k) = k*n + k - n, 1 <= k <= n.
  • A209301 (program): Table T(n,k) n, k > 0, T(n,k)=n-k+1, if n>=k, T(n,k)=k-n+2, if n < k. Table read by sides of squares from T(1,n) to T(n,n), then from T(n,n) to T(n,1).
  • A209302 (program): Table T(n,k) = max{n+k-1, n+k-1} n, k > 0, read by sides of squares from T(1,n) to T(n,n), then from T(n,n) to T(n,1).
  • A209304 (program): Table T(n,k)=n+4*k-4 n, k > 0, read by antidiagonals.
  • A209319 (program): Number of functions f:{1,2,…,n}->{1,2,…,n} whose cycle lengths are <= 2.
  • A209323 (program): Values of omega(n) (A001221) as n runs through the triprimes (A014612).
  • A209328 (program): Decimal expansion of the sum of the inverse twin prime products.
  • A209330 (program): Triangle defined by T(n,k) = binomial(n^2, n*k), for n>=0, k=0..n, as read by rows.
  • A209331 (program): a(n) = Sum_{k=0..[n/2]} binomial((n-k)^2, n*k-k^2).
  • A209345 (program): Number of 4-bead necklaces labeled with numbers -n..n allowing reversal, with sum zero with no three beads in a row equal
  • A209350 (program): Number of initially rising meander words, where each letter of the cyclic n-ary alphabet occurs twice.
  • A209352 (program): Number of initially rising meander words, where each letter of the cyclic 6-ary alphabet occurs n times.
  • A209355 (program): Sequence with each term appearing in runs of every length infinitely often.
  • A209356 (program): The function g(n), the inverse of f(k) the shortest length of a binary linear intersecting code.
  • A209358 (program): G.f.: (1-4*x)^(-1/4) * (1-8*x)^(-1/8).
  • A209359 (program): a(n) = 2^n * (n^4 - 4*n^3 + 18*n^2 - 52*n + 75) - 75.
  • A209376 (program): 1/4 the number of (n+1) X 3 0..2 arrays with every 2 X 2 subblock having distinct edge sums.
  • A209388 (program): Product of positive odd integers smaller than n and relatively prime to n.
  • A209398 (program): Number of subsets of {1,…,n} containing two elements whose difference is 2.
  • A209399 (program): Number of subsets of {1,…,n} containing two elements whose difference is 3.
  • A209400 (program): Number of subsets of {1,…,n} containing a subset of the form {k,k+1,k+3} for some k.
  • A209404 (program): Negated coefficients of Chebyshev T polynomials: a(n) = -A053120(n+14, n), n >= 0.
  • A209408 (program): Number of subsets of {1,…,n} containing {a,a+4} for some a.
  • A209409 (program): Number of subsets of {1,…,n} containing {a,a+2,a+4} for some a.
  • A209410 (program): Number of subsets of {1,…,n} not containing {a,a+2,a+4} for any a.
  • A209413 (program): Triangle of coefficients of polynomials v(n,x) jointly generated with A209172; see the Formula section.
  • A209414 (program): Triangle of coefficients of polynomials u(n,x) jointly generated with A112351; see the Formula section.
  • A209415 (program): Triangle of coefficients of polynomials u(n,x) jointly generated with A209416; see the Formula section.
  • A209416 (program): Triangle of coefficients of polynomials v(n,x) jointly generated with A209415; see the Formula section.
  • A209419 (program): Triangle of coefficients of polynomials u(n,x) jointly generated with A209420; see the Formula section.
  • A209420 (program): Triangle of coefficients of polynomials v(n,x) jointly generated with A209419; see the Formula section.
  • A209421 (program): Triangle of coefficients of polynomials u(n,x) jointly generated with A209422; see the Formula section.
  • A209427 (program): T(n,k) = binomial(n,k)^n.
  • A209428 (program): a(n) = Sum_{k=0..[n/2]} binomial(n-k,k)^(n-k).
  • A209429 (program): Numerator of l(n), where l(1)=1, l(2)=2, l(n)=l(n-1)+2*l(n-2)/n.
  • A209430 (program): Denominator of l(n), where l(1)=1, l(2)=2, l(n)=l(n-1)+2*l(n-2)/n.
  • A209443 (program): a(n) = Pell(n)*A000118(n) for n>=1 with a(0)=1, where A000118(n) is the number of ways of writing n as a sum of 4 squares.
  • A209444 (program): a(n) = Pell(n)*A000143(n) for n>=1 with a(0)=1, where A000143(n) is the number of ways of writing n as a sum of 8 squares.
  • A209445 (program): a(n) = Pell(n)*A001227(n) for n >= 1, where A001227(n) is the number of odd divisors of n.
  • A209446 (program): a(n) = Pell(n)*A004016(n) for n >= 1, with a(0)=1, where A004016(n) is the number of integer solutions (x,y) to x^2 + x*y + y^2 = n.
  • A209447 (program): a(n) = Pell(n)*A008653(n) for n>=1, with a(0)=1, where A008653 is the theta series of direct sum of 2 copies of hexagonal lattice.
  • A209449 (program): a(n) = Pell(n)*A113973(n) for n>=1, with a(0)=1, where A113973 lists the coefficients in phi(x^3)^3/phi(x) and phi() is a Ramanujan theta function.
  • A209450 (program): a(n) = Pell(n)*A132973(n) for n>=1, with a(0)=1, where A132973 lists the coefficients in psi(-q)^3/psi(-q^3) and where psi() is a Ramanujan theta function.
  • A209451 (program): a(n) = Pell(n)*A034896(n) for n >= 1, with a(0)=1, where A034896 lists the number of solutions to a^2 + b^2 + 3*c^2 + 3*d^2 = n.
  • A209452 (program): a(n) = Pell(n)*A122859(n) for n>=1, with a(0)=1, where A122859 lists the coefficients in phi(-q)^3/phi(-q^3) and phi() is a Ramanujan theta function.
  • A209453 (program): a(n) = Pell(n)*A109041(n) for n>=1, with a(0)=1, where A109041 lists the coefficients in eta(q)^9/eta(q^3)^3.
  • A209454 (program): a(n) = Pell(n)*A033719(n) for n>=1, with a(0)=1, where A033719 lists the coefficients in theta_3(q)*theta_3(q^7).
  • A209455 (program): a(n) = Pell(n)*A002652(n) for n>=1, with a(0)=1, where A002652 lists the coefficients in theta series of Kleinian lattice Z[(-1+sqrt(-7))/2].
  • A209456 (program): a(n) = Pell(n)*A028594(n) for n>=1, with a(0)=1, where A028594 lists the coefficients in (theta_3(x)*theta_3(7*x)+theta_2(x)*theta_2(7*x))^2.
  • A209466 (program): Final digit of n^n - n.
  • A209492 (program): a(0)=1; for n >= 1, let k = floor((1 + sqrt(8*n-7))/2), m = n - (k^2 - k+2)/2. Then a(n) = 2^k + 2^(m+1) - 1.
  • A209495 (program): G.f. A(x) = Product_{n>=1} 1/(1 - 3^(n^2)*x^n).
  • A209505 (program): Half the number of (n+1) X 3 0..2 arrays with every 2 X 2 subblock having two or four distinct clockwise edge differences.
  • A209506 (program): Half the number of (n+1) X 4 0..2 arrays with every 2 X 2 subblock having two or four distinct clockwise edge differences.
  • A209518 (program): Triangle by rows, reversal of A104712.
  • A209529 (program): Half the number of (n+1)X(n+1) 0..2 arrays with every 2X2 subblock having exactly two distinct clockwise edge differences
  • A209530 (program): Half the number of (n+1) X 3 0..2 arrays with every 2 X 2 subblock having exactly two distinct clockwise edge differences.
  • A209531 (program): Half the number of (n+1) X 5 0..2 arrays with every 2 X 2 subblock having exactly two distinct clockwise edge differences.
  • A209532 (program): Half the number of (n+1) X 7 0..2 arrays with every 2 X 2 subblock having exactly two distinct clockwise edge differences.
  • A209533 (program): Half the number of (n+1)X8 0..2 arrays with every 2X2 subblock having exactly two distinct clockwise edge differences
  • A209534 (program): T(n,k)=Half the number of (n+1)X(k+1) 0..2 arrays with every 2X2 subblock having exactly two distinct clockwise edge differences
  • A209535 (program): Number of partitions of 0 of the form [x(1)+x(2)+…+x (j)] - [y(1)+y(2)+…+y(k)] where the x(i) are distinct positive integers <=n and the y(i) are distinct positive integers <= n.
  • A209536 (program): Number of partitions of 0 having positive part-sum <= n.
  • A209544 (program): Primes not expressed in form n<+>2, where operation <+> defined in A206853.
  • A209546 (program): 1/4 the number of (n+1) X 2 0..3 arrays with every 2 X 2 subblock having exactly two distinct clockwise edge differences.
  • A209554 (program): Primes that expressed in none of the forms n<+>2 and n<+>3, where the operation <+> is defined in A206853.
  • A209555 (program): Triangle of coefficients of polynomials u(n,x) jointly generated with A209556; see the Formula section.
  • A209556 (program): Triangle of coefficients of polynomials v(n,x) jointly generated with A209555; see the Formula section.
  • A209559 (program): Triangle of coefficients of polynomials u(n,x) jointly generated with A209560; see the Formula section.
  • A209560 (program): Triangle of coefficients of polynomials v(n,x) jointly generated with A209559; see the Formula section.
  • A209561 (program): Triangle of coefficients of polynomials u(n,x) jointly generated with A209562; see the Formula section.
  • A209562 (program): Triangle of coefficients of polynomials v(n,x) jointly generated with A209561; see the Formula section.
  • A209563 (program): Triangle of coefficients of polynomials u(n,x) jointly generated with A209564; see the Formula section.
  • A209564 (program): Triangle of coefficients of polynomials v(n,x) jointly generated with A209559; see the Formula section.
  • A209567 (program): Triangle of coefficients of polynomials u(n,x) jointly generated with A209568; see the Formula section.
  • A209568 (program): Triangle of coefficients of polynomials v(n,x) jointly generated with A209567; see the Formula section.
  • A209569 (program): Triangle of coefficients of polynomials u(n,x) jointly generated with A209570; see the Formula section.
  • A209577 (program): Triangle of coefficients of polynomials u(n,x) jointly generated with A209578; see the Formula section.
  • A209586 (program): Number of n X n 0..1 arrays with every element equal to a diagonal or antidiagonal reflection
  • A209594 (program): Number of 3 X 3 0..n arrays with every element equal to a diagonal or antidiagonal reflection.
  • A209595 (program): Number of 4X4 0..n arrays with every element equal to a diagonal or antidiagonal reflection
  • A209596 (program): Number of 5X5 0..n arrays with every element equal to a diagonal or antidiagonal reflection
  • A209599 (program): Triangle T(n,k), read by rows, given by (2, -1/2, -1/2, 0, 0, 0, 0, 0, 0, 0, …) DELTA (0, 1/2, -1/2, 0, 0, 0, 0, 0, 0, 0, …) where DELTA is the operator defined in A084938.
  • A209603 (program): Number of n X 1 1..2 arrays with every element value z a city block distance of exactly z from another element value z.
  • A209614 (program): G.f.: Sum_{n>=1} Fibonacci(n^3)*x^(n^3).
  • A209615 (program): Completely multiplicative with a(p^e) = 1 if p == 1 (mod 4), a(p^e) = (-1)^e otherwise.
  • A209618 (program): Primes separated from their adjacent next primes by a composite number of successive composites.
  • A209623 (program): Primes separated from their adjacent next primes by a prime number of successive composites.
  • A209624 (program): Primes separated from their previous adjacent primes by a prime number of successive composites.
  • A209628 (program): Number of squarefree numbers < n that are not prime.
  • A209629 (program): The number of partitions of the set [n] where each element can be colored 1 or 2 avoiding the patterns 1^12^2 and 1^22^1 in the pattern sense.
  • A209632 (program): Digits of E read in decimal as if written in hexadecimal.
  • A209634 (program): Triangle with (1,4,7,10,13,16…,(3*n-2),…) in every column, shifted down twice.
  • A209635 (program): Möbius mu-function applied to the odd part of n: a(n) = A008683(A000265(n)).
  • A209639 (program): Bisection of A209859.
  • A209642 (program): A014486-codes for rooted plane trees where non-leaf branching can occur only at the leftmost branch of any level, but nowhere else. Reflected from the corresponding rightward branching codes in A071162, thus not in ascending order.
  • A209646 (program): Number of n X 4 0..1 arrays avoiding 0 0 1 and 1 0 0 horizontally and 0 0 1 and 1 0 1 vertically.
  • A209647 (program): Number of n X 5 0..1 arrays avoiding 0 0 1 and 1 0 0 horizontally and 0 0 1 and 1 0 1 vertically.
  • A209648 (program): Number of n X 6 0..1 arrays avoiding 0 0 1 and 1 0 0 horizontally and 0 0 1 and 1 0 1 vertically.
  • A209649 (program): Number of n X 7 0..1 arrays avoiding 0 0 1 and 1 0 0 horizontally and 0 0 1 and 1 0 1 vertically.
  • A209658 (program): Partition numbers p(n) having the same parity as n.
  • A209659 (program): Partition numbers p(n) having opposite parity of n.
  • A209661 (program): a(n) = (-1)^A083025(n).
  • A209662 (program): a(n) = (-1)^A083025(n)*n.
  • A209673 (program): a(n) = count of monomials, of degree k=n, in the Schur symmetric polynomials s(mu,k) summed over all partitions mu of n.
  • A209675 (program): Radon function at even positions: a(n) = A003484(2*n).
  • A209676 (program): Expansion of f(x)^12 in powers of x where f() is a Ramanujan theta function.
  • A209688 (program): Triangle of coefficients of polynomials v(n,x) jointly generated with A115241; see the Formula section.
  • A209689 (program): Triangle of coefficients of polynomials u(n,x) jointly generated with A209690; see the Formula section.
  • A209690 (program): Triangle of coefficients of polynomials v(n,x) jointly generated with A209689; see the Formula section.
  • A209695 (program): Triangle of coefficients of polynomials u(n,x) jointly generated with A209696; see the Formula section.
  • A209696 (program): Triangle of coefficients of polynomials v(n,x) jointly generated with A209695; see the Formula section.
  • A209705 (program): Triangle of coefficients of polynomials u(n,x) jointly generated with A209706; see the Formula section.
  • A209706 (program): Triangle of coefficients of polynomials v(n,x) jointly generated with A209705; see the Formula section.
  • A209721 (program): 1/4 the number of (n+1) X 3 0..2 arrays with every 2 X 2 subblock having distinct clockwise edge differences.
  • A209722 (program): 1/4 the number of (n+1) X 4 0..2 arrays with every 2 X 2 subblock having distinct clockwise edge differences.
  • A209723 (program): 1/4 the number of (n+1) X 5 0..2 arrays with every 2 X 2 subblock having distinct clockwise edge differences.
  • A209724 (program): 1/4 the number of (n+1) X 6 0..2 arrays with every 2 X 2 subblock having distinct clockwise edge differences.
  • A209725 (program): 1/4 the number of (n+1) X 7 0..2 arrays with every 2 X 2 subblock having distinct clockwise edge differences.
  • A209726 (program): 1/4 the number of (n+1) X 8 0..2 arrays with every 2 X 2 subblock having distinct clockwise edge differences.
  • A209729 (program): 1/4 the number of (n+1) X 2 0..3 arrays with every 2 X 2 subblock having distinct edge sums.
  • A209747 (program): Triangle of coefficients of polynomials u(n,x) jointly generated with A209748; see the Formula section.
  • A209757 (program): Triangle of coefficients of polynomials v(n,x) jointly generated with A013609; see the Formula section.
  • A209758 (program): Triangle of coefficients of polynomials v(n,x) jointly generated with A210041; see the Formula section.
  • A209761 (program): Triangle of coefficients of polynomials u(n,x) jointly generated with A209762; see the Formula section.
  • A209762 (program): Triangle of coefficients of polynomials v(n,x) jointly generated with A209761; see the Formula section.
  • A209771 (program): Triangle of coefficients of polynomials u(n,x) jointly generated with A209772; see the Formula section.
  • A209772 (program): Triangle of coefficients of polynomials v(n,x) jointly generated with A209771; see the Formula section.
  • A209789 (program): Half the number of (n+1) X 2 0..2 arrays with every 2 X 2 subblock having exactly one duplicate clockwise edge difference.
  • A209798 (program): The number of partitions of the set [n] where each element can be colored 1 or 2 avoiding the patterns 1^11^2, 1^12^2, and 1^22^1 in the pattern sense.
  • A209801 (program): The number of partitions of the set [n] where each element can be colored 1 or 2 avoiding the patterns 1^11^2 in the equality sense.
  • A209803 (program): a(n) = Sum_{d|n} d*2^(n*d).
  • A209804 (program): a(n) = Sum_{d|n} d*3^(n*d).
  • A209822 (program): Number of (n+1) X 2 0..2 arrays with every 2 X 2 subblock having one or two distinct values, and new values 0..2 introduced in row major order.
  • A209835 (program): Smallest k >= 0 such that 2k + (n-th average of twin prime pairs) is oblong number.
  • A209841 (program): Number of (n+1) X 2 0..3 arrays with every 2 X 2 subblock having one or two distinct values, and new values 0..3 introduced in row major order.
  • A209859 (program): Rewrite the binary expansion of n from the most significant end, 1 -> 1, 0+1 (one or more zeros followed by one) -> 0, drop the trailing zeros of the original n.
  • A209871 (program): Quasi-Niven (or Quasi-Harshad) numbers: numbers that divided by the sum of their digits leave 1 as remainder.
  • A209876 (program): a(n) = 36*n - 6.
  • A209880 (program): RATS: Reverse Add Then Sort the digits applied to previous term, starting with 29.
  • A209884 (program): E.g.f. A(x) satisfies: A(x/(1-x))/(1-x) = (1/x) * d/dx x^2*A(x)/2.
  • A209888 (program): Number of binary words of length n containing no subword 01101.
  • A209890 (program): Number of (n+1) X 2 0..2 arrays with every 2 X 2 subblock having two distinct values, and new values 0..2 introduced in row major order.
  • A209899 (program): Floor of the expected number of empty cells in a random placement of 2n balls into n cells.
  • A209900 (program): Floor of the expected number of occupied cells in a random placement of 2n balls into n cells.
  • A209901 (program): 7^p - 6^p - 2 with p = prime(n).
  • A209917 (program): E.g.f. A(x) satisfies: A(x/(1-x))/(1-x) = (1/x^2) * d/dx x^3*A(x)/3.
  • A209921 (program): Position of positive values in A209661 and A209662.
  • A209922 (program): Position of negative values in A209661 and A209662.
  • A209927 (program): Decimal expansion of sqrt(3 + sqrt(3 + sqrt(3 + sqrt(3 + … )))).
  • A209928 (program): Largest digit of all divisors of n.
  • A209929 (program): Smallest digit of all divisors of n.
  • A209931 (program): Numbers n such that smallest digit of all divisors of n is 1.
  • A209938 (program): Number of groups of order prime(n)^5 with nontrivial unramified Brauer groups.
  • A209940 (program): Expansion of psi(x^4) * phi(-x^4)^4 / phi(x) in powers of x where phi(), psi() are Ramanujan theta function.
  • A209941 (program): Expansion of f(x)^6 in powers of x where f() is a Ramanujan theta function.
  • A209944 (program): Half the number of (n+1) X 2 0..2 arrays with every 2 X 2 subblock having at most one duplicate clockwise edge difference.
  • A209953 (program): Number of (n+1) X 2 0..2 arrays with every 2 X 2 subblock having one, three or four distinct clockwise edge differences.
  • A209970 (program): a(n) = 2^n - A000031(n).
  • A209971 (program): a(n) = A000129(n) + n.
  • A209973 (program): Number of 2 X 2 matrices having all elements in {0,1,…,n} and determinant 2.
  • A209974 (program): a(n) = A209973(n)/4.
  • A209978 (program): a(n) = A196227(n)/2.
  • A209979 (program): Number of unimodular 2 X 2 matrices having all elements in {1,2,…,n}.
  • A209980 (program): (A197168)/2.
  • A209981 (program): Number of singular 2 X 2 matrices having all elements in {-n,…,n}.
  • A209982 (program): Number of 2 X 2 matrices having all elements in {-n,…,n} and determinant 1.
  • A209983 (program): (A209982)/2.
  • A210000 (program): Number of unimodular 2 X 2 matrices having all terms in {0,1,…,n}.
  • A210003 (program): Number of binary words of length n containing no subword 10001.
  • A210021 (program): Number of binary words of length n containing no subword 11011.
  • A210024 (program): Floor of the expected value of number of trials until all cells are occupied in a random distribution of 2n balls in n cells.
  • A210029 (program): Number of sequences over the alphabet of n symbols of length 2n which have n distinct symbols. Also number of placements of 2n balls into n cells where no cell is empty.
  • A210030 (program): Expansion of phi(-q) / phi(q^2) in powers of q where phi() is a Ramanujan theta function.
  • A210031 (program): Number of binary words of length n containing no subword 100001.
  • A210032 (program): a(n)=n for n=1,2,3 and 4; a(n)=5 for n>=5.
  • A210033 (program): Triangle of coefficients of polynomials u(n,x) jointly generated with A210034; see the Formula section.
  • A210034 (program): Triangle of coefficients of polynomials v(n,x) jointly generated with A210033; see the Formula section.
  • A210036 (program): Triangle of coefficients of polynomials v(n,x) jointly generated with A210035; see the Formula section.
  • A210037 (program): Triangle of coefficients of polynomials u(n,x) jointly generated with A210038; see the Formula section.
  • A210038 (program): Triangle of coefficients of polynomials v(n,x) jointly generated with A210037; see the Formula section.
  • A210039 (program): Array of coefficients of polynomials u(n,x) jointly generated with A210040; see the Formula section.
  • A210040 (program): Array of coefficients of polynomials v(n,x) jointly generated with A210039; see the Formula section.
  • A210042 (program): Triangle of coefficients of polynomials u(n,x) jointly generated with A124927; see the Formula section.
  • A210054 (program): Number of (n+1) X 2 0..3 arrays with every 2 X 2 subblock having one, two or four distinct values, and new values 0..3 introduced in row major order.
  • A210062 (program): Number of digits in 7^n.
  • A210064 (program): Total number of 231 patterns in the set of permutations avoiding 123.
  • A210065 (program): Expansion of phi(q^2) / phi(q) in powers of q where phi() is a Ramanujan theta function.
  • A210066 (program): Expansion of (phi(q^2) / phi(q))^2 in powers of q where phi() is a Ramanujan theta function.
  • A210067 (program): Expansion of (phi(-q) / phi(q^2))^2 in powers of q where phi() is a Ramanujan theta function.
  • A210088 (program): Number of (n+1) X 2 0..2 arrays containing all values 0..2 with every 2 X 2 subblock having one or two distinct values, and new values 0..2 introduced in row major order.
  • A210098 (program): Somos-5 sequence variant: a(n) = (a(n-1) * a(n-4) - a(n-2) * a(n-3)) / a(n-5), a(0) = 0, a(1) = a(2) = a(3) = a(4) = 1, a(5) = 2.
  • A210100 (program): Number of (n+1) X 2 0..2 arrays with every 2 X 2 subblock having one or three distinct values, and new values 0..2 introduced in row major order.
  • A210101 (program): Number of (n+1) X 3 0..2 arrays with every 2 X 2 subblock having one or three distinct values, and new values 0..2 introduced in row major order.
  • A210112 (program): Floor of the expected value of number of trials until exactly one cell is empty in a random distribution of n balls in n cells.
  • A210127 (program): Number of (n+1) X 2 0..3 arrays with every 2 X 2 subblock having one, three or four distinct values, and new values 0..3 introduced in row major order.
  • A210147 (program): Numbers expressible as 2*p+q, p and q distinct primes.
  • A210188 (program): Triangle of coefficients of polynomials v(n,x) jointly generated with A210187; see the Formula section.
  • A210189 (program): Triangle of coefficients of polynomials u(n,x) jointly generated with A210190; see the Formula section.
  • A210192 (program): Triangle of coefficients of polynomials v(n,x) jointly generated with A210191; see the Formula section.
  • A210195 (program): Triangle of coefficients of polynomials u(n,x) jointly generated with A210196; see the Formula section.
  • A210196 (program): Triangle of coefficients of polynomials v(n,x) jointly generated with A210195; see the Formula section.
  • A210197 (program): Triangle of coefficients of polynomials u(n,x) jointly generated with A210198; see the Formula section.
  • A210203 (program): Triangle of coefficients of polynomials u(n,x) jointly generated with A210204; see the Formula section.
  • A210204 (program): Triangle of coefficients of polynomials v(n,x) jointly generated with A210203; see the Formula section.
  • A210209 (program): GCD of all sums of n consecutive Fibonacci numbers.
  • A210213 (program): Triangle of coefficients of polynomials u(n,x) jointly generated with A210214; see the Formula section.
  • A210214 (program): Triangle of coefficients of polynomials v(n,x) jointly generated with A210213; see the Formula section.
  • A210215 (program): Triangle of coefficients of polynomials u(n,x) jointly generated with A210216; see the Formula section.
  • A210216 (program): Triangle of coefficients of polynomials v(n,x) jointly generated with A210215; see the Formula section.
  • A210219 (program): Triangle of coefficients of polynomials u(n,x) jointly generated with A210220; see the Formula section.
  • A210220 (program): T(n, k) = -binomial(2*n-k+2, k+1)*hypergeom([2*n-k+3, 1], [k+2], 2). Triangle read by rows, T(n, k) for 1 <= k <= n.
  • A210222 (program): Triangle of coefficients of polynomials v(n,x) jointly generated with A104698; see the Formula section.
  • A210229 (program): Triangle of coefficients of polynomials u(n,x) jointly generated with A210230; see the Formula section.
  • A210230 (program): Triangle of coefficients of polynomials v(n,x) jointly generated with A210229; see the Formula section.
  • A210241 (program): Partial sums of A073093.
  • A210243 (program): Hanoi solutions (odd), the disks are moved from pillar 1 to pillar 3. For disks = 2k+1 use the first 2^(2k+2)-2 number pairs.
  • A210245 (program): Signs of the polylogarithm li(-n,-1/2).
  • A210246 (program): Polylogarithm li(-n,-1/3) multiplied by (4^(n+1))/3.
  • A210247 (program): a(n) = sign of the polylogarithm li(-n,-1/3) for n > 0, with a(0) = 1.
  • A210249 (program): Number of partitions of n in which all parts are less than n/2.
  • A210251 (program): Residues modulo 100 of odd squares.
  • A210256 (program): Differences of the sum of distinct values of {floor(n/k), k=1,…,n}.
  • A210269 (program): Half the number of (n+1) X 2 0..2 arrays with every 2 X 2 subblock having two or three distinct clockwise edge differences.
  • A210277 (program): a(n) = (3*n)!/3^n.
  • A210278 (program): (5n)!/5^n.
  • A210288 (program): Number of 2 X 2 matrices with all elements in {0,1,…,n} and permanent = trace.
  • A210290 (program): Number of 2 X 2 matrices with all elements in {0,1,…,n} and nonnegative determinant.
  • A210323 (program): Number of 2-divided words of length n over a 3-letter alphabet.
  • A210341 (program): Triangle generated by T(n,k) = Fibonacci(n-k+2)^k.
  • A210342 (program): Row sums of triangle A210341.
  • A210343 (program): a(n) = Fibonacci(n+1)^n.
  • A210356 (program): Maximum modulus in the inverse of Hilbert’s matrix.
  • A210357 (program): Location of the maximum modulus in the inverse of Hilbert’s matrix.
  • A210360 (program): Prime numbers p such that x^2 + x + p produces primes for x = 0..1 but not x = 2.
  • A210369 (program): Number of 2 X 2 matrices with all terms in {0,1,…,n} and even determinant.
  • A210370 (program): Number of 2 X 2 matrices with all elements in {0,1,…,n} and odd determinant.
  • A210373 (program): Number of 2 X 2 matrices with all elements in {0,1,…,n} and positive odd determinant.
  • A210374 (program): Number of 2 X 2 matrices with all terms in {0,1,…,n} and (sum of terms) = n+2.
  • A210375 (program): Number of 2 X 2 matrices with all terms in {0,1,…,n} and (sum of terms) = n + 3.
  • A210378 (program): Number of 2 X 2 matrices with all terms in {0,1,…,n} and even trace.
  • A210379 (program): Number of 2 X 2 matrices with all terms in {0,1,…,n} and odd trace.
  • A210381 (program): Triangle by rows, derived from the beheaded Pascal’s triangle, A074909.
  • A210383 (program): Number of (n+1) X 2 0..2 arrays with every 2 X 2 subblock having one, two or three distinct clockwise edge differences.
  • A210397 (program): Number of (n+1) X 2 0..3 arrays with every 2 X 2 subblock having one or three distinct values, and new values 0..3 introduced in row major order.
  • A210406 (program): Number of (n+1) X 2 0..3 arrays with every 2 X 2 subblock having three or four distinct values, and new values 0..3 introduced in row major order.
  • A210424 (program): Number of 2-divided words of length n over a 4-letter alphabet.
  • A210427 (program): Number of semistandard Young tableaux over all partitions of 5 with maximal element <= n.
  • A210433 (program): Natural numbers k such that floor(v) * ceiling(v)^2 = k, where v = k^(1/3).
  • A210434 (program): Number of digits in 4^n.
  • A210435 (program): Number of digits in 5^n.
  • A210436 (program): Number of digits in 6^n.
  • A210437 (program): Greatest prime factor of reversal of digits of n.
  • A210440 (program): a(n) = 2*n*(n+1)*(n+2)/3.
  • A210445 (program): Least positive integer k with k*n practical.
  • A210448 (program): Total number of different letters summed over all ternary words of length n.
  • A210449 (program): Numbers that are the sum of three triangular numbers an odd number of ways.
  • A210454 (program): Cipolla pseudoprimes to base 2: (4^p-1)/3 for any prime p greater than 3.
  • A210455 (program): Characteristic function of pseudoperfect (or semiperfect) numbers.
  • A210457 (program): Triangular array read by rows: T(n,k) is the number of elements x in {1,2,…,n} such that |(f^-1)(x)| = k over all functions f:{1,2,…,n}->{1,2,…,n}; n>=0, 0<=k<=n.
  • A210460 (program): Expansion of x*(1+x)/(1-x-2*x^2-2*x^3-x^4).
  • A210461 (program): Cipolla pseudoprimes to base 3: (9^p-1)/8 for any odd prime p.
  • A210462 (program): Decimal expansion of the real part of the complex roots of x^3-x^2+1.
  • A210464 (program): Number of bracelets with 2 blue, 2 red, and n black beads.
  • A210469 (program): a(n) = n - primepi(2n).
  • A210474 (program): The number of different lattice paths from (0,0) to (2n,0) using steps of S={(i,i) or (i,-i): i=1,2,…,n} with j flaws(j=1,2,…,n-1), where the j flaws is the sum of lengths of down steps below the x-axis. (For down steps that are partly above and partly below the x-axis we just count the part below the x-axis.) This number is independent of the number of flaws.
  • A210477 (program): Product of adjacent primes with a gap of 6.
  • A210486 (program): Number of paths starting at {3}^n to a border position where one component equals 0 using steps that decrement one component by 1.
  • A210489 (program): Array read by ascending antidiagonals where row n contains the second partial sums of row n of Pascal’s triangle.
  • A210490 (program): Union of positive squares (A000290 \ {0}) and squarefree numbers (A005117).
  • A210495 (program): Numbers n such that d(n)*n + 1 is prime, d(n) = number of divisors of n.
  • A210497 (program): 2*prime(n+1) - prime(n).
  • A210504 (program): Numbers n for which 2*n+5, 4*n+5, 6*n+5, and 8*n+5 are primes.
  • A210521 (program): Array read by downward antidiagonals: T(n,k) = (n+k-1)*(n+k-2) + n + floor((n+k)/2)*(1-2*floor((n+k)/2)), for n, k > 0
  • A210522 (program): Decimal expansion of 10^(3/4).
  • A210524 (program): a(n) = n - sum of even digits of n.
  • A210527 (program): a(n) = 9*n^2 + 39*n + 83.
  • A210530 (program): T(n,k) = (k + 3*n - 2 - (k+n-2)*(-1)^(k+n))/2 n, k > 0, read by antidiagonals.
  • A210535 (program): Second inverse function (numbers of columns) for pairing function A209293.
  • A210540 (program): Number of arrays of n nonnegative integers with value i>0 appearing only after i-1 has appeared at least 3 times.
  • A210541 (program): Number of arrays of n nonnegative integers with value i>0 appearing only after i-1 has appeared at least 4 times
  • A210542 (program): Number of arrays of n nonnegative integers with value i>0 appearing only after i-1 has appeared at least 5 times
  • A210543 (program): Number of arrays of n nonnegative integers with value i>0 appearing only after i-1 has appeared at least 6 times.
  • A210544 (program): Number of arrays of n nonnegative integers with value i>0 appearing only after i-1 has appeared at least 7 times
  • A210551 (program): Triangle of coefficients of polynomials v(n,x) jointly generated with A172431; see the Formula section.
  • A210552 (program): Triangle of coefficients of polynomials u(n,x) jointly generated with A210553; see the Formula section.
  • A210553 (program): Triangle of coefficients of polynomials v(n,x) jointly generated with A210552; see the Formula section.
  • A210554 (program): Triangle of coefficients of polynomials v(n,x) jointly generated with A208341; see the Formula section.
  • A210555 (program): Triangle of coefficients of polynomials u(n,x) jointly generated with A210556; see the Formula section.
  • A210556 (program): Triangle of coefficients of polynomials v(n,x) jointly generated with A210555; see the Formula section.
  • A210557 (program): Triangle of coefficients of polynomials u(n,x) jointly generated with A210558; see the Formula section.
  • A210558 (program): Triangle of coefficients of polynomials v(n,x) jointly generated with A210557; see the Formula section.
  • A210561 (program): Triangle of coefficients of polynomials u(n,x) jointly generated with A210562; see the Formula section.
  • A210562 (program): Triangle of coefficients of polynomials v(n,x) jointly generated with A210561; see the Formula section.
  • A210565 (program): Triangle of coefficients of polynomials u(n,x) jointly generated with A210595; see the Formula section.
  • A210569 (program): a(n) = (n-3)*(n-2)*(n-1)*n*(n+1)/30.
  • A210576 (program): Positive integers that cannot be expressed as sum of one or more nontrivial binomial coefficients.
  • A210583 (program): Decimal expansion of (9/2)*Pi.
  • A210595 (program): Triangle of coefficients of polynomials v(n,x) jointly generated with A209999; see the Formula section.
  • A210596 (program): Triangle read by rows of coefficients of polynomials v(n,x) jointly generated with A210221; see the Formula section.
  • A210615 (program): Least semiprime dividing n, or 0 if no semiprime divides n.
  • A210616 (program): Digit reversal of n-th semiprime.
  • A210619 (program): Triangle of numbers with n 1’s and n 0’s in their representation in base of Fibonacci numbers (A014417).
  • A210620 (program): Nontrivial solution to x = 2*x^2 - 1 mod 10^n.
  • A210621 (program): Decimal expansion of 256/81.
  • A210622 (program): Decimal expansion of 377/120.
  • A210625 (program): Least semiprime dividing digit reversal of n, or 0 if no such factor.
  • A210626 (program): Values of the prime-generating polynomial 4*n^2 - 284*n + 3449.
  • A210627 (program): Constants r_n arising in study of polynomials of least deviation from zero in several variables.
  • A210628 (program): Expansion of (-1 + 2*x + sqrt( 1 - 4*x^2)) / (2*x) in powers of x.
  • A210635 (program): Array read by antidiagonals: row n (n >= 1) gives a permutation of the nonnegative integers for rotating an image of width n.
  • A210636 (program): Riordan array ((1-x)/(1-2*x-x^2), x*(1+x)/(1-2*x-x^2)).
  • A210645 (program): Area A of the triangles such that A, the sides and one of the altitudes are four consecutive integers of an arithmetic progression d.
  • A210657 (program): a(0)=1; thereafter a(n) = -2*Sum_{k=1..n} binomial(2n,2k)*a(n-k).
  • A210658 (program): Triangle of partial sums of Catalan numbers.
  • A210665 (program): Least semiprime dividing digit reversal of n-th semiprime, or 0 if no such factor.
  • A210670 (program): Central coefficients of triangle A210658.
  • A210671 (program): Number of equivalence classes of S_n under transformations of positionally adjacent elements of the form abc <–> acb <–> bac <–> cba, where a<b<c.
  • A210672 (program): a(0)=1; thereafter a(n) = 2*Sum_{k=1..n} binomial(2n,2k)*a(n-k).
  • A210673 (program): a(n) = a(n-1)+a(n-2)+n-4, a(0)=0, a(1)=1.
  • A210674 (program): a(0)=1; thereafter a(n) = 3*Sum_{k=1..n} binomial(2n,2k)*a(n-k).
  • A210675 (program): a(n)=a(n-1)+a(n-2)+n+4, a(0)=0, a(1)=1.
  • A210676 (program): a(0)=1; thereafter a(n) = -3*Sum_{k=1..n} binomial(2n,2k)*a(n-k).
  • A210677 (program): a(n)=a(n-1)+a(n-2)+n+1, a(0)=a(1)=1.
  • A210678 (program): a(n)=a(n-1)+a(n-2)+n+2, a(0)=a(1)=1.
  • A210679 (program): Number of distinct prime factors <= 7 of n.
  • A210685 (program): a(1)=-1, a(2)=2, thereafter a(n) = (1/(2n))*((7n-22)a(n-1)+2(2n-1)a(n-2)).
  • A210692 (program): Number of parts that are visible in one of the three views of the shell model of partitions with n regions mentioned in A210991.
  • A210694 (program): T(n,k)=Number of (n+1)X(n+1) -k..k symmetric matrices with every 2X2 subblock having sum zero
  • A210695 (program): a(n) = 6*a(n-1) - a(n-2) + 6 with n>1, a(0)=0, a(1)=1.
  • A210698 (program): Number of 2 X 2 matrices having all terms in {1,…,n} and determinant = 0 (mod 3).
  • A210700 (program): A047160(3n): smallest m >= 0 with both 3n - m and 3n + m prime.
  • A210709 (program): Number of trivalent connected simple graphs with 2n nodes and girth at least 9.
  • A210728 (program): a(n) = a(n-1) + a(n-2) + n + 2 with n>1, a(0)=1, a(1)=2.
  • A210729 (program): a(n) = a(n-1) + a(n-2) + n + 3 with n>1, a(0)=1, a(1)=2.
  • A210730 (program): a(n) = a(n-1) + a(n-2) + n + 2 with n>1, a(0)=a(1)=0.
  • A210731 (program): a(n) = a(n-1) + a(n-2) + n + 3 with n>1, a(0) = a(1) = 0.
  • A210736 (program): Expansion of (1 + sqrt( (1 + 2*x) / (1 - 2*x))) / 2 in powers of x.
  • A210741 (program): Triangle of coefficients of polynomials u(n,x) jointly generated with A210742; see the Formula section.
  • A210742 (program): Triangle of coefficients of polynomials v(n,x) jointly generated with A210741; see the Formula section.
  • A210745 (program): The leaf weight sequence w_{2,3,4}.
  • A210746 (program): A leaf weight sequence.
  • A210751 (program): Triangle of coefficients of polynomials u(n,x) jointly generated with A210752; see the Formula section.
  • A210752 (program): Triangle of coefficients of polynomials v(n,x) jointly generated with A210751; see the Formula section.
  • A210753 (program): Triangle of coefficients of polynomials u(n,x) jointly generated with A210754; see the Formula section.
  • A210754 (program): Triangle of coefficients of polynomials v(n,x) jointly generated with A210753; see the Formula section.
  • A210765 (program): Triangle read by rows in which row n lists the number of partitions of n together with n-1 ones.
  • A210770 (program): a(1) = 1, a(2) = 2; for n > 1, a(2*n+2) = smallest number not yet seen, a(2*n+1) = a(2*n) + a(2*n+2).
  • A210772 (program): Number of partitions of 2^n into powers of 2 less than or equal to 8.
  • A210826 (program): G.f.: Sum_{n>=1} a(n)*x^n/(1 - x^n) = Sum_{n>=1} x^(n^3).
  • A210840 (program): Sum of the 8th powers of the digits of n.
  • A210843 (program): Level of the n-th plateau of the column k of the square array A195825, when k -> infinity.
  • A210845 (program): Values n for which A055034(n) is squarefree.
  • A210848 (program): a(n) = (A048898(n)^2 + 1)/5^n, n >= 0.
  • A210849 (program): a(n) = (A048899(n)^2 + 1)/5^n, n >= 0.
  • A210850 (program): Digits of one of the two 5-adic integers sqrt(-1).
  • A210851 (program): Digits of one of the two 5-adic integers sqrt(-1).
  • A210852 (program): Approximations up to 7^n for one of the three 7-adic integers (-1)^(1/3).
  • A210868 (program): Triangle of coefficients of polynomials u(n,x) jointly generated with A210869; see the Formula section.
  • A210872 (program): Triangle of coefficients of polynomials u(n,x) jointly generated with A210873; see the Formula section.
  • A210873 (program): Triangle of coefficients of polynomials u(n,x) jointly generated with A210873; see the Formula section.
  • A210874 (program): Triangular array U(n,k) of coefficients of polynomials defined in Comments.
  • A210876 (program): Triangle of coefficients of polynomials u(n,x) jointly generated with A210877; see the Formula section.
  • A210882 (program): a(1)=1, a(n)=a(n-1)-1 if a(n-1)-1 > 0 is not in the set {a(k)| 1<=k<n}, else a(n)=p, where p is the least prime number not yet in the sequence.
  • A210934 (program): Sum of prime factors of prime(n)+1 (counted with multiplicity).
  • A210936 (program): Sum of prime factors of prime(n)-1 (counted with multiplicity).
  • A210939 (program): Nonprime nearest-neighbors of the primes.
  • A210940 (program): The prime numbers and their nonprime nearest-neighbors.
  • A210958 (program): Decimal expansion of 1 - (Pi/4).
  • A210962 (program): Decimal expansion of 4*(2 - Pi/3).
  • A210963 (program): Decimal expansion of sqrt(163).
  • A210970 (program): Total area of the shadows of the three views of a three-dimensional version of the shell model of partitions with n shells.
  • A210973 (program): Decimal expansion of cube root of (3/4).
  • A210975 (program): Decimal expansion of square root of (Pi/6).
  • A210977 (program): A005475 and positive terms of A000566 interleaved.
  • A210978 (program): A186029 and positive terms of A001106 interleaved.
  • A210981 (program): A062725 and positive terms of A051682 interleaved.
  • A210982 (program): Zero together with A126264 and positive terms of A051624 interleaved.
  • A210983 (program): Total number of pairs of states of the first n subshells of the nuclear shell model in which the subshells are ordered by energy level in increasing order.
  • A210984 (program): Total number of states of the first n subshells of the nuclear shell model in which the subshells are ordered by energy level in increasing order.
  • A210994 (program): Numbers n such that A000005(n) <> 4.
  • A210998 (program): Composite numbers that are in the gap between an even-indexed prime and an odd-indexed prime.
  • A210999 (program): Composite numbers that are in the gap between an odd-indexed prime and an even-indexed prime.
  • A211004 (program): Number of distinct regions in the set of partitions of n.
  • A211005 (program): Pair (i, j) where i = number of adjacent nonprimes and j = number of adjacent primes.
  • A211006 (program): Pair (n,p) where n is the sum of adjacent nonprimes and p is the sum of adjacent primes.
  • A211007 (program): Surface area of the first n faces of the structure mentioned in A211006.
  • A211010 (program): Value on the axis “x” of the endpoint of the structure of A211000 at n-th stage.
  • A211012 (program): Total area of all squares and rectangles after 2^n stages in the toothpick structure of A139250, assuming the toothpicks have length 2.
  • A211013 (program): Second 13-gonal numbers: a(n) = n*(11*n+9)/2.
  • A211014 (program): Second 14-gonal numbers: n*(6*n+5).
  • A211033 (program): Number of 2 X 2 matrices having all elements in {0,1,…,n} and determinant = 0 (mod 3).
  • A211034 (program): Number of 2 X 2 matrices having all elements in {0,1,…,n} and determinant = 1 (mod 3).
  • A211056 (program): Number of 2 X 2 nonsingular matrices having all terms in {1,…,n}.
  • A211058 (program): Number of 2 X 2 matrices having all terms in {1,…,n} and nonnegative determinant.
  • A211059 (program): Number of 2 X 2 matrices having all terms in {1,…,n} and positive determinant.
  • A211064 (program): Number of 2 X 2 matrices having all terms in {1,…,n} and even determinant.
  • A211065 (program): Number of 2 X 2 matrices having all terms in {1,…,n} and odd determinant.
  • A211068 (program): Number of 2 X 2 matrices having all terms in {1,…,n} and positive odd determinant.
  • A211071 (program): Number of 2 X 2 matrices having all terms in {1,…,n} and determinant = 1 (mod 3).
  • A211074 (program): Decimal expansion of 4/Pi - 1/2.
  • A211114 (program): Number of (n+1) X (n+1) -2..2 symmetric matrices with every 2 X 2 subblock having sum zero and one or three distinct values.
  • A211117 (program): Number of (n+1) X (n+1) -2..2 symmetric matrices with every 2 X 2 subblock having sum zero and two, three or four distinct values.
  • A211154 (program): Number of 2 X 2 matrices having all terms in {-n,…,0,..,n} and even determinant.
  • A211155 (program): Number of 2 X 2 matrices having all terms in {-n,…,0,..,n} and odd determinant.
  • A211158 (program): Number of 2 X 2 matrices having all terms in {-n,…,0,..,n} and positive odd determinant.
  • A211159 (program): Number of integer pairs (x,y) such that 0<x<y<=n and x*y=n+1.
  • A211161 (program): Table T(n,k) = n, if k is odd, k/2 if k is even; n, k > 0, read by antidiagonals.
  • A211163 (program): Numerator of (-1/Pi^n) * integral_{0..1} (log(1-1/x)^n) dx.
  • A211164 (program): Number of compositions of n with at most one odd part.
  • A211168 (program): Exponent of alternating group An.
  • A211171 (program): Exponent of general linear group GL(n,2).
  • A211173 (program): (2n)!^n (modulo 2n+1).
  • A211174 (program): Johannes Kepler’s polyhedron circumscribing constant.
  • A211191 (program): List of odd values of k for which k^2+4 has a factor that is a square number larger than 1.
  • A211197 (program): Table T(n,k) = 2*n + ((-1)^n)*(1/2 - (k-1) mod 2) - 1/2; n, k > 0, read by antidiagonals.
  • A211199 (program): Sum of the 16th powers of the decimal digits of n.
  • A211202 (program): Positive numbers n such that Lambda_n = A002336(n) is divisible by n.
  • A211213 (program): n-alternating permutations of length 3n.
  • A211216 (program): Expansion of (1-8*x+21*x^2-20*x^3+5*x^4)/(1-9*x+28*x^2-35*x^3+15*x^4-x^5).
  • A211221 (program): For any partition of n consider the product of the sigma of each element. Sequence gives the maximum of such values.
  • A211227 (program): Row sums of A211226.
  • A211228 (program): Shallow diagonal sums of A211226.
  • A211231 (program): Row sums of A211230.
  • A211241 (program): Order of 5 mod n-th prime: least k such that prime(n) divides 5^k-1.
  • A211242 (program): Order of 6 mod n-th prime: least k such that prime(n) divides 6^k-1.
  • A211243 (program): Order of 7 mod n-th prime: least k such that prime(n) divides 7^k-1.
  • A211244 (program): Order of 8 mod n-th prime: least k such that prime(n) divides 8^k-1.
  • A211245 (program): Order of 9 mod n-th prime: least k such that prime(n) divides 9^k-1.
  • A211248 (program): G.f. satisfies: A(x) = (1 + x*A(x)^3) * (1 + x^2*A(x)^4).
  • A211249 (program): G.f. satisfies: A(x) = (1 + x*A(x)^3) * (1 + x^2*A(x)^5).
  • A211253 (program): Number of (n+1) X (n+1) -6..6 symmetric matrices with every 2 X 2 subblock having sum zero and one or two distinct values.
  • A211261 (program): Number of integer pairs (x,y) such that 0<x<y<=n and x*y=2n.
  • A211262 (program): Number of integer pairs (x,y) such that 0<x<y<=n and x*y=3n.
  • A211263 (program): Number of integer pairs (x,y) such that 0<x<y<=n and x*y=floor(n/2).
  • A211264 (program): Number of integer pairs (x,y) such that 0 < x < y <= n and x*y <= n.
  • A211265 (program): Number of integer pairs (x,y) such that 0<x<y<=n and x*y<=n+1.
  • A211266 (program): Number of integer pairs (x,y) such that 0<x<y<=n and x*y<=2n.
  • A211270 (program): Number of integer pairs (x,y) such that 0<x<=y<=n and x*y=2n.
  • A211271 (program): Number of integer pairs (x,y) such that 0<x<=y<=n and x*y=3n.
  • A211272 (program): Number of integer pairs (x,y) such that 0<x<=y<=n and x*y=floor(n/2).
  • A211273 (program): Number of integer pairs (x,y) such that 0<x<=y<=n and x*y<=2n.
  • A211275 (program): Number of integer pairs (x,y) such that 0 < x <= y <= n and x*y <= floor(n/2).
  • A211278 (program): a(n) = number of n-lettered words in the alphabet {1, 2, 3} with as many occurrences of the substring (consecutive subword) [1, 1] as of [2, 3].
  • A211279 (program): a(n) = number of n-lettered words in the alphabet {1, 2, 3} with as many occurrences of the substring (consecutive subword) [1, 2] as of [1, 3].
  • A211280 (program): Numerator of prime(n+1) - prime(n)/2.
  • A211288 (program): a(n) = number of n-lettered words in the alphabet {1, 2, 3} with as many occurrences of the substring (consecutive subword) [1, 1, 2] as of [1, 1, 3].
  • A211312 (program): Square array of Delannoy numbers D(i,j) mod 3 (i >= 0, j >= 0) read by antidiagonals.
  • A211313 (program): Square array of Delannoy numbers D(i,j) mod 5 (i >= 0, j >= 0) read by antidiagonals.
  • A211314 (program): Square array of Delannoy numbers D(i,j) mod 7 (i >= 0, j >= 0) read by antidiagonals.
  • A211315 (program): Square array of Delannoy numbers D(i,j) mod 11 (i >= 0, j >= 0) read by antidiagonals.
  • A211316 (program): Maximal size of sum-free set in additive group of integers mod n.
  • A211317 (program): A211316(2n+1).
  • A211322 (program): Number of (n+1) X (n+1) -3..3 symmetric matrices with every 2 X 2 subblock having sum zero and one or two distinct values.
  • A211323 (program): Number of (n+1) X (n+1) -3..3 symmetric matrices with every 2 X 2 subblock having sum zero and three distinct values.
  • A211324 (program): Number of (n+1) X (n+1) -3..3 symmetric matrices with every 2 X 2 subblock having sum zero and one or three distinct values.
  • A211327 (program): Number of (n+1) X (n+1) -3..3 symmetric matrices with every 2 X 2 subblock having sum zero and one, three or four distinct values.
  • A211329 (program): Number of (n+1) X (n+1) -5..5 symmetric matrices with every 2 X 2 subblock having sum zero and one or two distinct values.
  • A211337 (program): Numbers k for which the number of divisors, tau(k), is congruent to 1 modulo 3.
  • A211338 (program): Numbers k for which the number of divisors, tau(k), is congruent to 2 modulo 3.
  • A211339 (program): Number of integer pairs (x,y) such that 1 < x <= y <= n and x^2 + y^2 <= n.
  • A211340 (program): Number of integer pairs (x,y) such that 1<x<=y<=n and x^2+y^2<=n^2.
  • A211341 (program): a(n) = (n^n mod n!)/n.
  • A211344 (program): Atomic Boolean functions interpreted as binary numbers.
  • A211369 (program): Array read by antidiagonals: T(m,n) = m*(m+n-1)! + Sum( n <= i <= m+n-2 ) i!
  • A211370 (program): Array read by antidiagonals: T(m,n) = Sum( n <= i <= m+n-1 ) i!.
  • A211372 (program): Side length of smallest square containing n L’s with short sides 1, 2, …, n.
  • A211374 (program): Product of all the parts in the partitions of n into exactly 2 parts.
  • A211379 (program): Number of pairs of parallel diagonals in a regular n-gon.
  • A211380 (program): Number of pairs of intersecting diagonals in the interior and exterior of a regular n-gon.
  • A211381 (program): Number of pairs of intersecting diagonals in the exterior of a regular n-gon.
  • A211385 (program): Values of n for which product_{p|n, p prime} 1 + 1/p > e^gamma*log(log(n)).
  • A211386 (program): Expansion of 1/((1-2*x)^5*(1-x)).
  • A211388 (program): Expansion of 1/((1-2*x)^6*(1-x)).
  • A211390 (program): The minimum cardinality of an n-qubit unextendible product basis.
  • A211394 (program): T(n,k) = (k+n)*(k+n-1)/2-(k+n-1)*(-1)^(k+n)-k+2; n , k > 0, read by antidiagonals.
  • A211412 (program): a(n) = 4*n^4 + 1.
  • A211419 (program): Integral factorial ratio sequence: a(n) = (6*n)!*(2*n)!/((4*n)!*(3*n)!*n!).
  • A211420 (program): Integral factorial ratio sequence: a(n) = (8*n)!*n!/((4*n)!*(3*n)!*(2*n)!).
  • A211421 (program): Integral factorial ratio sequence: a(n) = (8*n)!*(3*n)!/((6*n)!*(4*n)!*n!).
  • A211422 (program): Number of ordered triples (w,x,y) with all terms in {-n,…,0,…,n} and w^2 + x*y = 0.
  • A211430 (program): Number of ordered triples (w,x,y) with all terms in {-n,…,0,…,n} and w^2+x+y=0.
  • A211431 (program): Number of ordered triples (w,x,y) with all terms in {-n,…,0,…,n} and w^3+(x+y)^2=0.
  • A211432 (program): Number of ordered triples (w,x,y) with all terms in {-n,…,0,…,n} and w^2=x^2+y^2.
  • A211433 (program): Number of ordered triples (w,x,y) with all terms in {-n,…,0,…,n} and w+2x+4y=0.
  • A211434 (program): Number of ordered triples (w,x,y) with all terms in {-n,…,0,…,n} and w+2x+5y=0.
  • A211435 (program): Number of ordered triples (w,x,y) with all terms in {-n,…,0,…,n} and w+4x+5y=0.
  • A211437 (program): Number of ordered triples (w,x,y) with all terms in {-n,…,0,…,n} and w*x*y=n.
  • A211438 (program): Number of ordered triples (w,x,y) with all terms in {-n,…,0,…,n} and w+2x+2y=0.
  • A211439 (program): Number of ordered triples (w,x,y) with all terms in {-n,…,0,…,n} and w+3x+3y=0.
  • A211440 (program): Number of ordered triples (w,x,y) with all terms in {-n,…,0,…,n} and 2w+3x+3y=0.
  • A211441 (program): Number of ordered triples (w,x,y) with all terms in {-n,…,0,…,n} and w + x + y = 2.
  • A211453 (program): (p-1)/x, where p = prime(n) and x = ord(8,p), the smallest positive integer such that 8^x == 1 mod p.
  • A211466 (program): Number of (n+1) X (n+1) -8..8 symmetric matrices with every 2 X 2 subblock having sum zero and one or two distinct values.
  • A211476 (program): Number of -1..1 arrays x(i) of n+1 elements i=1..n+1 with x(i)+x(j), x(i+1)+x(j+1), -(x(i)+x(j+1)), and -(x(i+1)+x(j)) having one or three distinct values for every i<=n and j<=n.
  • A211479 (program): Number of -1..1 arrays x(i) of n+1 elements i=1..n+1 with x(i)+x(j), x(i+1)+x(j+1), -(x(i)+x(j+1)), and -(x(i+1)+x(j)) having two, three or four distinct values for every i<=n and j<=n.
  • A211480 (program): Number of ordered triples (w,x,y) with all terms in {-n,…,0,…,n} and w + 2x + 3y = 1.
  • A211481 (program): Number of ordered triples (w,x,y) with all terms in {-n,…,0,…,n} and w+2x+3y=n.
  • A211483 (program): Number of ordered triples (w,x,y) with all terms in {-n,…,0,…,n} and (w+n)^2=x+y.
  • A211487 (program): Characteristic sequence of numbers n having a primitive root modulo n.
  • A211488 (program): Fibonacci(n^2) - Fibonacci(n).
  • A211490 (program): Number of (n+1) X (n+1) -4..4 symmetric matrices with every 2 X 2 subblock having sum zero and one or two distinct values.
  • A211508 (program): Number of ordered triples (w,x,y) with all terms in {1,…,n} and w^2=n-x*y.
  • A211516 (program): Number of ordered triples (w,x,y) with all terms in {1,…,n} and w^2=x+y.
  • A211517 (program): Number of ordered triples (w,x,y) with all terms in {1,…,n} and w^3=(x+y)^2.
  • A211519 (program): Number of ordered triples (w,x,y) with all terms in {1,…,n} and w=2x-3y.
  • A211520 (program): Number of ordered triples (w,x,y) with all terms in {1,…,n} and w + 4y = 2x.
  • A211521 (program): Number of ordered triples (w,x,y) with all terms in {1,…,n} and w + 2x = 4y.
  • A211522 (program): Number of ordered triples (w,x,y) with all terms in {1,…,n} and w + 5y = 2x.
  • A211523 (program): Number of ordered triples (w,x,y) with all terms in {1,…,n} and w+2x=5y.
  • A211524 (program): Number of ordered triples (w,x,y) with all terms in {1,…,n} and w=3x+5y.
  • A211525 (program): Number of -1..1 arrays x(i) of n+1 elements i=1..n+1 with set{t,u,v in 0,1}((x[i+t]+x[j+u]+x[k+v])*(-1)^(t+u+v)) having two or four distinct values for every i,j,k<=n.
  • A211526 (program): Number of -1..1 arrays x(i) of n+1 elements i=1..n+1 with set{t,u,v in 0,1}((x[i+t]+x[j+u]+x[k+v])*(-1)^(t+u+v)) having two, four or five distinct values for every i,j,k<=n.
  • A211528 (program): Number of -1..1 arrays x(i) of n+1 elements i=1..n+1 with set{t,u,v in 0,1}((x[i+t]+x[j+u]+x[k+v])*(-1)^(t+u+v)) having two, four or six distinct values for every i,j,k<=n.
  • A211529 (program): Number of -1..1 arrays x(i) of n+1 elements i=1..n+1 with set{t,u,v in 0,1}((x[i+t]+x[j+u]+x[k+v])*(-1)^(t+u+v)) having two, four, five or six distinct values for every i,j,k<=n.
  • A211533 (program): Number of ordered triples (w,x,y) with all terms in {1,…,n} and w=3x-5y.
  • A211534 (program): Number of ordered triples (w,x,y) with all terms in {1,…,n} and w = 3x + 3y.
  • A211535 (program): Number of ordered triples (w,x,y) with all terms in {1,…,n} and w=4x+5y.
  • A211538 (program): Number of ordered triples (w,x,y) with all terms in {1,…,n} and 2w=2n-2x-y.
  • A211539 (program): Number of ordered triples (w,x,y) with all terms in {1,…,n} and 2w = 2n - 2x + y.
  • A211540 (program): Number of ordered triples (w,x,y) with all terms in {1..n} and 2w = 3x + 4y.
  • A211541 (program): Number of ordered triples (w,x,y) with all terms in {1,…,n} and 2w=3x-4y.
  • A211542 (program): Number of ordered triples (w,x,y) with all terms in {1,…,n} and 2w=4y-3x.
  • A211543 (program): Number of ordered triples (w,x,y) with all terms in {1,…,n} and 2w=3x+5y.
  • A211544 (program): Number of ordered triples (w,x,y) with all terms in {1,…,n} and 2w=3x-5y.
  • A211545 (program): Number of ordered triples (w,x,y) with all terms in {-n,…-1,1,…,n} and w+x+y>0.
  • A211546 (program): Number of ordered triples (w,x,y) with all terms in {1,…,n} and w=3x-3y.
  • A211547 (program): The squares n^2, n >= 0, each one written three times.
  • A211549 (program): Number of (n+1) X (n+1) -9..9 symmetric matrices with every 2 X 2 subblock having sum zero and one or two distinct values.
  • A211557 (program): Number of nonnegative integer arrays of length n+3 with new values 0 upwards introduced in order, and containing the value 3
  • A211562 (program): Number of nonnegative integer arrays of length n+2 with new values 0 upwards introduced in order, and containing the value n-1.
  • A211603 (program): Triangular array read by rows: T(n,k) is the number of n-permutations that are pure cycles having exactly k fixed points; n>=2, 0<=k<=n-2.
  • A211606 (program): Total number of inversions over all involutions of length n.
  • A211610 (program): a(n) = Sum_{k=1..n-1} binomial (2*k, k)^n.
  • A211612 (program): Number of ordered triples (w,x,y) with all terms in {-n,…-1,1,…,n} and w+x+y>=0.
  • A211613 (program): Number of ordered triples (w,x,y) with all terms in {-n,…-1,1,…,n} and w+x+y>1.
  • A211614 (program): Number of ordered triples (w,x,y) with all terms in {-n,…-1,1,…,n} and w+x+y>2.
  • A211615 (program): Number of ordered triples (w,x,y) with all terms in {-n,…-1,1,…,n} and -1<=w+x+y<=1.
  • A211616 (program): Number of ordered triples (w,x,y) with all terms in {-n,…-1,1,…,n} and -2<=w+x+y<=2.
  • A211617 (program): Number of ordered triples (w,x,y) with all terms in {-n,…-1,1,…,n} and 2w+x+y>0.
  • A211618 (program): Number of ordered triples (w,x,y) with all terms in {-n,…-1,1,…,n} and 2w+x+y>1.
  • A211620 (program): Number of ordered triples (w,x,y) with all terms in {-n,…-1,1,…,n} and -1<=2w+x+y<=1.
  • A211622 (program): Number of ordered triples (w,x,y) with all terms in {-n,…-1,1,…,n} and w+2x+3y>1.
  • A211623 (program): Number of ordered triples (w,x,y) with all terms in {-n,…-1,1,…,n} and -1<=w+2x+3y<=1.
  • A211631 (program): Number of ordered triples (w,x,y) with all terms in {-n,…-1,1,…,n} and w^2>x^2+y^2.
  • A211634 (program): Number of ordered triples (w,x,y) with all terms in {1,…,n} and w^2<=x^2+y^2.
  • A211635 (program): Number of ordered triples (w,x,y) with all terms in {1,…,n} and w^2<x^2+y^2.
  • A211636 (program): Number of ordered triples (w,x,y) with all terms in {1,…,n} and w^2>=x^2+y^2.
  • A211637 (program): Number of ordered triples (w,x,y) with all terms in {1,…,n} and w^2>x^2+y^2.
  • A211638 (program): Number of ordered triples (w,x,y) with all terms in {1,…,n} and w^2+x^2+y^2<n.
  • A211639 (program): Number of ordered triples (w,x,y) with all terms in {1,…,n} and w^2+x^2+y^2<=n.
  • A211640 (program): Number of ordered triples (w,x,y) with all terms in {1,…,n} and w^2+x^2+y^2>n.
  • A211641 (program): Number of ordered triples (w,x,y) with all terms in {1,…,n} and w^2+x^2+y^2>=n.
  • A211642 (program): Number of ordered triples (w,x,y) with all terms in {1,…,n} and w^2+x^2+y^2<2n.
  • A211643 (program): Number of ordered triples (w,x,y) with all terms in {1,…,n} and w^2+x^2+y^2<=2n.
  • A211644 (program): Number of ordered triples (w,x,y) with all terms in {1,…,n} and w^2+x^2+y^2>2n.
  • A211645 (program): Number of ordered triples (w,x,y) with all terms in {1,…,n} and w^2+x^2+y^2>=2n.
  • A211646 (program): Number of ordered triples (w,x,y) with all terms in {1,…,n} and w^2+x^2+y^2<3n.
  • A211647 (program): Number of ordered triples (w,x,y) with all terms in {1,…,n} and w^2+x^2+y^2<=3n.
  • A211648 (program): Number of ordered triples (w,x,y) with all terms in {1,…,n} and w^2+x^2+y^2=3n.
  • A211649 (program): Number of ordered triples (w,x,y) with all terms in {1,…,n} and w^2+x^2+y^2=2n.
  • A211661 (program): Number of iterations log_3(log_3(log_3(…(n)…))) such that the result is < 1.
  • A211662 (program): Number of iterations log_3(log_3(log_3(…(n)…))) such that the result is < 2.
  • A211663 (program): Number of iterations log(log(log(…(n)…))) such that the result is < 1, where log is the natural logarithm.
  • A211664 (program): Number of iterations (…f_4(f_3(f_2(n))))…) such that the result is < 1, where f_j(x):=log_j(x).
  • A211665 (program): Minimal number of iterations of log_10 applied to n until the result is < 1.
  • A211666 (program): Number of iterations log_10(log_10(log_10(…(n)…))) such that the result is < 2.
  • A211667 (program): Number of iterations sqrt(sqrt(sqrt(…(n)…))) such that the result is < 2.
  • A211668 (program): Number of iterations sqrt(sqrt(sqrt(…(n)…))) such that the result is < 3.
  • A211669 (program): Number of iterations f(f(f(…(n)…))) such that the result is < 2, where f(x) = cube root of x.
  • A211670 (program): Number of iterations (…f_4(f_3(f_2(n))))…) such that the result is < 2, where f_j(x):=x^(1/j).
  • A211694 (program): Number of nonnegative integer arrays of length n+2*2-2 with new values introduced in order 0 upwards and every value appearing only in runs of at least 2
  • A211695 (program): Number of nonnegative integer arrays of length n+2*3-2 with new values introduced in order 0 upwards and every value appearing only in runs of at least 3
  • A211696 (program): Number of nonnegative integer arrays of length n+2*4-2 with new values introduced in order 0 upwards and every value appearing only in runs of at least 4
  • A211697 (program): Number of nonnegative integer arrays of length n+2*5-2 with new values introduced in order 0 upwards and every value appearing only in runs of at least 5
  • A211698 (program): Number of nonnegative integer arrays of length n+2*6-2 with new values introduced in order 0 upwards and every value appearing only in runs of at least 6
  • A211699 (program): Number of nonnegative integer arrays of length n+2*7-2 with new values introduced in order 0 upwards and every value appearing only in runs of at least 7
  • A211701 (program): Rectangular array by antidiagonals, n >= 1, k >= 1: R(n,k) = n + [n/2] + … + [n/k], where [ ]=floor.
  • A211702 (program): Rectangular array: R(n,k)=[n/F(1)]+[n/F(2)]+…+[n/F(k)], where [ ]=floor and F=A000045 (Fibonacci numbers), by antidiagonals.
  • A211703 (program): a(n) = n + [n/2] + [n/3] + [n/4], where [] = floor.
  • A211704 (program): a(n) = n + [n/2] + [n/3] + [n/4] + [n/5], where []=floor.
  • A211707 (program): Rectangular array: R(n,k)=n+[n/2+1/2]+…+[n/k+1/2], where [ ]=floor and k>=1, by antidiagonals.
  • A211710 (program): Number of (n+1) X (n+1) -11..11 symmetric matrices with every 2 X 2 subblock having sum zero and two distinct values.
  • A211715 (program): Number of (n+1) X (n+1) -11..11 symmetric matrices with every 2 X 2 subblock having sum zero and two or four distinct values.
  • A211719 (program): Number of (n+1) X (n+1) -11..11 symmetric matrices with every 2 X 2 subblock having sum zero.
  • A211773 (program): Prime-generating polynomial: 2*n^2 - 108*n + 1259.
  • A211774 (program): Number of rooted 2-regular labeled graphs on n nodes.
  • A211775 (program): a(n) = 2*n^2 - 212*n + 5419.
  • A211776 (program): a(n) = Product_{d | n} tau(d).
  • A211779 (program): a(n) = Sum_{d_<n | n} sigma(d_<n), where d_<n = divisors of n that are less than n, sigma(x) = A000203(x).
  • A211780 (program): a(n) = Sum_{d_<n | n} (d_<n) * tau(n / d_<n), where d_<n = divisors of n that are less than n, tau(x) = A000005(x).
  • A211782 (program): Rectangular array: R(n,k)=[n/F(2)]+[n/F(3)]+…+[n/F(k+1)], where [ ]=floor and F=A000045 (Fibonacci numbers), by antidiagonals.
  • A211783 (program): Rectangular array: R(n,k)=n^2+[(n^2)/2)]+…+[(n^2)/k], where [ ]=floor, by antidiagonals.
  • A211784 (program): n^2 + floor(n^2/2) + floor(n^2/3).
  • A211785 (program): Rectangular array: R(n,k)=n^3+[(n^3)/2)]+…+[(n^3)/k], where [ ]=floor, by antidiagonals.
  • A211786 (program): n^3 + floor(n^3/2).
  • A211788 (program): Triangle enumerating certain two-line arrays of positive integers.
  • A211789 (program): Row sums of A211788.
  • A211813 (program): Number of (n+1) X (n+1) -10..10 symmetric matrices with every 2 X 2 subblock having sum zero and two distinct values.
  • A211829 (program): Number of nonnegative integer arrays of length n+2 with new values 0 upwards introduced in order, no three adjacent elements equal, and containing the value 2
  • A211837 (program): Number of nonnegative integer arrays of length n+4 with new values 0 upwards introduced in order, no three adjacent elements equal, and containing the value n+1.
  • A211842 (program): Number of nonnegative integer arrays of length n+3 with new values 0 upwards introduced in order, no three adjacent elements all unequal, and containing the value 2.
  • A211850 (program): Number of nonnegative integer arrays of length 2n+5 with new values 0 upwards introduced in order, no three adjacent elements all unequal, and containing the value n+1.
  • A211864 (program): Powers of three read in base 2.
  • A211866 (program): (9^n - 5) / 4.
  • A211867 (program): a(n) = A097609(2*n-1,n), n>0; a(0)=1.
  • A211873 (program): Numbers b >= 0 such that 2 b^2 + 3 b + 5 is prime.
  • A211891 (program): G.f.: exp( Sum_{n>=1} 2 * Pell(n^2) * x^n/n ), where Pell(n) = A000129(n).
  • A211892 (program): G.f.: exp( Sum_{n>=1} 3 * Jacobsthal(n^2) * x^n/n ), where Jacobsthal(n) = A001045(n).
  • A211893 (program): G.f.: exp( Sum_{n>=1} 3 * Jacobsthal(n)^n * x^n/n ), where Jacobsthal(n) = A001045(n).
  • A211894 (program): G.f.: exp( Sum_{n>=1} 3 * Jacobsthal(n)^2 * x^n/n ), where Jacobsthal(n) = A001045(n).
  • A211898 (program): G.f.: exp( Sum_{n>=1} (2^n - (-1)^n)^n * x^n/n ).
  • A211899 (program): Number of triangular n X n X n arrays colored with integers 0 upwards introduced in row major order, with no element equal to any neighbor, and containing the value n(n+1)/2-2.
  • A211905 (program): Number of lower triangular n X n arrays colored with integers 0 upwards introduced in row major order, with no element equal to any horizontal or vertical neighbor, and containing the value n(n+1)/2-2.
  • A211911 (program): Number of lower triangular n X n arrays colored with integers 0 upwards introduced in row major order, with no element equal to any horizontal, vertical, diagonal or antidiagonal neighbor, and containing the value n(n+1)/2-2.
  • A211924 (program): Number of lower triangular n X n arrays colored with integers 0 upwards introduced in row major order, with no element equal to any horizontal, vertical or antidiagonal neighbor, and containing the value n(n+1)/2-2
  • A211932 (program): a(n) = Sum_{ m=1..n and gcd(n,m)>1 } tau(m), tau(m)=A000005(m).
  • A211939 (program): Number of distinct regular languages over unary alphabet, whose minimum regular expression has reverse Polish length n.
  • A211940 (program): Number of distinct finite languages over unary alphabet, whose minimum regular expression has reverse Polish length 2n-1.
  • A211947 (program): Number of distinct regular languages over unary alphabet, whose minimum regular expression has ordinary length n.
  • A211948 (program): Number of distinct finite languages over unary alphabet, whose minimum regular expression has ordinary length n.
  • A211955 (program): Triangle of coefficients of a polynomial sequence related to the Morgan-Voyce polynomials A085478.
  • A211957 (program): Triangle of coefficients of a polynomial sequence related to the Morgan-Voyce polynomials A085478.
  • A211958 (program): Number of lower triangular n X n arrays colored with integers 0 upwards introduced in row major order, with no element equal to any diagonal or antidiagonal neighbor, and containing the value n(n+1)/2-2.
  • A211971 (program): Column 0 of square array A211970 (in which column 1 is A000041).
  • A211991 (program): Difference between the arithmetic derivative of n and the sum of proper divisors of n.
  • A211995 (program): a(n) = floor(7^n / 2^n) mod 2^n.
  • A212000 (program): Triangle read by rows: T(n,k) = total number of parts in the last n-k+1 shells of n.
  • A212001 (program): Triangle read by rows: T(n,k) = sum of all parts of the last n-k+1 shells of n.
  • A212002 (program): Decimal expansion of (2*Pi)^2.
  • A212003 (program): Decimal expansion of (2*Pi)^3.
  • A212004 (program): Decimal expansion of (2*Pi)^4.
  • A212005 (program): Decimal expansion of (2*Pi)^5.
  • A212006 (program): Decimal expansion of (2*Pi)^6.
  • A212010 (program): Triangle read by rows: T(n,k) = total number of parts in the last k shells of n.
  • A212011 (program): Triangle read by rows: T(n,k) = sum of all parts of the last k shells of n.
  • A212012 (program): Triangle read by rows in which row n lists the number of states of the subshells of the n-th shell of the nuclear shell model ordered by energy level in increasing order.
  • A212013 (program): Triangle read by rows: total number of pairs of states of the first n subshells of the nuclear shell model in which the subshells are ordered by energy level in increasing order.
  • A212014 (program): Total number of states of the first n subshells of the nuclear shell model in which the subshells are ordered by energy level in increasing order.
  • A212031 (program): Number of lower triangular n X n arrays colored with integers 0 upwards introduced in row major order, with no element equal to any element at a city block distance of two, and containing the value n(n+1)/2-2.
  • A212039 (program): Number of lower triangular n X n arrays colored with integers 0 upwards introduced in row major order, with no element equal to any element within a city block distance of two, and containing the value n(n+1)/2-2.
  • A212057 (program): Number of (w,x,y,z) with all terms in {1,…,n} and w<x*y*z.
  • A212058 (program): Number of (w,x,y,z) with all terms in {1,…,n} and w>=x*y*z.
  • A212059 (program): Number of (w,x,y,z) with all terms in {1,…,n} and w=x*y*z-1.
  • A212060 (program): Number of (w,x,y,z) with all terms in {1,…,n} and w=x*y*z-2.
  • A212068 (program): Number of (w,x,y,z) with all terms in {1,…,n} and 2w=x+y+z.
  • A212069 (program): Number of (w,x,y,z) with all terms in {1,…,n} and 3*w = x+y+z.
  • A212071 (program): G.f. satisfies: A(x) = (1 + x*A(x)^3)^2.
  • A212072 (program): G.f. satisfies: A(x) = (1 + x*A(x)^2)^3.
  • A212073 (program): G.f. satisfies: A(x) = (1 + x*A(x)^(3/2))^4.
  • A212088 (program): Number of (w,x,y,z) with all terms in {1,…,n} and w<average{x,y,z}.
  • A212089 (program): Number of (w,x,y,z) with all terms in {1,…,n} and w>=average{x,y,z}.
  • A212090 (program): Number of (w,x,y,z) with all terms in {1,…,n} and w<x+y+z.
  • A212091 (program): Number of (w,x,y,z) with all terms in {1,…,n} and w^2=x^2+y^2+z^2.
  • A212096 (program): Number of (w,x,y,z) with all terms in {1,…,n} and w^3=x^3+y^3+z^3.
  • A212126 (program): Period 13: repeat (0,0,1,0,0,1,0,1,0,0,1,0,1).
  • A212127 (program): Numbers n whose arithmetic derivative equals the sum of its proper divisors.
  • A212133 (program): Number of (w,x,y,z) with all terms in {1,…,n} and median=mean.
  • A212134 (program): Number of (w,x,y,z) with all terms in {1,…,n} and median<=mean.
  • A212135 (program): Number of (w,x,y,z) with all terms in {1,…,n} and median<mean.
  • A212151 (program): Number of 2 X 2 matrices M of positive integers such that permanent(M) < n.
  • A212152 (program): Digits of one of the three 7-adic integers (-1)^(1/3).
  • A212153 (program): Approximations up to 7^n for one of the three 7-adic integers (-1)^(1/3).
  • A212155 (program): Digits of one of the three 7-adic integers (-1)^(1/3).
  • A212156 (program): ((6*A023000(n))^3 + 1)/7^n, n >= 0.
  • A212158 (program): ((prime(n)- 1)/2)!, n >= 2.
  • A212159 (program): a(n) = (-1)^((prime(n) + 1)/2).
  • A212160 (program): Numbers that are congruent to {2, 10} mod 13.
  • A212161 (program): Numbers congruent to 6 or 10 mod 17.
  • A212164 (program): Numbers n such that the maximal exponent in its prime factorization is greater than the number of positive exponents (A051903(n) > A001221(n)).
  • A212165 (program): Numbers n such that the maximal exponent in its prime factorization is not less than the number of positive exponents (A051903(n) >= A001221(n)).
  • A212166 (program): Numbers n such that the maximal exponent in its prime factorization equals the number of positive exponents (A051903(n) = A001221(n)).
  • A212167 (program): Numbers n such that the maximal exponent in its prime factorization is not greater than the number of positive exponents (A051903(n) <= A001221(n)).
  • A212168 (program): Numbers n such that the maximal exponent in its prime factorization is less than the number of positive exponents (A051903(n) < A001221(n)).
  • A212173 (program): First integer with same second signature as n (cf. A212172).
  • A212181 (program): Largest odd divisor of tau(n): a(n) = A000265(A000005(n)).
  • A212190 (program): Squares that are the sum of exactly three distinct powers of 2.
  • A212191 (program): Numbers whose squares are the sum of exactly three distinct powers of 2.
  • A212205 (program): G.f.: ((1+2*x)*sqrt(1-6*x^2+x^4)-1+5*x^2-2*x^3)/(2*x*(1-6*x^2)).
  • A212233 (program): Number of 0..2 arrays of length 2*n with sum no more than 2*n in any length 2n subsequence (=50% duty cycle).
  • A212240 (program): Number of 2 X 2 matrices M of with all terms in {1,…,n} and permanent(M) >= n.
  • A212241 (program): Number of 2 X 2 matrices M of with terms in {1,…,n} such that permanent(M) > n.
  • A212243 (program): Number of (w,x,y,z) with all terms in {1,…,n} and 2wx+yz=n.
  • A212244 (program): Number of (w,x,y,z) with all terms in {1,…,n} and w + n = x*y*z.
  • A212246 (program): Number of (w,x,y,z) with all terms in {1,…,n} and w <= x > y <= z.
  • A212247 (program): Number of (w,x,y,z) with all terms in {1,…,n} and 3w=x+y+z+n.
  • A212251 (program): Number of (w,x,y,z) with all terms in {1,…,n} and 3w = x + y + z + n + 1.
  • A212252 (program): Number of (w,x,y,z) with all terms in {1,…,n} and 3w=x+y+z+n+2.
  • A212254 (program): Number of (w,x,y,z) with all terms in {1,…,n} and w=x+2y+3z-n.
  • A212257 (program): Number of (v,w,x,y,z) with all terms in {0,1,…,n} and v=average(w,x,y,z).
  • A212262 (program): a(n) = 3^n + Fibonacci(n).
  • A212272 (program): a(n) = Fibonacci(n) + n^3.
  • A212278 (program): Number of adjacent pairs of zeros (possibly overlapping) in the representation of n in base of Fibonacci numbers (A014417).
  • A212291 (program): Number of permutations of n elements with at most one fixed point.
  • A212294 (program): Sums of (zero or more) distinct twin primes.
  • A212303 (program): a(n) = n!/([(n-1)/2]!*[(n+1)/2]!) for n>0, a(0)=0, and where [ ] = floor.
  • A212307 (program): Numerator of n!/3^n.
  • A212309 (program): a(n) = n! mod 3^n.
  • A212310 (program): a(n) = n! mod 4^n.
  • A212315 (program): Numbers m such that B(m) = B(triangular(m)), where B(m) is the binary weight of m (A000120).
  • A212323 (program): a(n) = 3^n - Fibonacci(n).
  • A212325 (program): Prime-generating polynomial: n^2 + 3*n - 167.
  • A212328 (program): Smallest k such that k^3 + 17 is divisible by 3^n.
  • A212329 (program): Expansion of x*(5+x)/(1-7*x+7*x^2-x^3).
  • A212331 (program): a(n) = 5*n*(n+5)/2.
  • A212332 (program): The difference between the largest and smallest prime factor of n as n runs through the numbers with at least two distinct prime factors.
  • A212333 (program): n-th power of the n-th pentagonal number.
  • A212335 (program): Expansion of 1/(1-22*x+22*x^2-x^3).
  • A212336 (program): Expansion of 1/(1 - 23*x + 23*x^2 - x^3).
  • A212337 (program): Expansion of 1/(1-4*x+3*x^2)^2.
  • A212338 (program): Sequence of coefficients of x in marked mesh pattern generating function Q_{n,132}^(0,0,2,0)(x).
  • A212340 (program): G.f.: 1/(1-x-x^2-2*x^3-5*x^4).
  • A212342 (program): Sequence of coefficients of x^0 in marked mesh pattern generating function Q_{n,132}^(0,3,0,0)(x).
  • A212343 (program): a(n) = (n+1)*(n-2)*(n-3)/2.
  • A212344 (program): Sequence of coefficients of x^(n-3) in marked mesh pattern generating function Q_{n,132}^(0,3,0,0)(x).
  • A212346 (program): Sequence of coefficients of x^0 in marked mesh pattern generating function Q_{n,132}^(0,4,0,0)(x).
  • A212347 (program): Sequence of coefficients of x^1 in marked mesh pattern generating function Q_{n,132}^(0,4,0,0)(x).
  • A212350 (program): Maximal number of “good” manifolds in an n-serial polytope.
  • A212351 (program): Maximal number of “good” manifolds in an n-nice polytope.
  • A212356 (program): Number of terms of the cycle index polynomial Z(D_n) for the dihedral group D_n.
  • A212362 (program): Triangle by rows, binomial transform of the beheaded Pascal’s triangle A074909.
  • A212364 (program): Number of Dyck n-paths all of whose ascents and descents have lengths equal to 1 (mod 5).
  • A212365 (program): Number of Dyck n-paths all of whose ascents and descents have lengths equal to 1 (mod 6).
  • A212366 (program): Number of Dyck n-paths all of whose ascents and descents have lengths equal to 1 (mod 7).
  • A212367 (program): Number of Dyck n-paths all of whose ascents and descents have lengths equal to 1 (mod 8).
  • A212374 (program): Primes congruent to 1 mod 23.
  • A212377 (program): Primes congruent to 1 mod 53.
  • A212378 (program): Primes congruent to 1 mod 61.
  • A212379 (program): Primes congruent to 1 mod 41.
  • A212383 (program): Number of Dyck n-paths all of whose ascents have lengths equal to 1 (mod 3).
  • A212384 (program): Number of Dyck n-paths all of whose ascents have lengths equal to 1 (mod 4).
  • A212385 (program): Number of Dyck n-paths all of whose ascents have lengths equal to 1 (mod 5).
  • A212386 (program): Number of Dyck n-paths all of whose ascents have lengths equal to 1 (mod 6).
  • A212387 (program): Number of Dyck n-paths all of whose ascents have lengths equal to 1 (mod 7).
  • A212389 (program): Number of Dyck n-paths all of whose ascents have lengths equal to 1 (mod 9).
  • A212395 (program): Number of move operations required to sort all permutations of [n] by insertion sort.
  • A212396 (program): Numerator of the average number of move operations required by an insertion sort of n (distinct) elements.
  • A212397 (program): Denominator of the average number of move operations required by an insertion sort of n (distinct) elements.
  • A212403 (program): Number of binary arrays of length 2*n+1 with no more than n ones in any length 2n subsequence (=50% duty cycle).
  • A212404 (program): Number of binary arrays of length 2*n+2 with no more than n ones in any length 2n subsequence (=50% duty cycle)
  • A212415 (program): Number of (w,x,y,z) with all terms in {1,…,n} and w=y<=z.
  • A212419 (program): Size of the equivalence class of S_n containing the identity permutation under transformations of positionally adjacent elements of the form abc <–> acb <–> bac <–> cba, where a<b<c.
  • A212427 (program): a(n) = 17*n + A000217(n-1).
  • A212428 (program): a(n) = 18*n + A000217(n-1).
  • A212435 (program): Expansion of e.g.f.: exp(-x) / cosh(2*x).
  • A212445 (program): a(n) = floor( n + log(n) ).
  • A212450 (program): Ceiling(n + log(n)).
  • A212484 (program): Expansion of c(q^2) * b(q^6) / (b(q) * c(q) * b(q^3) * c(q^3))^(1/2) in powers of q where b(), c() are cubic AGM theta functions.
  • A212492 (program): Prime p such that p, p+10, p+12 are all primes.
  • A212495 (program): Numbers all of whose base 11 digits are even.
  • A212496 (program): a(n) = Sum_{k=1..n} (-1)^{k-Omega(k)} with Omega(k) the total number of prime factors of k (counted with multiplicity).
  • A212497 (program): A finite sequence (of length 12) in which every permutation of [1..4] is a substring.
  • A212499 (program): Numbers k that divide the product of digits of k.
  • A212500 (program): a(n) is the difference between multiples of 5 with even and odd digit sum in base 4 in interval [0,4^n).
  • A212501 (program): Number of (w,x,y,z) with all terms in {1,…,n} and w > x < y >= z.
  • A212503 (program): Number of (w,x,y,z) with all terms in {1,…,n} and w<2x and y<2z.
  • A212504 (program): Number of (w,x,y,z) with all terms in {1,…,n} and w<2x and y>2z.
  • A212505 (program): Number of (w,x,y,z) with all terms in {1,…,n} and w<2x and y>=2z.
  • A212506 (program): Number of (w,x,y,z) with all terms in {1,…,n} and w<=2x and y<=2z.
  • A212507 (program): Number of (w,x,y,z) with all terms in {1,…,n} and w<2x and y<=2z.
  • A212508 (program): Number of (w,x,y,z) with all terms in {1,…,n} and w<2x and y<3z.
  • A212509 (program): Number of (w,x,y,z) with all terms in {1,…,n} and w<2x and y<=3z.
  • A212510 (program): Number of (w,x,y,z) with all terms in {1,…,n} and w<2x and y>3z.
  • A212511 (program): Number of (w,x,y,z) with all terms in {1,…,n} and w<2x and y>=3z.
  • A212512 (program): Number of (w,x,y,z) with all terms in {1,…,n} and w<=2x and y<3z.
  • A212513 (program): Number of (w,x,y,z) with all terms in {1,…,n} and w<=2x and y<=3z.
  • A212514 (program): Number of (w,x,y,z) with all terms in {1,…,n} and w<=2x and y>3z.
  • A212515 (program): Number of (w,x,y,z) with all terms in {1,…,n} and w<=2x and y>=3z.
  • A212516 (program): Number of (w,x,y,z) with all terms in {1,…,n} and w>2x and y<3z.
  • A212517 (program): Number of (w,x,y,z) with all terms in {1,…,n} and w>2x and y<=3z.
  • A212518 (program): Number of (w,x,y,z) with all terms in {1,…,n} and w>2x and y>3z.
  • A212519 (program): Number of (w,x,y,z) with all terms in {1,…,n} and w>2x and y>=3z.
  • A212520 (program): Number of (w,x,y,z) with all terms in {1,…,n} and w>=2x and y<3z.
  • A212521 (program): Number of (w,x,y,z) with all terms in {1,…,n} and w>=2x and y<=3z.
  • A212522 (program): Number of (w,x,y,z) with all terms in {1,…,n} and w>=2x and y>3z.
  • A212523 (program): Number of (w,x,y,z) with all terms in {1,…,n} and w+x<y+z.
  • A212525 (program): Primes containing a digit 3.
  • A212529 (program): Negative numbers in base -2.
  • A212530 (program): Difference between the sum of the first n primes s(n) and the nearest square < s(n).
  • A212555 (program): Values of ||G*(n)|| related to construction of graphs which contain all small trees.
  • A212559 (program): Number of functions f:{1,2,…,n}->{1,2,…,n} such that every non-recurrent element has at most one preimage.
  • A212560 (program): Number of (w,x,y,z) with all terms in {1,…,n} and w+x<=y+z.
  • A212561 (program): Number of (w,x,y,z) with all terms in {1,…,n} and w + x = 2y + 2z.
  • A212562 (program): Number of (w,x,y,z) with all terms in {1,…,n} and w+x<2y+2z.
  • A212563 (program): Number of (w,x,y,z) with all terms in {1,…,n} and w+x<=2y+2z.
  • A212564 (program): Number of (w,x,y,z) with all terms in {1,…,n} and w+x>2y+2z.
  • A212565 (program): Number of (w,x,y,z) with all terms in {1,…,n} and w+x>=2y+2z.
  • A212566 (program): Number of (w,x,y,z) with all terms in {1,…,n} and w+x=3y+3z.
  • A212568 (program): Number of (w,x,y,z) with all terms in {1,…,n} and w<|x-y|+|y-z|.
  • A212569 (program): Number of (w,x,y,z) with all terms in {0,…,n} such that range{w,x,y,z} is not one of the numbers w,x,y,z.
  • A212570 (program): Number of (w,x,y,z) with all terms in {1,…,n} and |w-x|=|x-y|+|y-z|.
  • A212571 (program): Number of (w,x,y,z) with all terms in {1,…,n} and |w-x|<|x-y|+|y-z|.
  • A212572 (program): Number of (w,x,y,z) with all terms in {1,…,n} and |w-x| <= |x-y| + |y-z|.
  • A212573 (program): Number of (w,x,y,z) with all terms in {1,…,n} and |w-x|>|x-y|+|y-z|.
  • A212574 (program): Number of (w,x,y,z) with all terms in {1,…,n} and |w-x|>=|x-y|+|y-z|.
  • A212578 (program): Number of (w,x,y,z) with all terms in {1,…,n} and |w-x| = 2*|x-y| - |y-z|.
  • A212584 (program): Nonnegative walks of length n on the x-axis starting at the origin using steps {1,-1} and visiting no point more than twice.
  • A212586 (program): Nonnegative walks of length n on the x-axis starting at the origin using steps {1,0,-1} and visiting no point more than twice.
  • A212589 (program): Walks with n steps on the x-axis using steps {1,0,-1} and visiting no point more than twice.
  • A212591 (program): a(n) is the smallest value of k for which A020986(k) = n.
  • A212595 (program): Let f(n) = 2n-7. Difference between f(n) and the nearest prime < f(n).
  • A212596 (program): Number of cards required to build a Menger sponge of level n in origami.
  • A212598 (program): a(n) = n - m!, where m is the largest number such that m! <= n.
  • A212633 (program): Triangle read by rows: T(n,k) is the number of dominating subsets with cardinality k of the path tree P_n (n>=1, 1<=k<=n).
  • A212634 (program): Triangle read by rows: T(n,k) is the number of dominating subsets with cardinality k of the cycle C_n (n >= 1, 1 <= k <= n).
  • A212650 (program): Number of permutations of n elements with at least one fixed point and at least one 2-cycle (transposition).
  • A212652 (program): a(n) = least positive integer M such that n = T(M) - T(k), for k an integer, 0 <= k <= M, where T(r) = A000217(r) is the r-th triangular number.
  • A212653 (program): Number of steps to reach 1 in the Collatz (3x+1) problem starting with 3^n + 1.
  • A212655 (program): Denominator of Bernoulli(2*n,1/2) / Period of length 2: repeat 12, 60.
  • A212656 (program): a(n) = 5*n^2 + 1.
  • A212660 (program): Partial products of A001037.
  • A212668 (program): a(n) = (16/3)*(n+1)*n*(n-1) + 8*n^2 + 1.
  • A212669 (program): a(n) = 2/15 * (32*n^5 + 80*n^4 + 40*n^3 - 20*n^2 + 3*n).
  • A212671 (program): A001037(n)!.
  • A212672 (program): Partial products of A212671.
  • A212673 (program): Number of (w,x,y,z) with all terms in {1,…,n} and w<=|x-y|+|y-z|.
  • A212674 (program): Number of (w,x,y,z) with all terms in {1,…,n} and w > |x-y| + |y-z|.
  • A212675 (program): Number of (w,x,y,z) with all terms in {1,…,n} and w >= |x-y| + |y-z|.
  • A212676 (program): Number of (w,x,y,z) with all terms in {1,…,n} and w+x=|x-y|+|y-z|.
  • A212677 (program): Number of (w,x,y,z) with all terms in {1,…,n} and w+y=|x-y|+|y-z|.
  • A212679 (program): Number of (w,x,y,z) with all terms in {1,…,n} and |x-y|=|y-z|.
  • A212680 (program): Number of (w,x,y,z) with all terms in {1,…,n} and |x-y|=|y-z|+1.
  • A212681 (program): Number of (w,x,y,z) with all terms in {1,…,n} and |x-y|<|y-z|.
  • A212682 (program): Number of (w,x,y,z) with all terms in {1,…,n} and |x-y|>=|y-z|.
  • A212683 (program): Number of (w,x,y,z) with all terms in {1,…,n} and |x-y| = w + |y-z|.
  • A212684 (program): Number of (w,x,y,z) with all terms in {1,…,n} and |x-y|=n-w+|y-z|.
  • A212685 (program): Number of (w,x,y,z) with all terms in {1,…,n} and |w-x|=w+|y-z|.
  • A212686 (program): Number of (w,x,y,z) with all terms in {1,…,n} and 2|w-x|=n+|y-z|.
  • A212687 (program): Number of (w,x,y,z) with all terms in {1,…,n} and 2|w-x|<n+|y-z|.
  • A212688 (program): Number of (w,x,y,z) with all terms in {1,…,n} and 2|w-x|>=n+|y-z|.
  • A212689 (program): Number of (w,x,y,z) with all terms in {1,…,n} and 2|w-x|>n+|y-z|.
  • A212690 (program): Number of (w,x,y,z) with all terms in {1,…,n} and 2|w-x|<=n+|y-z|.
  • A212691 (program): Number of (w,x,y,z) with all terms in {1,…,n} and w+|x-y|<=|x-z|+|y-z|.
  • A212692 (program): Number of (w,x,y,z) with all terms in {1,…,n} and w<|x-y|+|y-z|.
  • A212695 (program): Decimal expansion of the uniform exponent of simultaneous approximation of Q-linearly independent triples (1,x,x^3) by rational numbers.
  • A212696 (program): Central coefficient of the triangle A097609.
  • A212697 (program): a(n) = 2*n*3^(n-1).
  • A212698 (program): Main transitions in systems of n particles with spin 3/2.
  • A212699 (program): Main transitions in systems of n particles with spin 2.
  • A212700 (program): a(n) = 5*n*6^(n-1).
  • A212701 (program): Main transitions in systems of n particles with spin 3.
  • A212702 (program): Main transitions in systems of n particles with spin 7/2.
  • A212703 (program): Main transitions in systems of n particles with spin 4.
  • A212704 (program): a(n) = 9*n*10^(n-1).
  • A212707 (program): Semiprimes of the form 5*n^2 + 1.
  • A212714 (program): Number of (w,x,y,z) with all terms in {1,…,n} and |w-x| >= w + |y-z|.
  • A212722 (program): E.g.f. satisfies: A(x) = exp( x/(1 - x*A(x)^2) ).
  • A212730 (program): Number of 0..2 arrays of length 2*n with sum less than 2*n in any length 2n subsequence (=less than 50% duty cycle)
  • A212739 (program): a(n) = 2^(n^2) - 1.
  • A212740 (program): Number of (w,x,y,z) with all terms in {0,…,n} and max{w,x,y,z}<2*min{w,x,y,z}.
  • A212741 (program): Number of (w,x,y,z) with all terms in {0,…,n} and max{w,x,y,z}>=2*min{w,x,y,z}.
  • A212742 (program): Number of (w,x,y,z) with all terms in {0,…,n} and max{w,x,y,z}<=2*min{w,x,y,z}.
  • A212743 (program): Number of (w,x,y,z) with all terms in {0,…,n} and max{w,x,y,z}>2*min{w,x,y,z}.
  • A212744 (program): Number of (w,x,y,z) with all terms in {0,…,n} and w=max{w,x,y,z}-min{w,x,y,z}; i.e., the range of (w,x,y,z) is its first term.
  • A212746 (program): Number of (w,x,y,z) with all terms in {0,…,n} and at least one of them is the range of {w,x,y,z}.
  • A212747 (program): Number of (w,x,y,z) with all terms in {0,…,n} and 2w=floor((x+y+z)/2)).
  • A212748 (program): Number of (w,x,y,z) with all terms in {0,…,n} and w=2*floor((x+y+z)/2)).
  • A212753 (program): Number of (w,x,y,z) with all terms in {0,…,n} and at least one of these conditions holds: w<R, x<R, y>R, z>R, where R = max{w,x,y,z} - min{w,x,y,z}.
  • A212754 (program): Number of (w,x,y,z) with all terms in {0,…,n} and at least one of these conditions holds: w<R, x>R, y>R, z>R, where R = max{w,x,y,z} - min{w,x,y,z}.
  • A212755 (program): Number of (w,x,y,z) with all terms in {0,…,n} and |w-x|=max{w,x,y,z}-min{w,x,y,z}.
  • A212759 (program): Number of (w,x,y,z) with all terms in {0,…,n} and w, x, and y even.
  • A212760 (program): Number of (w,x,y,z) with all terms in {0,…,n}, w even, and x = y + z.
  • A212761 (program): Number of (w,x,y,z) with all terms in {0,…,n}, w odd, x and y even.
  • A212762 (program): Number of (w,x,y,z) with all terms in {0,…,n}, w and x odd, y even.
  • A212763 (program): Number of (w,x,y,z) with all terms in {0,…,n}, and w, x and y odd.
  • A212764 (program): Number of (w,x,y,z) with all terms in {0,…,n}, w, x and y odd, and z odd.
  • A212765 (program): Number of (w,x,y,z) with all terms in {0,…,n}, w even and x, y, and z odd.
  • A212766 (program): Number of (w,x,y,z) with all terms in {0,…,n}, w even and x odd.
  • A212767 (program): Number of (w,x,y,z) with all terms in {0,…,n}, w even, x even, and w+x=y+z.
  • A212769 (program): p*q modulo (p+q) with p, q consecutive primes.
  • A212770 (program): Expansion of q / (chi(q) * chi(q^2) * chi(q^3) * chi(q^6))^2 in powers of q where chi() is a Ramanujan theta function.
  • A212772 (program): Floor((n+1)*(n-3)*(n-4)/12).
  • A212776 (program): Half the number of 0..2 arrays of length n+2 with second differences nonzero
  • A212790 (program): (prime(n) + n) mod (prime(n) - n).
  • A212791 (program): Central binomial coefficient CB(n) purged of all primes exceeding (n+1)/2.
  • A212792 (program): Product of all primes in the interval ((n+1)/2,n].
  • A212793 (program): Characteristic function of cubefree numbers, A004709.
  • A212794 (program): Triangular numbers (A000217) which are also hypotenuse numbers (A009003).
  • A212797 (program): Row 2 of array in A212796.
  • A212798 (program): Row 3 of array in A212796.
  • A212804 (program): Expansion of (1 - x)/(1 - x - x^2).
  • A212810 (program): Iterate the morphism 1->122, 2->1112 starting with 1.
  • A212823 (program): Number of 0..2 arrays of length n with no adjacent pair equal to its immediately preceding adjacent pair, and new values introduced in 0..2 order.
  • A212824 (program): Number of 0..3 arrays of length n with no adjacent pair equal to its immediately preceding adjacent pair, and new values introduced in 0..3 order.
  • A212825 (program): Number of 0..4 arrays of length n with no adjacent pair equal to its immediately preceding adjacent pair, and new values introduced in 0..4 order.
  • A212826 (program): Number of 0..5 arrays of length n with no adjacent pair equal to its immediately preceding adjacent pair, and new values introduced in 0..5 order.
  • A212827 (program): Number of 0..6 arrays of length n with no adjacent pair equal to its immediately preceding adjacent pair, and new values introduced in 0..6 order
  • A212831 (program): a(4*n) = 2*n, a(2*n+1) = 2*n+1, a(4*n+2) = 2*n+2.
  • A212832 (program): Decimal expansion of 5/24.
  • A212833 (program): Number of 0..n arrays of length n+1 with 0 never adjacent to n
  • A212834 (program): Number of 0..7 arrays of length n+1 with 0 never adjacent to 7.
  • A212835 (program): T(n,k)=Number of 0..k arrays of length n+1 with 0 never adjacent to k
  • A212836 (program): Number of 0..n arrays of length 3 with 0 never adjacent to n.
  • A212837 (program): Number of 0..n arrays of length 4 with 0 never adjacent to n.
  • A212838 (program): Number of 0..n arrays of length 5 with 0 never adjacent to n.
  • A212839 (program): Number of 0..n arrays of length 6 with 0 never adjacent to n.
  • A212840 (program): Number of 0..n arrays of length 7 with 0 never adjacent to n.
  • A212841 (program): Number of 0..n arrays of length 8 with 0 never adjacent to n.
  • A212844 (program): a(n) = 2^(n+2) mod n.
  • A212846 (program): Polylogarithm li(-n,-1/2) multiplied by (3^(n+1))/2.
  • A212847 (program): Polylogarithm li(-n,-2/3) multiplied by (5^(n+1))/3.
  • A212848 (program): Least prime factor of n-th central trinomial coefficient (A002426).
  • A212849 (program): Numbers whose sum of prime factors (counted with multiplicity) is a triangular number.
  • A212850 (program): Number of n X 3 arrays with rows being permutations of 0..2 and no column j greater than column j-1 in all rows.
  • A212856 (program): Number of 3 X n arrays with rows being permutations of 0..n-1 and no column j greater than column j-1 in all rows.
  • A212857 (program): Number of 4 X n arrays with rows being permutations of 0..n-1 and no column j greater than column j-1 in all rows.
  • A212859 (program): Number of 6 X n arrays with rows being permutations of 0..n-1 and no column j greater than column j-1 in all rows.
  • A212860 (program): Number of 7 X n arrays with rows being permutations of 0..n-1 and no column j greater than column j-1 in all rows.
  • A212864 (program): Number of nondecreasing sequences of n 1..4 integers with no element dividing the sequence sum.
  • A212885 (program): Expansion of phi(q) * phi(-q)^2 in powers of q where phi() is a Ramanujan theta function.
  • A212886 (program): Decimal expansion of 2/(3*sqrt(3)) = 2*sqrt(3)/9.
  • A212889 (program): Number of (w,x,y,z) with all terms in {0,…,n} and even range.
  • A212890 (program): Number of (w,x,y,z) with all terms in {0,…,n} and odd range.
  • A212891 (program): Rectangular array: (row n) = b**c, where b(h) = h, c(h) = (n-1+h)^2, n>=1, h>=1, and ** = convolution.
  • A212892 (program): a(n) = n^4/8 if n is even, a(n) = (n^2-1)^2/8 if n is odd.
  • A212893 (program): Number of quadruples (w,x,y,z) with all terms in {0,…,n} such that w-x, x-y, and y-z all have the same parity.
  • A212894 (program): Number of (w,x,y,z) with all terms in {0,…,n} and (least gapsize)=1.
  • A212896 (program): Number of (w,x,y,z) with all terms in {0,…,n} and (least gapsize)<2.
  • A212897 (program): Number of (w,x,y,z) with all terms in {0,…,n} and (least gapsize)>1.
  • A212901 (program): Number of (w,x,y,z) with all terms in {0,…,n} and equal consecutive gap sizes.
  • A212905 (program): Number of (w,x,y,z) with all terms in {0,…,n} and |w-x|+|x-y+|y-z|=2n.
  • A212907 (program): Expansion of x^(-1/3) * psi(x^3) * c(x) / 3 in powers of x where psi() is a Ramanujan theta function and c() is a cubic AGM theta function.
  • A212917 (program): E.g.f. satisfies: A(x) = exp( x/(1 - x*A(x)^3) ).
  • A212925 (program): Number of n X 3 0..2 arrays with no column j greater than column j-1 in all rows.
  • A212952 (program): Decimal expansion of 3*sqrt(3)/16.
  • A212959 (program): Number of (w,x,y) such that w,x,y are all in {0,…,n} and |w-x| = |x-y|.
  • A212960 (program): Number of (w,x,y) with all terms in {0,…,n} and |w-x| != |x-y|.
  • A212962 (program): Expansion of x*(3+x-x^3)/((1-3*x-x^2)*(1-x)*(1+x)).
  • A212963 (program): a(n) = number of ordered triples (w,x,y) such that w,x,y are all in {0,…,n} and the numbers |w-x|, |x-y|, |y-w| are distinct.
  • A212964 (program): Number of (w,x,y) with all terms in {0,…,n} and |w-x| < |x-y| < |y-w|.
  • A212965 (program): Number of triples (w,x,y) with all terms in {0,…,n} and such that w = max(w,x,y) - min(w,x,y).
  • A212966 (program): Number of (w,x,y) with all terms in {0,…,n} and 2*w=range{w,x,y}.
  • A212967 (program): Number of (w,x,y) with all terms in {0,…,n} and w < range{w,x,y}.
  • A212968 (program): Number of (w,x,y) with all terms in {0,…,n} and w>=range{w,x,y}.
  • A212969 (program): Number of (w,x,y) with all terms in {0,…,n} and w!=x and x>range{w,x,y}.
  • A212970 (program): Number of (w,x,y) with all terms in {0,…,n} and w!=x and x>range{w,x,y}.
  • A212971 (program): Number of (w,x,y) with all terms in {0,…,n} and w<floor((x+y)/3)).
  • A212972 (program): Number of (w,x,y) with all terms in {0,…,n} and w<floor((x+y)/3)).
  • A212973 (program): Number of (w,x,y) with all terms in {0,…,n} and w<=floor((x+y)/3)).
  • A212974 (program): Number of (w,x,y) with all terms in {0,…,n} and w>floor((x+y)/3)).
  • A212975 (program): Number of (w,x,y) with all terms in {0,…,n} and even range.
  • A212976 (program): Number of (w,x,y) with all terms in {0,…,n} and odd range.
  • A212977 (program): Number of (w,x,y) with all terms in {0,…,n} and n/2 < w+x+y <= n.
  • A212978 (program): Number of (w,x,y) with all terms in {0,…,n} and range = 2*n-w-x.
  • A212979 (program): Number of (w,x,y) with all terms in {0,…,n} and range=average.
  • A212980 (program): Number of (w,x,y) with all terms in {0,…,n} and w<x+y and x<y.
  • A212981 (program): Number of (w,x,y) with all terms in {0,…,n} and w <= x + y and x < y.
  • A212982 (program): Number of (w,x,y) with all terms in {0,…,n} and w<x+y and x<=y.
  • A212983 (program): Number of (w,x,y) with all terms in {0,…,n} and w<=x+y and x<=y.
  • A212984 (program): Number of (w,x,y) with all terms in {0..n} and 3w = x+y.
  • A212985 (program): Number of (w,x,y) with all terms in {0,…,n} and 3w = 3x + y.
  • A212986 (program): Number of (w,x,y) with all terms in {0,…,n} and 2w = 3x+y.
  • A212987 (program): Number of (w,x,y) with all terms in {0,…,n} and 3*w = 2*x+2*y.
  • A212988 (program): Number of (w,x,y) with all terms in {0,…,n} and 4*w = x+y.
  • A212989 (program): Number of (w,x,y) with all terms in {0,…,n} and 4*w = 4*x+y.
  • A213012 (program): Trajectory of 26 under the Reverse and Add! operation carried out in base 2.
  • A213014 (program): Number of zeros following the initial 1 in n-th absolute difference of primes.
  • A213015 (program): Numbers n such that the sum of prime factors of n (counted with multiplicity) is 2 times a prime.
  • A213022 (program): Expansion of phi(x)^2 * psi(x) in powers of x where phi(), psi() are Ramanujan theta functions.
  • A213023 (program): Expansion of psi(x)^2 * psi(-x^3) / chi(-x^2) in powers of x where psi(), chi() are Ramanujan theta functions.
  • A213024 (program): The number of solutions to x^2 + y^2 + 2*z^2 = n in positive integers x,y,z.
  • A213029 (program): a(n) = floor(n/2)^2 - floor(n/3)^2.
  • A213030 (program): [2n/3]^2 -[n/3]^2, where []=floor.
  • A213031 (program): [n/2]^3 -[n/3]^3, where []=floor.
  • A213033 (program): n*[n/2]*[n/3], where [] = floor.
  • A213034 (program): [3n/2]*[n/3], where [] = floor.
  • A213035 (program): n^2-[n/3]^2, where [] = floor.
  • A213036 (program): n^2-[2n/3]^2, where [] = floor.
  • A213037 (program): a(n) = n^2 - 2*floor(n/2)^2.
  • A213038 (program): a(n) = n^2 - 3*floor(n/2)^2.
  • A213039 (program): n^3-[n/3]^3, where [] = floor.
  • A213040 (program): Partial sums of A004738, leftmost column of the sequence of triangles defined in A206492.
  • A213041 (program): Number of (w,x,y) with all terms in {0..n} and 2|w-x| = max(w,x,y)-min(w,x,y).
  • A213042 (program): Convolution of (1,0,2,0,3,0,…) and (1,0,0,2,0,0,3,0,0,…); i.e., (A027656(n)) and (A175676(n+2)).
  • A213043 (program): Convolution of (1,-1,2,-2,3,-3,…) and A000045 (Fibonacci numbers).
  • A213044 (program): Convolution of Fibonacci numbers and positive integers repeated three times (A000045 and A008620).
  • A213045 (program): Number of (w,x,y) with all terms in {0,…,n} and 2|w-x|>max(w,x,y)-min(w,x,y).
  • A213046 (program): Convolution of Lucas numbers and positive integers repeated (A000032 and A008619).
  • A213050 (program): Primes of the form 4*k+1 with primitive root +2.
  • A213051 (program): Primes of the form 4*k+3 with primitive root +2.
  • A213056 (program): Expansion of chi(x) * f(x^3)^3 in powers of x where chi(), f() are Ramanujan theta functions.
  • A213060 (program): Lucas(n) mod n, Lucas(n)= A000032(n).
  • A213061 (program): Triangle of Stirling numbers of second kind (A048993) read mod 2.
  • A213064 (program): Bitwise AND of 2n with the one’s-complement of n.
  • A213071 (program): 3*n*(9n + 2)*(18n - 1), where n runs through the odd numbers 1, 3, 5,…
  • A213075 (program): Second diagonal of A213074.
  • A213077 (program): a(n) = round(n^2 - sqrt(n)).
  • A213082 (program): Values of n for which the number of roots of the function sin(x)/x - 1/n increases.
  • A213083 (program): Each square n^2 appears n^2 number of times.
  • A213084 (program): Numbers consisting of ones and eights.
  • A213088 (program): The Manhattan distance to the origin while traversing the first quadrant in a taxicab geometry.
  • A213119 (program): Number of binary arrays of length 2*n+1 with fewer than n ones in any length 2n subsequence (=less than 50% duty cycle).
  • A213120 (program): Number of binary arrays of length 2*n+2 with fewer than n ones in any length 2n subsequence (=less than 50% duty cycle).
  • A213127 (program): Polylogarithm li(-n,-1/4) multiplied by (5^(n+1))/4.
  • A213128 (program): Polylogarithm li(-n,-1/5) multiplied by (6^(n+1))/5.
  • A213129 (program): Polylogarithm li(-n,-1/6) multiplied by (7^(n+1))/6.
  • A213130 (program): Polylogarithm li(-n,-1/7) multiplied by (8^(n+1))/7.
  • A213131 (program): Polylogarithm li(-n,-1/8) multiplied by (9^(n+1))/8.
  • A213132 (program): Polylogarithm li(-n,-1/9) multiplied by (10^(n+1))/9.
  • A213133 (program): Polylogarithm li(-n,-1/10) multiplied by (11^(n+1))/10.
  • A213134 (program): Polylogarithm li(-n,-2/5) multiplied by (7^(n+1))/5.
  • A213135 (program): Polylogarithm li(-n,-2/7) multiplied by (9^(n+1))/7.
  • A213136 (program): Polylogarithm li(-n,-2/9) multiplied by (11^(n+1))/9.
  • A213137 (program): Polylogarithm li(-n,-3/4) multiplied by (7^(n+1))/4.
  • A213138 (program): Polylogarithm li(-n,-3/5) multiplied by (8^(n+1))/5.
  • A213139 (program): Polylogarithm li(-n,-3/7) multiplied by (10^(n+1))/7.
  • A213140 (program): Polylogarithm li(-n,-3/8) multiplied by (11^(n+1))/8.
  • A213141 (program): Polylogarithm li(-n,-3/10) multiplied by (13^(n+1))/10.
  • A213142 (program): Polylogarithm li(-n,-4/5) multiplied by (9^(n+1))/5.
  • A213143 (program): Polylogarithm li(-n,-4/7) multiplied by (11^(n+1))/7.
  • A213144 (program): Polylogarithm li(-n,-4/9) multiplied by (13^(n+1))/9.
  • A213145 (program): Polylogarithm li(-n,-5/6) multiplied by (11^(n+1))/6.
  • A213146 (program): Polylogarithm li(-n,-5/7) multiplied by (12^(n+1))/7.
  • A213147 (program): Polylogarithm li(-n,-5/8) multiplied by (13^(n+1))/8.
  • A213148 (program): Polylogarithm li(-n,-5/9) multiplied by (14^(n+1))/9.
  • A213150 (program): Polylogarithm li(-n,-7/8) multiplied by (15^(n+1))/8.
  • A213152 (program): Polylogarithm li(-n,-7/10) multiplied by (17^(n+1))/10.
  • A213154 (program): Polylogarithm li(-n,-9/10) multiplied by (19^(n+1))/10.
  • A213155 (program): Polylogarithm li(-n,-1/100) multiplied by (101^(n+1))/100.
  • A213156 (program): Polylogarithm li(-n,-1/1000) multiplied by (1001^(n+1))/1000.
  • A213163 (program): Sequence of coefficients of x in marked mesh pattern generating function Q_{n,132}^(3,0,-,0)(x).
  • A213164 (program): Sequence of coefficients of x in marked mesh pattern generating function Q_{n,132}^(4,0,-,0)(x).
  • A213167 (program): a(n) = n! - (n-2)!.
  • A213168 (program): a(n) = n!/2 - (n-1)! - n + 2.
  • A213169 (program): n!+n+1.
  • A213170 (program): E.g.f.: exp(2*(1-exp(x))).
  • A213171 (program): T(n,k) = ((k+n)^2 - 4*k + 3 - (-1)^n - (k+n)*(-1)^(k+n))/2; n, k > 0, read by antidiagonals.
  • A213172 (program): Floor of the Euclidean distance of a point on the (1, 2, 3; 4, 5, 6) 3D walk.
  • A213173 (program): a(n) = 4^floor(n/2), Powers of 4 repeated.
  • A213178 (program): Total cell count of the expansion of a single cell, utilizing S1/B1 Game of Life cellular automata rules.
  • A213179 (program): Numbers k such that 2*k is a partition number.
  • A213181 (program): Number of chains of even numbers of length 2 or more in the Collatz (3x+1) trajectory of n.
  • A213182 (program): Numbers which may represent a date in “condensed European notation” DDMMYY.
  • A213183 (program): Initialize a(1)=R=1. Repeat: copy the last R preceding terms to current position; increment R; do twice: append the least integer that has not appeared in the sequence yet.
  • A213184 (program): Numbers which may represent a date in “condensed American notation” MMDDYY.
  • A213190 (program): a(0)=1, a(1)=1, a(n) = n*a(n-1) + 3*a(n-2).
  • A213194 (program): First inverse function (numbers of rows) for pairing function A211377.
  • A213195 (program): Second inverse function (of columns) for pairing function A211377.
  • A213199 (program): Numbers n such that at least one member of its Collatz (3x+1) trajectory is greater than n.
  • A213203 (program): The sum of the first n! integers, with every n-th integer taken as negative.
  • A213211 (program): Triangular array read by rows: T(n,k) is the number of size k subsets of {1,2,…,n} such that (when the elements are arranged in increasing order) the smallest element is congruent to 1 mod 3 and the difference of every pair of successive elements is also congruent to 1 mod 3.
  • A213214 (program): Number of steps to reach 1 in the Collatz (3x+1) problem starting with 3^n - 1.
  • A213222 (program): Minimum number of distinct slopes formed by n noncollinear points in the plane.
  • A213223 (program): 10^n + 10*n.
  • A213234 (program): Triangle read by rows: coefficients of auxiliary Rudin-Shapiro polynomials A_{ns}(omega) written in descending powers of x.
  • A213236 (program): a(n) = (-n)^(n-1).
  • A213243 (program): Number of nonzero elements in GF(2^n) that are cubes.
  • A213244 (program): Number of nonzero elements in GF(2^n) that are 5th powers.
  • A213245 (program): Number of nonzero elements in GF(2^n) that are 7th powers.
  • A213246 (program): Number of nonzero elements in GF(2^n) that are 9th powers.
  • A213247 (program): Number of nonzero elements in GF(2^n) that are 11th powers.
  • A213248 (program): Number of nonzero elements in GF(2^n) that are 13th powers.
  • A213250 (program): Numbers n such that the coefficient of x^n in the expansion of Product_{k>=1} (1-x^k)^2 is zero.
  • A213252 (program): G.f. satisfies: A(x) = 1 + x/A(-x)^2.
  • A213255 (program): 2^(n-1) - floor((2^(n-1) - 1)/(n-1)).
  • A213257 (program): a(1) = 1, a(2) = 2 and, for n > 2, a(n) is the smallest integer greater than a(n - 1) such that no three terms of the sequence form a geometric progression of the form {x, 2 x, 4 x}.
  • A213258 (program): Positive integers that are not in A213257.
  • A213265 (program): Expansion of psi(q) * psi(q^2) * psi(q^6) / psi(q^3)^3 in powers of q where psi() is a Ramanujan theta function.
  • A213267 (program): Expansion of phi(q^9) / (psi(-q) * chi(q^3)) in powers of q where phi(), psi(), chi() are Ramanujan theta functions.
  • A213268 (program): Denominators of the Inverse semi-binomial transform of A001477(n) read downwards antidiagonals.
  • A213269 (program): The number of edges in the directed graph of the 2-opt landscape of the symmetric TSP
  • A213272 (program): Costas arrays such that the terms in each row of the difference table are unique modulo n.
  • A213278 (program): Least common multiple of A001175(n) and n.
  • A213282 (program): G.f. satisfies: A(x) = G(x/(1-x)^3) where G(x) = 1 + x*G(x)^3 is the g.f. of A001764.
  • A213283 (program): Number of 4-length words w over n-ary alphabet such that for every prefix z of w we have #(z,a_i) = 0 or #(z,a_i) >= #(z,a_j) for all j>i and #(z,a_i) counts the occurrences of the i-th letter in z.
  • A213290 (program): Number of n-length words w over binary alphabet such that for every prefix z of w we have #(z,a_i) = 0 or #(z,a_i) >= #(z,a_j) for all j>i and #(z,a_i) counts the occurrences of the i-th letter in z.
  • A213326 (program): a(n) = (n+2)^n - (n+1)^n.
  • A213327 (program): Analog of Fermat quotients: a(n) = ((round((phi_2)^p)-2)/p, where phi_2 is silver ratio 1+sqrt(2) and p = prime(n).
  • A213336 (program): G.f. satisfies: A(x) = G(x/(1-x)^4) where G(x) = 1 + x*G(x)^4 is the g.f. of A002293.
  • A213340 (program): Numbers which are the values of the quadratic polynomial 5+8t+12k+16kt on nonnegative integers.
  • A213367 (program): Numbers that are not squares of primes.
  • A213369 (program): The twisted Stern sequence: a(0) = 0, a(1) = 1 and a(2n) = -a(n), a(2n + 1) = -a(n)-a(n + 1) for n>=1.
  • A213370 (program): a(n) = n AND 2*n, where AND is the bitwise AND operator.
  • A213380 (program): a(n) = 132*binomial(n,12).
  • A213381 (program): a(n) = n^n mod (n+2).
  • A213384 (program): Expansion of phi(-q)^3 in powers of q where phi() is a Ramanujan theta function.
  • A213387 (program): a(n) = 5*2^(n-1)-2-3*n.
  • A213388 (program): Number of (w,x,y) with all terms in {0,…,n} and 2|w-x| >= max(w,x,y)-min(w,x,y).
  • A213389 (program): Number of (w,x,y) with all terms in {0,…,n} and max(w,x,y) < 2*min(w,x,y).
  • A213390 (program): Number of (w,x,y) with all terms in {0,…,n} and max(w,x,y) >= 2*min(w,x,y).
  • A213391 (program): Number of (w,x,y) with all terms in {0,…,n} and 2*max(w,x,y) < 3*min(w,x,y).
  • A213392 (program): Number of (w,x,y) with all terms in {0,…,n} and 2*max(w,x,y) >= 3*min(w,x,y).
  • A213393 (program): Number of (w,x,y) with all terms in {0,…,n} and 2*max(w,x,y) > 3*min(w,x,y).
  • A213394 (program): The difference between n and the product of the digits of the n-th prime.
  • A213395 (program): Number of (w,x,y) with all terms in {0,…,n} and max(|w-x|,|x-y|) = w.
  • A213396 (program): Number of (w,x,y) with all terms in {0,…,n} and 2*w < |x+y-w|.
  • A213397 (program): Number of (w,x,y) with all terms in {0,…,n} and 2*w >= |x+y-z|.
  • A213398 (program): Number of (w,x,y) with all terms in {0,…,n} and min(|w-x|,|x-y|) = x.
  • A213399 (program): Number of (w,x,y) with all terms in {0,…,n} and max(|w-x|,|x-y|) = x.
  • A213402 (program): Expansion of exp( Sum_{n>=1} binomial(2*n^2-1, n^2) * x^n/n ).
  • A213403 (program): G.f.: exp( Sum_{n>=1} binomial(6*n-1, 3*n) * x^n/n ).
  • A213406 (program): G.f.: exp( Sum_{n>=1} binomial(12*n-1, 6*n) * x^n/n ).
  • A213408 (program): Sequence A002654 with the zero terms omitted.
  • A213409 (program): G.f.: exp( Sum_{n>=1} binomial(3*n^2,n^2) * x^n/n ).
  • A213413 (program): Half the number of n X 3 binary arrays with no 3 X 3 submatrix formed with any three rows and columns equal to J-I.
  • A213421 (program): Real part of Q^n, Q being the quaternion 2+i+j+k.
  • A213432 (program): 2^(n-3)*binomial(n,4).
  • A213436 (program): Principal diagonal of the convolution array A212891.
  • A213441 (program): Number of 2-colored graphs on n labeled nodes.
  • A213443 (program): a(0)=5, thereafter a(n) = chromatic number (or Heawood number) Chi(n) of surface of genus n.
  • A213444 (program): Numbers n such that decimal expansion of n^2 contains a 2.
  • A213445 (program): Squares containing a digit 2.
  • A213449 (program): Denominators of higher order Bernoulli numbers.
  • A213455 (program): 90*A002451(n).
  • A213472 (program): Period 20, repeat [1, 4, 0, 9, 1, 6, 4, 5, 9, 6, 6, 9, 5, 4, 6, 1, 9, 0, 4, 1].
  • A213479 (program): Number of (w,x,y) with all terms in {0,…,n} and |w-x|+|x-y| = w+x+y.
  • A213480 (program): Number of (w,x,y) with all terms in {0,…,n} and |w-x| + |x-y| != w+x+y.
  • A213481 (program): Number of triples (w,x,y) with all terms in {0,…,n} and |w-x| + |x-y| <= w+x+y.
  • A213482 (program): Number of (w,x,y) with all terms in {0,…,n} and |w-x| + |x-y| > w+x+y.
  • A213483 (program): Number of (w,x,y) with all terms in {0,…,n} and |w-x| + |x-y| >= w+x+y.
  • A213484 (program): Number of (w,x,y) with all terms in {0,…,n} and |w-x| + |x-y| + |y-w| >= w+x+y.
  • A213485 (program): Number of (w,x,y) with all terms in {0,…,n} and |w-x|+|x-y|+|y-w| != w+x+y.
  • A213486 (program): Number of (w,x,y) with all terms in {0,…,n} and |w-x|+|x-y|+|y-w| > w+x+y.
  • A213487 (program): Number of (w,x,y) with all terms in {0,…,n} and |w-x|+|x-y|+|y-w| <= w+x+y.
  • A213488 (program): Number of (w,x,y) with all terms in {0,…,n} and |w-x|+|x-y|+|y-w| < w+x+y.
  • A213489 (program): Number of (w,x,y) with all terms in {0,…,n} and |w-x| + |x-y| + |y-w| >= w + x + y.
  • A213492 (program): Number of (w,x,y) with all terms in {0,…,n} and w != min(|w-x|,|x-y|,|y-w|).
  • A213495 (program): Number of (w,x,y) with all terms in {0,…,n} and w = min(|w-x|,|x-y|,|y-w|).
  • A213496 (program): Number of (w,x,y) with all terms in {0,…,n} and x != max(|w-x|,|x-y|)
  • A213497 (program): Number of (w,x,y) with all terms in {0,…,n} and w = min(|w-x|,|x-y|)
  • A213498 (program): Number of (w,x,y) with all terms in {0,…,n} and w != max(|w-x|,|x-y|,|y-w|)
  • A213499 (program): Number of (w,x,y) with all terms in {0,…,n} and w != min(|w-x|,|x-y|)
  • A213500 (program): Rectangular array T(n,k): (row n) = b**c, where b(h) = h, c(h) = h + n - 1, n >= 1, h >= 1, and ** = convolution.
  • A213501 (program): Number of (w,x,y) with all terms in {0,…,n} and w != max(|w-x|,|x-y|)
  • A213502 (program): Number of (w,x,y) with all terms in {0,…,n} and x != min(|w-x|,|x-y|)
  • A213503 (program): Rectangular array: (row n) = b**c, where b(h) = h^2, c(h) = n-1+h, n>=1, h>=1, and ** = convolution.
  • A213504 (program): Principal diagonal of the convolution array A213590.
  • A213505 (program): Rectangular array: (row n) = b**c, where b(h) = h^2, c(h) = (n-1+h)^2, n>=1, h>=1, and ** = convolution.
  • A213506 (program): Number of nonisomorphic 2-generator p-groups of class at most 2 and order p^n.
  • A213507 (program): E.g.f.: exp( Sum_{n>=1} A000108(n)*x^n/n ), where A000108(n) = binomial(2*n,n)/(n+1) forms the Catalan numbers.
  • A213508 (program): The sequence Z(n) arising in the enumeration of balanced binary trees.
  • A213509 (program): The sequence Z’(n) arising in the enumeration of balanced binary trees.
  • A213510 (program): The sequence N(n) arising in the enumeration of balanced ternary trees.
  • A213511 (program): The sequence N’(n) arising in the enumeration of balanced ternary trees.
  • A213515 (program): L.g.f.: log( Sum_{n>=0} A000108(n)^2*x^n ) = Sum_{n>=1} a(n)*x^n/n, where A000108(n) = binomial(2*n,n)/(n+1) forms the Catalan numbers.
  • A213526 (program): a(n) = 3*n AND n, where AND is the bitwise AND operator.
  • A213527 (program): E.g.f.: exp( Sum_{n>=1} Fibonacci(n+1)*x^n/n ), where Fibonacci(n) = A000045(n).
  • A213528 (program): E.g.f.: exp( Sum_{n>=1} Pell(n+1)*x^n/n ), where Pell(n) = A000129(n).
  • A213536 (program): Cousin prime recurrence sequence: a(1)=14, and for n>1, a(n) = a(n-1) + gcd(n+5, a(n-1)), if n is even, else a(n) = a(n-1) + gcd(n+1, a(n-1)).
  • A213538 (program): Maximum deviation from n in Collatz trajectory of n.
  • A213540 (program): Numbers k such that k AND k*2 = 2, where AND is the bitwise AND operator.
  • A213541 (program): a(n) = n AND n^2, where AND is the bitwise AND operator.
  • A213543 (program): a(n) = n AND 3^n, where AND is the bitwise AND operator.
  • A213544 (program): Sum of numerators of Farey Sequence of order n.
  • A213546 (program): Principal diagonal of the convolution array A213505.
  • A213547 (program): Antidiagonal sums of the convolution array A213505.
  • A213548 (program): Rectangular array: (row n) = b**c, where b(h) = h, c(h) = m(m+1)/2, m = n-1+h, n>=1, h>=1, and ** = convolution.
  • A213549 (program): Principal diagonal of the convolution array A213548.
  • A213550 (program): Rectangular array: (row n) = b**c, where b(h) = h*(h+1)/2, c(h) = n-1+h, n>=1, h>=1, and ** = convolution.
  • A213551 (program): Rectangular array: (row n) = b**c, where b(h) = h*(h+1)/2, c(h) = b(n-1+h), n>=1, h>=1, and ** = convolution.
  • A213552 (program): Principal diagonal of the convolution array A213551.
  • A213553 (program): Rectangular array: (row n) = b**c, where b(h) = h, c(h) = (n-1+h)^3, n>=1, h>=1, and ** = convolution.
  • A213554 (program): Principal diagonal of the convolution array A213553.
  • A213555 (program): Rectangular array: (row n) = b**c, where b(h) = h^3, c(h) = n-1+h, n>=1, h>=1, and ** = convolution.
  • A213556 (program): Principal diagonal of the convolution array A213555.
  • A213557 (program): Antidiagonal sums of the convolution array A213590.
  • A213558 (program): Rectangular array: (row n) = b**c, where b(h) = h^3, c(h) = (n-1+h)^3, n>=1, h>=1, and ** = convolution.
  • A213559 (program): Principal diagonal of the convolution array A213558.
  • A213560 (program): Antidiagonal sums of the convolution array A213558.
  • A213561 (program): Rectangular array: (row n) = b**c, where b(h) = h^2, c(h) = m*(m+1)/2, m=n-1+h, n>=1, h>=1, and ** = convolution.
  • A213562 (program): Principal diagonal of the convolution array A213561.
  • A213563 (program): Antidiagonal sums of the convolution array A213561.
  • A213564 (program): Rectangular array: (row n) = b**c, where b(h) = h*(h+1)/2, c(h) = (n-1+h)^2, n>=1, h>=1, and ** = convolution.
  • A213565 (program): Principal diagonal of the convolution array A213564.
  • A213566 (program): Rectangular array: (row n) = b**c, where b(h) = F(h), c(h) = (n-1+h)^2, F = A000045 (Fibonacci numbers), n>=1, h>=1, and ** = convolution.
  • A213567 (program): Principal diagonal of the convolution array A213566.
  • A213568 (program): Rectangular array: (row n) = b**c, where b(h) = 2^(h-1), c(h) = n-1+h, n>=1, h>=1, and ** = convolution.
  • A213569 (program): Principal diagonal of the convolution array A213568.
  • A213570 (program): Antidiagonal sums of the convolution array A213566.
  • A213571 (program): Rectangular array: (row n) = b**c, where b(h) = h, c(h) = (n-1+h)^2, n>=1, h>=1, and ** = convolution.
  • A213572 (program): Principal diagonal of the convolution array A213571.
  • A213573 (program): Rectangular array: (row n) = b**c, where b(h) = 2^(h-1), c(h) = (n-1+h)^2, n>=1, h>=1, and ** = convolution.
  • A213574 (program): Principal diagonal of the convolution array A213573.
  • A213575 (program): Antidiagonal sums of the convolution array A213573.
  • A213577 (program): Principal diagonal of the convolution array A213576.
  • A213578 (program): Antidiagonal sums of the convolution array A213576.
  • A213579 (program): Rectangular array: (row n) = b**c, where b(h) = F(h), c(h) = n-1+h, where F=A000045 (Fibonacci numbers), n>=1, h>=1, and ** = convolution.
  • A213580 (program): Principal diagonal of the convolution array A213579.
  • A213581 (program): Antidiagonal sums of the convolution array A213571.
  • A213582 (program): Rectangular array: (row n) = b**c, where b(h) = -1 + 2^h, c(h) = n-1+h, n>=1, h>=1, and ** = convolution.
  • A213583 (program): Principal diagonal of the convolution array A213582.
  • A213584 (program): Rectangular array: (row n) = b**c, where b(h) = F(h+1), c(h) = n-1+h, where F=A000045 (Fibonacci numbers), n>=1, h>=1, and ** = convolution.
  • A213585 (program): Principal diagonal of the convolution array A213584.
  • A213586 (program): Antidiagonal sums of the convolution array A213584.
  • A213588 (program): Principal diagonal of the convolution array A213587.
  • A213589 (program): Antidiagonal sums of the convolution array A213587.
  • A213592 (program): Expansion of q^(-1/3) * phi(q^2) * c(q) / 3 in powers of q where phi() is a Ramanujan theta function and c() is a cubic AGM theta function.
  • A213593 (program): Stirling transform of the first kind of the Lucas numbers A000032.
  • A213594 (program): Greatest number k such that A048784(n) / 2^k is an integer.
  • A213595 (program): A048784(n) / 2^A213594(n).
  • A213600 (program): Triangle T(n,k) read by rows: Number of Dyck n-paths with midpoint at height k.
  • A213602 (program): Numerator of expected minimum number of yes-no questions required to determine the value of a card randomly selected from a deck consisting of one 1, two 2’s, three 3’s, …, and n n’s.
  • A213603 (program): Denominator of expected minimum number of yes-no questions required to determine the value of a card randomly selected from a deck consisting of one 1, two 2’s, three 3’s, …, and n n’s.
  • A213604 (program): Cumulative sums of digital roots of A005891(n).
  • A213607 (program): Expansion of psi(x^4) * f(-x^3)^3 / f(-x) in powers of x where psi(), f() are Ramanujan theta functions.
  • A213617 (program): Expansion of psi(x) * f(-x^3)^3 in powers of x where psi() and f() are Ramanujan theta functions.
  • A213622 (program): Expansion of phi(x) * psi(x) * phi(x^2) in powers of x where phi(), psi() are Ramanujan theta functions.
  • A213624 (program): Expansion of psi(x)^2 * psi(x^4) in powers of x where psi() is a Ramanujan theta function.
  • A213625 (program): Expansion of psi(x)^2 * phi(x^2) in powers of x where phi(), psi() are Ramanujan theta functions.
  • A213627 (program): Expansion of psi(x)^4 / psi(x^3) in powers of x where psi() is a Ramanujan theta function.
  • A213633 (program): [A000027/A007978], where [ ] = floor.
  • A213634 (program): n-[n/m], where m is the least nondivisor of n (as in A007978) and [ ] = floor.
  • A213635 (program): m*[n/m], where m is the least nondivisor of n (as in A007978) and [ ] = floor.
  • A213636 (program): Remainder when n is divided by its least nondivisor.
  • A213637 (program): Values of n for which A213636(n) = 1.
  • A213638 (program): Positions of 2 in A213636.
  • A213642 (program): Primes with subscript that equals odd part of n.
  • A213643 (program): E.g.f. satisfies: A(x) = x + A(x)^2*exp(A(x)).
  • A213644 (program): E.g.f. satisfies: A(x) = 1 + x*A(x)^2*exp(x*A(x)).
  • A213648 (program): The minimum number of 1’s in the relation n*[n,1,1,…,1,n] = [x,…,x] between simple continued fractions.
  • A213655 (program): Number of dominating subsets of the theta-graph TH(2,2,n) (n>=1). A tribonacci sequence with initial values 13, 23, and 41.
  • A213659 (program): a(n) = 3^n + 2^(2*n + 1).
  • A213661 (program): Number of dominating subsets of the wheel graph W_n.
  • A213663 (program): Number of dominating subsets of the graph G(n) obtained by joining each vertex of the path graph P_{n+1} on n+1 vertices with an additional vertex (the join of K_1 and P_{n+1}).
  • A213665 (program): Number of dominating subsets of the graph G(n) obtained by joining a vertex with two consecutive vertices of the cycle graph C_n (n >=3).
  • A213667 (program): Number of dominating subsets with k vertices in all the graphs G(n) (n>=1) obtained by taking n copies of the path P_3 and identifying one of their endpoints (a star with n branches of length 2).
  • A213671 (program): The odd part of n^2 - n + 2.
  • A213673 (program): (n^2 - A000695(n))/4.
  • A213675 (program): a(n) = Chowla’s function(n) + anti-Chowla’s function(n).
  • A213684 (program): Logarithmic derivative of A001002.
  • A213685 (program): Arises in enumerating maximal antichains of minimum size.
  • A213687 (program): Numbers which are the values of the quadratic polynomial 3+4*k+7*t+8*k*t on nonnegative integers.
  • A213688 (program): a(n) = Sum_{i=0..n} A000129(i)^3.
  • A213705 (program): a(n)=n if n <= 3, otherwise a(n) = A007477(n-1) + A007477(n).
  • A213706 (program): Partial sums of A071542.
  • A213707 (program): Positions of zeros in A218254.
  • A213708 (program): a(n) is the least inverse of A071542, i.e., minimal i such that A071542(i) = n.
  • A213711 (program): a(n) = minimal k for which A218600(k) >= n.
  • A213712 (program): a(n) = A000120(A179016(n)).
  • A213713 (program): Complement of A179016.
  • A213714 (program): Inverse function for injection A005187.
  • A213715 (program): a(n) = position of A179016(n) in A005187.
  • A213718 (program): n occurs A213712(n) times.
  • A213719 (program): Characteristic function for A179016.
  • A213720 (program): a(0)=0, a(1)=0; for n>1, a(n) = a(n-1) + (n+2)*a(n-2) + 1.
  • A213723 (program): a(n) = smallest natural number x such that x=n+A000120(x), otherwise zero.
  • A213724 (program): Largest natural number x such that x = n + A000120(x), or zero if no such number exists.
  • A213728 (program): Binary complement of A213729.
  • A213729 (program): Sequence A179016 reduced modulo 2.
  • A213742 (program): Triangle of numbers C^(3)(n,k) of combinations with repetitions from n different elements over k for each of them not more than three appearances allowed.
  • A213747 (program): Rectangular array: (row n) = b**c, where b(h) = -1 + 2^h, c(h) = b(n-1+h), n>=1, h>=1, and ** = convolution.
  • A213748 (program): Principal diagonal of the convolution array A213747.
  • A213749 (program): Antidiagonal sums of the convolution array A213747.
  • A213750 (program): Rectangular array: (row n) = b**c, where b(h) = h, c(h) = 2*(n-1+h)-1, n>=1, h>=1, and ** = convolution.
  • A213751 (program): Rectangular array: (row n) = b**c, where b(h) = 2*h-1, c(h) = n-1+h, n>=1, h>=1, and ** = convolution.
  • A213752 (program): Rectangular array: (row n) = b**c, where b(h) = 2*h-1, c(h) = b(n-1+h), n>=1, h>=1, and ** = convolution.
  • A213753 (program): Rectangular array: (row n) = b**c, where b(h) = 2*h-1, c(h) = -1 + 2^(n-1+h), n>=1, h>=1, and ** = convolution.
  • A213754 (program): Principal diagonal of the convolution array A213753.
  • A213755 (program): Antidiagonal sums of the convolution array A213753.
  • A213756 (program): Rectangular array: (row n) = b**c, where b(h) = -1 + 2^h, c(h) = 2*n - 3 + 2*h, n>=1, h>=1, and ** = convolution.
  • A213757 (program): Principal diagonal of the convolution array A213756.
  • A213758 (program): Antidiagonal sums of the convolution array A213756.
  • A213759 (program): Principal diagonal of the convolution array A213783.
  • A213760 (program): Antidiagonal sums of the convolution array A213783.
  • A213761 (program): Rectangular array: (row n) = b**c, where b(h) = h, c(h) = 3*n-5+3*h, n>=1, h>=1, and ** = convolution.
  • A213762 (program): Rectangular array: (row n) = b**c, where b(h) = 2^(h-1), c(h) = 2*n-3+2*h, n>=1, h>=1, and ** = convolution.
  • A213763 (program): Principal diagonal of the convolution array A213762.
  • A213764 (program): Antidiagonal sums of the convolution array A213762.
  • A213766 (program): Principal diagonal of the convolution array A213765.
  • A213767 (program): Antidiagonal sums of the convolution array A213765.
  • A213768 (program): Rectangular array: (row n) = b**c, where b(h) = F(h), c(h) = 2*n-3+2*h, F=A000045 (Fibonacci numbers), n>=1, h>=1, and ** = convolution.
  • A213769 (program): Principal diagonal of the convolution array A213768.
  • A213770 (program): Antidiagonal sums of the convolution array A213768.
  • A213771 (program): Rectangular array: (row n) = b**c, where b(h) = 3*h-2, c(h) = n-1+h, n>=1, h>=1, and ** = convolution.
  • A213772 (program): Principal diagonal of the convolution array A213771.
  • A213773 (program): Rectangular array: (row n) = b**c, where b(h) = 3*h-2, c(h) = 3*n-5+3*h, n>=1, h>=1, and ** = convolution.
  • A213774 (program): Rectangular array: (row n) = b**c, where b(h) = F(h+1), c(h) = 2*n-3+2*h, F=A000045 (Fibonacci numbers), n>=1, h>=1, and ** = convolution.
  • A213775 (program): Principal diagonal of the convolution array A213774.
  • A213776 (program): Antidiagonal sums of the convolution array A213774.
  • A213778 (program): Rectangular array: (row n) = b**c, where b(h) = h, c(h) = 1+[(n-1+h)/2], n>=1, h>=1, [ ] = floor, and ** = convolution.
  • A213779 (program): Principal diagonal of the convolution array A213778.
  • A213780 (program): Antidiagonal sums of the convolution array A213778.
  • A213781 (program): Rectangular array: (row n) = b**c, where b(h) = 1+[h/2], c(h) = n-1+h, n>=1, h>=1, [ ] = floor, and ** = convolution.
  • A213782 (program): Principal diagonal of the convolution array A213781.
  • A213785 (program): a(n) = Sum(P(i)*P(j), 1<=i<j<=n), where P(k) is the k-th Pell number A000129(k).
  • A213786 (program): a(n)=Sum(b(i)*b(j), 1<=i<j<=n), where b(k) = A020985(k).
  • A213787 (program): a(n) = Sum_{1<=i<j<k<=n} F(i)*F(j)*F(k), where F(m) is the m-th Fibonacci number.
  • A213788 (program): a(n) = Sum_{1<=i<j<k<=n} (P(i)*P(j)*P(k), where P(m) is the k-th Pell number A000129(m).
  • A213791 (program): Expansion of psi(-x)^6 in powers of x where psi() is a Ramanujan theta function.
  • A213801 (program): Number of 3 X 3 0..n symmetric arrays with all rows summing to floor(n*3/2).
  • A213807 (program): a(n)=Sum(L(i)*L(j)*L(k), 0<=i<j<k<=n), where L(m) is the m-th Lucas number A000032(m).
  • A213809 (program): Position of the maximum element in the simple continued fraction of Fibonacci(n+1)^5/Fibonacci(n)^5.
  • A213810 (program): a(n) = 4*n^2 - 482*n + 14561.
  • A213816 (program): Tribonacci sequences A000073 and A001590 interleaved.
  • A213818 (program): Antidiagonal sums of the convolution array A213773.
  • A213819 (program): Rectangular array: (row n) = b**c, where b(h) = h, c(h) = 3*n-4+3*h, n>=1, h>=1, and ** = convolution.
  • A213820 (program): Principal diagonal of the convolution array A213819.
  • A213821 (program): Rectangular array: (row n) = b**c, where b(h) = 3*h-1, c(h) = n-1+h, n>=1, h>=1, and ** = convolution.
  • A213822 (program): Rectangular array: (row n) = b**c, where b(h) = 3*h-1, c(h) = 3*n-4+3*h, n>=1, h>=1, and ** = convolution.
  • A213823 (program): Principal diagonal of the convolution array A213822.
  • A213824 (program): Antidiagonal sums of the convolution array A213822.
  • A213825 (program): Rectangular array: (row n) = b**c, where b(h) = 3*h-1, c(h) = 3*n-5+3*h, n>=1, h>=1, and ** = convolution.
  • A213826 (program): Principal diagonal of the convolution array A213825.
  • A213827 (program): a(n) = n^2*(n+1)*(3*n+1)/4.
  • A213828 (program): Rectangular array: (row n) = b**c, where b(h) = 3*h-2, c(h) = 3*n-4+3*h, n>=1, h>=1, and ** = convolution.
  • A213829 (program): Principal diagonal of the convolution array A213828.
  • A213830 (program): Antidiagonal sums of the convolution array A213828.
  • A213831 (program): Rectangular array: (row n) = b**c, where b(h) = 2*h-1, c(h) = 3*n-5+3*h, n>=1, h>=1, and ** = convolution.
  • A213832 (program): Principal diagonal of the convolution array A213831.
  • A213833 (program): Rectangular array: (row n) = b**c, where b(h) = 3*h-2, c(h) = 2*n-3+2*h, n>=1, h>=1, and ** = convolution.
  • A213834 (program): Antidiagonal sums of the convolution array A213833.
  • A213835 (program): Rectangular array: (row n) = b**c, where b(h) = h, c(h) = 4*n-7+4*h, n>=1, h>=1, and ** = convolution.
  • A213836 (program): Rectangular array: (row n) = b**c, where b(h) = 4*h-3, c(h) = n-1+h, n>=1, h>=1, and ** = convolution.
  • A213837 (program): Principal diagonal of the convolution array A213836.
  • A213838 (program): Rectangular array: (row n) = b**c, where b(h) = 4*h-3, c(h) = 2*n-3+2*h, n>=1, h>=1, and ** = convolution.
  • A213839 (program): Principal diagonal of the convolution array A213838.
  • A213840 (program): a(n) = n*(1 + n)*(3 - 4*n + 4*n^2)/6.
  • A213841 (program): Rectangular array: (row n) = b**c, where b(h) = 2*h-1, c(h) = 4*n-7+4*h, n>=1, h>=1, and ** = convolution.
  • A213842 (program): Principal diagonal of the convolution array A213841.
  • A213843 (program): Antidiagonal sums of the convolution array A213841.
  • A213844 (program): Rectangular array: (row n) = b**c, where b(h) = 2*h-1, c(h) = 4*n-5+4*h, n>=1, h>=1, and ** = convolution.
  • A213845 (program): Principal diagonal of the convolution array A213844.
  • A213846 (program): Antidiagonal sums of the convolution array A213844.
  • A213847 (program): Rectangular array: (row n) = b**c, where b(h) = 4*h-1, c(h) = 2*n-3+2*h, n>=1, h>=1, and ** = convolution.
  • A213848 (program): Principal diagonal of the convolution array A213847.
  • A213850 (program): Antidiagonal sums of the convolution array A213849.
  • A213851 (program): Least m such that m!*2^m >= n!
  • A213852 (program): Least m>0 such that n+1+m and n-m are relatively prime.
  • A213853 (program): Rectangular array: (row n) = b**c, where b(h) = h, c(h) = binomial(2*n-4+2*h,n-2+h), n>=1, h>=1, and ** = convolution.
  • A213854 (program): Least m>0 such that m!*3^m >= n!.
  • A213855 (program): Least m > 0 such that m! * 4^m >= n!.
  • A213856 (program): Least m such that m!*5^m >= n!.
  • A213857 (program): Least m such that n! <= 3^m.
  • A213858 (program): Least m such that n! <= 4^m.
  • A213859 (program): a(n) = 2^n mod (n+2).
  • A213887 (program): Triangle of coefficients of representations of columns of A213743 in binomial basis.
  • A213890 (program): For any n >= 0, write all permutations of {0,1,…,n} in reverse lexicographic order. The last elements of the permutations will be the initial terms of this sequence.
  • A213900 (program): The minimum number of 11’s in the relation n*[n,11,11,…,11,n] = [x,…,x] between simple terminating continued fractions.
  • A213902 (program): Number of integers of the form 6*k+1 and 6*k-1 between prime(n) and prime(n+1).
  • A213907 (program): a(n) = 1 + n + n*{n/2} + n*{n/2}*{n/3} + n*{n/2}*{n/3}*{n/4} +… where {x} = [x+1/2] = round(x).
  • A213908 (program): Minimal number of terms in the series 1/n + 1/(n+1) + 1/(n+2) + … to obtain a sum >= 1.
  • A213909 (program): Sum of all even numbers in Collatz (3x+1) trajectory of n.
  • A213911 (program): Number of runs of consecutive zeros in the Zeckendorf (binary) representation of n.
  • A213916 (program): Sum of all odd numbers in Collatz (3x+1) trajectory of n.
  • A213917 (program): Difference between sum of all even and the sum of all odd numbers in Collatz (3x+1) trajectory of n.
  • A213926 (program): prime(n^2) - prime(n).
  • A213933 (program): G.f.: (1+x+x^2+2*x^5-2*x^10)/(1-3*x^3).
  • A213936 (program): Number triangle with entry a(n,k), n>=1, m=1, 2, …, n, giving the number of representative necklaces with n beads (C_n symmetry) corresponding to the color multinomial c[1]^k*c[2]*…*c[n+1-k].
  • A213937 (program): Row sums a(n) of triangle A213936: number of representative necklaces with n beads (C_N symmetry) corresponding to all color signatures given by the partitions [1^n], [2,1^(n-2)], …, [n-1,1], [n].
  • A213944 (program): Triangle read by rows, with column k defined by partial sums of the finite sequence that contains k three times.
  • A213967 (program): a(n)=n for n<=3; thereafter a(n)=a(n-1)+a(n-2)+a(n-3)+1.
  • A213976 (program): a(n) = n-th term of A106750 reversed.
  • A213983 (program): Smallest integer x >= 0 satisfying x^2 - y^2 = n^3.
  • A214002 (program): Number of compositions of n into ceiling(n/2) parts with 1 <= each part <=4.
  • A214028 (program): Entry points for the Pell sequence: smallest k such that n divides A000129(k).
  • A214036 (program): Numbers n such that floor(sqrt(1)) + floor(sqrt(2)) + floor(sqrt(3)) + … + floor(sqrt(n)) is prime.
  • A214039 (program): a(n) = a(n-1) - floor((a(n-2) + a(n-3))/2), with a(n)=n for n < 3.
  • A214040 (program): a(n)=a(n-1)+floor((a(n-2)+a(n-3))/2), with a(n)=n for n<3.
  • A214041 (program): a(n) = a(n-1) + floor((a(n-2) + a(n-3))/2), with a(n)=1 for n < 3.
  • A214045 (program): Least m>0 such that n! <= 5^m.
  • A214048 (program): Least m>0 such that n! <= r^m, where r = (1+sqrt(5))/2, the golden ratio.
  • A214050 (program): Least m>0 such that n! <= F(m), the m-th Fibonacci number, A000045(m).
  • A214051 (program): Least m>0 such that (1+r)^m >= n!, where r = (1+sqrt(5))/2, the golden ratio.
  • A214054 (program): Least m>0 such that n!!+m and n-m have a common divisor > 1.
  • A214055 (program): Least m>0 such that n!+2+m and n-m have a common divisor > 1.
  • A214056 (program): Least m>0 such that 2^n+m and n-m have a common divisor > 1.
  • A214057 (program): Least m>0 such that 2^n-1+m and n-m have a common divisor > 1.
  • A214059 (program): Least m>0 such that gcd(n^2+1+m, n-m) > 1.
  • A214060 (program): Least m>0 such that gcd(2*n-1+m, n-m) > 1.
  • A214061 (program): Least m>0 such that gcd(2*n-1+m, 2*n-m) > 1.
  • A214062 (program): Least m>0 such that gcd(2*n+m, 2*n-1-m) > 1.
  • A214066 (program): a(n) = floor( (3/2)*floor(5*n/2) ).
  • A214067 (program): [(5/2)*[(5/2)*n]], where [ ] = floor.
  • A214068 (program): a(n) = floor((3/2)*floor((3/2)*n)).
  • A214071 (program): Least m>0 such that 2^n-m and n-m are relatively prime.
  • A214073 (program): Least m>0 such that 2^n-m and n^2-m are relatively prime.
  • A214076 (program): a(n) = ceiling(e^(n/3)).
  • A214077 (program): a(n) = floor(e^(n/3)).
  • A214078 (program): a(n) = (ceiling (sqrt(n)))!.
  • A214079 (program): a(n) = ceiling( n^(1/3) )!.
  • A214080 (program): a(n) = (floor(sqrt(n)))!
  • A214081 (program): a(n) = floor( n^(1/3) )!.
  • A214085 (program): n^2 * (n^4 - n^2 + n + 1) / 2.
  • A214090 (program): Period 6: repeat [0, 0, 1, 0, 1, 1].
  • A214091 (program): a(n) = 3^n - 2^(n+2).
  • A214092 (program): Principal diagonal of the convolution array A213773.
  • A214099 (program): Number of 0..2 colorings on an n X 7 array circular in the 7 direction with new values 0..2 introduced in row major order.
  • A214107 (program): Number of 0..3 colorings on an nX4 array circular in the 4 direction with new values 0..3 introduced in row major order
  • A214108 (program): Number of 0..3 colorings on an nX5 array circular in the 5 direction with new values 0..3 introduced in row major order
  • A214123 (program): Smallest positive k such that n+k(n-1) is prime
  • A214126 (program): a(2n)=a(n-1)+a(n) and a(2n+1)=a(n+1) for n>=1, with a(0)=a(1)=1.
  • A214127 (program): a(2n) = a(n-1) + a(n) and a(2n+1) = a(n+1) for n>=1, with a(0)=1, a(1)=2.
  • A214135 (program): Number of 0..4 colorings on an nX3 array circular in the 3 direction with new values 0..4 introduced in row major order
  • A214142 (program): Number of 0..4 colorings of a 1 X (n+1) array circular in the n+1 direction with new values 0..4 introduced in row major order.
  • A214151 (program): Numbers n from the set == 5 (mod 6) with the property that 3^((3*n-1)/2) == 3 (mod n) and 2^((n-1)/2) == (n-1) (mod n)
  • A214153 (program): Numbers k for which k and tau(k) are both congruent to 1 modulo 3.
  • A214167 (program): Number of 0..5 colorings of a 1 X (n+1) array circular in the n+1 direction with new values 0..5 introduced in row major order.
  • A214177 (program): Sum of the 4 nearest neighbors of n in a spiral with positive integers.
  • A214188 (program): Number of 0..6 colorings of a 1 X (n+1) array circular in the n+1 direction with new values 0..6 introduced in row major order.
  • A214195 (program): Numbers with the number of distinct prime factors a multiple of 3.
  • A214206 (program): a(n) = largest m such that m*(m+1)/2 <= 14*n.
  • A214209 (program): Numbers appearing in A214208 excluding powers 2^i with i>0.
  • A214210 (program): Trebled Thue-Morse sequence: the A010060 sequence replacing 0 with 0,0,0 and 1 with 1,1,1.
  • A214211 (program): Doubled Fibonacci word: the A003842 sequence replacing 1 with 1,1 and 2 with 2,2.
  • A214212 (program): Number of right special factors of length n in the Thue-Morse sequence A010060.
  • A214214 (program): Partial sums of A214212.
  • A214225 (program): E.g.f. satisfies: A(x) = x/(1 - tanh(A(x))).
  • A214239 (program): Number of 0..7 colorings of a 1 X (n+1) array circular in the n+1 direction with new values 0..7 introduced in row major order.
  • A214259 (program): Number of compositions of n where the difference between largest and smallest parts equals one.
  • A214260 (program): First differences of A052980.
  • A214263 (program): Expansion of f(x^1, x^7) in powers of x where f() is Ramanujan’s general theta function.
  • A214264 (program): Expansion of f(x^3, x^5) in powers of x where f() is Ramanujan’s two-variable theta function.
  • A214270 (program): Number of compositions of n where the difference between largest and smallest parts equals 1 and adjacent parts are unequal.
  • A214281 (program): Triangle by rows, row n contains the ConvOffs transform of the first n terms of 1, 1, 3, 2, 5, 3, 7, … (A026741 without leading zero).
  • A214282 (program): Largest Euler characteristic of a downset on an n-dimensional cube.
  • A214283 (program): Smallest Euler characteristic of a downset on an n-dimensional cube.
  • A214284 (program): Characteristic function of squares or five times squares.
  • A214286 (program): a(n) = floor(Fibonacci(n)/7).
  • A214287 (program): Primes of the form phi(n)-1 sorted by increasing n, where phi is the Euler totient function.
  • A214288 (program): Primes of the form phi(n)+1 sorted by increasing n, where phi is the Euler totient function.
  • A214289 (program): Numbers k such that 2*k^3 - 1 is prime.
  • A214292 (program): Triangle read by rows: T(n,k) = T(n-1,k-1) + T(n-1,k), 0 < k < n with T(n,0) = n and T(n,n) = -n.
  • A214293 (program): a(n) = 1 if n is a square, -1 if n is five times a square.
  • A214294 (program): The maximum number of V-pentominoes covering the cells of square n × n.
  • A214295 (program): a(n) = 1 if n is a square, -1 if n is three times a square, 0 otherwise.
  • A214297 (program): a(0)=-1, a(1)=0, a(2)=-3; thereafter a(n+2) - 2*a(n+1) + a(n) has period 4: repeat -4, 8, -4, 2.
  • A214298 (program): Number of n-th order connected Feynman diagrams.
  • A214300 (program): Sum of the terms of the Pisano period mod n.
  • A214302 (program): Expansion of f(-x^2, -x^4) * f(x^3, x^5) in powers of x where f(,) is Ramanujan’s two-variable theta function.
  • A214303 (program): Expansion of f(-x^2, -x^4) * f(x^1, x^7) in powers of x where f(,) is Ramanujan’s two-variable theta function.
  • A214304 (program): Expansion of phi(q) + phi(q^2) - phi(q^4) in powers of q where phi() is a Ramanujan theta function.
  • A214308 (program): a(n) is the number of all two colored bracelets (necklaces with turning over allowed) with n beads with the two colors from a repertoire of n distinct colors, for n>=2.
  • A214315 (program): Floor of the real part of the zeros of the complex Fibonacci function on the right half-plane.
  • A214317 (program): a(n) = length-n prefix of the Fibonacci word A003842.
  • A214318 (program): Replace the word A214317(n) with its position in A007931.
  • A214319 (program): First differences of A182028.
  • A214322 (program): a(n) = A214551(n-1) + A214551(n-3), with a(0) = a(1) = a(2) = 1.
  • A214323 (program): a(n) = gcd( A214551(n-1), A214551(n-3) ) with a(0) = a(1) = a(2) = 1.
  • A214330 (program): a(n) = A214551(n) mod 2.
  • A214331 (program): a(n) = (a(n-1) + a(n-3))/gcd(a(n-1), a(n-3)) with a(0) =2, a(1) = 3, a(2) = 5.
  • A214333 (program): Trajectory of 1 under evenly many applications of the morphism 1 -> 2, 2 -> 114, 3 -> 4, 4 -> 233.
  • A214340 (program): Number of contiguous blocks of novel occurrences of length-n factors for the Thue-Morse sequence A010060.
  • A214345 (program): Interleaved reading of A073577 and A053755.
  • A214361 (program): Expansion of c(q^2) * (c(q) + 2 * c(q^4)) / 9 in powers of q where c() is a cubic AGM theta function.
  • A214372 (program): G.f. satisfies: A(x) = x + A(x)^2*(1 + A(x))^2.
  • A214377 (program): G.f. satisfies: A(x) = 1 + 4*x*A(x)^(3/2).
  • A214392 (program): If n mod 4 = 0 then a(n) = n/4, otherwise a(n) = n.
  • A214393 (program): Numbers of the form (4k+3)^2+4 or (4k+5)^2-8.
  • A214394 (program): If n mod 6 = 0 then n/6 else n.
  • A214395 (program): Decimal expansion of 16/27.
  • A214398 (program): Triangle where the g.f. of column k is 1/(1-x)^(k^2) for k>=1, as read by rows n>=1.
  • A214400 (program): a(n) = binomial(n^2 + 3*n, n).
  • A214401 (program): Denominator of Sum_{k=0..n} n^k/k!.
  • A214402 (program): Cancellation factor in reducing Sum_{k=0…n} n^k/k! to lowest terms.
  • A214405 (program): Numbers of the form (4k+3)^2-8 or (4k+5)^2+4.
  • A214411 (program): The maximum exponent k of 7 such that 7^k divides n.
  • A214416 (program): Inverse permutation to A105025.
  • A214417 (program): Inverse permutation to A105027.
  • A214429 (program): Integers of the form (n^2 - 49) / 120.
  • A214438 (program): Numerator of correlation kernels arising in adding a list of numbers in base 3 considering the distribution of number of carries.
  • A214439 (program): Denominators of correlation kernels arising in adding a list of numbers in base 3 considering the distribution of number of carries.
  • A214441 (program): Catalan numbers at square positions: a(n) = A000108(n^2).
  • A214445 (program): Euler(2*n)*binomial(4*n,2*n).
  • A214446 (program): n*(n^2-2*n-1)
  • A214447 (program): (-2)^n * Euler_polynomial(n,1) * binomial(2*n,n).
  • A214448 (program): Least m>0 such that m^4 >= n!.
  • A214456 (program): Expansion of b(q^2) * (b(q) + 2 * b(q^4)) / 3 in powers of q where b() is a cubic AGM theta function.
  • A214457 (program): Table read by antidiagonals in which entry T(n,k) in row n and column k gives the number of possible rhombus tilings of an octagon with interior angles of 135 degrees and sequences of side lengths {n, k, 1, 1, n, k, 1, 1} (as the octagon is traversed), n,k in {1,2,3,…}.
  • A214489 (program): Numbers m such that A070939(m) = A070939(m + A070939(m)), A070939 = length of binary representation.
  • A214493 (program): Numbers of the form ((6k+5)^2+9)/2 or 2(3k+4)^2-9.
  • A214505 (program): a(n) = 1 if n is four times a triangular number, -1 if one more than twelve times a triangular number else 0.
  • A214507 (program): a(n) = 1 if n is one or two times an even square, -1 if one or two times an odd square else 0.
  • A214509 (program): a(n) = 1 if n is an odd square or twice a nonzero even square, -1 if a nonzero even square or twice an odd square else 0.
  • A214516 (program): Differences between the numbers n such that n^2 + 1 is prime.
  • A214517 (program): Differences between the numbers n such that 4n^2 + 1 is prime.
  • A214526 (program): Manhattan distances between n and 1 in a square spiral with positive integers and 1 at the center.
  • A214546 (program): First differences of A140472.
  • A214549 (program): Decimal expansion of 4*Pi^2/27.
  • A214551 (program): Reed Kelly’s sequence: a(n) = (a(n-1) + a(n-3))/gcd(a(n-1), a(n-3)) with a(0) = a(1) = a(2) = 1.
  • A214553 (program): G.f. satisfies: A(x) = 1 + 4*x*A(x)^(5/2).
  • A214555 (program): Subsequence of fixed points A099009 of the Kaprekar mapping with numbers of the form 5(n)//4//9(n+1)//4(n)//5.
  • A214556 (program): Subsequence of fixed points A099009 of the Kaprekar mapping with numbers of the form 6//3(n)//17//6(n)//4.
  • A214560 (program): Number of 0’s in binary expansion of n^2.
  • A214561 (program): Number of 1’s in binary expansion of n^n.
  • A214562 (program): Number of 0’s in binary expansion of n^n.
  • A214576 (program): Triangle read by rows: T(n,k) is the number of partitions of n in which each part is divisible by the next and have last part equal to k (1<=k<=n).
  • A214579 (program): Number of partitions of n in which each part is divisible by the next and have no parts equal to 1.
  • A214582 (program): Riordan array (1/(1-x-x^2), x*(1+2*x)).
  • A214584 (program): Integers whose decimal representation has only digits in {4,5,7}.
  • A214585 (program): Numbers k such that gcd(k!!+1,k-1) > 1.
  • A214586 (program): Numbers k such that gcd(k!!+1,k-1) = 1.
  • A214587 (program): Greatest common divisor of a number and its last decimal digit: a(n) = gcd(n, n mod 10).
  • A214588 (program): Primes p such that p mod 16 < 8.
  • A214589 (program): Number of nXnXn triangular 0..2 arrays with every horizontal row having the same average value
  • A214590 (program): Number of nXnXn triangular 0..3 arrays with every horizontal row having the same average value
  • A214604 (program): Odd numbers by transposing the right half of A176271, triangle read by rows: T(n,k) = A176271(n - 1 + k, n), 1 <= k <= n.
  • A214606 (program): a(n) = gcd(n, 2^n - 2).
  • A214615 (program): Row sums of A060338.
  • A214616 (program): n*(n+1)*(n+2)*(n+3)*(20*n^2+72*n+43)/360.
  • A214617 (program): Primes written in the factorial base.
  • A214623 (program): Braid numbers B((n,n)->(n,n)).
  • A214624 (program): Braid numbers B((2)^n->(2)^n).
  • A214626 (program): a(n) = (a(n-1) + a(n-3)) / gcd(a(n-1), a(n-3)) with a(0) = a(1) = 1 and a(2) = 3.
  • A214628 (program): Intersections of radii with the cycloid.
  • A214630 (program): a(n) is the reduced numerator of 1/4 - 1/A109043(n)^2 = (1 - 1/A026741(n)^2)/4.
  • A214640 (program): A ternary sequence : closed under 1 -> 123, 2 -> 12, 3 -> 2 . Start with 1 .
  • A214641 (program): Indices of a in the sequence closed under a -> abc, b -> ab, c -> b . Start with a.
  • A214642 (program): Indices of b in the sequence a -> abc, b -> ab, c -> b . Start with a.
  • A214643 (program): Primes p such that p XOR 22 = p + 22.
  • A214644 (program): Indices of c in the sequence closed under a -> abc, b -> ab, c -> b . Start with a.
  • A214646 (program): a(n) = (a(n-2) + a(n-3))/gcd(a(n-2), a(n-3)) with a(1) = a(2) = a(3) = 1.
  • A214647 (program): (n^n + n^2)/2.
  • A214649 (program): a(-1) = 1 and g.f. A(x) satisfies A(x) - 1/A(x) = 1/x - 1.
  • A214651 (program): Count down from n to 1, n times.
  • A214653 (program): Where A214551(n) and A214551(n+2) are coprime.
  • A214656 (program): Floor of the imaginary part of the zeros of the complex Fibonacci function on the left half-plane.
  • A214657 (program): Floor of the moduli of the zeros of the complex Fibonacci function.
  • A214659 (program): a(n) = n*(7*n^2 - 3*n - 1)/3.
  • A214660 (program): 9*n^2 - 11*n + 3.
  • A214661 (program): Odd numbers by transposing the left half of A176271, triangle read by rows: T(n,k) = A176271(n - 1 + k, k), 1 <= k <= n.
  • A214663 (program): Number of permutations of 1..n for which the partial sums of signed displacements do not exceed 2.
  • A214664 (program): The x-coordinates of prime numbers in an Ulam spiral oriented counterclockwise with first step east.
  • A214665 (program): The y-coordinates of prime numbers in an Ulam spiral oriented counterclockwise with first step east.
  • A214666 (program): The x-coordinates of prime numbers in an Ulam spiral oriented counterclockwise with first step west.
  • A214667 (program): The y-coordinates of prime numbers in an Ulam spiral oriented counterclockwise with first step west.
  • A214668 (program): G.f. satisfies: A(x) = 1 + 9*x*A(x)^(4/3).
  • A214671 (program): Floor of the real parts of the zeros of the complex Lucas function on the right half-plane.
  • A214672 (program): Floor of the imaginary parts of the zeros of the complex Lucas function on the left half-plane.
  • A214673 (program): Floor of the moduli of the zeros of the complex Lucas function.
  • A214675 (program): 9*n^2 - 13*n + 5.
  • A214677 (program): a(n) = n represented in bijective base-7 numeration.
  • A214678 (program): a(n) = n represented in bijective base-8 numeration.
  • A214681 (program): a(n) is obtained from n by removing factors of 2 and 3 that do not contribute to a factor of 6.
  • A214682 (program): Remove 2’s that do not contribute to a factor of 4 from the prime factorization of n.
  • A214683 (program): a(n+3) = -a(n+2) + 2a(n+1) + a(n) with a(0)=-1, a(1)=0, a(2)=-3.
  • A214684 (program): a(1)=1, a(2)=1, and, for n>2, a(n)=(a(n-1)+a(n-2))/5^k, where 5^k is the highest power of 5 dividing a(n-1)+a(n-2).
  • A214688 (program): E.g.f. equals the series reversion of x - x^2*exp(2*x).
  • A214689 (program): E.g.f. satisfies: A(x) = exp( 2*x*Catalan(x*A(x)) ), where Catalan(x) = (1-sqrt(1-4*x))/(2*x) is the g.f. of A000108.
  • A214691 (program): G.f.: A(x) = Sum_{n>=0} x^n * Product_{k=1..n} (2^(2*k-1) - 1) / (1 + 2^(2*k-1)*x).
  • A214698 (program): (n^n - n^2)/2.
  • A214699 (program): a(n) = 3*a(n-2) - a(n-3) with a(0)=0, a(1)=3, a(2)=0.
  • A214706 (program): a(n) = a(n-1)*a(n-2) with a(0)=1, a(1)=5.
  • A214710 (program): Least m>0 such that n!-m and n!!-m are relatively prime.
  • A214716 (program): Least m>0 such that 3^n-m and n-m are relatively prime.
  • A214717 (program): Least m>0 such that 4^n-m and n-m are relatively prime.
  • A214718 (program): Least m>0 such that 5^n-m and n-m are relatively prime.
  • A214719 (program): Least m>0 such that 6^n-m and n-m are relatively prime.
  • A214720 (program): Least m>0 such that n^2-m and n-m are relatively prime.
  • A214721 (program): Least m>0 such that 2*n+1+m and n-m are not relatively prime.
  • A214724 (program): E.g.f.: exp( Sum_{n>=0} x^(n^2+1)/(n^2+1) ).
  • A214726 (program): Decimal expansion of the perimeter of Cairo and Prismatic tiles.
  • A214727 (program): a(n) = a(n-1) + a(n-2) + a(n-3) with a(0)=1, a(1) = a(2) = 2.
  • A214728 (program): Least k such that n + (n+1) + … + (n+k-1) is a square.
  • A214729 (program): Member m=6 of the m-family of sums b(m,n) = Sum_{k=0..n} F(k+m)*F(k), m >= 0, n >= 0, with the Fibonacci numbers F.
  • A214731 (program): a(n) = n^3 - 2*n^2 - 1.
  • A214732 (program): a(n) = 25*n^2 + 15*n + 1021.
  • A214733 (program): a(n) = -a(n-1) - 3*a(n-2) with n>1, a(0)=0, a(1)=1.
  • A214736 (program): Least m>0 such that n-m divides n+1+m.
  • A214739 (program): Least m>0 such that n-m divides 2^(n-1)+m.
  • A214740 (program): Least m>0 such that n-m divides 2^n+m.
  • A214745 (program): Least m>0 such that n-m divides 2*n-1+m.
  • A214748 (program): Least m>0 such that n-m divides (2*n-1)!!+m.
  • A214749 (program): Least m>0 such that n-m divides n^2+m.
  • A214750 (program): Least m>0 such that n-m divides n^2+m^2.
  • A214774 (program): Number of ways of obtaining a weight of n grams using eight weights of denominations 1, 1, 2, 5, 10, 10, 20 and 50 grams.
  • A214776 (program): Number A(n,k) of standard Young tableaux of shape [n*k,n]; square array A(n,k), n>=0, k>=0, read by antidiagonals.
  • A214778 (program): a(n) = 3*a(n-1) + 6*a(n-2) + a(n-3), with a(0) = 3, a(1) = 3, and a(2) = 21.
  • A214779 (program): a(n) = 3*a(n-2) - a(n-3) with a(0)=-1, a(1)=1, a(2)=-4.
  • A214783 (program): a(n) = smallest k such that n divides Fibonacci(k-1)+3.
  • A214789 (program): a(n) is the smallest k>=2 such that n divides A000045(k-1)+8.
  • A214795 (program): a(n) is the smallest k>=2 such that n divides Fibonacci(k-1)+21.
  • A214799 (program): Let S be a set of n positive numbers such that all n choose 2 pairwise GCD’s are distinct, and let max(S) denote the largest element of S; a(n) is the minimal value of max(S) over all choices for S.
  • A214824 (program): Number of solid standard Young tableaux of shape [[(2)^n],[2]].
  • A214825 (program): a(n) = a(n-1) + a(n-2) + a(n-3), with a(0) = 1, a(1) = a(2) = 3.
  • A214826 (program): a(n) = a(n-1) + a(n-2) + a(n-3), with a(0) = 1, a(1) = a(2) = 4.
  • A214827 (program): a(n) = a(n-1) + a(n-2) + a(n-3), with a(0) = 1, a(1) = a(2) = 5.
  • A214828 (program): a(n) = a(n-1) + a(n-2) + a(n-3), with a(0) = 1, a(1) = a(2) = 6.
  • A214829 (program): a(n) = a(n-1) + a(n-2) + a(n-3), with a(0) = 1, a(1) = a(2) = 7.
  • A214830 (program): a(n) = a(n-1) + a(n-2) + a(n-3), with a(0) = 1, a(1) = a(2) = 8.
  • A214831 (program): a(n) = a(n-1) + a(n-2) + a(n-3), with a(0) = 1, a(1) = a(2) = 9.
  • A214838 (program): Triangular numbers of the form k^2 + 2.
  • A214840 (program): Averages y of twin prime pairs that satisfy y = x^2 + x - 2.
  • A214848 (program): First difference of A022846.
  • A214849 (program): Number of n-permutations having all cycles of odd length and at most one fixed point.
  • A214855 (program): Fibonacci numbers divisible by 10.
  • A214856 (program): Number of triangular numbers in interval ](n-1)^2, n^2] for n>0, a(0)=1.
  • A214857 (program): Number of triangular numbers in interval [0, n^2].
  • A214858 (program): Natural numbers missing from A214857.
  • A214860 (program): First differences of round(n*sqrt(3)) (A022847).
  • A214861 (program): First differences of round(n*sqrt(5)) (A022848).
  • A214863 (program): Numbers n such that n XOR 11 = n - 11.
  • A214864 (program): Numbers n such that n XOR 10 = n - 10.
  • A214865 (program): n such that n XOR 9 = n - 9.
  • A214867 (program): Quotients of (first) primorial numbers and denominators of Bernoulli numbers B 0, B 1, B 2, B 4, B 6,… .
  • A214869 (program): Decimal expansion of Sum_{n >= 1} n!/(2*n)!.
  • A214877 (program): n ^ (last digit of n).
  • A214879 (program): Numbers that cannot be written as sum of the squares of two primes.
  • A214881 (program): 2-adic valuation of A016090.
  • A214882 (program): A007185(n)/5^n.
  • A214883 (program): A016090(n)/2^n.
  • A214884 (program): a(n) = Sum_{k=0..n} (-1)^k*F(k)*F(k+2), where F=A000045 (Fibonacci numbers).
  • A214885 (program): a(n) = Sum_{k=0..n} (-1)^k*F(k)*F(k+3), where F=A000045 (Fibonacci numbers).
  • A214886 (program): Primes of the form n^3-2*n^2-1.
  • A214887 (program): a(n) = a(n-1)*a(n-2) with a(0)=1, a(1)=7.
  • A214888 (program): Primes congruent to {2, 3} mod 11.
  • A214889 (program): Primes congruent to {2, 3} mod 13.
  • A214890 (program): Primes congruent to {2, 3} mod 17.
  • A214899 (program): a(n) = a(n-1) + a(n-2) + a(n-3) with a(0)=2, a(1)=1, a(2)=2.
  • A214901 (program): Number of nXnXn triangular 0..3 arrays with every horizontal row nondecreasing and having the same average value
  • A214912 (program): Primes p such that A215029(p) = 0.
  • A214916 (program): a(0) = a(1) = 1, a(n) = n! / a(n-2).
  • A214917 (program): a(n) is the least m > 0 such that Fibonacci(n-m) divides Fibonacci(n+1+m).
  • A214918 (program): a(n) is the least m > 0 such that Fibonacci(n-m) divides Fibonacci(n+2+m).
  • A214919 (program): a(n) is the least m > 0 such that Lucas(n-m) divides Fibonacci(n+m).
  • A214920 (program): a(n) is the least m > 0 such that Fibonacci(n-m) divides Lucas(n+m).
  • A214922 (program): Numbers of the form x^2 + y^2 + z^3 + w^3 (x, y, z, w >= 0).
  • A214923 (program): Total count of 1’s in binary representation of Fibonacci(n) and previous Fibonacci numbers, minus total count of 0’s. That is, partial sums of b(n) = -A037861(Fibonacci(n)).
  • A214927 (program): Number of n-digit numbers N that do not end with 0 and are such that the reversal of N divides N but is different from N.
  • A214936 (program): a(0) = 1, a(n) = a(n - 1) * (length of binary representation of n).
  • A214937 (program): Square numbers that can be expressed as sums of a positive square number and a positive triangular number.
  • A214938 (program): Number of Motzkin n-paths avoiding even-numbered steps that are flat steps.
  • A214944 (program): Number of squarefree words of length 5 in an (n+1)-ary alphabet.
  • A214945 (program): Number of squarefree words of length 6 in an (n+1)-ary alphabet.
  • A214946 (program): Number of squarefree words of length 7 in an (n+1)-ary alphabet.
  • A214951 (program): a(n) = 3*a(n-1) + 6*a(n-2) + a(n-3) with a(0)=2, a(1)=5, a(2)=26.
  • A214954 (program): a(n) = 3*a(n-1) + 6*a(n-2) + a(n-3), with a(0) = 0, a(1) = 2, and a(2) = 7.
  • A214955 (program): Number of solid standard Young tableaux of shape [[n,n-1],[1]].
  • A214960 (program): Expansion of psi(x^2) - x * psi(x^10) in powers of x where psi() is a Ramanujan theta function.
  • A214962 (program): a(n) is the least m > 0 such that Fibonacci(n-m) divides Fibonacci(2n+2m).
  • A214971 (program): Integers k for which the base-phi representation of k includes 1.
  • A214972 (program): a(n) = a(floor(2*(n-1)/3)) + 1, where a(0) = 0.
  • A214977 (program): Number of terms in Lucas representations of 1,2,…,n.
  • A214982 (program): a(n) = (Fibonacci(5n)/Fibonacci(n) - 5)/50.
  • A214988 (program): Beatty sequence for sqrt(r), where r = (1+sqrt(5))/2 = golden ratio; complement of A214989.
  • A214989 (program): Beatty sequence [sqrt(phi)/(sqrt(phi)-1) * n], where phi = (1 + sqrt(5))/2 = golden ratio; complement of A214988.
  • A214990 (program): Second nearest integer to n*r, where r = (1+ sqrt(5))/2, the golden ratio.
  • A214991 (program): Second nearest integer to n*(1+golden ratio).
  • A214992 (program): Power ceiling-floor sequence of (golden ratio)^4.
  • A214993 (program): Power floor sequence of (golden ratio)^5.
  • A214994 (program): Power ceiling sequence of (golden ratio)^5.
  • A214995 (program): Power ceiling-floor sequence of (golden ratio)^6.
  • A214996 (program): Power floor-ceiling sequence of 2+sqrt(2).
  • A214997 (program): Power ceiling-floor sequence of 2+sqrt(2).
  • A214998 (program): Power ceiling-floor sequence of 2 + sqrt(3).
  • A214999 (program): Power floor sequence of sqrt(5).
  • A215003 (program): E.g.f. satisfies: A(x) = x + A(x)^2*exp(A(x))/2.
  • A215004 (program): a(0) = a(1) = 1; for n>1, a(n) = a(n-1) + a(n-2) + floor(n/2).
  • A215005 (program): a(n) = a(n-2) + a(n-1) + floor(n/2) + 1 for n > 1 and a(0)=0, a(1)=1.
  • A215006 (program): a(0)=0, a(n+1) is the least k>a(n) such that k+a(n)+n+1 is a Fibonacci number.
  • A215007 (program): a(n) = 7*a(n-1) - 14*a(n-2) + 7*a(n-3), a(0)=1, a(1)=3, a(2)=9.
  • A215008 (program): a(n) = 7*a(n-1) - 14*a(n-2) + 7*a(n-3), a(0)=0, a(1)=1, a(2)=5.
  • A215010 (program): Integer side lengths in arithmetic progression of simple convex hexagons with equal interior angles. Sequence gives the values of m for sides of lengths t+m*d, counterclockwise, for the two primitive solutions.
  • A215011 (program): a(n) = least k>0 such that triangular(n) divides Fibonacci(k).
  • A215016 (program): Decimal expansion of the product of 1 - 1/2^2^n over all n >= 0.
  • A215020 (program): a(n) = log_2( A182105(n) ).
  • A215026 (program): Reluctant Fibonacci sequence.
  • A215027 (program): a(n+1) = (concatenation of n and n+1) - a(n), a(0) = 0.
  • A215028 (program): a(1) = 1; for n >= 1, a(n+1) = (concatenation of n+1 and n) - a(n).
  • A215030 (program): a(n) = A215029(A000040(n)), where A000040(n) is the n-th prime.
  • A215031 (program): Primes p such that A215029(p) = 2.
  • A215032 (program): Numbers n such that A215029(n) = -1.
  • A215035 (program): Numbers n such that A215029(n) = 2.
  • A215036 (program): 2 followed by “1,0” repeated.
  • A215037 (program): a(n) = sum(fibonomial(k+3,3), k=0..n), n>=0.
  • A215038 (program): Partial sums of A066259: a(n) = sum(F(k+1)^2*F(k),k=0..n), n>=0, with the Fibonacci numbers F=A000045.
  • A215039 (program): a(n) = Fibonacci(2*n)^3, n>=0.
  • A215040 (program): a(n) = F(2*n+1)^3, n>=0, with F = A000045 (Fibonacci).
  • A215042 (program): a(n) = F(8*n)/L(2*n) with n >= 0, F = A000045 (Fibonacci numbers) and L = A000032 (Lucas numbers).
  • A215044 (program): a(n) = F(2*n)^5 with F=A000045 (Fibonacci numbers).
  • A215045 (program): a(n) = F(2*n+1)^5 with n >= 0, F=A000045 (Fibonacci numbers).
  • A215046 (program): Increasingly ordered list of those values m for which the degree of the minimal polynomial of 2*cos(Pi/m) (see A187360) is prime.
  • A215052 (program): a(n) = (binomial(n,5) - floor(n/5)) / 5.
  • A215053 (program): a(n) = 1/7*( binomial(n,7) - floor(n/7) ).
  • A215054 (program): a(n) = 1/11*(binomial(n,11) - floor(n/11)).
  • A215061 (program): Triangle read by rows, e.g.f. exp(x*(z-1/2))*((exp(3*x/2)+2*cos(sqrt(3)*x/2))/3).
  • A215063 (program): Triangle read by rows, e.g.f. exp(x*(z-3/2))*((exp(3*x/2)+2*cos(sqrt(3)*x/2))/3.
  • A215069 (program): Natural numbers that when squared can be expressed as sums of a positive square number and a positive triangular number
  • A215076 (program): a(n) = 3*a(n-1) + 4*a(n-2) + a(n-3) with a(0)=3, a(1)=3, a(2)=17.
  • A215077 (program): Binomial convolution of sum of consecutive powers.
  • A215078 (program): Array of sums of the first k n-th powers multiplied by binomial(n,k), read by rows.
  • A215079 (program): Triangle T(n,k) = k^n * sum(binomial(n,n-k-j),j=0..n-k)
  • A215080 (program): T(n,k) = sum( (k-j)^n * binomial(n,j), j=0..k).
  • A215083 (program): Triangle T(n,k) = sum of the k first n-th powers
  • A215084 (program): a(n) = sum of the sums of the k first n-th powers.
  • A215088 (program): a(n)=Sum{d(i)*2^i: i=0,1,…,m}, where Sum{d(i)*5^i: i=0,1,…,m} is the base 5 representation of n.
  • A215089 (program): a(n)=Sum{d(i)*6^i: i=0,1,…,m}, where Sum{d(i)*2^i: i=0,1,…,m} is the base 2 representation of n.
  • A215090 (program): a(n) = Sum_{i=0..m} d(i)*3^i, where Sum_{i=0..m} d(i)*4^i is the base-4 representation of n.
  • A215091 (program): Power floor-ceiling sequence of sqrt(5).
  • A215092 (program): a(n) = Sum_{i=0..m} d(i)*3^i, where Sum_{i=0..m} d(i)*6^i is the base-6 representation of n.
  • A215095 (program): a(0)=0, a(1)=1, a(n) = least k>a(n-1) such that k+a(n-2) is a Jacobsthal number.
  • A215096 (program): a(0)=0, a(1)=1, a(n) = n! - a(n-2).
  • A215097 (program): a(n) = n^3 - a(n-2) for n >= 2 and a(0)=0, a(1)=1.
  • A215098 (program): a(0)=0, a(1)=1, a(n) = n*(n-1) - a(n-2).
  • A215100 (program): a(n) = 3*a(n-1) + 4*a(n-2) + a(n-3) with a(0)=2, a(1)=5, a(2)=22.
  • A215101 (program): Primes congruent to {2, 3} mod 19.
  • A215108 (program): a(n) = A215082(2*n)
  • A215109 (program): a(n) = A215082(2*n+1).
  • A215112 (program): a(n) = -2*a(n-1) + a(n-2) + a(n-3) with a(0)=a(1)=-1, a(2)=1.
  • A215125 (program): E.g.f.: Sum_{n>=0} d^n/dx^n (x + x^2)^(2*n) / (2*n)!.
  • A215126 (program): E.g.f.: Sum_{n>=0} D^(n*(n-1)/2) (x + x^2)^(n*(n+1)/2) / (n*(n+1)/2)!, where operator D^n = d^n/dx^n.
  • A215127 (program): E.g.f.: Sum_{n>=0} D^(n^2-n) (x + x^2)^(n^2) / (n^2)!, where operator D^n = d^n/dx^n.
  • A215128 (program): G.f.: Sum_{n>=0} d^n/dx^n (x + x^2)^(2*n) / n!.
  • A215131 (program): Primes congruent to {3, 5, 6} mod 13.
  • A215133 (program): Primes congruent to {3, 5, 6} mod 19.
  • A215134 (program): Primes congruent to {1, 2, 3} mod 11.
  • A215135 (program): Primes congruent to {1, 2, 3} mod 13.
  • A215137 (program): a(n) = 17*n + 1.
  • A215143 (program): a(n) = 7*a(n-1) -14*a(n-2) +7*a(n-3), with a(0)=1, a(1)=2, a(2)=7.
  • A215144 (program): a(n) = 19*n + 1.
  • A215145 (program): a(n) = 20*n + 1.
  • A215146 (program): a(n) = 21*n + 1.
  • A215147 (program): For n odd, a(n)= 1^2+2^2+3^2+…+n^2; for n even, a(n)=(1^2+2^2+3^2+…+n^2) + 1.
  • A215148 (program): a(n) = 23*n + 1.
  • A215149 (program): a(n) = n * (1 + 2^(n-1)).
  • A215159 (program): a(n) = floor(n^n / (n+1)).
  • A215163 (program): Primes congruent to {1, 4} mod 11.
  • A215164 (program): Primes congruent to {1, 4} mod 13.
  • A215165 (program): Primes congruent to {1, 4} mod 17.
  • A215166 (program): Primes congruent to {1, 4} mod 19.
  • A215167 (program): Primes congruent to {2, 5} mod 11.
  • A215168 (program): Primes congruent to {2, 5} mod 13.
  • A215169 (program): Primes congruent to {2, 5} mod 17.
  • A215170 (program): Primes congruent to {2, 5} mod 19.
  • A215172 (program): a(0)=1, a(n) = a(n-1)*4^n + 2^n - 1. That is, add n 0’s and n 1’s to the binary representation of previous term.
  • A215176 (program): Number of nXnXn triangular 0..2 arrays with every horizontal row nondecreasing, first elements of rows nonincreasing, last elements of rows nondecreasing, and every row having the same average value
  • A215191 (program): Number of arrays of 4 0..n integers with no sum of consecutive elements equal to a disjoint adjacent sum of an equal number of elements.
  • A215203 (program): a(0) = 0, a(n) = a(n - 1)*2^(n + 1) + 2^n - 1. That is, add one 0 and n 1’s to the binary representation of previous term.
  • A215205 (program): a(n) = (-1)^n * (A060819(n) + A060819(n+1)).
  • A215206 (program): Primes congruent to {2, 7} mod 11.
  • A215207 (program): Primes congruent to {2, 7} mod 13.
  • A215208 (program): Primes congruent to {2, 7} mod 17.
  • A215209 (program): Primes congruent to {2, 7} mod 19.
  • A215211 (program): Primes congruent to {2, 5, 7} mod 13.
  • A215229 (program): Number of length-6 0..k arrays connected end-around, with no sequence of L<n elements immediately followed by itself (periodic “squarefree”).
  • A215230 (program): Number of length-7 0..k arrays connected end-around, with no sequence of L<n elements immediately followed by itself (periodic “squarefree”).
  • A215247 (program): A Beatty sequence: a(n) = floor((n-1/2)*(2 + 2*sqrt(2))).
  • A215258 (program): Smallest number h such that (2n+1)*h is a repunit (A002275), or 0 if no such h exists.
  • A215265 (program): (n-1)^(n+1) - n^n.
  • A215268 (program): Concatenation of the decimal digits of n^2-1 and n^2.
  • A215270 (program): a(n) = a(n-1)*a(n-2) with a(0)=1, a(1)=6.
  • A215271 (program): a(n) = a(n-1)*a(n-2) with a(0)=1, a(1)=8.
  • A215272 (program): a(n) = a(n-1)*a(n-2) with a(0)=1, a(1)=9.
  • A215279 (program): Primes congruent to {2, 3, 4} mod 11.
  • A215280 (program): Primes congruent to {2, 3, 4} mod 13.
  • A215287 (program): Number of permutations of 0..floor((n*3-1)/2) on even squares of an n X 3 array such that each row and column of even squares is increasing.
  • A215288 (program): Number of permutations of 0..floor((n*4-1)/2) on even squares of an n X 4 array such that each row and column of even squares is increasing.
  • A215294 (program): Number of permutations of 0..floor((n*3-2)/2) on odd squares of an n X 3 array such that each row and column of odd squares is increasing.
  • A215302 (program): Primes congruent to {1, 2, 3, 4} mod 11.
  • A215310 (program): Primes congruent to {1, 2, 3, 4, 5} mod 11.
  • A215311 (program): Primes congruent to {1, 2, 3, 4, 5} mod 13.
  • A215314 (program): Primes congruent to {2, 3, 4, 5} mod 11.
  • A215339 (program): a(n) = A001608(n) mod n.
  • A215340 (program): Expansion of series_reversion( x/(1 + sum(k>=1, x^A032766(k)) ) ) / x.
  • A215341 (program): Expansion of series_reversion( x/(1+x^4*sum(k>=0, x^k)) ) / x.
  • A215342 (program): Expansion of series reversion of x*(1-x^3*sum(k>=1, x^k)).
  • A215375 (program): Primes congruent to {0, 2, 3} mod 13.
  • A215377 (program): Primes congruent to {0, 2, 3} mod 19.
  • A215378 (program): Primes congruent to {0, 1, 2, 3} mod 11.
  • A215390 (program): Primes congruent to {1, 2} mod 11.
  • A215391 (program): Primes congruent to {1, 2} mod 13.
  • A215392 (program): Primes congruent to {1, 2} mod 17.
  • A215393 (program): Primes congruent to {1, 2} mod 19.
  • A215404 (program): a(n) = 4*a(n-1) - 3*a(n-2) - a(n-3), with a(0)=0, a(1)=0 and a(2)=1.
  • A215405 (program): Largest prime factor of the n-th n-almost prime.
  • A215410 (program): a(0) = 0; a(n+1) = 2*a(n) + k where k = 0 if prime(n+2)/prime(n+1) < prime(n+1)/prime(n), otherwise k = 1.
  • A215411 (program): a(0) = 0; a(n+1) = 2*a(n) + k where k = 0 if prime(n+2)/prime(n+1) > prime(n+1)/prime(n), otherwise k = 1.
  • A215414 (program): Unix epoch timestamp for start of year, beginning with 1970.
  • A215415 (program): a(2*n) = n, a(4*n+1) = 2*n-1, a(4*n+3) = 2*n+3.
  • A215418 (program): Number of Regular and Stellar polytopes in n-dimensional Euclidean space, or -1 if infinite.
  • A215448 (program): a(0)=1, a(1)=0, a(n) = a(n-1) + a(n-2) + Sum_{i=0…n-1} a(i).
  • A215450 (program): a(0)=0, a(1)=1, a(n) = a(n-1) + (Sum_{i=0…n-1)a(i)) mod n.
  • A215451 (program): a(0)=1, a(n) = (sum of previous terms) mod (a(n-1)+n).
  • A215452 (program): a(1)=1, a(n) = (sum of previous terms) mod (a(n-1)+n).
  • A215454 (program): a(n) = least positive k such that n^2 divides k!
  • A215455 (program): a(n) = 6*a(n-1) - 9*a(n-2) + a(n-3), with a(0)=3, a(1)=6 and a(2)=18.
  • A215456 (program): a(n)=(4n-1)!! modulo 2n, n=1,2,…
  • A215458 (program): a(n) = 4*a(n-1) - 7*a(n-2) + 8*a(n-3) - 4*a(n-4) starting 0, 1, 4, 7.
  • A215459 (program): Arises in quick gossiping without duplicate transmission.
  • A215460 (program): Floor(n!^2 / n^n).
  • A215462 (program): Number of decompositions of 2n into ordered sums of two odd nonprimes.
  • A215465 (program): a(n) = (Lucas(4n) - Lucas(2n))/4.
  • A215466 (program): Expansion of x*(1-4*x+x^2) / ( (x^2-7*x+1)*(x^2-3*x+1) ).
  • A215467 (program): Length of longest palindromic prefix of (n base 2).
  • A215469 (program): a(n) = A215467(2n+1).
  • A215476 (program): Minimum number of comparisons needed to find the median of n elements.
  • A215480 (program): Characteristic function of numbers n with exactly two distinct prime factors.
  • A215484 (program): a(n) = 21*a(n-2) + 7*a(n-3), with a(0)=a(1)=0, a(2)=9.
  • A215486 (program): n - 1 mod phi(n), where phi(n) is Euler’s totient function.
  • A215492 (program): a(n) = 21*a(n-2) + 7*a(n-3), with a(0)=0, a(1)=3, and a(2)=6.
  • A215493 (program): a(n) = 7*a(n-1) - 14*a(n-2) + 7*a(n-3) with a(0)=0, a(1)=1, a(2)=4.
  • A215494 (program): a(n) = 7*a(n-1) - 14*a(n-2) + 7*a(n-3) with a(1)=7, a(2)=21, a(3)=70.
  • A215495 (program): a(4*n) = a(4*n+2) = a(2*n+1) = 2*n + 1.
  • A215500 (program): a(n) = ((sqrt(5) + 3)^n + (-sqrt(5) -1)^n + (-sqrt(5) + 3)^n + (sqrt(5) - 1)^n) / 2^n.
  • A215502 (program): a(n) = (1+sqrt(3))^n + (-2)^n + (1-sqrt(3))^n + 1.
  • A215510 (program): a(n) = 7*a(n-1) - 14*a(n-2) + 7*a(n-3) with a(0)=0, a(1)=7, a(2)=35.
  • A215512 (program): a(n) = 5*a(n-1) - 6*a(n-2) + a(n-3), with a(0)=1, a(1)=3, a(2)=8.
  • A215523 (program): Slowest increasing sequence of alternate-parity integers m such that 2m+1 is prime.
  • A215530 (program): The limit of the string “0, 1” under the operation ‘repeat string twice and append 0’.
  • A215531 (program): The limit of the string “0, 1” under the operation ‘append first k terms, k=k+2’ with k=1 initially.
  • A215532 (program): The limit of the string “0, 1” under the operation ‘append first k terms, increment k’ with k=2 initially.
  • A215534 (program): Matrix inverse of triangle A088956.
  • A215537 (program): Lowest k such that k is representable as both the sum of n and of n+1 nonzero squares.
  • A215541 (program): a(n) = binomial(5*n,n)*(3*n+1)/(4*n+1).
  • A215542 (program): a(n) = binomial(6*n,n)*(4*n+1)/(5*n+1).
  • A215543 (program): Number of standard Young tableaux of shape [3n,3].
  • A215544 (program): Number of standard Young tableaux of shape [4n,4].
  • A215545 (program): Number of standard Young tableaux of shape [5n,5].
  • A215546 (program): Number of standard Young tableaux of shape [6n,6].
  • A215547 (program): Number of standard Young tableaux of shape [7n,7].
  • A215548 (program): Number of standard Young tableaux of shape [8n,8].
  • A215549 (program): Number of standard Young tableaux of shape [9n,9].
  • A215550 (program): Number of standard Young tableaux of shape [10n,10].
  • A215551 (program): a(n) = binomial(7*n,n)*(5*n+1)/(6*n+1).
  • A215552 (program): a(n) = binomial(8*n,n)*(6*n+1)/(7*n+1).
  • A215553 (program): a(n) = binomial(9*n,n)*(7*n+1)/(8*n+1).
  • A215554 (program): a(n) = binomial(10*n,n)*(8*n+1)/(9*n+1).
  • A215555 (program): a(n) = binomial(11*n,n)*(9*n+1)/(10*n+1).
  • A215557 (program): Number of standard Young tableaux of shape [n^2,n].
  • A215560 (program): a(n) = 3*a(n-1) + 46*a(n-2) + a(n-3) with a(0)=a(1)=3, a(2)=101.
  • A215569 (program): a(n) = 3*a(n-1) + 46*a(n-2) + a(n-3) with a(0)=0, a(1)=14, a(2)=49.
  • A215572 (program): a(n) = 3*a(n-1) + 46*a(n-2) + a(n-3) with a(0)=2, a(1)=5, a(2)=106.
  • A215573 (program): a(n) = n*(n+1)*(2n+1)/6 modulo n.
  • A215575 (program): a(n) = 7*(a(n-1) - a(n-2) - a(n-3)), with a(0)=3, a(1)=7, a(2)=35.
  • A215576 (program): G.f. satisfies: A(x) = (1 + x^2)*(1 + x*A(x)^2).
  • A215580 (program): Partial sums of A215602.
  • A215595 (program): Number of strings of length n, formed from the 26-letter English alphabet, which contain the substring xy.
  • A215596 (program): Expansion of psi(-x) * f(-x^4)^3 in powers of x where psi(), f() are Ramanujan theta functions.
  • A215598 (program): Expansion of phi(-x^2) * f(x)^3 in powers of x where phi(), f() are Ramanujan theta functions.
  • A215602 (program): a(n) = L(n)*L(n+1), where L = A000032 (Lucas numbers).
  • A215603 (program): O.g.f.: exp( Sum_{n>=1} -(sigma(2*n^2) - sigma(n^2)) * (-x)^n/n ).
  • A215604 (program): a(0)=0, a(n) = (n + a(floor(n/2))) mod 3.
  • A215623 (program): G.f.: A(x) = (1 + x*A(x)) * (1 + x*A(x)^4).
  • A215624 (program): G.f.: A(x) = (1 + x*A(x)) * (1 + x*A(x)^5).
  • A215630 (program): Triangle read by rows: T(n,k) = n^2 - n*k + k^2, 1 <= k <= n.
  • A215631 (program): Triangle read by rows: T(n,k) = n^2 + n*k + k^2, 1 <= k <= n.
  • A215633 (program): Decimal expansion of Sum_{n>=1} 1/n^(n^prime(n)).
  • A215634 (program): a(n) = - 6*a(n-1) - 9*a(n-2) - 3*a(n-3) with a(0)=3, a(1)=-6, a(2)=18.
  • A215646 (program): n * (11*n^2 + 6*n + 1) / 6.
  • A215652 (program): Exponential Riordan array [exp(x*exp(-x)),x].
  • A215653 (program): a(n) = smallest positive m such that m^2=1+k*n with positive k.
  • A215654 (program): G.f. satisfies: A(x) = (1 + x*A(x)^2) * (1 + x*A(x)^3).
  • A215655 (program): Irregular triangle read by rows: reading the n-th row describes all the numbers seen in the triangle up to the end of the n-th row.
  • A215661 (program): G.f. satisfies: A(x) = (1 + 2*x*A(x)) * (1 + x*A(x)^2).
  • A215664 (program): a(n) = 3*a(n-2) - a(n-3), with a(0)=3, a(1)=0, and a(2)=6.
  • A215665 (program): a(n) = 3*a(n-2) - a(n-3), with a(0)=0, a(1)=a(2)=-3.
  • A215666 (program): a(n) = 3*a(n-2) - a(n-3), with a(0)=0, a(1)=-3, and a(2)=6.
  • A215667 (program): 22n+1 is prime.
  • A215673 (program): a(1) = 1, a(2n) = a(n)+1, a(2n+1) = a(n)+a(n+1)+1.
  • A215674 (program): a(1) = 1, a(n) = 2 if 1<n<=3, a(3n) = a(n)+1, a(3n+1) = a(3n+2) = a(n)+a(n+1)+1 otherwise.
  • A215675 (program): a(1) = 1, a(n) = 2 if 1<n<=3, a(2n+1) = a(n)+1, a(2n+2) = a(n)+a(n+1)+1 otherwise.
  • A215676 (program): a(1) = 1, a(n) = 2 if 1<n<=4, a(3n+1) = a(n)+1, a(3n+2) = a(3n+3) = a(n)+a(n+1)+1 otherwise.
  • A215687 (program): Number of solid standard Young tableaux of shape [[2*n,2],[2]].
  • A215694 (program): a(n) = 5*a(n-1) - 6*a(n-2) + a(n-3) with a(0)=1, a(1)=2, a(2)=7.
  • A215695 (program): a(n) = 5*a(n-1) - 6*a(n-2) + a(n-3) with a(0)=1, a(1)=0, a(2)=-2.
  • A215696 (program): a(n)=smallest positive k>n+2 such that k*n+1 is a square.
  • A215712 (program): Numerator of sum(i=1..n, 3*i/4^i )
  • A215713 (program): Denominator of sum(i=1..n, 3*i/4^i).
  • A215715 (program): G.f. satisfies: A(x) = (1 + x*A(x)^2) * (1 + x*A(x)^4).
  • A215720 (program): The number of functions f:{1,2,…,n}->{1,2,…,n}, endofunctions, such that exactly one nonrecurrent element is mapped into each recurrent element.
  • A215726 (program): Numbers k such that the k-th triangular number is squarefree.
  • A215746 (program): Numerator of Sum_{i=0..n} (-1)^i*4/(2*i + 1).
  • A215747 (program): a(n) = (-2)^n mod n.
  • A215761 (program): Numbers m with property that 36m+11 is prime.
  • A215762 (program): a(n) = smallest prime > a(n-1) + 2(n-1), a(1)=2.
  • A215773 (program): Number of undirected labeled graphs on n+3 nodes with exactly n cycle graphs as connected components.
  • A215781 (program): a(n) = ceiling(n*(sqrt(3)-1)).
  • A215784 (program): Number of permutations of 0..floor((n*6-1)/2) on even squares of an n X 6 array such that each row, column, diagonal and (downwards) antidiagonal of even squares is increasing.
  • A215814 (program): 60516*n^2 - 61008*n + 2481403.
  • A215829 (program): a(n) = -3*a(n-1) + 9*a(n-2) + 3*a(n-3), with a(0)=3, a(1)=-3, a(2)=27.
  • A215848 (program): Primes > 3.
  • A215850 (program): Primes p such that 2*p + 1 divides Lucas(p).
  • A215851 (program): Number of simple labeled graphs on n nodes with exactly 1 connected component that is a tree or a cycle.
  • A215862 (program): Number of simple labeled graphs on n+2 nodes with exactly n connected components that are trees or cycles.
  • A215863 (program): Number of simple labeled graphs on n+3 nodes with exactly n connected components that are trees or cycles.
  • A215866 (program): Number of permutations of 0..floor((n*6-2)/2) on odd squares of an n X 6 array such that each row, column, diagonal and (downwards) antidiagonal of odd squares is increasing.
  • A215878 (program): Lengths of loops in the P2 Penrose tiling.
  • A215879 (program): Written in base 3, n ends in a(n) consecutive nonzero digits.
  • A215883 (program): When written in base 4, n ends in a(n) consecutive nonzero digits.
  • A215884 (program): Written in base 5, n ends in a(n) consecutive nonzero digits.
  • A215885 (program): a(n) = 3*a(n-1) - a(n-3), with a(0) = 3, a(1) = 3, and a(2) = 9.
  • A215887 (program): Written in decimal, n ends in a(n) consecutive nonzero digits.
  • A215892 (program): a(n) = 2^n - n^k, where k is the largest integer such that 2^n >= n^k.
  • A215894 (program): a(n) = floor(2^n / n^k), where k is the largest integer such that 2^n >= n^k.
  • A215898 (program): a(4n) = 1+4n, a(1+4n) = -2-6n, a(2+4n) = 4+6n, a(3+4n) = -3-4n.
  • A215916 (program): The total number of components (cycles) in all alignments.
  • A215917 (program): a(n) = -3*a(n-1) + a(n-3), with a(0)=0, a(1)=6, and a(2)=-15.
  • A215918 (program): Numbers n such that 6*n + {1, 5, 7} are all primes.
  • A215919 (program): a(n) = -3*a(n-1) + a(n-3), with a(0)=0, a(1)=-3, a(2)=12.
  • A215925 (program): The number of distinct (up to unitary similarity) *-subalgebras of the n X n complex matrices.
  • A215928 (program): a(n) = 2*a(n-1) + a(n-2) for n > 2, a(0) = a(1) = 1, a(2) = 2.
  • A215931 (program): Product of Fibonacci and Catalan numbers: a(n) = A000045(2*n+2)*A000108(n).
  • A215936 (program): a(n) = -2*a(n-1) + a(n-2) for n > 2, with a(0) = a(1) = 1, a(2) = 0.
  • A215940 (program): Difference between the n-th and the first (identity) permutation of (0,…,m-1), interpreted as a decimal number, divided by 9 (for any m for which 10! >= m! >= n).
  • A215942 (program): a(n) = sigma(6*n) - 12*n.
  • A215947 (program): Difference between the sum of the even divisors and the sum of the odd divisors of 2n.
  • A215960 (program): First differences of A016759.
  • A215990 (program): Numerator of sum( k!/2^k, k=1..n ).
  • A216021 (program): a(n) = modlg(n^n, 2^n), where modlg is the function defined in A215894: modlg(a,b) = floor(a / b^floor(logb(a))), logb is the logarithm base b.
  • A216022 (program): Largest number m such that the Collatz trajectory starting at n contains all numbers not greater than m.
  • A216038 (program): Number of isomorphism classes of unstretchable simplicial arrangements of n pseudolines in the real projective plane that satisfy Pappus’s theorem.
  • A216046 (program): Expansion of (chi(-x) / chi^3(-x^3))^2 in powers of x where chi() is a Ramanujan theta function.
  • A216053 (program): a(n) is the position of the last two-tuple within the reverse lexicographic set of partitions of 2n and 2n+1, with a(1)-a(n) representing the positions of every 2-tuple partition of 2n and 2n+1.
  • A216059 (program): Smallest number not in Collatz trajectory starting at n.
  • A216066 (program): a(n) = card {cos((2^k)*Pi/(2*n-1)): k in N}.
  • A216073 (program): The list of the a(n)-values in the common solutions to k+1=b^2 and 6*k+1=a^2.
  • A216078 (program): Number of horizontal and antidiagonal neighbor colorings of the odd squares of an n X 2 array with new integer colors introduced in row major order.
  • A216079 (program): Number of horizontal and antidiagonal neighbor colorings of the odd squares of an n X 3 array with new integer colors introduced in row major order.
  • A216092 (program): a(n) = 2^(2*5^(n-1)) mod 10^n.
  • A216093 (program): a(n) = 10^n - (5^(2^n) mod 10^n).
  • A216095 (program): a(n) = 2^n mod 10000.
  • A216096 (program): a(n) = 3^n mod 1000.
  • A216097 (program): 3^n mod 10000.
  • A216099 (program): Period of powers of 3 mod 10^n.
  • A216100 (program): 11^n mod 100.
  • A216106 (program): The Wiener index of the tetrameric 1,3-adamantane TA(n) (see the Fath-Tabar et al. reference).
  • A216108 (program): The Wiener index of the ortho-polyphenyl chain with n hexagons (see the Dou et al. and the Deng references).
  • A216109 (program): The hyper-Wiener index of the ortho-polyphenyl chain with n hexagons (see the Dou et al. and the Deng references).
  • A216110 (program): The Wiener index of the meta-polyphenyl chain with n hexagons (see the Dou et al. and the Deng references).
  • A216111 (program): The hyper-Wiener index of the meta-polyphenyl chain with n hexagons (see the Dou et al. and the Deng references).
  • A216112 (program): The Wiener index of the para-polyphenyl chain with n hexagons (see the Dou et al. and the Deng references).
  • A216113 (program): The hyper-Wiener index of the meta-polyphenyl chain with n hexagons (see the Dou et al. and the Deng references).
  • A216114 (program): The Wiener index of a link of n fullerenes C_{20} (see the Ghorbani and Hosseinzadeh reference).
  • A216116 (program): G.f. satisfies: A(x) = (1 + x*A(x)) * (1 + x^4*A(x)).
  • A216119 (program): Number of stretching pairs in all permutations in S_n.
  • A216125 (program): a(n) = 5^n mod 1000.
  • A216126 (program): 5^n mod 10000.
  • A216127 (program): a(n) = 6^n mod 1000.
  • A216128 (program): 6^n mod 10000.
  • A216129 (program): a(n) = 7^n mod 1000.
  • A216130 (program): 7^n mod 10000.
  • A216131 (program): a(n) = 11^n mod 1000.
  • A216132 (program): 11^n mod 10000.
  • A216134 (program): Numbers k such that 2 * A000217(k) + 1 is triangular.
  • A216144 (program): Square root of smallest square greater than the product of first n primes.
  • A216147 (program): 2*n^n + 1.
  • A216152 (program): A205957(n) where n is a nonprime number.
  • A216153 (program): The partial products of a(n) are the distinct values of the exponential of the von Mangoldt function modified by restricting the divisors to prime divisors (A205957).
  • A216154 (program): Triangle read by rows, T(n,k) n>=0, k>=0, generalization of A000255.
  • A216156 (program): Period of powers of 11 mod 10^n.
  • A216157 (program): Difference between the sum of the even divisors and the sum of the odd divisors of phi(n).
  • A216160 (program): 2^(2p-2) modulo p^3 for p=odd primes.
  • A216164 (program): Period of powers of 7 mod 10^n.
  • A216172 (program): Number of all possible tetrahedra of any size, having reverse orientation to the original regular tetrahedron, formed when intersecting the latter by planes parallel to its sides and dividing its edges into n equal parts.
  • A216173 (program): Number of all possible tetrahedra of any size and orientation, formed when intersecting the original regular tetrahedron by planes parallel to its sides and dividing its edges into n equal parts.
  • A216175 (program): Number of all polyhedra (tetrahedra of any orientation and octahedra) of any size, formed when intersecting a regular tetrahedron by planes parallel to its sides and dividing its edges into n equal parts.
  • A216178 (program): Period 4: repeat [4, 1, 0, -3].
  • A216179 (program): a(n) = 10^n + 3.
  • A216182 (program): Riordan array ((1+x)/(1-x)^2, x(1+x)^2/(1-x)^2).
  • A216194 (program): a(n) = Smallest b for which the base b representation of n contains at least one 2 (or 0 if no such base exists).
  • A216195 (program): Abelian complexity function of the period-doubling sequence (A096268).
  • A216197 (program): Abelian complexity function of A064990.
  • A216200 (program): Number of disjoint trees that appear while iterating the sum of divisors function up to n.
  • A216206 (program): a(n) = product_{i=1..n} ((-2)^i-1).
  • A216209 (program): Triangle read by rows: T(n,k) = n+k with 0 <= k <= 2*n.
  • A216212 (program): Number of n step walks (each step +-1 starting from 0) which are never more than 4 or less than -4.
  • A216216 (program): Square array T, read by antidiagonals: T(n,k) = 0 if n-k>=3 or if k-n>=3, T(2,0) = T(1,0) = T(0,0) = T(0,1) = T(0,2) = 1, T(n,k) = T(n-1,k) + T(n,k-1).
  • A216218 (program): Square array T, read by antidiagonals: T(n,k) = 0 if n-k>=2 or if k-n>=2, T(1,0) = T(0,0) = T(0,1) = 1, T(n,k) = T(n-1,k) + T(n,k-1).
  • A216223 (program): Distance from Fibonacci(n) to the next perfect square.
  • A216224 (program): Natural growth of an aliquot sequence driven by a perfect number 2^(p-1)*((2^p)-1), but starting at 27.
  • A216225 (program): Distance between n^2 and next higher Fibonacci number.
  • A216227 (program): Prime numbers that do not appear in the Euclid-Mullin sequence (A000946).
  • A216228 (program): Square array T, read by antidiagonals: T(n,k) = 0 if n-k>=1 or if k-n>=3, T(0,0) = T(0,1) = T(0,2) = 1, T(n,k) = T(n-1,k) + T(n,k-1).
  • A216230 (program): Square array T, read by antidiagonals: T(n,k) = 0 if n-k>=1 or if k-n>=2, T(0,0) = T(0,1) = 1, T(n,k) = T(n-1,k) + T(n,k-1).
  • A216234 (program): Cumulated number of increasing admissible cuts of rooted plane trees of size n.
  • A216241 (program): Number of n-step walks (each step +-1 starting from 0) which are never more than 5 or less than -5.
  • A216243 (program): Partial sums of the squares of Lucas numbers (A000032).
  • A216244 (program): a(n) = (prime(n)^2 - 1)/2 for n >= 2.
  • A216255 (program): Triangle read by rows: T(n,k) is the number of labeled rooted trees of height at most 2 that have exactly k nodes at a distance 2 from the root; n>=1, 0<=k<=n-1.
  • A216256 (program): Minimum length of a longest unimodal subsequence of a permutation of n elements.
  • A216257 (program): a(n) = 840*n^2-23100*n+86861.
  • A216263 (program): Expansion of 1 / ((1-2*x)*(1-4*x+x^2)).
  • A216265 (program): Number of primes between n^3 - n and n^3.
  • A216266 (program): Number of primes between n^3 and n^3+n (inclusive).
  • A216271 (program): Expansion of (1-x)/((1-2x)(1-4x+x^2)).
  • A216274 (program): Square array A(n,k) = maximal number of regions into which k-space can be divided by n hyperplanes (k >= 1, n >= 0), read by antidiagonals.
  • A216277 (program): Primes which cannot be written as x^2 + 5*y^2, where x >= 0, y >= 0.
  • A216278 (program): Number of solutions to the equation x^2+2y^2 = n with x and y > 0.
  • A216279 (program): Number of solutions to the equation x^2+5y^2 = n with x and y > 0.
  • A216282 (program): Number of nonnegative solutions to the equation x^2 + 2*y^2 = n.
  • A216283 (program): Number of nonnegative solutions to the equation x^2+5*y^2 = n.
  • A216286 (program): Primes which cannot be written as x^2+5*y^2, where x > 0, y > 0.
  • A216295 (program): Values of k such that 10k + 1 is the only prime between 10k and 10k + 9.
  • A216298 (program): Values of k such that 10k + 9 is the only prime between 10k and 10k + 9.
  • A216305 (program): Values of k such that 10*k+1 and 10*k+9 alone are prime between 10*k and 10*k+9.
  • A216309 (program): The prime ending in 1 is the only prime in a decade.
  • A216312 (program): The prime ending in 9 is the only prime in a decade.
  • A216313 (program): Total number of cycles in all partial permutations of {1,2,…,n}.
  • A216314 (program): G.f. satisfies: A(x) = (1 + x*A(x)) * (1 + 2*x*A(x)^2).
  • A216315 (program): Primes congruent to 1 mod 59.
  • A216316 (program): G.f.: 1/( (1-8*x)*(1+x)^2 )^(1/3).
  • A216317 (program): G.f.: 1/( (1-8*x)*(1+x)^2 )^(1/6).
  • A216318 (program): Number of peaks in all Dyck n-paths after changing each valley to a peak by the transform DU -> UD.
  • A216319 (program): Irregular triangle: row n lists the odd numbers of the reduced residue system modulo n.
  • A216321 (program): phi(delta(n)), n >= 1, with phi = A000010 (Euler’s totient) and delta = A055034 (degree of minimal polynomials with coefficients given in A187360).
  • A216325 (program): Number of divisors of the degree of the minimal polynomial for 2*cos(Pi/n), n >= 1.
  • A216326 (program): Number of divisors of the degree of the minimal polynomial of 2*cos(Pi/prime(n)), with prime = A000040, n >= 1.
  • A216332 (program): Number of horizontal and antidiagonal neighbor colorings of the even squares of an n X 2 array with new integer colors introduced in row major order.
  • A216333 (program): Number of horizontal and antidiagonal neighbor colorings of the even squares of an nX3 array with new integer colors introduced in row major order
  • A216345 (program): Position of the beginning of the n-th run in A000002.
  • A216348 (program): Numbers that appear in either both A156242(n) + 1 and A156243(n) or both A156242(n) and A156243(n) + 1.
  • A216352 (program): G.f.: A(x) = exp( Sum_{n>=1} A000172(n)^2*x^n/n ) where Franel number A000172(n) = Sum_{k=0..n} C(n,k)^3.
  • A216353 (program): G.f.: A(x) = exp( Sum_{n>=1} A000172(n)^3*x^n/n ) where Franel number A000172(n) = Sum_{k=0..n} C(n,k)^3.
  • A216354 (program): G.f.: A(x) = exp( Sum_{n>=1} A000172(n)^n*x^n/n ) where Franel number A000172(n) = Sum_{k=0..n} C(n,k)^3.
  • A216355 (program): G.f.: A(x) = exp( Sum_{n>=1} A000172(n^2)*x^n/n ) where Franel number A000172(n) = Sum_{k=0..n} C(n,k)^3.
  • A216356 (program): a(n) = A000172(n^2), where Franel number A000172(n) = Sum_{k=0..n} C(n,k)^3.
  • A216357 (program): Expansion of 1/( (1-16*x)*(1+4*x)^2 )^(1/4).
  • A216358 (program): G.f.: 1/( (1-32*x)*(1+11*x-x^2)^2 )^(1/5).
  • A216359 (program): G.f. satisfies: A(x) = (1 + x*A(x)^2) * (1 + x/A(x)).
  • A216361 (program): a(n) = (A216315(n) - 1)/118.
  • A216369 (program): a(n) = !(n-1) mod n.
  • A216371 (program): Odd primes with one coach: primes p such that A135303((p-1)/2) = 1.
  • A216377 (program): The most significant digit in base n representation of n!.
  • A216401 (program): E.g.f.: arctanh(x*exp(x)).
  • A216402 (program): Least prime p such that p = n (mod 59).
  • A216406 (program): G.f.: Product_{n>=1} ((1-x^n)/(1+x^n))^(2*n).
  • A216407 (program): Sum of decimal digits not appearing in n.
  • A216411 (program): Number of bases in which n begins with a “1”.
  • A216414 (program): a(n) = (-1)^(n-3)*binomial(n,3) - 1.
  • A216415 (program): a(n) = smallest positive m such that 2n-1 | 10^m-1, or 0 if no such m exists.
  • A216416 (program): a(n) = smallest m such that 2n-1 | 10^m+1, or 0 if no such m exists.
  • A216430 (program): (-1)^A081603(n), parity of the number of 2’s in the ternary expansion of n.
  • A216431 (program): a(0)=0; thereafter a(n+1) = a(n) + 1 + number of 0’s in binary representation of a(n), counted with A023416.
  • A216440 (program): a(n) = smallest m such that 2n-1 | 2^m+1, or 0 if no such m exists.
  • A216441 (program): a(n) = n! mod !n.
  • A216443 (program): a(n) = n!! mod !n.
  • A216450 (program): a(n) = -10*a(n-1) - 3*a(n-2) + a(n-3) with a(0) = 3, a(1) = -10, and a(2) = 94.
  • A216453 (program): Number of points hidden from the central point by a closer point in a hexagonal orchard of order n.
  • A216457 (program): Number of horizontal, diagonal and antidiagonal neighbor colorings of the even squares of an nX3 array with new integer colors introduced in row major order
  • A216466 (program): n!! mod n!
  • A216469 (program): a(n) = smallest m such that 2n-1 | (2^m+1)/3, or 0 if no such m exists.
  • A216470 (program): a(n) = smallest m such that 2n-1 | (10^m+1)/11, or 0 if no such m exists.
  • A216473 (program): a(n) = smallest m such that 2n-1 | (10^m-1)/9, or 0 if no such m exists.
  • A216475 (program): The number of numbers coprime to and less than n+2, excluding 2.
  • A216477 (program): The sequence of the parts in the partition binary diagram represented as an array.
  • A216483 (program): a(n) = Sum_{k=0..n} binomial(n,k)^3 * 4^k.
  • A216490 (program): G.f. satisfies: A(x) = 1 + x*A(x)^2 + x^3*A(x)^5.
  • A216491 (program): a(n) = 12*5^n.
  • A216494 (program): G.f. satisfies: A(x) = 1 + x*A(x)^3/(1 - x^4*A(x)^10).
  • A216495 (program): Primes p with property that there exists a number d>0 such that numbers p-d, p-2*d are primes.
  • A216509 (program): Primes which cannot be written in the form a^2 + 6*b^2.
  • A216510 (program): Number of positive integer solutions to the equation a^2 + 6*b^2 = n.
  • A216511 (program): Number of positive integer solutions to the equation a^2 + 7*b^2 = n.
  • A216512 (program): Number of nonnegative integer solutions to the equation a^2 + 7*b^2 = n.
  • A216513 (program): Number of nonnegative integer solutions to the equation x^2 + 6*y^2 = n.
  • A216522 (program): Integers of the form 2*x + 3*y with nonnegative x and y, with repetitions.
  • A216534 (program): Number of cycles in all partial functions on {1,2,…,n}.
  • A216541 (program): Product of Lucas and Catalan numbers: a(n) = A000032(n+1)*A000108(n).
  • A216568 (program): Smallest k such that prime(n)*k-1 is prime.
  • A216577 (program): Number of nonnegative integer solutions to the equation x^2 + 10*y^2 = n.
  • A216584 (program): a(n) = A002426(n)*A000984(n); product of central trinomial coefficients and central binomial coefficients.
  • A216585 (program): G.f.: exp( Sum_{n>=1} A000984(n)*A002426(n)*x^n/n ), where A000984 is the central binomial coefficients and A002426 is the central trinomial coefficients.
  • A216586 (program): G.f.: exp( Sum_{n>=1} A002426(n)/2 * A002426(n) * x^n/n ), where A002426 is the central binomial coefficients and A002426 is the central trinomial coefficients.
  • A216603 (program): Indices n for which A216557(n)=0, i.e., n does not reappear as substring in its orbit under A216556.
  • A216604 (program): G.f. satisfies: A(x) = (1 + x*(1-x)*A(x)) * (1 + x^2*A(x)).
  • A216606 (program): Decimal expansion of 360/7.
  • A216607 (program): The sequence used to represent partition binary diagram as an array.
  • A216609 (program): Number of horizontal, diagonal and antidiagonal neighbor colorings of the odd squares of an nX3 array with new integer colors introduced in row major order
  • A216628 (program): a(n) = A163085(n)/n!.
  • A216636 (program): a(n) = Sum_{k=0..n} binomial(n,k)^3 * 5^k.
  • A216647 (program): a(n) := card{cos((2^(k-1))*Pi/n): k=1,2,…}.
  • A216650 (program): Maximum length of each subsequence whose elements are the greatest prime divisors of the integers 2, 3, 4, … in increasing order.
  • A216651 (program): Lengths of decreasing blocks of A006530, the greatest prime factor of n, starting from the second term.
  • A216658 (program): Number of n-digit 8th powers.
  • A216676 (program): Digital roots of squares of Fibonacci numbers.
  • A216685 (program): A(n) is the number of 1’s in binary expansion of n + a(n-1), with a(0)=0.
  • A216687 (program): Odd numbers > 10 that can be written as m*s - m + 1, where s is the sum of their digits and m >= 1.
  • A216688 (program): Expansion of e.g.f. exp( x * exp(x^2) ).
  • A216689 (program): E.g.f. exp( x * exp(x)^2 ).
  • A216696 (program): a(n) = Sum_{k=0..n} binomial(n,k)^4 * 2^k.
  • A216698 (program): a(n) = Sum_{k=0..n} binomial(n,k)^3 * 6^k.
  • A216699 (program): Digital root of cubes of Fibonacci numbers.
  • A216702 (program): a(n) = Product_{k=1..n} (16 - 4/k).
  • A216703 (program): a(n) = Product_{k=1..n} (49 - 7/k).
  • A216704 (program): a(n) = Product_{k=1..n} (64 - 8/k).
  • A216705 (program): a(n) = Product_{k=1..n} (81 - 9/k).
  • A216706 (program): a(n) = Product_{k=1..n} (100 - 10/k).
  • A216710 (program): Expansion of (1-3*x+x^2)^2/(1-9*x+28*x^2-35*x^3+15*x^4-x^5).
  • A216711 (program): Expansion of q * (phi(q) * psi(-q))^8 in powers of q where phi(), psi() are Ramanujan theta functions.
  • A216714 (program): a(n) = 2^(n-5) - A000931(n).
  • A216728 (program): (2*n)!*((2*n+1)/2)^n/(2*n+1).
  • A216754 (program): Digital root of fourth power of Fibonacci numbers.
  • A216755 (program): Digital root of the fifth power of Fibonacci(n).
  • A216757 (program): a(n) = 6*a(n-1) - 9*a(n-2) + 3*a(n-3).
  • A216761 (program): n * floor(log_2(n)) * floor(log_2(log_2(n))) * floor(log_2(log_2(log_2(n)))) ….
  • A216762 (program): a(n) = n * ceiling(log_2(n)) * ceiling(log_2(log_2(n))) * ceiling(log_2(log_2(log_2(n)))) ….
  • A216765 (program): Perfect powers (squares, cubes, etc.) plus 1.
  • A216776 (program): Primes p such that x^62 = -2 has no solution mod p.
  • A216778 (program): Number of derangements on n elements with an even number of cycles.
  • A216779 (program): Number of derangements on n elements with an odd number of cycles.
  • A216780 (program): Numbers n such that numerator(sigma(n)/n) and denominator(sigma(n)/n) are both odd.
  • A216781 (program): Numbers such that numerator(sigma(n)/n) is odd and denominator(sigma(n)/n) is even.
  • A216782 (program): Numbers such that numerator(sigma(n)/n) is even and denominator(sigma(n)/n) is odd.
  • A216786 (program): a(n) = Product_{k=1..n} (121 - 11/k).
  • A216787 (program): a(n) = Product_{k=1..n} (144 - 12/k).
  • A216788 (program): a(n) = Product_{k=1..n} (169 - 13/k).
  • A216789 (program): Table read by antidiagonals: T(n,k) is the digital sum of k in base n displayed in decimal.
  • A216794 (program): Number of set partitions of {1,2,…,n} with labeled blocks and a (possibly empty) subset of designated elements in each block.
  • A216795 (program): a(n) = sum_{k=0..n} binomial(n,k)^4 * 3^k.
  • A216815 (program): Primes congruent to 1 or 9 mod 20.
  • A216816 (program): Primes congruent to 3 or 7 mod 20.
  • A216829 (program): 2*a(n) is the multiplicative order of 2 mod 3*(2n-1).
  • A216831 (program): a(n) = Sum_{k=0..n} binomial(n,k)^3 * k!.
  • A216833 (program): Multiplicative order of 2 mod 3*(2n-1).
  • A216844 (program): 4k^2-8k+2 interleaved with 4k^2-4k+2 for k>=0.
  • A216845 (program): Numbers n such that the polynomial 1 + x + x^2 + x^3 + x^4 + … + x^(n-1) is reducible over GF(2).
  • A216848 (program): Odd numbers for which 2 is not a primitive root.
  • A216850 (program): Number of distinct infinite sets of primes congruent to a subset of 1..n mod n.
  • A216851 (program): a(n) = T^(floor(log(n)/log(2)))(n) (see comment).
  • A216852 (program): 18k^2-36k+9 interleaved with 18k^2-18k+9 for k>=0.
  • A216853 (program): 18k^2-12k-7 interleaved with 18k^2+6k+5 for k>=0.
  • A216857 (program): Number of connected functions from {1,2,…,n} into a subset of {1,2,…,n} that have a fixed point summed over all subsets.
  • A216864 (program): Number of squares that divide the product of divisors of n.
  • A216865 (program): 16k^2-32k+8 interleaved with 16k^2-16k+8 for k>=0.
  • A216871 (program): 16k^2-16k-4 interleaved with 16k^2+4 for k>=0.
  • A216875 (program): 20k^2-40k+10 interleaved with 20k^2-20k+10 for k>=0.
  • A216876 (program): 20k^2-20k-5 interleaved with 20k^2+5 for k=>0.
  • A216880 (program): Numbers of the form 3p - 2 where p and 6p + 1 are prime.
  • A216886 (program): Primes p such that x^59 = 2 has a solution mod p.
  • A216913 (program): a(n) = Gauss_primorial(3*n, 3) / Gauss_primorial(3*n, 3*n).
  • A216918 (program): Odd numbers with at least 3 distinct prime factors.
  • A216938 (program): Number of side-2 hexagonal 0..n arrays with values nondecreasing E, SW and SE
  • A216949 (program): G.f.: (1-6*x+7*x^2)/(1-7*x+11*x^2-x^3).
  • A216953 (program): Triangle read by rows: T(n,k) (n>=1, 1<=k<=n) = number of binary sequences of length n with minimal period k.
  • A216954 (program): Triangle read by rows: A216953/2.
  • A216957 (program): a(1)=2; for n > 1, a(n) = 2^(n-2) + (1/(2n-2)) * Sum_{ d divides n-1 } phi(2d)*2^((n-1)/d).
  • A216968 (program): Numbers n such that 2*n^2 + 3 is prime.
  • A216970 (program): Primes congruent to 1 mod 37.
  • A216972 (program): a(4n+2) = 2, otherwise a(n) = n.
  • A216973 (program): Exponential Riordan array [x*exp(x),x].
  • A216982 (program): Anti-Chowla’s function: sum of anti-divisors of n except the largest.
  • A216983 (program): The integers sieved by 7, 5, 3, and 2.
  • A216985 (program): Number of city-block distance 1, pressure limit 2 movements in an n X 2 array with each element moving exactly one horizontally or vertically, no element acquiring more than two neighbors, and without 2-loops.
  • A216994 (program): Multiples of 7 such that the digit sum is divisible by 7.
  • A216996 (program): Numbers n such that the digit sum of n*7 is a multiple of 7.
  • A216997 (program): Multiples of 8 that have a digit sum which is a multiple of 8.
  • A216998 (program): Digit sum of n*7 mod 7.
  • A217000 (program): Triangular numbers of the form 2p-1 where p is prime.
  • A217001 (program): Numbers k such that (k^2 + k + 2)/4 is prime.
  • A217004 (program): Numbers arising in computing the Turan function of cycles of length 4.
  • A217009 (program): Multiples of 7 in base 8.
  • A217017 (program): E.g.f. satisfies: A(x) = Sum_{n>=0} x^n * cosh(n^2*x).
  • A217022 (program): Number of city-block distance 1, pressure limit 2 movements in an n X 2 array with each element moving exactly one horizontally or vertically and no element acquiring more than two neighbors.
  • A217029 (program): Array T(i,j) read by antidiagonals, where T(i,j) is the height of i/j, that is max(|m|,|n|) with m/n = i/j and gcd(m, n) = 1.
  • A217032 (program): Minimum number of steps to reach n! starting from 1 and using the operations of multiplication, addition, or subtraction.
  • A217036 (program): Term preceding the first zero in the Fibonacci numbers modulo n.
  • A217038 (program): Number of powerful numbers < n.
  • A217039 (program): Primes whose decimal representation has only digits in {4,5,7}.
  • A217052 (program): a(n) = 3*a(n-1) + 24*a(n-2) + a(n-3), with a(0)=a(1)=1, and a(2)=19.
  • A217053 (program): a(n) = 3*a(n-1) + 24*a(n-2) + a(n-3), with a(0) = 2, a(1) = 5, and a(2) = 62.
  • A217058 (program): Van der Waerden numbers w(j+2; t_0,t_1,…,t_{j-1}, 3, 4) with t_0 = t_1 = … = t_{j-1} = 2.
  • A217067 (program): Number of unlabeled graphs on n nodes whose components are cycles or complete graphs.
  • A217069 (program): a(n) = 3*a(n-1) + 24*a(n-2) + a(n-3), with a(0)=0, a(1)=2, and a(2)=7.
  • A217093 (program): Number of partitions of n objects of 3 colors.
  • A217094 (program): Least index k such that A011540(k) >= 10^n.
  • A217096 (program): Characteristic function of numbers that have a nonleading zero in their decimal representation (A011540). 0 itself is also included, so a(0) = 1.
  • A217110 (program): Number of pandigital numbers with n places.
  • A217111 (program): Number of pandigital numbers <= 10^n.
  • A217123 (program): Number of possible ordered pairs (x, y) where x is the number of beads adjacent to at least one black bead and y the number of beads adjacent to at least one white bead in a binary necklace of length n.
  • A217124 (program): Semiprimes whose decimal representation has only digits in {4,5,7}.
  • A217128 (program): Numbers n such that (2n)^4 + 1 is not prime.
  • A217129 (program): Numbers n such that n^4 + 1 is not prime.
  • A217140 (program): a(n) = m/n where m is the least number divisible by n such that phi(m) = phi(m+6n).
  • A217143 (program): Sum of squares of Bell numbers (A000110).
  • A217144 (program): Alternating sums of squares of Bell numbers (A000110).
  • A217175 (program): a(n) is the first digit (from the left) to appear n times in succession in the decimal representation of the Fibonacci(A217165(n)).
  • A217176 (program): a(n) is the first digit (from the left) to appear n times in succession in the decimal representation of the Lucas(A217166(n)).
  • A217200 (program): Number of permutations in S_{n+2} containing an increasing subsequence of length n.
  • A217203 (program): First column of A217202.
  • A217213 (program): 2*A002740(n).
  • A217218 (program): Trajectory of 44 under the map k -> A006368(k).
  • A217219 (program): Theta series of planar hexagonal net (honeycomb) with respect to deep hole.
  • A217220 (program): Theta series of Kagome net with respect to an atom.
  • A217221 (program): Theta series of Kagome net with respect to a deep hole.
  • A217233 (program): Expansion of (1-2*x+x^2)/(1-3*x-3*x^2+x^3).
  • A217238 (program): a(n) = n! * Sum_{k=1..n} k!.
  • A217239 (program): a(n) = n!*(!n - 1) = n! * Sum_{k=1..n-1} k!.
  • A217254 (program): a(n) = round(primepi(n) * prime(n)/n).
  • A217258 (program): Threshold for the P(n)-avoidance edge-coloring game with two colors and fixed tree size restriction, where P(n) denotes the path on n edges (see the comments and reference for precise definition).
  • A217260 (program): E.g.f. 2*arctan(1+x) - Pi/2.
  • A217274 (program): a(n) = 7*a(n-1) - 14*a(n-2) + 7*a(n-3) with a(0)=0, a(1)=1, a(2)=7.
  • A217275 (program): Expansion of 2/(1-x+sqrt(1-2*x-27*x^2)).
  • A217280 (program): a(n) = Sum_{k=0..n} binomial(n,k)^3 * 2^k * 3^(n-k).
  • A217283 (program): Expansion of 1/(1 -x -x^2 -x^6 -x^24 - … -x^(k!) - … ).
  • A217284 (program): a(n) = Sum_{k=0..n} (n!/k!)^3.
  • A217285 (program): Irregular triangle read by rows: T(n,k) is the number of labeled relations on n nodes with exactly k edges; n>=0, 0<=k<=n^2.
  • A217287 (program): Length of chain of consecutive integers starting with n, where each new integer in the chain has a prime factor which no previous member in the chain has.
  • A217290 (program): Integers n such that 2*cos(2*Pi/n) is an integer.
  • A217312 (program): Number of Motzkin paths of length n with no level steps at height 1.
  • A217319 (program): Numbers with binary representation ending in 4*k+2 or 4*k+3 zeros.
  • A217323 (program): Number of self-inverse permutations in S_n with longest increasing subsequence of length 3.
  • A217329 (program): Esumprimes: prime(k), where k is the sum of the first n digits of E.
  • A217330 (program): The number of integer solutions to the equation x1 + x2 + x3 + x4 = n, with xi >= 0, and with x2 + x3 divisible by 3.
  • A217331 (program): Number of inequivalent ways to color a 3 X 3 checkerboard using at most n colors allowing rotations and reflections.
  • A217333 (program): G.f.: exp( Sum_{n>=1} x^n/n * Sum_{k=0..n} binomial(n,k)^2 * x^k/(1-x)^k ).
  • A217340 (program): Number of n X 2 arrays of occupancy after each element moves to some horizontal or vertical neighbor but without 2-loops
  • A217358 (program): Series reversion of x-x^3-x^4.
  • A217359 (program): Series reversion of x+x^3+x^4.
  • A217360 (program): a(n) = 2^n*binomial(4*n, n)/(3*n+1).
  • A217361 (program): Series reversion of x+x^2+2*x^3.
  • A217363 (program): Series reversion of x - 3*x^3.
  • A217364 (program): a(n) = 2^n*binomial(5*n, n)/(4*n+1).
  • A217365 (program): Series reversion of x + x^2 + x^3 + x^4 + x^5.
  • A217366 (program): a(n) = ((n+6) / gcd(n+6,4)) * (n / gcd(n,4)).
  • A217367 (program): a(n) = ((n+7) / gcd(n+7,4)) * (n / gcd(n,4)).
  • A217388 (program): Alternating sums of the ordered Bell numbers (number of preferential arrangements) A000670.
  • A217389 (program): Partial sums of the ordered Bell numbers (number of preferential arrangements) A000670.
  • A217391 (program): Partial sums of the squares of the ordered Bell numbers (number of preferential arrangements) A000670.
  • A217392 (program): Alternating sums of the squares of the ordered Bell numbers (number of preferential arrangements) A000670.
  • A217394 (program): Numbers starting with 2.
  • A217395 (program): Numbers starting with 3.
  • A217397 (program): Numbers starting with 4.
  • A217398 (program): Numbers starting with 5.
  • A217399 (program): Numbers starting with 6.
  • A217400 (program): Numbers starting with 7.
  • A217401 (program): Numbers starting with 8.
  • A217402 (program): Numbers starting with 9.
  • A217434 (program): n divided by the product of all its prime divisors smaller than the largest prime divisor.
  • A217436 (program): Triangular array read by rows. T(n,k) is the number of labeled relations on n elements with exactly k vertices of indegree and outdegree = 0.
  • A217441 (program): Numbers k such that 26*k+1 is a square.
  • A217445 (program): Numbers n such that n! has the same number of terminating zeros in bases 3 and 4.
  • A217447 (program): Number of n x n permutation matrices that disconnect their zeros.
  • A217450 (program): Number of n X 1 arrays of the minimum value of corresponding elements and their horizontal and vertical neighbors in a random 0..2 n X 1 array.
  • A217460 (program): Odd values of n such that the polynomial 1+x+x^2+…+x^(n-1) is reducible over GF(2).
  • A217464 (program): L.g.f.: Sum_{n>=1} x^n/n * Sum_{k=0..n} binomial(n,k)^2 * x^k*(1-x)^(n-k).
  • A217469 (program): Multiplicative order of 5 (mod 5*n + 1).
  • A217471 (program): Partial sum of fifth power of the even-indexed Fibonacci numbers.
  • A217473 (program): Product of the first n+1 odd-indexed Lucas numbers A000032.
  • A217477 (program): Z-sequence for the Riordan triangle A111125;
  • A217478 (program): Triangle of coefficients of polynomials providing the second term of the numerator for the generating function for odd powers (2*m+1) of Chebyshev S-polynomials. The present polynomials are called P(m;1,x^2).
  • A217481 (program): Decimal expansion of sqrt(2*Pi)/4.
  • A217482 (program): Quarter-square tetrahedrals: a(n) = k*(k - 1)*(k - 2)/6, k = A002620(n).
  • A217483 (program): Alternating sums of the numbers in sequence A080253.
  • A217484 (program): Partial sums of the numbers in sequence A080253.
  • A217486 (program): Binomial convolution of the numbers in sequence A080253.
  • A217487 (program): Partial sums of the squares of the numbers in sequence A080253.
  • A217488 (program): Alternating sums of the squares of the numbers in sequence A080253
  • A217494 (program): Primes of the form 2*n^2 + 34*n + 15.
  • A217495 (program): Primes of the form 2*n^2 + 46*n + 21.
  • A217496 (program): Primes of the form 2*n^2 + 50*n + 23.
  • A217497 (program): Primes of the form 2*n^2 + 54*n + 25.
  • A217498 (program): Primes of the form 2*n^2 + 58*n + 27.
  • A217499 (program): Primes of the form 2*n^2 + 70*n + 33.
  • A217501 (program): Primes of the form 2*n^2 + 78*n + 37.
  • A217513 (program): Partial sums of nonzero terms in A005926.
  • A217515 (program): Base-n state complexity of partitioned deterministic finite automaton (PDFA) for the periodic sequence (123)*.
  • A217516 (program): Base-n state complexity of partitioned deterministic finite automaton (PDFA) for the periodic sequence (1234)*.
  • A217517 (program): Base-n state complexity of partitioned deterministic finite automaton (PDFA) for the periodic sequence (12345)*.
  • A217518 (program): Base-n state complexity of partitioned deterministic finite automaton (PDFA) for the periodic sequence (123456)*.
  • A217522 (program): Squarefree ternary sequence derived from bi-infinite squarefree ternary sequence of Kurosaki.
  • A217526 (program): From the enumeration of involutions avoiding the pattern 4321.
  • A217527 (program): a(n) = 2^(n-2)*(n-2)^2+2^(n-1).
  • A217528 (program): a(n) = (n-2)*(n-3)*2^(n-2)+2^n-2.
  • A217529 (program): a(n) = 2^(n-4)*(4*n^2 - 16*n + 23).
  • A217530 (program): n^4/2-5*n^3/2+21*n-30.
  • A217539 (program): Number of Dyck paths of semilength n which satisfy the condition: number of returns + number of hills < number of peaks.
  • A217553 (program): G.f.: exp( Sum_{n>=1} 4^A001511(n) * x^n/n ), where 2^A001511(n) is the highest power of 2 that divides 2*n.
  • A217557 (program): The difference between the reversal of an 8-bit integer and the original integer.
  • A217562 (program): Even numbers not divisible by 5.
  • A217564 (program): Number of primes between prime(n)/2 and prime(n+1)/2.
  • A217570 (program): Numbers n such that floor(sqrt(n)) = floor(n/(floor(sqrt(n))-1))-1.
  • A217571 (program): a(n) = (2*n*(n+5) + (2*n+1)*(-1)^n - 1)/8.
  • A217573 (program): Number of integers between -(2*n+1)*Pi and (2*n+2)*Pi.
  • A217574 (program): (n^2)*(n^2-1)*(n^2-2)*(n^2-3).
  • A217575 (program): Numbers n such that floor(sqrt(n)) = floor(n/floor(sqrt(n)))-1.
  • A217579 (program): a(1) = 1; for n > 1, a(n) = max(d*lpf(d) : d|n, d > 1), where lpf is the least prime factor function (A020639).
  • A217580 (program): Triangular array read by rows. T(n,k) is the number of labeled digraphs on n nodes with exactly k isolated nodes. 0<=k<=n.
  • A217581 (program): Largest prime divisor of n <= sqrt(n), 1 if n is prime or 1.
  • A217585 (program): Number of triangles with endpoints of the form (x,x^2), x in {-n,…,n}, having at least one angle of 45 degrees.
  • A217586 (program): a(1) = 1 and, for all n >= 1, if a(n) = 0 then a(2*n) = 1 and a(2*n+1) = 0 whereas if a(n) = 1 then a(2*n) = 0 and a(2*n+1) = 0.
  • A217587 (program): Primes p of the form 420k + 1 for some k.
  • A217588 (program): Primes of the form 2520k + 1 for some k.
  • A217589 (program): Bit reversed 16-bit numbers.
  • A217596 (program): G.f.: x / reversion(x - x^2 - x^3).
  • A217607 (program): Smallest k > 1 such that n divides binomial(n,k).
  • A217612 (program): Difference between n-th prime and the smallest semiprime greater than it.
  • A217615 (program): G.f.: Sum_{n>=0} x^n * Sum_{k=0..n} binomial(n,k)^2 * x^k*(1-x)^(n-k).
  • A217616 (program): G.f.: Sum_{n>=0} x^n * Sum_{k=0..n} binomial(n,k)^2 * x^k*(2-x)^(n-k).
  • A217619 (program): a(n) = m/(12*n) where m is the least multiple of n that satisfies phi(m) = phi(m+6*n).
  • A217620 (program): Primes of the form 2*n^2 + 82*n + 39.
  • A217621 (program): Primes of the form 2*n^2 + 90*n + 43.
  • A217622 (program): Prime(prime(2*n)).
  • A217624 (program): Prime(prime(3*n)).
  • A217626 (program): First differences of A215940, or first differences of permutations of (0,1,2,…,m-1) reading them as decimal numbers, divided by 9 (with 10>=m, and m! > n).
  • A217627 (program): a(n) is the sum of the products of the nonzero digits of the numbers from 1 to n.
  • A217628 (program): a(n) = 3^((n-1)*(n+2)/2).
  • A217629 (program): Triangle, read by rows, where T(n,k) = k!*C(n, k)*3^(n-k) for n>=0, k=0..n.
  • A217631 (program): Number of nX2 arrays of the minimum value of corresponding elements and their horizontal and vertical neighbors in a random 0..1 nX2 array
  • A217639 (program): Number of nX2 arrays of the minimum value of corresponding elements and their horizontal, vertical or antidiagonal neighbors in a random 0..2 nX2 array
  • A217649 (program): a(n) = n!! mod n!!!
  • A217652 (program): Number of isolated nodes over all labeled directed graphs on n nodes.
  • A217656 (program): Primes p such that p = 361 + 420*k for some k.
  • A217659 (program): Larger of two consecutive primes which both equal 1 (mod 3).
  • A217661 (program): G.f.: Sum_{n>=0} x^n * Sum_{k=0..n} binomial(n,k)^2 * x^k/(1-x)^k.
  • A217664 (program): G.f.: Sum_{n>=0} x^n * Sum_{k=0..n} binomial(n,k)^2 * x^k/(1-2*x)^k.
  • A217668 (program): G.f.: Sum_{n>=0} x^n*(1 + x^n)^n.
  • A217669 (program): G.f.: Sum_{n>=0} (x + x^n)^n.
  • A217670 (program): G.f.: Sum_{n>=0} x^n/(1 + x^n)^n.
  • A217693 (program): Numbers of distinct integers obtained from summing up subsets of {1, 1/2, 1/3, …, 1/n}.
  • A217694 (program): Number of n-variations of the set {1,2,…,n+1} satisfying p(i)-i in {-2,0,2}, i=1..n (an n-variation of the set N_{n+s} = {1,2,…,n+s} is any 1-to-1 mapping p from the set N_n = {1,2,…,n} into N_{n+s} = {1,2,…,n+s}).
  • A217701 (program): Permanent of the n X n matrix with all diagonal entries n and all off diagonal entries 1.
  • A217703 (program): a(0)=1, a(1)=0, and a(n+1) = 2*n*(n+1)*a(n)-n^4*a(n-1) for n>0.
  • A217707 (program): Numbers n such that both 4*n-1 and 4*n+1 are composite.
  • A217710 (program): Cardinality of the set of possible heights of AVL trees with n (leaf-) nodes.
  • A217713 (program): Integer part of log(n)^2.
  • A217714 (program): Modified Euler numbers.
  • A217723 (program): a(n) = (sum of first n primorial numbers) minus 1.
  • A217729 (program): Trajectory of 40 under the map n-> A006369(n).
  • A217730 (program): Expansion of (1+2*x-x^3)/(1-4*x^2+2*x^4).
  • A217733 (program): Expansion of (1+x-x^2)/((1-x)*(1-3*x^2-x^3)).
  • A217736 (program): Sum of first n squares of semiprimes.
  • A217737 (program): a(n) = Fibonacci(n) mod n*(n+1).
  • A217739 (program): Decimal expansion of 8/Pi^2.
  • A217740 (program): Abundant numbers with abundant subscripts.
  • A217742 (program): Numbers n with the property that if the base-8 representation of n is read backwards, the result is 5*n.
  • A217747 (program): Numbers whose digits sum to a perfect number.
  • A217748 (program): Number of regions with infinite area in the exterior of a regular n-gon with all diagonals drawn.
  • A217754 (program): Number of different kinds of polygonal regions with finite area in the exterior of a regular n-gon with all diagonals drawn.
  • A217755 (program): Numbers n such that ((n^2 + n)/2)^2 + 1 is prime.
  • A217757 (program): Product_{i=0..n} (i! + 1).
  • A217758 (program): Triangular numbers of the form k^2 + k - 1.
  • A217761 (program): Numbers whose square has a square number of decimal digits.
  • A217767 (program): Denominators for a rational approximation to Euler constant.
  • A217771 (program): Expansion of (phi(-x) / phi(-x^3))^2 in powers of x where phi() is a Ramanujan theta function.
  • A217772 (program): a(n) = ((p+1)*(3p)!/((2p-1)!*(p+1)!*2p) - 3)/(3p^3), where p is the n-th prime.
  • A217775 (program): a(n) = n*(n+1) + (n+2)*(n+3) + (n+4)*(n+5).
  • A217776 (program): a(n) = n*(n+1) + (n+2)*(n+3) + (n+4)*(n+5) + (n+6)*(n+7).
  • A217777 (program): Expansion of (1+x)*(1+2*x)*(1-x)/(1-5*x^2+5*x^4).
  • A217778 (program): Expansion of (1-x)^2*(1-3*x)/((1-3*x+x^2)*(1-5*x+5*x^2)).
  • A217779 (program): Expansion of (1-4x+4*x^2)/((1-5x+5*x^2)*(1-3x+x^2)).
  • A217782 (program): Expansion of (1-x)*(1-2x)*(1-3x)/((1-5x+5*x^2)*(1-3x+x^2)).
  • A217783 (program): Expansion of (1-x)*(1-2x)/((1-5x+5*x^2)*(1-3x+x^2)).
  • A217786 (program): Expansion of (psi(x^3) / psi(x))^2 in powers of x where psi() is a Ramanujan theta function.
  • A217787 (program): a(n) = (a(n-1)*a(n-3) + 1) / a(n-4) with a(0) = a(1) = a(2) = a(3) = 1.
  • A217789 (program): Least difference between 2 palindromic numbers of length n.
  • A217800 (program): Number of alternating permutations on 2n+1 letters that avoid a certain pattern of length 4 (see Lewis, 2012, Appendix, for precise definition).
  • A217831 (program): Triangle read by rows: label the entries T(0,0), T(1,0), T(0,1), T(2,0), T(1,1), T(0,2), T(3,0), … Then T(n,k)=T(k,n), T(0,0)=0, T(1,0)=1, and for n>1, T(n,0)=0 and T(n,in+j)=T(n-j,j) (i,j >= 0, not both 0).
  • A217834 (program): Total number of solutions to the equation x^2+k*y^2 = n with x > 0, y > 0, k > 0. (Order matters for the equation x^2+y^2 = n).
  • A217838 (program): Number of n element 0..1 arrays with each element the minimum of 7 adjacent elements of a random 0..1 array of n+6 elements.
  • A217839 (program): T(n,k)=Number of n element 0..1 arrays with each element the minimum of k adjacent elements of a random 0..1 array of n+k-1 elements
  • A217852 (program): Multiplicative order of 5 (mod 5*n - 1).
  • A217854 (program): Product of all divisors of n, positive or negative.
  • A217855 (program): Numbers m such that 16*m*(3*m+1)+1 is a square.
  • A217856 (program): Numbers with three prime factors, not necessarily distinct, except cubes of primes.
  • A217858 (program): Odd part of lcm(1,2,3,…,n).
  • A217862 (program): Primes p of the form p = 1 + 840*k for some k.
  • A217863 (program): a(n) = phi(lcm(1,2,3,…,n)), where phi is Euler’s totient function.
  • A217871 (program): a(n)=b(n,1) where b(0,m)=m, b(n,m)=b(floor(n/4),m*2).
  • A217872 (program): a(n) = sigma(n)^n.
  • A217873 (program): 4*n*(n^2+2)/3.
  • A217874 (program): Table A142978 (figurate numbers for n-dimensional cross polytope) extended by a top row.
  • A217893 (program): 50k^2-40k-17 interleaved with 50k^2+10k+13 for k=>0.
  • A217894 (program): 50k^2-20k-23 interleaved with 50k^2+30k+17 for k=>0.
  • A217895 (program): Sum of d/Gpf(d) for all divisors d of n, with Gpf(d) the greatest prime factor of d.
  • A217907 (program): Numbers whose each digit squared sums to a semiprime.
  • A217914 (program): O.g.f.: Sum_{n>=0} (n^4)^n * exp(-n^4*x) * x^n / n!.
  • A217915 (program): O.g.f.: Sum_{n>=1} (n^5)^n * exp(-n^5*x) * x^n / n!.
  • A217920 (program): Column 1 of A217916 (when formed into a number triangle).
  • A217923 (program): F-block elements for Janet periodic table.
  • A217924 (program): Row sums of triangle A217537.
  • A217928 (program): Sum of distinct decimal digits appearing in n.
  • A217947 (program): a(n) = (n+1)*(n^3+15*n^2+74*n+132)/12.
  • A217948 (program): List of numbers 2n for which the riffle permutation permutes all except the first and last of the 2n cards.
  • A217956 (program): Total number of solutions to the equation x^2+k*y^2 = n with x > 0, y > 0, k >= 0, or 0 if infinite. (Order matters for the equation x^2+y^2 = n).
  • A217958 (program): Number of n X 2 arrays of the minimum value of corresponding elements and their horizontal or antidiagonal neighbors in a random 0..2 n X 2 array.
  • A217971 (program): a(n) = 2^(2*n+1) * (2*n+1)*n^(2*n).
  • A217975 (program): 2*n^2 - 7 is a square.
  • A217983 (program): a(A130290(n) * A000040(n)^n1) = A000040(n), n >= 1 and n1 >= 1, and a(n) = 1 elsewhere.
  • A217988 (program): Binomial transform of A215495(n).
  • A217990 (program): Size of largest semigroup generated by one Boolean n X n matrix.
  • A217994 (program): a(n) = 2^((2 + n + n^2)/2).
  • A218002 (program): E.g.f.: exp( Sum_{n>=1} x^prime(n) / prime(n) ).
  • A218003 (program): Number of degree-n permutations of order a power of 3.
  • A218004 (program): Number of equivalence classes of compositions of n where two compositions a,b are considered equivalent if the summands of a can be permuted into the summands of b with an even number of transpositions.
  • A218008 (program): Sum of successive absolute differences of the binomial coefficients = 2*A014495(n)
  • A218009 (program): Binomial transform of A212831(n).
  • A218016 (program): Triangle, read by rows, where T(n,k) = k!*C(n, k)*5^(n-k) for n>=0, k=0..n.
  • A218017 (program): Triangle, read by rows, where T(n,k) = k!*C(n, k)*7^(n-k) for n>=0, k=0..n.
  • A218018 (program): Triangle, read by rows, where T(n,k) = k!*C(n, k)*11^(n-k) for n>=0, k=0..n.
  • A218034 (program): Number of ways to seat 4 types of people in n labeled seats around a circle such that no two adjacent people are of the same type.
  • A218036 (program): a(n) = (n+1) + (n+3/2)*H(n) - (H(n)^3)/2, where H(n)=A002024(n).
  • A218043 (program): Base 3 numbers that have digits that sum to 3.
  • A218045 (program): Number of truth tables of bracketed formulas (case 3).
  • A218051 (program): Number of n X 1 arrays of the minimum value of corresponding elements and their horizontal, vertical, diagonal or antidiagonal neighbors in a random 0..3 n X 1 array.
  • A218059 (program): Number of n X 3 arrays of the minimum value of corresponding elements and their horizontal or antidiagonal neighbors in a random 0..1 n X 3 array.
  • A218065 (program): Number of 2 X n arrays of the minimum value of corresponding elements and their horizontal or antidiagonal neighbors in a random 0..1 2 X n array.
  • A218072 (program): Product of the nonzero digits (in base 10) of n^2.
  • A218073 (program): Number of profiles in domino tiling of a 2*n checkboard.
  • A218075 (program): a(n) = 2^(prime(n+1) - prime(n)).
  • A218078 (program): Number of n X 2 arrays of the minimum value of corresponding elements and their horizontal, vertical or antidiagonal neighbors in a random 0..1 n X 2 array.
  • A218088 (program): a(n) is the largest term in period of continued fraction expansion of square root of n!.
  • A218089 (program): a(n) = n*((n+1)^n - n^(n-1)).
  • A218101 (program): The number of simple labeled graphs on n nodes that have exactly n(n-1)/4 edges.
  • A218117 (program): G.f.: A(x) = exp( Sum_{n>=1} A005261(n)*x^n/n ) where A005261(n) = Sum_{k=0..n} C(n,k)^5.
  • A218118 (program): G.f.: A(x) = exp( Sum_{n>=1} A005261(n)/2*x^n/n ) where A005261(n) = Sum_{k=0..n} C(n,k)^5.
  • A218119 (program): G.f.: A(x) = exp( Sum_{n>=1} A069865(n)*x^n/n ) where A069865(n) = Sum_{k=0..n} C(n,k)^6.
  • A218120 (program): G.f.: A(x) = exp( Sum_{n>=1} A069865(n)/2*x^n/n ) where A069865(n) = Sum_{k=0..n} C(n,k)^6.
  • A218124 (program): Number of 7-ary sequences with primitive period n.
  • A218125 (program): Number of 8-ary sequences with primitive period n.
  • A218126 (program): Number of 9-ary sequences with primitive period n.
  • A218127 (program): Number of 10-ary sequences with primitive period n.
  • A218130 (program): Number of length 6 primitive (=aperiodic or period 6) n-ary words.
  • A218131 (program): Number of length 8 primitive (=aperiodic or period 8) n-ary words.
  • A218132 (program): Number of length 9 primitive (=aperiodic or period 9) n-ary words.
  • A218133 (program): Number of length 10 primitive (=aperiodic or period 10) n-ary words.
  • A218134 (program): Norm of coefficients in the expansion of 1/(1 - 2*x - i*x^2), where i is the imaginary unit.
  • A218135 (program): Norm of coefficients in the expansion of 1 / (1 - x - 2*I*x^2), where I^2=-1.
  • A218141 (program): a(n) = Stirling2(n^2, n).
  • A218143 (program): a(n) = Stirling2(n*(n+1)/2, n).
  • A218145 (program): Product of the nonzero digits (in base 10) of n^3.
  • A218147 (program): Degree of minimal polynomial satisfied by exp(8*Pi*phi_2(1/n,1/n)), where phi_2 is defined in the Comments.
  • A218148 (program): a(n) = 2^((6+5*n+n^3)/6).
  • A218149 (program): a(n) = 3^((6+5*n+n^3)/6).
  • A218150 (program): 5^((6+5*n+n^3)/6).
  • A218151 (program): a(n) = 2*3^n*5^(n(n-1)/2).
  • A218152 (program): a(n) = 1 + n + ((n-1)*n^2)/2.
  • A218155 (program): Numbers congruent to 2, 3, 6, 11 mod 12.
  • A218171 (program): Expansion of f(x^11, x^13) - x * f(x^5, x^19) in powers of x where f(, ) is Ramanujan’s general theta function.
  • A218172 (program): Centered 12-gonal numbers which are semiprimes, intersection of A003154 and A001358.
  • A218173 (program): Expansion of f(x^7, x^17) - x^2 * f(x, x^23) in powers of x where f(,) is Ramanujan’s two-variable theta function.
  • A218186 (program): Number of rows with the value true in the truth tables of all bracketed formulas with n distinct propositions p_1, …, p_n connected by the binary connective of m-implication (case 1).
  • A218189 (program): Hilltop maps: number of n X 1 binary arrays indicating the locations of corresponding elements not exceeded by any horizontal or vertical neighbor in a random 0..3 n X 1 array.
  • A218199 (program): Hilltop maps: number of n X 1 binary arrays indicating the locations of corresponding elements not exceeded by any horizontal or vertical neighbor in a random 0..2 n X 1 array
  • A218215 (program): Product of the nonzero digits (in base 10) of n^4.
  • A218219 (program): Define a(x,y) to be 1 if x is 0 or 1 and y*a(x-1,y)-a(x-2,y) otherwise. Then the n-th term of the sequence is a(n,n).
  • A218220 (program): Array a(n,m) read by antidiagonals where a(0,m)=a(1,m)=1 and a(n,m) = m*a(n-1,m)-a(n-2,m) for n>=2.
  • A218225 (program): G.f. A(x) satisfies: (1 - x*A(x)) / (1 - x^2*A(x)^2)^2 = 1 - x.
  • A218227 (program): Hilltop maps: number of n X 2 binary arrays indicating the locations of corresponding elements not exceeded by any horizontal, vertical or antidiagonal neighbor in a random 0..2 n X 2 array.
  • A218234 (program): Infinitesimal generator for padded Pascal matrix A097805 (as lower triangular matrices).
  • A218236 (program): Hilltop maps: number of n X 2 binary arrays indicating the locations of corresponding elements not exceeded by any king-move neighbor in a random 0..3 n X 2 array.
  • A218245 (program): Nicolas’s sequence, whose nonnegativity is equivalent to the Riemann hypothesis.
  • A218250 (program): G.f. satisfies: A(x) = (1 + x*A(x)) * (1 + x^2*A(x))^2.
  • A218251 (program): G.f. satisfies: A(x) = (1 + x*A(x))^2 * (1 + x^3*A(x)).
  • A218255 (program): Next prime after 10*n.
  • A218260 (program): E.g.f.: Sum_{n>=0} Product_{k=1..n} tanh((2*k-1)*x).
  • A218263 (program): Number of standard Young tableaux of n cells and height >= 3.
  • A218272 (program): Infinitesimal generator for transpose of the Pascal matrix A007318 (as upper triangular matrices).
  • A218281 (program): Hilltop maps: number of n X 1 binary arrays indicating the locations of corresponding elements not exceeded by any horizontal or vertical neighbor in a random 0..4 n X 1 array.
  • A218289 (program): Denominator of the sixth increasing diagonal of the autosequence of the second kind from (-1)^n/(n+1).
  • A218290 (program): Multiples of 5 such that the sum of their digits is also a multiple of 5.
  • A218291 (program): Multiples of 6 such that the sum of their digits is also a multiple of 6.
  • A218292 (program): Multiples of 10 such that the sum of their digits is also a multiple of 10.
  • A218296 (program): E.g.f.: Sum_{n>=0} n^n * cosh(n*x) * x^n/n!.
  • A218297 (program): E.g.f.: Sum_{n>=0} (n^2)^n * cosh(n^2*x) * x^n/n!.
  • A218300 (program): E.g.f. A(x) satisfies: A( x/(exp(x)*cosh(x)) ) = exp(2*x)*cosh(2*x).
  • A218302 (program): E.g.f. A(x) satisfies: A( x/(exp(x)*cosh(x)) ) = exp(4*x)*cosh(4*x).
  • A218303 (program): E.g.f. A(x) satisfies: A( x/(exp(2*x)*cosh(2*x)) ) = exp(x)*cosh(x).
  • A218305 (program): E.g.f. A(x) satisfies: A( x/(exp(3*x)*cosh(3*x)) ) = exp(x)*cosh(x).
  • A218306 (program): E.g.f. A(x) satisfies: A( x/(exp(3*x)*cosh(3*x)) ) = exp(2*x)*cosh(2*x).
  • A218307 (program): E.g.f. A(x) satisfies: A( x/(exp(4*x)*cosh(4*x)) ) = exp(x)*cosh(x).
  • A218309 (program): E.g.f. A(x) satisfies: A( x/(exp(3*x)*cosh(3*x)) ) = exp(4*x)*cosh(4*x).
  • A218310 (program): E.g.f. A(x) satisfies: A( x/(exp(5*x)*cosh(5*x)) ) = exp(x)*cosh(x).
  • A218311 (program): Product of the nonzero digits (in base 10) of n^5.
  • A218313 (program): Hilltop maps: number of n X 2 binary arrays indicating the locations of corresponding elements not exceeded by any king-move neighbor in a random 0..2 n X 2 array.
  • A218314 (program): Hilltop maps: number of n X 3 binary arrays indicating the locations of corresponding elements not exceeded by any king-move neighbor in a random 0..2 n X 3 array.
  • A218317 (program): Hilltop maps: number of nX6 binary arrays indicating the locations of corresponding elements not exceeded by any king-move neighbor in a random 0..2 nX6 array
  • A218324 (program): Odd heptagonal pyramidal numbers
  • A218325 (program): Even heptagonal pyramidal numbers.
  • A218326 (program): Odd octagonal pyramidal numbers
  • A218327 (program): Even octagonal pyramidal numbers (A002414)
  • A218328 (program): Odd 9-gonal (nonagonal) pyramidal numbers.
  • A218329 (program): Even 9-gonal (nonagonal) pyramidal numbers.
  • A218330 (program): Odd decagonal pyramidal numbers.
  • A218331 (program): Even, nonzero decagonal pyramidal numbers.
  • A218344 (program): Smallest k such that k*(n-th composite)+1 is prime.
  • A218346 (program): Numbers of the form a^a + b^b, with a > b > 0.
  • A218348 (program): Hilltop maps: number of n X 2 binary arrays indicating the locations of corresponding elements not exceeded by any horizontal or vertical neighbor in a random 0..1 nX2 array.
  • A218376 (program): a(n) = 5^n*sum_{i=1..n} i^5/5^i.
  • A218385 (program): (n-2)!/n when an integer.
  • A218394 (program): Numbers such that sum(i<=n) binomial(n,i)*binomial(2*n-2*i, n-i) is not divisible by 5.
  • A218395 (program): If the sum of the squares of 11 consecutive numbers is a square, then a(n) is the square root of this sum.
  • A218420 (program): Hilltop maps: number of n X 2 binary arrays indicating the locations of corresponding elements not exceeded by any horizontal, vertical or antidiagonal neighbor in a random 0..1 n X 2 array.
  • A218438 (program): G.f.: 1 / ( (1 + x^2 - x^3)^2 * (1 - x - 2*x^2 - x^3) ).
  • A218439 (program): a(n) = A001609(n)^2, where g.f. of A001609 is x*(1+3*x^2)/(1-x-x^3).
  • A218441 (program): a(n) = A000108(n)*A001764(n).
  • A218442 (program): a(n) = Sum_{k=0..n} floor(n/(3*k + 1)).
  • A218443 (program): a(n) = Sum_{k=0..n} floor(n/(3k+2)).
  • A218444 (program): a(n) = Sum_{k>=0} floor(n/(5*k + 1)).
  • A218445 (program): a(n) = Sum_{k>=0} floor(n/(5*k + 2)).
  • A218446 (program): a(n) = Sum_{k>=0} floor(n/(5*k + 3)).
  • A218447 (program): a(n) = Sum_{k>=0} floor(n/(5*k + 4)).
  • A218449 (program): Gaussian binomial coefficient [2*n-1,n] for q=2, n>=0.
  • A218450 (program): Number of digits of n plus number of digits of n equal to 1, 2, 4, or 8.
  • A218451 (program): 10^n minus its binary weight.
  • A218460 (program): a(n) = prime(n)^(prime(n + 1) - prime(n)).
  • A218461 (program): Floor( prime(prime(n))/ prime(n) ).
  • A218470 (program): Partial sums of floor(n/9).
  • A218471 (program): a(n) = n*(7*n-3)/2.
  • A218473 (program): Number of 3n-length 3-ary words, either empty or beginning with the first letter of the alphabet, that can be built by repeatedly inserting triples of identical letters into the initially empty word.
  • A218474 (program): Number of 3n-length 4-ary words, either empty or beginning with the first letter of the alphabet, that can be built by repeatedly inserting triples of identical letters into the initially empty word.
  • A218475 (program): Number of 3n-length 5-ary words, either empty or beginning with the first letter of the alphabet, that can be built by repeatedly inserting triples of identical letters into the initially empty word.
  • A218476 (program): Number of 3n-length 6-ary words, either empty or beginning with the first letter of the alphabet, that can be built by repeatedly inserting triples of identical letters into the initially empty word.
  • A218477 (program): Number of 3n-length 7-ary words, either empty or beginning with the first letter of the alphabet, that can be built by repeatedly inserting triples of identical letters into the initially empty word.
  • A218478 (program): Number of 3n-length 8-ary words, either empty or beginning with the first letter of the alphabet, that can be built by repeatedly inserting triples of identical letters into the initially empty word.
  • A218479 (program): Number of 3n-length 9-ary words, either empty or beginning with the first letter of the alphabet, that can be built by repeatedly inserting triples of identical letters into the initially empty word.
  • A218480 (program): Number of 3n-length 10-ary words, either empty or beginning with the first letter of the alphabet, that can be built by repeatedly inserting triples of identical letters into the initially empty word.
  • A218481 (program): Binomial transform of the partition numbers (A000041).
  • A218482 (program): First differences of the binomial transform of the partition numbers (A000041).
  • A218485 (program): Positive numbers differing from next greater square by a square.
  • A218492 (program): a(n) = lcm(1,…,L(n)), where L(n) = n-th Lucas number.
  • A218496 (program): 4th iteration of the hyperbinomial transform on the sequence of 1’s.
  • A218497 (program): 5th iteration of the hyperbinomial transform on the sequence of 1’s.
  • A218498 (program): 6th iteration of the hyperbinomial transform on the sequence of 1’s.
  • A218499 (program): 7th iteration of the hyperbinomial transform on the sequence of 1’s.
  • A218500 (program): 8th iteration of the hyperbinomial transform on the sequence of 1’s.
  • A218501 (program): 9th iteration of the hyperbinomial transform on the sequence of 1’s.
  • A218502 (program): 10th iteration of the hyperbinomial transform on the sequence of 1’s.
  • A218503 (program): q-factorial numbers 5!_q.
  • A218505 (program): Decimal expansion of sum_{k=1..infinity} (H(k)/k)^2, where H(k) = sum_{j=1..k} 1/j.
  • A218506 (program): Number of partitions of n in which any two parts differ by at most 4.
  • A218507 (program): Number of partitions of n in which any two parts differ by at most 5.
  • A218509 (program): Number of partitions of n in which any two parts differ by at most 7.
  • A218510 (program): Number of partitions of n in which any two parts differ by at most 8.
  • A218511 (program): Number of partitions of n in which any two parts differ by at most 9.
  • A218516 (program): Number of n X 2 arrays of the minimum value of corresponding elements and their horizontal or antidiagonal neighbors in a random 0..3 n X 2 array.
  • A218529 (program): Binomial transform of -1, -1, 1, 2, -5, -16, … (signed variant of A000111).
  • A218530 (program): Partial sums of floor(n/11).
  • A218541 (program): First differences of A213715.
  • A218557 (program): Smallest prime >= n-th Lucas number.
  • A218585 (program): Number of ways to write n as x+y with 0<x<=y and x^2+xy+y^2 prime.
  • A218614 (program): a(n) = binary code (shown here in decimal) of the position of natural number n in the beanstalk-tree A218778.
  • A218615 (program): a(n) = binary code (shown here in decimal) of the position of natural number n in the beanstalk-tree A218776.
  • A218616 (program): The infinite trunk of beanstalk (A179016) with reversed subsections.
  • A218621 (program): a(n) = unique divisor d of n such that d + (n/d - 1)/2 is minimal and integral.
  • A218622 (program): a(n) = A183161(n) (mod 4), n>=0.
  • A218654 (program): Number of ways to write n as x+y with 0<x<=y and x^2+3xy+y^2 prime.
  • A218657 (program): Hilltop maps: number of n X 2 binary arrays indicating the locations of corresponding elements not exceeded by any king-move neighbor in a random 0..1 n X 2 array.
  • A218659 (program): Hilltop maps: number of n X 4 binary arrays indicating the locations of corresponding elements not exceeded by any king-move neighbor in a random 0..1 n X 4 array.
  • A218689 (program): Sum_{k=0..n} C(n,k)^6*C(n+k,k)^6.
  • A218690 (program): Sum_{k=0..n} C(n,k)^4*C(n+k,k)^2.
  • A218691 (program): Number of ways to paint some (possibly none or all) of the trees over all forests on n labeled nodes.
  • A218692 (program): Sum_{k=0..n} C(n,k)^6*C(n+k,k)^3.
  • A218693 (program): Sum_{k=0..n} C(n,k)*C(n+k,k)^3.
  • A218706 (program): Number of nonnegative integer solutions to x^2 + 2y^2 <= n^2.
  • A218709 (program): a(n) is smallest number such that a(n)^2 + 1 is divisible by 13^n.
  • A218710 (program): a(n) is smallest number such that a(n)^2 + 1 is divisible by 17^n.
  • A218711 (program): Number of nonnegative solutions to x^2 + y^2 + z^2 < n^2.
  • A218721 (program): a(n) = (18^n-1)/17.
  • A218722 (program): a(n) = (19^n-1)/18.
  • A218723 (program): a(n) = (256^n - 1)/255.
  • A218724 (program): a(n) = (21^n - 1)/20.
  • A218725 (program): a(n) = (22^n-1)/21.
  • A218726 (program): a(n) = (23^n-1)/22.
  • A218727 (program): a(n) = (24^n-1)/23.
  • A218728 (program): a(n) = (25^n-1)/24.
  • A218729 (program): a(n) = (26^n-1)/25.
  • A218730 (program): a(n) = (27^n-1)/26.
  • A218731 (program): a(n) = (28^n-1)/27.
  • A218732 (program): a(n) = (29^n-1)/28.
  • A218733 (program): a(n) = (30^n-1)/29.
  • A218734 (program): a(n) = (31^n-1)/30.
  • A218735 (program): Values of x in the solutions to x^2 - 3xy + y^2 + 29 = 0, where 0 < x < y.
  • A218736 (program): a(n) = (33^n-1)/32.
  • A218737 (program): a(n) = (34^n-1)/33.
  • A218738 (program): a(n) = (35^n-1)/34.
  • A218739 (program): a(n) = (36^n-1)/35.
  • A218740 (program): a(n) = (37^n-1)/36.
  • A218741 (program): a(n) = (38^n-1)/37.
  • A218742 (program): a(n) = (39^n-1)/38.
  • A218743 (program): a(n) = (40^n-1)/39.
  • A218744 (program): a(n) = (41^n-1)/40.
  • A218745 (program): a(n) = (42^n-1)/41.
  • A218746 (program): a(n) = (43^n-1)/42.
  • A218747 (program): a(n) = (44^n-1)/43.
  • A218748 (program): a(n) = (45^n-1)/44.
  • A218749 (program): a(n) = (46^n-1)/45.
  • A218750 (program): a(n) = (47^n-1)/46.
  • A218751 (program): a(n) = (48^n-1)/47.
  • A218752 (program): a(n) = (50^n-1)/49.
  • A218753 (program): a(n) = (49^n-1)/48.
  • A218767 (program): Total number of divisors and anti-divisors of n.
  • A218768 (program): a(n+2) = (2*n+1)^2*a(n+1) + (2*n+1)*(2*n-1)*a(n) with a(1)=1 and a(2)=2.
  • A218790 (program): a(n) = binary code (shown here in decimal) of the position of the predecessor of the natural number pair (2n,2n+1) in the compact beanstalk-tree A218782.
  • A218791 (program): a(n) = binary code (shown here in decimal) of the position of the predecessor of the natural number pair (2n,2n+1) in the compact beanstalk-tree A218780.
  • A218799 (program): Number of solutions to x^2 + 2y^2 = n^2.
  • A218800 (program): Number of nonnegative integer solutions to x^2 + 2y^2 = (3n)^2.
  • A218804 (program): Hilltop maps: number of n X 2 binary arrays indicating the locations of corresponding elements not exceeded by any horizontal or antidiagonal neighbor in a random 0..3 n X 2 array.
  • A218817 (program): Number of rooted factorizations of n-permutations into ordered cycles.
  • A218828 (program): Reluctant sequence of reverse reluctant sequence A004736.
  • A218832 (program): Number of positive integer solutions to the Diophantine equation x + y + 2z = n^2.
  • A218836 (program): Unmatched value maps: number of nX2 binary arrays indicating the locations of corresponding elements not equal to any horizontal or antidiagonal neighbor in a random 0..1 nX2 array.
  • A218837 (program): Unmatched value maps: number of n X 3 binary arrays indicating the locations of corresponding elements not equal to any horizontal or antidiagonal neighbor in a random 0..1 n X 3 array.
  • A218864 (program): Numbers of the form 9*k^2 + 8*k, k an integer.
  • A218898 (program): Number of 2 X n arrays of the minimum value of corresponding elements and their horizontal, diagonal or antidiagonal neighbors in a random 0..1 2 X n array.
  • A218906 (program): Number of different kernels of integer partitions of n.
  • A218929 (program): Number of maximal solvable conjugacy classes of subgroups of the symmetric group.
  • A218930 (program): Number of maximal supersolvable conjugacy classes of subgroups of the symmetric group.
  • A218933 (program): Number of maximal nilpotent conjugacy classes of subgroups of the symmetric group.
  • A218935 (program): Number of cyclic conjugacy classes of subgroups of the alternating group.
  • A218946 (program): Number of maximal solvable conjugacy classes of subgroups of the alternating group.
  • A218947 (program): Number of maximal supersolvable conjugacy classes of subgroups of the alternating group.
  • A218950 (program): Number of maximal nilpotent conjugacy classes of subgroups of the alternating group.
  • A218975 (program): Number of connected cyclic conjugacy classes of subgroups of the alternating group.
  • A218982 (program): Power ceiling-floor sequence of sqrt(5).
  • A218983 (program): Power ceiling sequence of sqrt(5).
  • A218984 (program): Power floor sequence of 2+sqrt(6).
  • A218985 (program): Power ceiling sequence of 2+sqrt(6).
  • A218986 (program): Power floor sequence of 2+sqrt(7).
  • A218987 (program): Power ceiling sequence of 2+sqrt(7).
  • A218988 (program): Power floor sequence of 2+sqrt(8).
  • A218989 (program): Power ceiling sequence of 2+sqrt(8).
  • A218990 (program): Power ceiling-floor sequence of 3+sqrt(8).
  • A218991 (program): Power floor sequence of 3+sqrt(10).
  • A218992 (program): Power ceiling sequence of 3+sqrt(10).
  • A218993 (program): Numerator of the least reduced fraction b/c > 1 using divisors b and c of n.
  • A219003 (program): Unmatched value maps: number of 2 X n binary arrays indicating the locations of corresponding elements not equal to any horizontal, diagonal or antidiagonal neighbor in a random 0..2 2 X n array.
  • A219009 (program): Coefficients of the Dirichlet series for zeta(4s)/zeta(s).
  • A219020 (program): Sum of the cubes of the first n even-indexed Fibonacci numbers divided by the sum of the first n terms.
  • A219021 (program): Sum of cubes of first n terms of Lucas sequence U(4,1) (A001353) divided by sum of their first powers.
  • A219024 (program): Number of length n mixed radix numbers with base [2, 3, 4, …] (factorial base) such that the parities of adjacent digits differ.
  • A219028 (program): Number of non-primitive roots for prime(n), less than prime(n).
  • A219029 (program): a(n) = n - 1 - phi(phi(n)).
  • A219034 (program): Triangular array read by rows: T(n,k) is the number of forests of rooted trees on n labeled nodes with exactly k isolated nodes; n>=0, 0<=k<=n.
  • A219054 (program): (8*n^3 + 3*n^2 + n) / 6.
  • A219056 (program): a(n) = 3*n^4.
  • A219069 (program): Triangle read by rows: T(n,k) = n^4 + (n*k)^2 + k^4, 1 <= k <= n.
  • A219070 (program): a(n) = (46*n^5 + 30*n^4 + 15*n^3 - n) / 30.
  • A219071 (program): Parity of pi(10^n).
  • A219079 (program): Hilltop maps: number of 2Xn binary arrays indicating the locations of corresponding elements not exceeded by any horizontal, diagonal or antidiagonal neighbor in a random 0..1 2Xn array
  • A219085 (program): a(n) = floor((n + 1/2)^3).
  • A219086 (program): a(n) = floor((n + 1/2)^4).
  • A219087 (program): a(n) = floor((n + 1/2)^(4/3)).
  • A219088 (program): Floor((n + 1/2)^5).
  • A219089 (program): Floor((n + 1/2)^6).
  • A219090 (program): a(n) = floor((n + 1/2)^7).
  • A219091 (program): a(n) = floor((n + 1/2)^8).
  • A219092 (program): a(n) = floor(e^(n + 1/2)).
  • A219093 (program): Denominator of the least reduced fraction b/c > 1 using divisors b and c of n.
  • A219094 (program): n/(b*c), where b/c is the least reduced fraction > 1 using divisors b and c of n.
  • A219095 (program): Numbers k such that if b/c > 1 is the least reduced fraction using divisors b and c of k, then c > 1.
  • A219100 (program): Unmatched value maps: number of n X 2 binary arrays indicating the locations of corresponding elements not equal to any horizontal, vertical or antidiagonal neighbor in a random 0..2 n X 2 array.
  • A219109 (program): The smallest k such that prime(k) == -1 (mod n).
  • A219113 (program): Sequence of integers which are simultaneously a sum of consecutive squares and a difference of consecutive cubes.
  • A219115 (program): Numbers whose squares have at least one 1 and one 2 in ternary representation.
  • A219116 (program): Number of semicomplete digraphs on n nodes with an “Emperor”.
  • A219143 (program): Unchanging value maps: number of 2 X n binary arrays indicating the locations of corresponding elements unequal to no horizontal, diagonal or antidiagonal neighbor in a random 0..2 2 X n array.
  • A219150 (program): Unchanging value maps: number of n X 2 binary arrays indicating the locations of corresponding elements unequal to no horizontal, antidiagonal or vertical neighbor in a random 0..1 n X 2 array.
  • A219167 (program): Number of n X 2 arrays of the minimum value of corresponding elements and their horizontal or vertical neighbors in a random, but sorted with lexicographically nondecreasing rows and columns, 0..2 n X 2 array.
  • A219174 (program): Numbers whose prime factors are either 2 or Mersenne primes.
  • A219176 (program): Smallest k > 1 such that k + n divides k^2 + n.
  • A219190 (program): Numbers of the form k*(5*k+1), where k = 0,-1,1,-2,2,-3,3,…
  • A219191 (program): Numbers of the form k*(7*k+1), where k = 0,-1,1,-2,2,-3,3,…
  • A219194 (program): a(n) = max(A218075(n+1), A218075(n)) / min(A218075(n+1), A218075(n)).
  • A219196 (program): A subsequence of the denominators of the Bernoulli numbers: a(n) = A027642(A131577(n)).
  • A219205 (program): 3^(n-1)*(3^n - 1), n >= 0.
  • A219206 (program): Triangle, read by rows, where T(n,k) = binomial(n,k)^k for n>=0, k=0..n.
  • A219207 (program): Triangle, read by rows, where T(n,k) = binomial(n,k)^(k+1) for n>=0, k=0..n.
  • A219211 (program): Number of n X 2 arrays of the minimum value of corresponding elements and their horizontal, vertical, diagonal or antidiagonal neighbors in a random, but sorted with lexicographically nondecreasing rows and columns, 0..2 n X 2 array.
  • A219218 (program): G.f. satisfies: A(x) = Sum_{n>=0} [A(x)^(2*n) (mod 3)]*x^n, where A(x)^(2*n) (mod 3) reduces all coefficients modulo 3 to {0,1,2}.
  • A219224 (program): G.f.: exp( Sum_{n>=1} A005063(n)*x^n/n ), where A005063(n) = sum of squares of primes dividing n.
  • A219226 (program): Number of rooted unlabeled ordered (plane) trees with 2n leaves such that i) every internal node has an even number of children and ii) every path from the root to a leaf is the same length.
  • A219227 (program): a(n) is the sum of n addends nested as follows: floor(f(floor(f(…(n)…)))) where f(x) = x^(1/3).
  • A219233 (program): Alternating row sums of Riordan triangle A110162.
  • A219244 (program): Differences of two consecutive primes which both equal 1 modulo 3, divided by 6.
  • A219257 (program): Numbers k such that 11*k+1 is a square.
  • A219258 (program): Numbers k such that 27*k+1 is a square.
  • A219259 (program): Numbers k such that 25*k+1 is a square.
  • A219266 (program): Logarithmic derivative of the superfactorials (A000178).
  • A219267 (program): Logarithmic derivative of the hyperfactorials (A002109).
  • A219268 (program): Logarithmic derivative of A001142, where A001142(n) = product{k=1..n} k^k/k!.
  • A219282 (program): Number of superdiagonal bargraphs with area n.
  • A219286 (program): Number of n X 3 arrays of the minimum value of corresponding elements and their horizontal or vertical neighbors in a random, but sorted with lexicographically nondecreasing rows and columns, 0..1 n X 3 array.
  • A219293 (program): Number of n X 2 arrays of the minimum value of corresponding elements and their horizontal, vertical or antidiagonal neighbors in a random, but sorted with lexicographically nondecreasing rows and columns, 0..2 n X 2 array.
  • A219312 (program): Composition of the binomial transform of Fibonacci numbers and the Catalan transform of Fibonacci numbers.
  • A219314 (program): Composition of the inverse binomial transform of Fibonacci numbers and the Catalan transform of Fibonacci numbers.
  • A219330 (program): Number of random selections (with replacement) needed from a normal population to assure a greater than one-half chance that the selected group contains the top 10th percentile individual, top 1st percentile individual, the 0.1 percentile, 0.01 percentile etc…
  • A219331 (program): L.g.f.: -log(1 - Sum_{n>=1} x^(n^2)) = Sum_{n>=1} a(n)*x^n/n.
  • A219347 (program): Number of partitions of n into distinct parts with smallest possible largest part.
  • A219349 (program): Number of n X 3 arrays of the minimum value of corresponding elements and their horizontal, vertical, diagonal or antidiagonal neighbors in a random, but sorted with lexicographically nondecreasing rows and columns, 0..1 n X 3 array.
  • A219355 (program): Size of the edge set of the Generalized Lucas Cube Q_n(111).
  • A219388 (program): Basic quantic arrangement for the 1 to 120 planetary electrons and elementary periods (circles I to XX) distributed by energy levels.
  • A219389 (program): Numbers k such that 13*k+1 is a square.
  • A219390 (program): Numbers k such that 14*k+1 is a square.
  • A219391 (program): Numbers k such that 21*k + 1 is a square.
  • A219392 (program): Numbers k such that 22*k+1 is a square.
  • A219393 (program): Numbers k such that 23*k+1 is a square.
  • A219394 (program): Numbers k such that 17*k+1 is a square.
  • A219395 (program): Numbers k such that 18*k+1 is a square.
  • A219396 (program): Numbers k such that 19*k+1 is a square.
  • A219405 (program): Unmatched value maps: number of n X 3 binary arrays indicating the locations of corresponding elements not equal to any horizontal or antidiagonal neighbor in a random 0..2 n X 3 array.
  • A219428 (program): a(n) = n - 1 - phi(n).
  • A219462 (program): a(n) = Sum_{k = 1..2*n} binomial(2*n,k) * Fibonacci(2*k).
  • A219463 (program): Triangle read by rows: T(n,k) = 1 - A047999(n,k), 0 <= k <= n.
  • A219498 (program): Number of n X 4 arrays of the minimum value of corresponding elements and their horizontal or vertical neighbors in a random, but sorted with lexicographically nondecreasing rows and nonincreasing columns, 0..1 n X 4 array.
  • A219499 (program): Number of n X 5 arrays of the minimum value of corresponding elements and their horizontal or vertical neighbors in a random, but sorted with lexicographically nondecreasing rows and nonincreasing columns, 0..1 n X 5 array.
  • A219527 (program): a(n) = (6*n^2 + 7*n - 9 + 2*n^3)/12 - (-1)^n*(n+1)/4.
  • A219529 (program): Coordination sequence for 3.3.4.3.4 Archimedean tiling.
  • A219530 (program): Number of functions f:{1,2,…,n}->{1,2,…,n} such that each component of f is a function on an interval of {1,2,…,n}.
  • A219531 (program): a(n) = Sum_{k=0..11} C(n, k).
  • A219534 (program): G.f. satisfies: A(x) = 1 + x*(A(x)^2 + A(x)^4).
  • A219535 (program): G.f. satisfies: A(x) = 1 + x*(2*A(x)^2 + A(x)^3).
  • A219536 (program): G.f. satisfies: A(x) = 1 + x*(A(x)^2 + 2*A(x)^3).
  • A219537 (program): G.f. satisfies: A(x) = 1 + x*(A(x)^2 - A(x)^3 + A(x)^4).
  • A219538 (program): G.f. satisfies: A(x) = 1 + x*A(x)^2*(1 + A(x))^2/2.
  • A219547 (program): Numbers k such that 2 times the least prime factor of 2^k + 1 is not the least m > 1 that divides sigma_k(m).
  • A219550 (program): Sum(m^p, m=1..p-1)/p as p runs through the odd primes.
  • A219562 (program): a(n) = Sum_{k=0..n} binomial(n+k,k)^4.
  • A219563 (program): Sum(binomial(n+k,k)^5, k=0..n).
  • A219564 (program): Sum(binomial(n+k,k)^6, k=0..n).
  • A219570 (program): Triangular array read by rows. T(n,k) is the number of necklaces (turning over is not allowed) of n labeled black or white beads having exactly k black beads.
  • A219586 (program): Greatest prime factor of Product_{x=1..n} (x^2 + 1).
  • A219587 (program): Noncrossing, nonnesting, 2-arc-colored permutations on the set {1..n} where lower arcs even of different colors do not cross.
  • A219589 (program): Number of n X 2 arrays of the minimum value of corresponding elements and their horizontal or vertical neighbors in a random, but sorted with lexicographically nondecreasing rows and nonincreasing columns, 0..2 n X 2 array.
  • A219601 (program): Number of partitions of n in which no parts are multiples of 6.
  • A219602 (program): Primes p such that p^2-2 is composite.
  • A219603 (program): a(n) = prime(n) * prime(2*n-1).
  • A219606 (program): Prime gaps and primes interleaved.
  • A219608 (program): Odd terms in A060142.
  • A219609 (program): Half of first differences of A219608.
  • A219612 (program): Numbers k that divide the sum of the first k Fibonacci numbers (beginning with F(0)).
  • A219613 (program): E.g.f. tan(x/(1-x)).
  • A219615 (program): a(n) = Sum_{k=0..12} binomial(n,k).
  • A219619 (program): a(n) = n! * (n^4 + n^2 + 1).
  • A219621 (program): Number of n X 2 arrays of the minimum value of corresponding elements and their horizontal or antidiagonal neighbors in a random, but sorted with lexicographically nondecreasing rows and columns, 0..2 n X 2 array.
  • A219636 (program): Complement of A035336.
  • A219637 (program): Numbers that occur twice in A219641.
  • A219638 (program): Complement of A219640. Natural numbers that do not occur in A219641.
  • A219639 (program): Numbers that occur only once in A219641.
  • A219640 (program): Numbers n for which there exists k such that n = k - (number of 1’s in Zeckendorf expansion of k); distinct values in A219641.
  • A219641 (program): a(n) = n minus (number of 1’s in Zeckendorf expansion of n).
  • A219642 (program): Number of steps to reach 0 starting with n and using the iterated process: x -> x - (number of 1’s in Zeckendorf expansion of x).
  • A219643 (program): Least inverse of A219642; a(n) = minimal i such that A219642(i) = n.
  • A219644 (program): Run lengths in A219642.
  • A219645 (program): Greatest inverse of A219642; a(n) = maximal i such that A219642(i) = n.
  • A219646 (program): Partial sums of A219642.
  • A219647 (program): Positions of zeros in A219649.
  • A219650 (program): The nonnegative integers n such that there exists a number k with A034968(n+k)=k.
  • A219651 (program): a(n) = n minus (sum of digits in factorial base expansion of n).
  • A219652 (program): Number of steps to reach 0 starting with n and using the iterated process: x -> x - (sum of digits in factorial expansion of x).
  • A219656 (program): Partial sums of A219652.
  • A219657 (program): Positions of zeros in A219659.
  • A219658 (program): Complement of A219650. Natural numbers that do not occur in A219651.
  • A219660 (program): a(n) = number of bit-positions where Fibonacci numbers F(n) and F(n+1) contain both an 1-bit in their binary representation.
  • A219664 (program): Repeating part of A220664: First differences of the numbers given as concatenation of permutations of (1,…,m) for sufficiently large m.
  • A219672 (program): a(n) = Sum_{k=0..n} binomial(n,k)^2*Fibonacci(k).
  • A219673 (program): a(n) = Sum_{k=0..n} binomial(n,k)^2*Lucas(k) where Lucas(n) = A000032(n).
  • A219675 (program): Starting with a(0)=0, a(n) = 1 + the sum of the digital sums of a(0) through a(n-1).
  • A219676 (program): a(n) = Sum_{k=0..13} binomial(n, k).
  • A219680 (program): Number of n X 2 arrays of the minimum value of corresponding elements and their horizontal, vertical or antidiagonal neighbors in a random, but sorted with lexicographically nondecreasing rows and nonincreasing columns, 0..2 n X 2 array.
  • A219694 (program): Triangular array read by rows: T(n,k) is the number of functions f:{1,2,…,n} -> {1,2,…,n} that have exactly k nonrecurrent elements; n>=1, 0<=k<=n-1.
  • A219695 (program): For odd numbers 2n - 1, half the difference between the largest divisor not exceeding the square root, and the least divisor not less than the square root.
  • A219699 (program): Number of n X 3 arrays of the minimum value of corresponding elements and their horizontal, vertical or antidiagonal neighbors in a random, but sorted with lexicographically nondecreasing rows and columns, 0..1 n X 3 array.
  • A219706 (program): Total number of nonrecurrent elements in all functions f:{1,2,…,n}->{1,2,…,n}.
  • A219721 (program): Expansion of (1+7*x+5*x^2+7*x^3+x^4)/(1-x-x^4+x^5).
  • A219729 (program): Sum_{x <= n} largest divisor of x that is <= sqrt(x).
  • A219730 (program): Sum_{x <= n} smallest divisor of x that is >= sqrt(x).
  • A219732 (program): a(n) = (Product_{i=1..n-1} (2^i + 1)) modulo (2^n - 1).
  • A219749 (program): In the string b12b2b12 replace b with n 1’s.
  • A219751 (program): Expansion of x^4*(2-3*x-x^2)/((1+x)*(1-2*x)^2).
  • A219754 (program): Expansion of x^4*(1-x-x^2)/((1+x)*(1-2*x)*(1-x-2*x^2)).
  • A219755 (program): Expansion of x^4*(1-3*x^2-x^3)/((1+x)*(1-2*x)*(1-x-2*x^2)).
  • A219762 (program): Start with 0; repeatedly apply the map {0->012, 1->120, 2->201} to the odd-numbered terms and {0->210, 1->021, 2->102} to the even-numbered terms.
  • A219768 (program): Number of n X 3 arrays of the minimum value of corresponding elements and their horizontal or antidiagonal neighbors in a random, but sorted with lexicographically nondecreasing rows and columns, 0..1 n X 3 array.
  • A219786 (program): Least number such that there are n-1 composite numbers between n+1 and a(n) (both inclusive).
  • A219788 (program): Consider the succession rule (x, y, z) -> (z, y+z, x+y+z). Sequence gives z values starting at (0, 1, 2).
  • A219789 (program): Least prime in the form x*y-1 with x > 0, y > 0 and x + y = n > 3.
  • A219791 (program): Number of ways to write n=x+y (0<x<=y) with (xy)^2+1 prime.
  • A219794 (program): First differences of 5-smooth numbers (A051037).
  • A219803 (program): Number of 2 X n arrays of the minimum value of corresponding elements and their horizontal, vertical, diagonal or antidiagonal neighbors in a random, but sorted with lexicographically nondecreasing rows and nonincreasing columns, 0..3 2 X n array.
  • A219810 (program): Number of n X 2 arrays of the minimum value of corresponding elements and their horizontal, vertical or diagonal neighbors in a random, but sorted with lexicographically nondecreasing rows and nonincreasing columns, 0..2 n X 2 array.
  • A219838 (program): Number of ways to write n as x + y with 0 < x <= y and (xy)^2 + xy + 1 prime.
  • A219839 (program): a(n) is the number of odd integers in 2..(n-1) that have a common factor (other than 1) with n.
  • A219842 (program): Number of ways to write n as x+y (0<x<=y) with 2x*y+1 prime.
  • A219843 (program): Rows of A219463 seen as numbers in binary representation.
  • A219846 (program): Number of n X 2 arrays of the minimum value of corresponding elements and their horizontal or antidiagonal neighbors in a random, but sorted with lexicographically nondecreasing rows and nonincreasing columns, 0..2 n X 2 array.
  • A219853 (program): Number of 2 X n arrays of the minimum value of corresponding elements and their horizontal or antidiagonal neighbors in a random, but sorted with lexicographically nondecreasing rows and nonincreasing columns, 0..2 2 X n array.
  • A219859 (program): Triangular array read by rows: T(n,k) is the number of endofunctions, functions f:{1,2,…,n}->{1,2,…,n}, that have exactly k elements with no preimage; n>=0, 0<=k<=n.
  • A219863 (program): Decimal expansion of 1 - 1/e^2.
  • A219901 (program): Number of isomorphism classes of IPR nanocones with 3 pentagons and a symmetric boundary of length n.
  • A219902 (program): Number of isomorphism classes of IPR nanocones with 3 pentagons and a nearsymmetric boundary of length n.
  • A219931 (program): Coefficients related to an asymptotic expansion of the logarithm of the central binomial.
  • A219954 (program): (A160414(n)-1)/4, n >= 1.
  • A219977 (program): Expansion of 1/(1+x+x^2+x^3).
  • A220000 (program): Sixty fourths of an inch in thousandths, rounded to nearest integer.
  • A220001 (program): Benes network size for permutations of n.
  • A220018 (program): Number of cyclotomic cosets of 3 mod 10^n.
  • A220020 (program): Number of cyclotomic cosets of 9 mod 10^n.
  • A220021 (program): Number of cyclotomic cosets of 11 mod 10^n.
  • A220029 (program): Number of n X 5 arrays of the minimum value of corresponding elements and their horizontal or diagonal neighbors in a random, but sorted with lexicographically nondecreasing rows and nonincreasing columns, 0..1 n X 5 array.
  • A220033 (program): Number of 3 X n arrays of the minimum value of corresponding elements and their horizontal or diagonal neighbors in a random, but sorted with lexicographically nondecreasing rows and nonincreasing columns, 0..1 3 X n array.
  • A220051 (program): Sum_{k=0..14} binomial(n,k).
  • A220053 (program): Partial sums in rows of A130517, triangle read by rows.
  • A220071 (program): Difference between number of halving steps and number of tripling steps needed to reach 1 in ‘3x+1’ problem.
  • A220073 (program): Mirror of the triangle A130517.
  • A220074 (program): Triangle read by rows giving coefficients T(n,k) of [x^(n-k)] in Sum_{i=0..n} (x-1)^i, 0 <= n <= k.
  • A220075 (program): Partial sums in rows of A220073, triangle read by rows.
  • A220081 (program): Primes of the form 15*n^2 - 15*n + 17.
  • A220082 (program): Numbers k such that 10*k-1 is a square.
  • A220083 (program): a(n) = (15*n^2 + 9*n + 2)/2.
  • A220084 (program): a(n) = (n + 1)*(20*n^2 + 19*n + 6)/6.
  • A220087 (program): 2^n - 27.
  • A220088 (program): a(n) = 2^n - 81.
  • A220089 (program): a(n) = 2^n - 243.
  • A220092 (program): a(n) = ((2*n-1)!! + (-1)^((n-1)*(n-2)/2))/2.
  • A220094 (program): Sum of the n-digit base-ten numbers whose digits are nonzero.
  • A220096 (program): a(1)=0, n-1 if n is prime, else largest proper divisor of n.
  • A220097 (program): Number of words on {1,1,2,2,3,3,…,n,n} avoiding the pattern 123.
  • A220098 (program): Manhattan distances between 2n and 1 in the double spiral with positive integers and 1 at the center.
  • A220101 (program): Number of ordered set partitions of {1,…,n} into n-1 blocks avoiding the pattern 123.
  • A220104 (program): n appears n*(n+1) times.
  • A220105 (program): 2^(n-1) mod n^2.
  • A220114 (program): Largest k >= 0 such that k = n - x - y where n = x*y, x > 0, y > 0, or -1 if no such k exists.
  • A220115 (program): a(n) = A000120(n) - A007895(n), the number of 1’s in binary expansion of n minus the number of terms in Zeckendorf representation of n.
  • A220116 (program): Numbers k such that the number of 1’s in binary expansion of k equals the number of terms in Zeckendorf representation of k.
  • A220128 (program): 1 followed by period 6: (1, 3, 2, 3, 1, 4) repeated; offset 0.
  • A220129 (program): 1 followed by period 12: (1, 5, 3, 9, 1, 7, 1, 9, 3, 5, 1, 11) repeated; offset 0.
  • A220139 (program): The highest value of the Collatz iteration (3x+1) starting at a(n-1) + 1, with a(1) = 1.
  • A220147 (program): Number of n X 2 arrays of the minimum value of corresponding elements and their horizontal or diagonal neighbors in a random, but sorted with lexicographically nondecreasing rows and nonincreasing columns, 0..2 n X 2 array.
  • A220154 (program): Number of 2 X n arrays of the minimum value of corresponding elements and their horizontal or diagonal neighbors in a random, but sorted with lexicographically nondecreasing rows and nonincreasing columns, 0..2 2 X n array.
  • A220171 (program): An ordered subset of primitive values of x^2 + x*y + y^2 where at least two ordered pairs (x1,y1) and (x2,y2) with x1 != x2, y1 != y2 and gcd(x1,y1) = gcd(x2,y2) = 1 yield identical primitive values.
  • A220178 (program): Triangle where the g.f. for row n equals d^n/dx^n (1+x+x^2)^n / n! for n>=0, as read by rows.
  • A220180 (program): E.g.f.: exp( Sum_{n>=1} (n+1)^(n-1) * x^n / n ).
  • A220181 (program): E.g.f.: Sum_{n>=0} (1 - exp(-n*x))^n.
  • A220182 (program): Number of changes of parity in the Collatz trajectory of n.
  • A220185 (program): Numbers n such that n^2 + n(n+1) is an oblong number (A002378).
  • A220186 (program): Numbers n >= 0 such that n^2 + n*(n+1)/2 is a square.
  • A220211 (program): The order of the one-dimensional affine group in the finite fields F_q with q >= 3.
  • A220212 (program): Convolution of natural numbers (A000027) with tetradecagonal numbers (A051866).
  • A220218 (program): Numbers where all exponents in its prime factorization are one less than a prime.
  • A220232 (program): Number of rooted labeled trees of height 2 such that every leaf is at a distance 2 from the root.
  • A220235 (program): (2^n + 3^n) modulo n.
  • A220236 (program): Binary palindromic numbers with only two 0 bits, both in the middle.
  • A220249 (program): Numbers of rows R of the Wythoff array such that R is the n-th multiple of a tail of the Lucas sequence.
  • A220250 (program): Sum of neighbor maps: number of nX2 binary arrays indicating the locations of corresponding elements equal to the sum mod 3 of their king-move neighbors in a random 0..2 nX2 array
  • A220280 (program): Reluctant sequence of reluctant sequence A002260.
  • A220335 (program): A modified Engel expansion for sqrt(3) - 1.
  • A220336 (program): A modified Engel expansion for 4*sqrt(2) - 5.
  • A220337 (program): A modified Engel expansion for 3*sqrt(15) - 11.
  • A220338 (program): A modified Engel expansion for 8*sqrt(6) - 19.
  • A220348 (program): Index of row where n occurs in A183079.
  • A220360 (program): a(n) = Fibonacci(n-1) * Fibonacci(n+1) * Fibonacci(n+2).
  • A220361 (program): a(n) = Fibonacci(n)^3 + (-1)^n*Fibonacci(n-2).
  • A220362 (program): a(n) = Fibonacci(n-1) * Fibonacci(n) * Fibonacci(n+2).
  • A220363 (program): a(n) = Fibonacci(n)^3 + (-1)^n*Fibonacci(n+2).
  • A220371 (program): a(n) = Product_{i=1..2*n} (4*i+2)*A060818(n).
  • A220399 (program): A convolution triangle of numbers obtained from A057682.
  • A220400 (program): Number of ways to write n as sum of at least 2 consecutive odd positive integers.
  • A220411 (program): The denominators of J. L. Fields generalized Bernoulli polynomials.
  • A220414 (program): a(n) = 6*a(n-1) - a(n-2), with a(1) = 13, a(2) = 73.
  • A220415 (program): Table T(n,k)= floor(n/k)+ floor(k/n), n,k >0 read by antidiagonals.
  • A220416 (program): Table T(n,k) = ((n+k-1)*(n+k-2)/2+n)^n, n,k >0 read by antidiagonals.
  • A220417 (program): Table T(n,k) = k^n - n^k, n, k > 0, read by descending antidiagonals.
  • A220422 (program): Numerators of coefficients of an expansion of the logarithm of the Catalan numbers.
  • A220425 (program): a(n) = n^2 + 2*n + 2^n.
  • A220427 (program): G.f.: exp( Sum_{n>=1} A005064(n)*x^n/n ), where A005064(n) = sum of cubes of primes dividing n.
  • A220436 (program): a(n) = A127546(n)^2.
  • A220442 (program): a(n) = 3^n + 6^n + 9^n + 12^n.
  • A220443 (program): a(n) = Sum_{i=1..n} (3i)^2.
  • A220449 (program): Define u(n) as in A220448; then a(1)=1, thereafter a(n) = u(n)*a(n-1).
  • A220452 (program): Number of unordered full binary trees with labels from a set of n labels.
  • A220464 (program): Reverse reluctant sequence of reluctant sequence A002260.
  • A220465 (program): Reverse reluctant sequence of reverse reluctant sequence A004736.
  • A220466 (program): a((2*n-1)*2^p) = 4^p*(n-1) + 2^(p-1)*(1+2^p), p >= 0 and n >= 1.
  • A220469 (program): Fibonacci 14-step numbers, a(n) = a(n-1) + a(n-2) + … + a(n-14).
  • A220486 (program): a(n) = n(p(n)-d(n)): sum of all of parts of all partitions of n with at least one distinct part.
  • A220492 (program): Number of primes p between quarter-squares, Q(n) < p <= Q(n+1), where Q(n) = A002620(n).
  • A220493 (program): Fibonacci 15-step numbers, a(n) = a(n-1) + a(n-2) + … + a(n-15).
  • A220494 (program): Number of toothpicks and D-toothpicks after n-th stage in the structure of the D-toothpick “wide” triangle of the first kind.
  • A220495 (program): Number of toothpicks or D-toothpicks added at n-th stage to the structure of A220494.
  • A220499 (program): Number of line segments in an H tree with n levels that have no correspondence with the toothpicks of the toothpick structure of A139250 after n-th stage.
  • A220506 (program): Number of primes <= n-th quarter-square.
  • A220508 (program): T(n,k) = n^2 + k if k <= n, otherwise T(n,k) = k*(k + 2) - n; square array T(n,k) read by ascending antidiagonals (n >= 0, k >= 0).
  • A220509 (program): n^3 + 3n + 3^n.
  • A220511 (program): n^5 + 5n + 5^n.
  • A220515 (program): Numbers n such that A183054(n) is not equal to A188569(n).
  • A220519 (program): Permutation of prime numbers in the order of sequential reading the antidiagonals of A220508.
  • A220528 (program): n^7 + 7n + 7^n.
  • A220547 (program): Number of ways to reciprocally link elements of an n X 2 array either to themselves or to exactly one horizontal, vertical or antidiagonal neighbor.
  • A220556 (program): Square array T(n,k) = ((n+k-1)*(n+k-2)/2+n)^k, n,k > 0 read by antidiagonals.
  • A220558 (program): Number of ways to reciprocally link elements of an n X 4 array either to themselves or to exactly one horizontal or antidiagonal neighbor.
  • A220563 (program): Number of ways to reciprocally link elements of an 2 X n array either to themselves or to exactly one horizontal or antidiagonal neighbor.
  • A220588 (program): a(n) = 2^n - n^2 - n.
  • A220589 (program): Number of simple skew-merged permutations with n elements.
  • A220590 (program): Number of ways to reciprocally link elements of an n X 2 array either to themselves or to exactly two king-move neighbors.
  • A220603 (program): First inverse function (numbers of rows) for pairing function A081344.
  • A220604 (program): Second inverse function (numbers of columns) for pairing function A081344.
  • A220616 (program): Number of ways to reciprocally link elements of an n X 3 array either to themselves or to exactly one horizontal, diagonal and antidiagonal neighbor.
  • A220633 (program): Number of ways to reciprocally link elements of an 3 X n array either to themselves or to exactly two horizontal or antidiagonal neighbors.
  • A220653 (program): n^11 + 11*n + 11^n.
  • A220655 (program): For n with a unique factorial base representation n = du*u! + … + d2*2! + d1*1! (each di in range 0..i, cf. A007623), a(n) = (du+1)*u! + … + (d2+1)*2! + (d1+1)*1!; a(n) = n + A007489(A084558(n)).
  • A220656 (program): The positions of those permutations in A030298 where the first element is not fixed.
  • A220657 (program): Partial sums of A084558+1.
  • A220658 (program): Irregular table, where the n-th row consists of A084558(n)+1 copies of n.
  • A220659 (program): Irregular table: row n (n >= 1) consists of numbers 0..A084558(n).
  • A220660 (program): Irregular table, where the n-th row consists of numbers 0..(n!-1).
  • A220661 (program): Irregular table, where the n-th row consists of numbers 1..n!
  • A220662 (program): Irregular table: row n (n>=1) consists of A084556(n) copies of A130664(n).
  • A220663 (program): Irregular table: row n (n>=1) consists of numbers 0..A084556(n)-1.
  • A220669 (program): Coefficient array for powers of x^2 of the square of Chebyshev’s C(2*n+1,x)/x =: tau(n,x) polynomials.
  • A220670 (program): Coefficient triangle for powers of x^2 of polynomials appearing in a generalized Melham conjecture on alternating sums of third powers of Chebyshev’s S polynomials with odd indices. Coefficients in powers of x^2 of 2 + (-1)^n*S(2*n,x).
  • A220673 (program): Coefficients of formal series in powers of (tan(x))^2 for tan(5*x)/tan(x).
  • A220690 (program): Number of acyclic graphs on {1,2,…,n} such that the node with label 1 is in the same connected component (tree) as the node with label 2.
  • A220694 (program): Irregular table: row n (n>=1) consists of numbers 1..A084556(n).
  • A220695 (program): Complement of A220655.
  • A220696 (program): The positions of those permutations in A030298 where the first element is one (fixed).
  • A220699 (program): a(0)=0, a(1)=0; for n>1, a(n) = a(n-1) + (n-4)*a(n-2) + 1
  • A220700 (program): a(0)=0, a(1)=0; for n>1, a(n) = a(n-1) + (n+3)*a(n-2) + 1
  • A220705 (program): Number of ways to reciprocally link elements of an n X 5 array either to themselves or to exactly two horizontal and antidiagonal neighbors, without consecutive collinear links.
  • A220726 (program): Number of ways to reciprocally link elements of a 2 X n array either to themselves or to exactly two horizontal, diagonal or antidiagonal neighbors.
  • A220739 (program): Number of ways to reciprocally link elements of an 2 X n array either to themselves or to exactly two horizontal, diagonal and antidiagonal neighbors, without consecutive collinear links.
  • A220747 (program): a(n) = (2*n+1)!! / ((floor((n-1)/3)*2+1))!!
  • A220753 (program): Expansion of (1+4*x+5*x^2-x^3)/((1-x)*(1+x)*(1-2*x^2)).
  • A220754 (program): Number of ordered triples (a,b,c) of elements of the symmetric group S_n such that the triple a,b,c generates a transitive group.
  • A220755 (program): Numbers n such that n^2 + n(n+1)/2 is an oblong number (A002378).
  • A220779 (program): Exponent of highest power of 2 dividing the sum 1^n + 2^n + … + n^n.
  • A220780 (program): Nonzero terms of A220779: exponent of highest power of 2 dividing an even sum 1^n + 2^n + … + n^n.
  • A220783 (program): Agreement numbers: number of n X 2 arrays of the count of horizontal and vertical neighbors equal to the corresponding element in a random 0..3 n X 2 array.
  • A220789 (program): Numbers n such that 2*prime(n)^2 - 1 is not prime.
  • A220806 (program): Equals one maps: number of n X 2 binary arrays indicating the locations of corresponding elements equal to exactly one of their horizontal, vertical and antidiagonal neighbors in a random 0..2 n X 2 array.
  • A220837 (program): Normalized position numbers of distant parents in complete binary trees.
  • A220838 (program): Tropical version of Somos-4 sequence A006720.
  • A220844 (program): Sum of inclusive heights of complete 4-ary trees on n nodes.
  • A220845 (program): Sum of exclusive heights of complete 3-ary trees on n nodes.
  • A220846 (program): a(n) = sum_(d|n) ((product_(d|n) d) / d).
  • A220847 (program): a(n) = numerator of the fraction whose Engel expansion has the positive divisors of n as its terms.
  • A220848 (program): a(n) = sum_(d|n) product_(d_x|n, d_x<=d) d_x.
  • A220849 (program): a(n) = Product_{d|n} Product_{d_x|n , d_x <= d} d_x.
  • A220853 (program): Denominators of the fraction (30*n+7) * binomial(2*n,n)^2 * 2F1([1/2 - n/2, -n/2], [1], 64)/(-256)^n, where 2F1 is the hypergeometric function.
  • A220855 (program): Number of mappings by Struijk et al. Design Space Explorations with n actors and one implementation alternative.
  • A220857 (program): Number of mappings by Struijk et al. Design Space Explorations with n actors and three implementation alternatives.
  • A220861 (program): Choose smallest m>0 such that the n-th rational prime p ramifies in the imaginary quadratic extension field K = Q(sqrt(-m)); a(n) = discriminant(K).
  • A220874 (program): Number of permutations of [n+1] avoiding 2413, 3142, 1324, 4231.
  • A220885 (program): a(3)=5, a(4)=8, a(5)=12; thereafter a(n) = a(n-1) + A000931(n+7).
  • A220888 (program): a(n) = F(n+7) - (1/2)*(n^3+2*n^2+13*n+26) where F(i) is a Fibonacci number (A000045).
  • A220889 (program): a(n) = F(n+8) - (1/6)*(n^4-2*n^3+26*n^2+47*n+132) where F(i) = Fibonacci numbers (A000045).
  • A220892 (program): G.f.: (1+8*x+22*x^2+8*x^3+x^4)/(1-x)^6.
  • A220893 (program): G.f.: 1/H(-x), where H(x) = (1+8*x+22*x^2+8*x^3+x^4)/(1-x)^6.
  • A220898 (program): Number of primitive maps on n edges.
  • A220899 (program): Number of 2-face-free maps on n edges.
  • A220902 (program): a(n) = Catalan(n) - A000245(n-2).
  • A220906 (program): Thue-Morse sequence (A010060) with 0 replaced by 2 and 1 replaced by 3,1.
  • A220909 (program): The second crank moment function M_2(n).
  • A220910 (program): Matchings avoiding the pattern 231.
  • A220932 (program): Equals two maps: number of n X 3 binary arrays indicating the locations of corresponding elements equal to exactly two of their horizontal and antidiagonal neighbors in a random 0..2 n X 3 array.
  • A220944 (program): Expansion of (1+3*x+5*x^2-x^3)/((1-x^2)*(1-3*x^2).
  • A220946 (program): Expansion of (1+2*x+2*x^2-x^3)/((1-x)*(1+x)*(1-3x^2)).
  • A220948 (program): Expansion of (1-x)^2*(1-3*x)/(1-9*x+28*x^2-35*x^3+15*x^4-x^5).
  • A220968 (program): Positions in A030229 where odd terms occur.
  • A220978 (program): a(n) = 3^(2*n+1) - 3^(n+1) + 1: The left Aurifeuillian factor of 3^(6*n+3) + 1.
  • A220979 (program): 5^(4n+2) - 5^(3n+2) + 3 * 5^(2n+1) - 5^(n+1) + 1: the left Aurifeuillian factor of 5^(10n+5) - 1.
  • A220980 (program): 5^(4n+2) + 5^(3n+2) + 3 * 5^(2n+1) + 5^(n+1) + 1: the right Aurifeuillian factor of 5^(10n+5) - 1.
  • A220989 (program): 12^(2n+1) - 6 * 12^n + 1: the left Aurifeuillian factor of 12^(6n+3) + 1.
  • A220990 (program): 12^(2n+1) + 6 * 12^n + 1: the right Aurifeuillian factor of 12^(6n+3) + 1.
  • A221048 (program): The odd semiprime numbers (A046315) which are orders of a non-Abelian group.
  • A221049 (program): Expansion of (1+2*x+3*x^2-x^3)/((1-x)*(1+x)*(1-2*x)*(1+2*x)).
  • A221055 (program): Primes of the form k*(k+1)*(k+2)/6+2 (i.e., two more than a tetrahedral number).
  • A221056 (program): Numbers k such that there is no square between prime(k) and prime(k+1).
  • A221058 (program): Number of inversions in all Dyck prefixes of length n.
  • A221082 (program): Number of n X 3 arrays of occupancy after each element moves to some horizontal or antidiagonal neighbor.
  • A221083 (program): Number of n X 4 arrays of occupancy after each element moves to some horizontal or antidiagonal neighbor.
  • A221088 (program): Number of 2 X n arrays of occupancy after each element moves to some horizontal or antidiagonal neighbor.
  • A221121 (program): Number of n X 3 arrays of occupancy after each element stays put or moves to some horizontal or antidiagonal neighbor.
  • A221130 (program): a(n) = 2^(2*n - 1) + n.
  • A221131 (program): Table, T, read by antidiagonals where T(-j,k) = ((1+sqrt(j))^k + (1-sqrt(j))^k)/2.
  • A221132 (program): a(n) = lcm(a(n-1), n^2 + n + 1) for n > 1 with a(1) = 1.
  • A221145 (program): a(n) is the number of permutations of n elements with exactly one fixed point and no transpositions.
  • A221146 (program): Table read by antidiagonals: (m+n) - (m XOR n).
  • A221150 (program): The generalized Fibonacci word f^[3].
  • A221151 (program): The generalized Fibonacci word f^[4].
  • A221152 (program): The generalized Fibonacci word f^[5].
  • A221159 (program): a(n) = Sum_{i=0..n} Stirling2(n,i)*2^(3i).
  • A221160 (program): G.f.: Sum_{n>=0} (4*n+1)^n * x^n / (1 + (4*n+1)*x)^n.
  • A221161 (program): G.f.: Sum_{n>=0} (4*n+3)^n * x^n / (1 + (4*n+3)*x)^n.
  • A221162 (program): Number of n X 2 arrays of occupancy after each element stays put or moves to some horizontal, vertical or antidiagonal neighbor.
  • A221166 (program): The infinite generalized Fibonacci word p^[2].
  • A221167 (program): The infinite generalized Fibonacci word p^[3].
  • A221172 (program): a(0)=-2, a(1)=3; thereafter a(n) = 2*a(n-1) + a(n-2).
  • A221173 (program): a(0)=-3, a(1)=4; thereafter a(n) = 2*a(n-1) + a(n-2).
  • A221174 (program): a(0)=-4, a(1)=5; thereafter a(n) = 2*a(n-1) + a(n-2).
  • A221175 (program): a(0)=-5, a(1)=6; thereafter a(n) = 2*a(n-1) + a(n-2).
  • A221176 (program): a(n) = Sum_{i=0..n} Stirling2(n,i)*2^(4i).
  • A221177 (program): Row sums of A141906.
  • A221179 (program): A convolution triangle of numbers obtained from A146559.
  • A221180 (program): Erroneous version of A000079.
  • A221196 (program): Number of n X 3 arrays of occupancy after each element moves to some horizontal, diagonal or antidiagonal neighbor, with no occupancy greater than 2.
  • A221215 (program): T(n,k)= ((n+k)^2-2*(n+k)+4-(n+3*k-2)*(-1)^(n+k))/2; n , k > 0, read by antidiagonals.
  • A221216 (program): T(n,k)= ((n+k)^2-2*(n+k)+4-(3*n+k-2)*(-1)^(n+k))/2; n , k > 0, read by antidiagonals.
  • A221217 (program): T(n,k) = ((n+k)^2-2*n+3-(n+k-1)*(1+2*(-1)^(n+k)))/2; n , k > 0, read by antidiagonals.
  • A221236 (program): Number of n X 2 arrays of occupancy after each element moves to some horizontal, vertical or antidiagonal neighbor, without 2-loops.
  • A221251 (program): Number of nX4 arrays of occupancy after each element moves to some horizontal or antidiagonal neighbor, with no occupancy greater than 2
  • A221264 (program): Numbers having fewer distinct prime factors of form 4*k+1 than of 4*k+3.
  • A221265 (program): Numbers having more distinct prime factors of form 4*k+1 than of 4*k+3.
  • A221266 (program): Number of n X 2 arrays of occupancy after each element stays put or moves to some king-move neighbor, with no occupancy greater than 2.
  • A221274 (program): Number of nX4 arrays of occupancy after each element moves to some horizontal, diagonal or antidiagonal neighbor, with every occupancy equal to zero or two
  • A221276 (program): Number of 2 X n arrays of occupancy after each element moves to some horizontal, diagonal or antidiagonal neighbor, with every occupancy equal to zero or two.
  • A221280 (program): Numbers m such that lambda(m) = lambda(m+1), where lambda(n) = A008836(n) is the Liouville function.
  • A221313 (program): Square root of number of nX4 arrays of occupancy after each element moves to some horizontal or vertical neighbor, with every occupancy equal to zero or two
  • A221315 (program): Number of nonnegative integer arrays of length n summing to n without equal adjacent values modulo 2
  • A221364 (program): The simple continued fraction expansion of F(x) := product {n = 0..inf} (1 - x^(4*n+3))/(1 - x^(4*n+1)) when x = 1/2*(3 - sqrt(5)).
  • A221365 (program): The simple continued fraction expansion of F(x) := product {n = 0..inf} (1 - x^(4*n+3))/(1 - x^(4*n+1)) when x = 1/2*(5 - sqrt(21)).
  • A221366 (program): The simple continued fraction expansion of F(x) := Product_{n >= 0} (1 - x^(4*n+3))/(1 - x^(4*n+1)) when x = 1/2*(7 - 3*sqrt(5)).
  • A221367 (program): The simple continued fraction expansion of F(x) := product {n = 0..inf} (1 - x^(4*n+3))/(1 - x^(4*n+1)) when x = 1/2*(9 - sqrt(77)).
  • A221371 (program): O.g.f.: Sum_{n>=0} n!^2 * x^n * Product_{k=1..n} (1 + x) / (1 + k^2*x + k^2*x^2).
  • A221374 (program): Number of n X 2 arrays of occupancy after each element stays put or moves to some horizontal, vertical or antidiagonal neighbor, with no occupancy greater than 2.
  • A221397 (program): Number of n X 3 arrays of occupancy after each element moves to some horizontal, diagonal or antidiagonal neighbor, with no 2-loops and with no occupancy greater than 2.
  • A221414 (program): Number of nX3 arrays of occupancy after each element stays put or moves to some horizontal or antidiagonal neighbor, with every occupancy equal to zero or two
  • A221425 (program): Number of n X 2 arrays of occupancy after each element moves to some horizontal or vertical neighbor, without consecutive moves in the same direction.
  • A221440 (program): Hilltop maps: number of n X 2 binary arrays indicating the locations of corresponding elements not exceeded by any horizontal or antidiagonal neighbor in a random 0..1 n X 2 array.
  • A221441 (program): Hilltop maps: number of n X 3 binary arrays indicating the locations of corresponding elements not exceeded by any horizontal or antidiagonal neighbor in a random 0..1 n X 3 array.
  • A221453 (program): Number of 0..n arrays of length n with each element unequal to at least one neighbor, with new values introduced in 0..n order
  • A221454 (program): Number of 0..3 arrays of length n with each element unequal to at least one neighbor, with new values introduced in 0..3 order.
  • A221455 (program): Number of 0..4 arrays of length n with each element unequal to at least one neighbor, with new values introduced in 0..4 order.
  • A221456 (program): Number of 0..5 arrays of length n with each element unequal to at least one neighbor, with new values introduced in 0..5 order.
  • A221460 (program): Number of 0..n arrays of length n with each element unequal to at least one neighbor, starting with 0
  • A221461 (program): Number of 0..6 arrays of length n with each element unequal to at least one neighbor, starting with 0
  • A221462 (program): Number of 0..7 arrays of length n with each element unequal to at least one neighbor, starting with 0
  • A221463 (program): T(n,k)=Number of 0..k arrays of length n with each element unequal to at least one neighbor, starting with 0
  • A221464 (program): Number of 0..n arrays of length 5 with each element unequal to at least one neighbor, starting with 0.
  • A221465 (program): Number of 0..n arrays of length 6 with each element unequal to at least one neighbor, starting with 0.
  • A221466 (program): Number of 0..n arrays of length 7 with each element unequal to at least one neighbor, starting with 0.
  • A221490 (program): Number of primes of the form k*n + k - n, 1 <= k <= n.
  • A221491 (program): Number of primes of the form k*n - k + n, 1 <= k <= n.
  • A221510 (program): Number of 0..3 arrays of length n with each element differing from at least one neighbor by 2 or more, starting with 0.
  • A221519 (program): Number of 0..3 arrays of length n with each element differing from at least one neighbor by 2 or more.
  • A221529 (program): Triangle read by rows: T(n,k) = A000203(k)*A000041(n-k), 1 <= k <= n.
  • A221530 (program): Triangle read by rows: T(n,k) = A000005(k)*A000041(n-k).
  • A221531 (program): Triangle read by rows: T(n,k) = A000005(n-k+1)*A000041(k-1), n>=1, k>=1.
  • A221536 (program): Number of 0..2 arrays of length n with each element differing from at least one neighbor by something other than 1, starting with 0.
  • A221537 (program): Number of 0..3 arrays of length n with each element differing from at least one neighbor by something other than 1, starting with 0.
  • A221543 (program): Number of 0..n arrays of length 5 with each element differing from at least one neighbor by something other than 1, starting with 0.
  • A221564 (program): The number of FO4C3 moves required to restore a packet of n playing cards to its original state (order and orientation), where each move Flips Over the top four (4) as a unit and then Cuts three (3) cards from the top to bottom.
  • A221567 (program): Number of 0..2 arrays of length n with each element differing from at least one neighbor by something other than 1
  • A221568 (program): Number of 0..3 arrays of length n with each element differing from at least one neighbor by something other than 1.
  • A221574 (program): Number of 0..n arrays of length 3 with each element differing from at least one neighbor by something other than 1.
  • A221575 (program): Number of 0..n arrays of length 5 with each element differing from at least one neighbor by something other than 1.
  • A221591 (program): Number of 0..2 arrays of length n with each element differing from at least one neighbor by 1 or less.
  • A221597 (program): Number of 0..n arrays of length 5 with each element differing from at least one neighbor by 1 or less.
  • A221604 (program): Number of n X 3 arrays of occupancy after each element moves to some horizontal or antidiagonal neighbor, without move-in move-out left turns.
  • A221619 (program): Number of n X 4 arrays with each row a permutation of 1..4 having at least as many downsteps as the preceding row.
  • A221651 (program): Numbers divisible by their first digit squared (excluding those whose first digit is 1).
  • A221652 (program): Number of n X 2 arrays of occupancy after each element moves to some horizontal, diagonal or antidiagonal neighbor, without move-in move-out left turns.
  • A221671 (program): Maximum number of squares in a non-constant arithmetic progression (AP) of length n.
  • A221672 (program): Length of shortest non-constant arithmetic progression (AP) containing n squares.
  • A221677 (program): Number of 0..2 arrays of length n with each element differing from at least one neighbor by 1 or less, starting with 0.
  • A221678 (program): Number of 0..3 arrays of length n with each element differing from at least one neighbor by 1 or less, starting with 0.
  • A221684 (program): Number of 0..n arrays of length 5 with each element differing from at least one neighbor by 1 or less, starting with 0
  • A221686 (program): Number of 0..n arrays of length 7 with each element differing from at least one neighbor by 1 or less, starting with 0.
  • A221714 (program): Numbers written in base 2 with digits rearranged to be in decreasing order.
  • A221718 (program): Floor(sqrt(3*2^n)).
  • A221719 (program): a(n) = 3*2^n - Fibonacci(n+3) - 1.
  • A221720 (program): An avoidance sequence for a pair of tree patterns that is not the avoidance sequence for any set of permutations.
  • A221731 (program): Number of n X 2 arrays of occupancy after each element stays put or moves to some horizontal or antidiagonal neighbor, without move-in move-out left turns.
  • A221740 (program): a(n) = -4*((n-1)*(n+1)^(n+1)+1)/(((-1)^n-3)*n^3).
  • A221741 (program): a(n) = -4*(((n+1)^(n+1)-(n+1))/((n+1)-1)^2-1)/((-3+(-1)^n)*n).
  • A221756 (program): Number of 2 X n arrays of occupancy after each element moves to some horizontal or antidiagonal neighbor, without move-in move-out straight through or left turns.
  • A221762 (program): Numbers m such that 11*m^2 + 5 is a square.
  • A221763 (program): Numbers m such that 11*m^2 - 7 is a square.
  • A221764 (program): Number of n X 3 arrays of occupancy after each element moves to some horizontal or vertical neighbor, without 2-loops or left turns.
  • A221783 (program): Number of nX4 arrays of occupancy after each element moves to some horizontal or antidiagonal neighbor, without 2-loops or left turns
  • A221793 (program): Partial sums of cuban primes A002407, that is, primes equal to the difference of two consecutive cubes.
  • A221795 (program): Number of n X 2 arrays of occupancy after each element moves to some horizontal or vertical neighbor, without move-in move-out straight through or left turns.
  • A221829 (program): Number of 2 X n arrays of occupancy after each element moves to some horizontal, vertical or antidiagonal neighbor, without 2-loops or left turns.
  • A221837 (program): Number of integer Heron triangles of height n such that the angles adjacent to the base are not right.
  • A221838 (program): Number of integer Heron triangles of height n.
  • A221840 (program): Number of sets of n squares providing dissections of a square.
  • A221855 (program): Number of cyclotomic cosets of 13 mod 10^n.
  • A221859 (program): Expansion of (1-3*x+x^2)*(1-2*x)/(1-9*x+28*x^2-35*x^3+15*x^4-x^5).
  • A221862 (program): Expansion of (1-3*x+x^2)*(1-x)/(1-9*x+28*x^2-35*x^3+15*x^4-x^5).
  • A221863 (program): Expansion of (1-3*x+x^2)/(1-9*x+28*x^2-35*x^3+15*x^4-x^5).
  • A221864 (program): Number of forests (sets) of rooted labeled trees on {1,2,…,n} such that the node with label 1 is in the same rooted tree as the node with label 2.
  • A221874 (program): Numbers m such that 10*m^2 + 6 is a square.
  • A221875 (program): Numbers m such that 10*m^2 - 6 is a square.
  • A221876 (program): T(n,k) is the number of order-preserving full contraction mappings (of an n-chain) with exactly k fixed points.
  • A221877 (program): Number of order-preserving or order-reversing full contraction mappings (of an n-chain) with height exactly k.
  • A221879 (program): Triangle T(n,k) read by rows: Number of order-reversing full contraction mappings (of an n-chain) with 1 fixed point and height exactly k.
  • A221880 (program): Number of order-preserving or order-reversing full contraction mappings (of an n-chain) with exactly 1 fixed point.
  • A221881 (program): Number of order-preserving or order-reversing full contraction mappings (of an n-chain) with (right) waist exactly k.
  • A221882 (program): Number of order-preserving or order-reversing full contraction mappings of an n-chain.
  • A221902 (program): Primes of the form 2*n^2 + 10*n + 3.
  • A221903 (program): Primes of the form 2*n^2 + 42*n + 19.
  • A221904 (program): 9^n + 10^n.
  • A221905 (program): 3^n + 3*n.
  • A221906 (program): 4^n + 4*n.
  • A221907 (program): 5^n + 5*n.
  • A221908 (program): 6^n + 6*n.
  • A221909 (program): 7^n + 7*n.
  • A221910 (program): a(n) = 8^n + 8*n.
  • A221911 (program): 9^n + 9*n.
  • A221912 (program): Partial sums of floor(n/12).
  • A221913 (program): Array of coefficients of numerator polynomials (divided by x) of the n-th approximation of the continued fraction x/(1+x/(2+x/(3+…
  • A221917 (program): Difference between area/L^2 and perimeter/L, with some length unit L, of a rectangle n X m, n >= m >= 0.
  • A221918 (program): Triangle of denominators of sum of two unit fractions: 1/n + 1/m, n >= m >= 1.
  • A221919 (program): Triangle of numerators of sum of two unit fractions: 1/n + 1/m, n >= m >= 1.
  • A221920 (program): a(n) = 3*n/gcd(3*n, n+3), n >= 3.
  • A221921 (program): a(n) = 4*n/gcd(4*n,n+4), n >= 4.
  • A221942 (program): a(n) = floor(sqrt(5*2^n)).
  • A221943 (program): Floor(sqrt(7*2^n)).
  • A221944 (program): Floor(sqrt(2*3^n)).
  • A221945 (program): a(n) = floor(sqrt(2*5^n)).
  • A221946 (program): a(n) = floor(sqrt(2*7^n)).
  • A221948 (program): Expansion of (x-5*x^2+11*x^3-12*x^4+7*x^5-2*x^6+x^7) / (1-6*x+15*x^2-20*x^3+15*x^4-6*x^5+x^6).
  • A221949 (program): Expansion of (-x+2*x^2-x^3-x^4-2*x^5)/(-1+3*x-2*x^2-x^4+x^5).
  • A221950 (program): G.f.: 1/(1 - x - x^2 - 2*x^3 - 3*x^4 - 2*x^5 - x^6).
  • A221952 (program): Number of subgroups of C_5 X C_n.
  • A221953 (program): a(n) = 5^(n-1) * n! * Catalan(n-1).
  • A221954 (program): a(n) = 3^(n-1) * n! * Catalan(n-1).
  • A221955 (program): a(n) = 6^(n-1) * n! * Catalan(n-1).
  • A221957 (program): Number of n X n rook placements avoiding the pattern 012.
  • A221962 (program): Number of -3..3 arrays of length n with the sum ahead of each element differing from the sum following that element by 3 or less.
  • A221963 (program): Number of -4..4 arrays of length n with the sum ahead of each element differing from the sum following that element by 4 or less.
  • A221968 (program): Number of -n..n arrays of length 5 with the sum ahead of each element differing from the sum following that element by n or less.
  • A221969 (program): Number of -n..n arrays of length 6 with the sum ahead of each element differing from the sum following that element by n or less.
  • A221975 (program): Triangle read by rows of the numbers that are the sum of some consecutive Mersenne numbers A000225.
  • A221992 (program): Number of binary arrays indicating the locations of trailing edge maxima of a random length-n 0..1 array extended with zeros and convolved with 1,4,6,4,1.
  • A222001 (program): Number of n X 3 arrays with each row a permutation of 1..3 having at least as many downsteps as the preceding row, with rows in lexicographically nonincreasing order.
  • A222021 (program): Number of binary arrays indicating the locations of trailing edge maxima of a random length-n 0..2 array extended with zeros and convolved with 1,3,3,1.
  • A222030 (program): Primes and quarter-squares.
  • A222050 (program): G.f. satisfies: A(x) = sqrt(1 + 2*x*A(x)^4 + 3*x^2*A(x)^6).
  • A222051 (program): Central terms in rows of triangle A220178.
  • A222052 (program): a(n) = A222051(n)/binomial(2*n,n), the central terms in rows of triangle A220178 divided by the central binomial coefficients.
  • A222066 (program): Decimal expansion of 1/sqrt(128).
  • A222067 (program): Decimal expansion of 1/(8*sqrt(3)).
  • A222068 (program): Decimal expansion of (1/16)*Pi^2.
  • A222071 (program): Decimal expansion of (1/105)*Pi^3.
  • A222072 (program): Decimal expansion of (1/384)*Pi^4.
  • A222073 (program): Decimal expansion of (32/25515)*Pi^4.
  • A222074 (program): Decimal expansion of (1/1920)*Pi^5.
  • A222080 (program): G.f.: 1 = Sum_{n>=0} a(n) * x^n * (1 - (2*n+1)*x)^2.
  • A222084 (program): Number of the least divisors of n whose LCM is equal to n.
  • A222085 (program): Sum of the least divisors of n whose LCM is equal to n.
  • A222098 (program): Number of n X 2 0..5 arrays with entries increasing mod 6 by 0, 1, 2 or 3 rightwards and downwards, starting with upper left zero.
  • A222115 (program): a(n) = 1 + Sum_{k=1..n} binomial(n,k) * sigma(k).
  • A222121 (program): Number of binary arrays indicating the locations of trailing edge maxima of a random length-n 0..2 array extended with zeros and convolved with 1,2,1.
  • A222122 (program): Number of binary arrays indicating the locations of trailing edge maxima of a random length-n 0..3 array extended with zeros and convolved with 1,2,1.
  • A222123 (program): Number of binary arrays indicating the locations of trailing edge maxima of a random length-n 0..4 array extended with zeros and convolved with 1,2,1.
  • A222132 (program): Decimal expansion of sqrt(4 + sqrt(4 + sqrt(4 + sqrt(4 + … )))).
  • A222133 (program): Decimal expansion of sqrt(4 - sqrt(4 - sqrt(4 - sqrt(4 - … )))).
  • A222134 (program): Decimal expansion of sqrt(5 + sqrt(5 + sqrt(5 + sqrt(5 + … )))).
  • A222135 (program): Decimal expansion of sqrt(5 - sqrt(5 - sqrt(5 - sqrt(5 - … )))).
  • A222138 (program): Number of nX2 0..4 arrays with no entry increasing mod 5 by 4 rightwards or downwards, starting with upper left zero
  • A222160 (program): Number of (n+2) X 1 arrays of occupancy after each element moves up to +-2 places but not 0 and without 2-loops.
  • A222170 (program): a(n) = n^2 + 2*floor(n^2/3).
  • A222171 (program): Decimal expansion of Pi^2/24.
  • A222182 (program): Numbers m such that 2*m+11 is a square.
  • A222210 (program): In the number n, replace all (decimal) digits ‘0’ with ‘1’ and vice versa.
  • A222211 (program): In the number n, replace all (decimal) digits ‘0’ with ‘2’ and vice versa.
  • A222213 (program): Replace all (decimal) digits ‘0’ with ‘4’ and vice versa.
  • A222217 (program): In the number n, replace all (decimal) digits ‘0’ with ‘8’ and vice versa.
  • A222220 (program): In the number n, replace all (decimal) digits ‘1’ with ‘3’ and vice versa.
  • A222221 (program): In the number n, replace all (decimal) digits ‘1’ with ‘4’ and vice versa.
  • A222222 (program): In the number n, replace all (decimal) digits ‘1’ with ‘5’ and vice versa.
  • A222224 (program): In the number n, replace all (decimal) digits ‘1’ with ‘7’ and vice versa.
  • A222225 (program): In the number n, replace all (decimal) digits ‘1’ with ‘8’ and vice versa.
  • A222226 (program): In the number n, replace all (decimal) digits ‘1’ with ‘9’ and vice versa.
  • A222228 (program): In the number n, replace all (decimal) digits ‘2’ with ‘4’ and vice versa.
  • A222229 (program): In the number n, replace all (decimal) digits ‘2’ with ‘5’ and vice versa.
  • A222230 (program): In the number n, replace all (decimal) digits ‘2’ with ‘6’ and vice versa.
  • A222232 (program): In the number n, replace all (decimal) digits ‘2’ with ‘8’ and vice versa.
  • A222233 (program): In the number n, replace all (decimal) digits ‘2’ with ‘9’ and vice versa.
  • A222234 (program): In the number n, replace all (decimal) digits ‘3’ with ‘4’ and vice versa.
  • A222235 (program): In the number n, replace all (decimal) digits ‘3’ with ‘5’ and vice versa.
  • A222236 (program): In the number n, replace all (decimal) digits ‘3’ with ‘6’ and vice versa.
  • A222237 (program): In the number n, replace all (decimal) digits ‘3’ with ‘7’ and vice versa.
  • A222239 (program): In the number n, replace all (decimal) digits ‘3’ with ‘9’ and vice versa.
  • A222240 (program): In the number n, replace all (decimal) digits ‘4’ with ‘5’ and vice versa.
  • A222241 (program): In the number n, replace all (decimal) digits ‘4’ with ‘6’ and vice versa.
  • A222242 (program): In the number n, replace all (decimal) digits ‘4’ with ‘7’ and vice versa.
  • A222243 (program): In the number n, replace all (decimal) digits ‘4’ with ‘8’ and vice versa.
  • A222245 (program): In the number n, replace all (decimal) digits ‘5’ with ‘6’ and vice versa.
  • A222246 (program): In the number n, replace all (decimal) digits ‘5’ with ‘7’ and vice versa.
  • A222247 (program): In the number n, replace all (decimal) digits ‘5’ with ‘8’ and vice versa.
  • A222248 (program): In the number n, replace all (decimal) digits ‘5’ with ‘9’ and vice versa.
  • A222249 (program): In the number n, replace all (decimal) digits ‘6’ with ‘7’ and vice versa.
  • A222250 (program): In the number n, replace all (decimal) digits ‘6’ with ‘8’ and vice versa.
  • A222251 (program): In the number n, replace all (decimal) digits ‘6’ with ‘9’ and vice versa.
  • A222252 (program): In the number n, replace all (decimal) digits ‘7’ with ‘8’ and vice versa.
  • A222253 (program): In the number n, replace all (decimal) digits ‘7’ with ‘9’ and vice versa.
  • A222254 (program): In the number n, replace all (decimal) digits ‘8’ with ‘9’ and vice versa.
  • A222256 (program): Lexicographically earliest injective sequence of nonnegative integers such that the sum of 6 consecutive terms is always divisible by 6.
  • A222257 (program): Lexicographically earliest injective sequence of positive integers such that the sum of 6 consecutive terms is always divisible by 6.
  • A222258 (program): Lexicographically earliest injective sequence of nonnegative integers such that the sum of 8 consecutive terms is always divisible by 8.
  • A222259 (program): Lexicographically earliest injective sequence of positive integers such that the sum of 8 consecutive terms is always divisible by 8.
  • A222260 (program): Lexicographically earliest injective sequence of nonnegative integers such that the sum of 10 consecutive terms is always divisible by 10.
  • A222261 (program): Lexicographically earliest injective sequence of positive integers such that the sum of 10 consecutive terms is always divisible by 10.
  • A222283 (program): Number of nX1 0..1 arrays with exactly floor(nX1/2) elements unequal to at least one horizontal or vertical neighbor, with new values introduced in row major 0..1 order
  • A222308 (program): Let P be a one-move “rider” with move set M={(1,2)}; a(n) is the number of non-attacking positions of two indistinguishable pieces P on an n X n board.
  • A222312 (program): a(n) = n + A001222(n) - 1.
  • A222329 (program): Number of binary arrays indicating the locations of trailing edge maxima of a random length-n 0..3 array extended with zeros and convolved with 1,1.
  • A222330 (program): Number of binary arrays indicating the locations of trailing edge maxima of a random length-n 0..4 array extended with zeros and convolved with 1,1.
  • A222331 (program): Number of binary arrays indicating the locations of trailing edge maxima of a random length-n 0..5 array extended with zeros and convolved with 1,1.
  • A222335 (program): Number of nX2 0..6 arrays with no entry increasing mod 7 by 6 rightwards or downwards, starting with upper left zero
  • A222341 (program): Number of (n+4) X 1 arrays of occupancy after each element moves up to +-4 places including 0.
  • A222346 (program): Number of (n+2) X 1 arrays of occupancy after each element moves up to +-n places including 0.
  • A222361 (program): Fibonacci-Legendre quotients: (Fibonacci(p) - L(p/5)) / p, where p = prime(n) and L(p/5) is the Legendre symbol.
  • A222382 (program): Sum of neighbor maps: number of n X 3 binary arrays indicating the locations of corresponding elements equal to the sum mod 3 of their horizontal and antidiagonal neighbors in a random 0..2 n X 3 array.
  • A222390 (program): Nonnegative integers m such that 10*m*(m+1)+1 is a square.
  • A222393 (program): Nonnegative integers m such that 18*m*(m+1)+1 is a square.
  • A222403 (program): Triangle read by rows: left and right edges are A000217, interior entries are filled in using the Pascal triangle rule.
  • A222404 (program): Triangle read by rows: left and right edges are A002378, interior entries are filled in using the Pascal triangle rule.
  • A222405 (program): Triangle read by rows: left and right edges are A002061 (1,3,7,13,21,…), interior entries are filled in using the Pascal triangle rule.
  • A222407 (program): Digital roots of tribonacci numbers A000073.
  • A222408 (program): Partial sums of A008531, or crystal ball sequence for {A_4}* lattice.
  • A222409 (program): Numbers of the form 8n + [0,3,6,4,7].
  • A222410 (program): Partial sums of A008534, or crystal ball sequence for {A_6}* lattice.
  • A222416 (program): If n = Product (p_j^k_j) then a(n) = Sum (p_j^k_j) (a(1) = 1 by convention).
  • A222423 (program): Sum of (n AND k) for k = 0, 1, 2, …, n, where AND is the bitwise AND operator.
  • A222439 (program): Number of n X 3 0..3 arrays with entries increasing mod 4 by 0, 1 or 2 rightwards and downwards, starting with upper left zero.
  • A222463 (program): n*5/gcd(n*5,n+5), n >= 5.
  • A222464 (program): a(n) = (n+6)/gcd(n*6,n+6), n >= 6.
  • A222465 (program): a(n) = 4*n^2 + 3.
  • A222466 (program): Decimal expansion of the limit of the continued fraction 1/(1+2/(2+2/(3+2/(4+… in terms of Bessel functions.
  • A222467 (program): Denominator sequence of the n-th convergent of the continued fraction 1/(1 + 2/(2 + 2/(3 + 2/(4 + …
  • A222468 (program): Numerator sequence of the n-th convergent of the continued fraction 1/(1+2/(2+2/(3+2/(4+…
  • A222469 (program): Denominator sequence of the n-th convergent of the continued fraction 1/(1 - 2/(2 - 2/(3 - 2/(4 - …)))).
  • A222470 (program): Numerator sequence of the n-th convergent of the continued fraction 1/(1-2/(2-2/(3-2/(4-…
  • A222471 (program): Decimal expansion of the negative of the limit of the continued fraction 1/(1-2/(2-2/(3-2/(4-… in terms of Bessel functions.
  • A222472 (program): Numerator sequence of the n-th convergent of the continued fraction 1/(1+3/(2+3/(3+3/(4+…
  • A222480 (program): Decimal expansion of cos(1)/(1+cos(1)).
  • A222526 (program): O.g.f.: Sum_{n>=0} (n^6)^n * exp(-n^6*x) * x^n / n!.
  • A222527 (program): O.g.f.: Sum_{n>=0} (n^7)^n * exp(-n^7*x) * x^n / n!.
  • A222528 (program): O.g.f.: Sum_{n>=0} (n^8)^n * exp(-n^8*x) * x^n / n!.
  • A222548 (program): a(n) = Sum_{k=1..n} floor(n/k)^2.
  • A222559 (program): a(0) = 0. If n is odd, a(n) = a(n-1) * n, otherwise a(n) = a(n-1) + n.
  • A222565 (program): Primes that are the largest anti-divisor of primes.
  • A222588 (program): Composites of the form 2^n-1 or 2^n+1 that are non-multiples of 3.
  • A222591 (program): Numerators of (n*(n - 3)/6) + 1, arising as the maximum possible number of triple lines for an n-element set.
  • A222609 (program): Decimal expansion of the dimensionless coefficient of Stefan-Boltzmann constant.
  • A222618 (program): Multiples of 10 that are sum of two consecutive primes.
  • A222621 (program): a(n) = (2n-1)^(2n).
  • A222627 (program): Poly-Cauchy numbers c_n^(-2) (for definition see Comments lines).
  • A222641 (program): Number of iterations in Collatz (3x+1) trajectory of n to reach 1 from the highest term.
  • A222655 (program): a(n) = 16n^4 + 4.
  • A222657 (program): a(n) = 2 * floor( (2*n + 1) / 3) + 1.
  • A222684 (program): Number of nX2 0..2 arrays with exactly floor(nX2/2) elements unequal to at least one horizontal or antidiagonal neighbor, with new values introduced in row major 0..2 order
  • A222716 (program): Numbers which are both the sum of n+1 consecutive triangular numbers and the sum of the n-1 immediately following triangular numbers.
  • A222724 (program): Palindromic nonprime numbers starting with a digit 1.
  • A222739 (program): Partial sums of the first 10^n terms in A181482.
  • A222740 (program): Denominators of 1/16 - 1/(4 + 8*n)^2.
  • A222763 (program): Number of nX2 0..1 arrays with exactly floor(nX2/2) elements unequal to at least one horizontal or antidiagonal neighbor, with new values introduced in row major 0..1 order
  • A222776 (program): Number of n X 1 0..6 arrays with no element equal to another at a city block distance of exactly two, and new values 0..6 introduced in row major order.
  • A222822 (program): Number of idempotent 3X3 0..n matrices
  • A222834 (program): Number of n X 4 0..3 arrays with no element equal to another at a city block distance of exactly two, and new values 0..3 introduced in row major order.
  • A222867 (program): Number of n X 1 0..5 arrays with no element equal to another at a city block distance of exactly two, and new values 0..5 introduced in row major order.
  • A222868 (program): Number of n X 2 0..5 arrays with no element equal to another at a city block distance of exactly two, and new values 0..5 introduced in row major order.
  • A222890 (program): Number of n X 1 0..7 arrays with no element equal to another at a city block distance of exactly two, and new values 0..7 introduced in row major order.
  • A222939 (program): Number of n X 1 0..4 arrays with no element equal to another at a city block distance of exactly two, and new values 0..4 introduced in row major order.
  • A222940 (program): Number of n X 2 0..4 arrays with no element equal to another at a city block distance of exactly two, and new values 0..4 introduced in row major order.
  • A222941 (program): Number of nX3 0..4 arrays with no element equal to another at a city block distance of exactly two, and new values 0..4 introduced in row major order
  • A222945 (program): Number of distinct sums i+j+k with |i|, |j|, |k|, |i*j*k| <= n.
  • A222946 (program): Triangle for hypotenuses of primitive Pythagorean triangles.
  • A222947 (program): Number of distinct sums i+j+k with |i|, |j|, |k|, |i*j*k| <= n and gcd(i,j,k) <= 1.
  • A222963 (program): a(n) = (p-3)*(p+3)/4 where p is the n-th prime.
  • A222964 (program): Numbers n such that 25n+36 is a square.
  • A222993 (program): Number of n X 2 0..2 arrays with successive rows and columns fitting to straight lines with nondecreasing slope, with a single point array taken as having zero slope
  • A223024 (program): Numbers n such that 3^n is odious (A000069).
  • A223025 (program): Gives the column number which contains n in the dual Wythoff array (beginning the column count at 1).
  • A223082 (program): Number of n-digit numbers N with distinct digits such that N divides the reversal of N.
  • A223083 (program): Trajectory of 64 under the map n-> A006369(n).
  • A223084 (program): Trajectory of 80 under the map n-> A006369(n).
  • A223085 (program): Trajectory of 82 under the map n-> A006369(n).
  • A223086 (program): Trajectory of 64 under the map n-> A006368(n).
  • A223087 (program): Trajectory of 80 under the map n-> A006368(n).
  • A223088 (program): Trajectory of 82 under the map n-> A006368(n).
  • A223089 (program): Numbers n, written in base 8, with the property that if the base-8 representation of n is read backwards, the result is 5*n.
  • A223092 (program): Triangle read by rows: let T(n,k) (for n >= 0, 0 <= k <= n) be the number of walks from (0,0) to (n,k) using steps (1,1), (1,0), (1,-1) and (0,-1); n-th row of triangle gives T(n,n), T(n,n-1), …, T(n,0).
  • A223133 (program): Number of distinct sums i+j+k with i,j,k >= 0, i*j*k <= n and gcd(i,j,k) <= 1.
  • A223134 (program): Number of distinct sums i+j+k with i,j,k >= 0, i*j*k <= n.
  • A223139 (program): Decimal expansion of (sqrt(13) - 1)/2.
  • A223140 (program): Decimal expansion of (sqrt(29) + 1)/2.
  • A223141 (program): Decimal expansion of (sqrt(29) - 1)/2.
  • A223173 (program): Poly-Cauchy numbers c_3^(-n).
  • A223181 (program): Rolling icosahedron footprints: number of n X 3 0..11 arrays starting with 0 where 0..11 label vertices of an icosahedron and every array movement to a horizontal, vertical or antidiagonal neighbor moves along an icosahedral edge.
  • A223197 (program): Rolling cube footprints: number of n X 3 0..5 arrays starting with 0 where 0..5 label faces of a cube and every array movement to a horizontal or vertical neighbor moves across a corresponding cube edge.
  • A223198 (program): Rolling cube footprints: number of n X 4 0..5 arrays starting with 0 where 0..5 label faces of a cube and every array movement to a horizontal or vertical neighbor moves across a corresponding cube edge.
  • A223204 (program): Rolling icosahedron face footprints: number of n X 3 0..19 arrays starting with 0 where 0..19 label faces of an icosahedron and every array movement to a horizontal or vertical neighbor moves across an icosahedral edge.
  • A223205 (program): Rolling icosahedron face footprints: number of n X 4 0..19 arrays starting with 0 where 0..19 label faces of an icosahedron and every array movement to a horizontal or vertical neighbor moves across an icosahedral edge.
  • A223211 (program): 3 X 3 X 3 triangular graph coloring a rectangular array: number of n X 1 0..5 arrays where 0..5 label nodes of a graph with edges 0,1 0,2 1,2 1,3 1,4 2,4 3,4 2,5 4,5 and every array movement to a horizontal or vertical neighbor moves along an edge of this graph.
  • A223212 (program): 3X3X3 triangular graph coloring a rectangular array: number of nX2 0..5 arrays where 0..5 label nodes of a graph with edges 0,1 0,2 1,2 1,3 1,4 2,4 3,4 2,5 4,5 and every array movement to a horizontal or vertical neighbor moves along an edge of this graph
  • A223228 (program): Rolling icosahedron footprints: number of n X 3 0..11 arrays starting with 0 where 0..11 label vertices of an icosahedron and every array movement to a horizontal, diagonal or antidiagonal neighbor moves along an icosahedral edge.
  • A223240 (program): 3-loop graph coloring a rectangular array: number of n X 1 0..6 arrays where 0..6 label nodes of a graph with edges 0,1 1,2 2,0 0,3 3,4 4,0 0,5 5,6 6,0 and every array movement to a horizontal or vertical neighbor moves along an edge of this graph.
  • A223241 (program): 3-loop graph coloring a rectangular array: number of n X 2 0..6 arrays where 0..6 label nodes of a graph with edges 0,1 1,2 2,0 0,3 3,4 4,0 0,5 5,6 6,0 and every array movement to a horizontal or vertical neighbor moves along an edge of this graph.
  • A223249 (program): Two-loop graph coloring a rectangular array: number of n X 2 0..4 arrays where 0..4 label nodes of a graph with edges 0,1 1,2 2,0 0,3 3,4 4,0 and every array movement to a horizontal or vertical neighbor moves along an edge of this graph.
  • A223265 (program): Rolling cube footprints: number of n X 4 0..5 arrays starting with 0 where 0..5 label faces of a cube and every array movement to a horizontal, diagonal or antidiagonal neighbor moves across a corresponding cube edge.
  • A223270 (program): Rolling cube footprints: number of 2 X n 0..5 arrays starting with 0 where 0..5 label faces of a cube and every array movement to a horizontal, diagonal or antidiagonal neighbor moves across a corresponding cube edge.
  • A223271 (program): Rolling cube footprints: number of 3 X n 0..5 arrays starting with 0 where 0..5 label faces of a cube and every array movement to a horizontal, diagonal or antidiagonal neighbor moves across a corresponding cube edge.
  • A223277 (program): Rolling icosahedron face footprints: number of n X 3 0..19 arrays starting with 0 where 0..19 label faces of an icosahedron and every array movement to a horizontal, diagonal or antidiagonal neighbor moves across an icosahedral edge.
  • A223278 (program): Rolling icosahedron face footprints: number of n X 4 0..19 arrays starting with 0 where 0..19 label faces of an icosahedron and every array movement to a horizontal, diagonal or antidiagonal neighbor moves across an icosahedral edge.
  • A223283 (program): Rolling icosahedron face footprints: number of 2 X n 0..19 arrays starting with 0 where 0..19 label faces of an icosahedron and every array movement to a horizontal, diagonal or antidiagonal neighbor moves across an icosahedral edge.
  • A223290 (program): 4-loop graph coloring a rectangular array: number of n X 1 0..8 arrays where 0..8 label nodes of a graph with edges 0,1 1,2 2,0 0,3 3,4 4,0 0,5 5,6 6,0 0,7 7,8 8,0 and every array movement to a horizontal or vertical neighbor moves along an edge of this graph.
  • A223291 (program): 4-loop graph coloring a rectangular array: number of n X 2 0..8 arrays where 0..8 label nodes of a graph with edges 0,1 1,2 2,0 0,3 3,4 4,0 0,5 5,6 6,0 0,7 7,8 8,0 and every array movement to a horizontal or vertical neighbor moves along an edge of this graph.
  • A223299 (program): 4 X 4 X 4 triangular graph coloring a rectangular array: number of n X 2 0..9 arrays where 0..9 label nodes of a graph with edges 0,1 0,2 1,2 1,3 1,4 2,4 3,4 2,5 4,5 3,6 3,7 4,7 6,7 4,8 5,8 7,8 5,9 8,9 and every array movement to a horizontal or vertical neighbor moves along an edge of this graph.
  • A223322 (program): Rolling icosahedron footprints: number of 2 X n 0..11 arrays starting with 0 where 0..11 label vertices of an icosahedron and every array movement to a horizontal or antidiagonal neighbor moves along an icosahedral edge.
  • A223337 (program): 5 X 5 X 5 triangular graph coloring a rectangular array: number of n X 1 0..14 arrays where 0..14 label nodes of a graph with edges 0,1 0,2 1,2 1,3 1,4 2,4 3,4 2,5 4,5 3,6 3,7 4,7 6,7 4,8 5,8 7,8 5,9 8,9 6,10 6,11 7,11 10,11 7,12 8,12 11,12 11,12 8,13 9,13 12,13 9,14 13,14 and every array movement to a horizontal or vertical neighbor moves along an edge of this graph.
  • A223346 (program): 3 X 3 X 3 triangular graph without horizontal edges coloring a rectangular array: number of n X 1 0..5 arrays where 0..5 label nodes of a graph with edges 0,1 0,2 1,3 1,4 2,4 2,5 and every array movement to a horizontal or vertical neighbor moves along an edge of this graph.
  • A223354 (program): Rolling cube footprints: number of n X 5 0..5 arrays starting with 0 where 0..5 label faces of a cube and every array movement to a horizontal or antidiagonal neighbor moves across a corresponding cube edge.
  • A223363 (program): 6 X 6 X 6 triangular graph coloring a rectangular array: number of n X 1 0..20 arrays where 0..20 label nodes of the fully triangulated graph and every array movement to a horizontal or vertical neighbor moves along an edge of this graph.
  • A223372 (program): 3X3 square grid graph coloring a rectangular array: number of nX1 0..8 arrays where 0..8 label nodes of the square grid graph and every array movement to a horizontal or vertical neighbor moves along an edge of this graph
  • A223373 (program): 3 X 3 square grid graph coloring a rectangular array: number of n X 2 0..8 arrays where 0..8 label nodes of the square grid graph and every array movement to a horizontal or vertical neighbor moves along an edge of this graph.
  • A223381 (program): Number of n X 2 0..2 arrays with all horizontally or vertically connected equal values in a straight line, and new values 0..2 introduced in row major order.
  • A223395 (program): 4 X 4 square grid graph coloring a rectangular array: number of n X 1 0..15 arrays where 0..15 label nodes of the square grid graph and every array movement to a horizontal or vertical neighbor moves along an edge of this graph.
  • A223417 (program): 3-level binary fanout graph coloring a rectangular array: number of nX1 0..6 arrays where 0..6 label nodes of a graph with edges 0,1 1,3 1,4 0,2 2,5 2,6 and every array movement to a horizontal or vertical neighbor moves along an edge of this graph
  • A223443 (program): 4-level binary fanout graph coloring a rectangular array: number of n X 2 0..14 arrays where 0..14 label nodes of a graph with edges 0,1 1,3 3,5 3,6 1,4 4,7 4,8 0,2 2,9 9,11 9,12 2,10 10,13 10,14 and every array movement to a horizontal or vertical neighbor moves along an edge of this graph.
  • A223451 (program): Number of idempotent 2X2 -n..n matrices of rank 1
  • A223454 (program): Number of idempotent 2 X 2 -n..n matrices.
  • A223474 (program): Least positive multiple of n that when written in base 10 has digits in nonincreasing order.
  • A223475 (program): Least k such that the decimal representation of k*n has digits in nonincreasing order.
  • A223477 (program): Rolling icosahedron face footprints: number of n X 5 0..19 arrays starting with 0 where 0..19 label faces of an icosahedron and every array movement to a horizontal or antidiagonal neighbor moves across an icosahedral edge.
  • A223490 (program): Smallest Fermi-Dirac factor of n.
  • A223491 (program): Largest Fermi-Dirac factor of n.
  • A223499 (program): Petersen graph (3,1) coloring a rectangular array: number of n X 3 0..5 arrays where 0..5 label nodes of a graph with edges 0,1 0,3 3,5 3,4 1,2 1,4 4,5 2,0 2,5 and every array movement to a horizontal, diagonal or antidiagonal neighbor moves along an edge of this graph, with the array starting at 0.
  • A223505 (program): Petersen graph (3,1) coloring a rectangular array: number of 2 X n 0..5 arrays where 0..5 label nodes of a graph with edges 0,1 0,3 3,5 3,4 1,2 1,4 4,5 2,0 2,5 and every array movement to a horizontal, diagonal or antidiagonal neighbor moves along an edge of this graph, with the array starting at 0.
  • A223523 (program): Triangle S(n, k) by rows: coefficients of 2^((n-1)/2))*(x^(1/2)*d/dx)^n, where n = 1, 3, 5, …
  • A223524 (program): Triangle S(n, k) by rows: coefficients of 2^(n/2)*(x^(1/2)*d/dx)^n, where n =0, 2, 4, 6, …
  • A223544 (program): Triangle T(n,k), 0 < k <= n, T(n,1) = n - 1, T(n,k) = T(n,k-1) + n; read by rows.
  • A223552 (program): Petersen graph (3,1) coloring a rectangular array: number of n X 4 0..5 arrays where 0..5 label nodes of a graph with edges 0,1 0,3 3,5 3,4 1,2 1,4 4,5 2,0 2,5 and every array movement to a horizontal or antidiagonal neighbor moves along an edge of this graph, with the array starting at 0.
  • A223557 (program): Petersen graph (3,1) coloring a rectangular array: number of 2 X n 0..5 arrays where 0..5 label nodes of a graph with edges 0,1 0,3 3,5 3,4 1,2 1,4 4,5 2,0 2,5 and every array movement to a horizontal or antidiagonal neighbor moves along an edge of this graph, with the array starting at 0.
  • A223563 (program): Number of n X n 0..1 arrays with antidiagonals unimodal
  • A223564 (program): Number of nX3 0..1 arrays with antidiagonals unimodal
  • A223565 (program): Number of nX4 0..1 arrays with antidiagonals unimodal
  • A223571 (program): Number of nX3 0..2 arrays with antidiagonals unimodal
  • A223577 (program): Positive integers n for which there is exactly one negative integer m such that -n = floor(cot(Pi/(2*m))).
  • A223578 (program): Positive integers n for which f(-n-1) < f(-n) < f(-n+1), where f(m) = floor(cot(Pi/(2m))).
  • A223580 (program): Number of nX3 0..3 arrays with antidiagonals unimodal
  • A223659 (program): Number of n X 1 [0..3] arrays with row sums unimodal and column sums inverted unimodal.
  • A223687 (program): Petersen graph (8,2) coloring a rectangular array: number of n X 3 0..15 arrays where 0..15 label nodes of a graph with edges 0,1 0,8 8,14 8,10 1,2 1,9 9,15 9,11 2,3 2,10 10,12 3,4 3,11 11,13 4,5 4,12 12,14 5,6 5,13 13,15 6,7 6,14 7,0 7,15 and every array movement to a horizontal or antidiagonal neighbor moves along an edge of this graph.
  • A223711 (program): Number of n X 2 0..1 arrays with row sums and column sums unimodal.
  • A223718 (program): Number of nX1 0..2 arrays with rows, antidiagonals and columns unimodal.
  • A223719 (program): Number of n X 2 0..2 arrays with rows, antidiagonals and columns unimodal.
  • A223756 (program): Number of n X 2 0..3 arrays with rows, antidiagonals and columns unimodal.
  • A223764 (program): Number of n X 2 0..1 arrays with rows, columns and antidiagonals unimodal and diagonals nondecreasing.
  • A223772 (program): Number of n X 3 0..1 arrays with rows and columns unimodal and antidiagonals nondecreasing.
  • A223833 (program): Number of n X 3 0..1 arrays with rows and antidiagonals unimodal and columns nondecreasing.
  • A223834 (program): Number of n X 4 0..1 arrays with rows and antidiagonals unimodal and columns nondecreasing.
  • A223839 (program): Number of 3 X n 0..1 arrays with rows and antidiagonals unimodal and columns nondecreasing.
  • A223851 (program): Poly-Cauchy numbers c_4^(-n).
  • A223906 (program): Poly-Cauchy numbers of the second kind -hat c_3^(-n).
  • A223907 (program): Poly-Cauchy numbers of the second kind hat c_4^(-n).
  • A223909 (program): Numbers for which the maximal run of 1’s in their binary representation contains odd number of 1’s.
  • A223910 (program): Numbers for which the maximal run of 1’s in their binary representation contains even number of 1’s.
  • A223925 (program): a(2n+1) = 2*n-1; a(2n)= 4^n.
  • A223940 (program): Sums of antidiagonals of A223968.
  • A223950 (program): Number of 3 X n 0..1 arrays with diagonals and antidiagonals unimodal and rows nondecreasing.
  • A223962 (program): Number of 2 X n 0..3 arrays with antidiagonals unimodal and rows and diagonals nondecreasing.
  • A224000 (program): Number of 2 X n 0..2 arrays with antidiagonals unimodal and rows and diagonals nondecreasing.
  • A224033 (program): Number of n X 3 0..1 arrays with antidiagonals unimodal and rows and diagonals nondecreasing.
  • A224039 (program): Number of 3 X n 0..1 arrays with antidiagonals unimodal and rows and diagonals nondecreasing.
  • A224071 (program): Number of Schroeder paths of semilength n in which there are no (2,0)-steps at level 1.
  • A224072 (program): Odd odious numbers divisible by 3.
  • A224128 (program): Number of n X 3 0..1 arrays with rows nondecreasing and antidiagonals unimodal.
  • A224129 (program): Number of n X 4 0..1 arrays with rows nondecreasing and antidiagonals unimodal.
  • A224134 (program): Number of 3 X n 0..1 arrays with rows nondecreasing and antidiagonals unimodal.
  • A224139 (program): Double 1’s in binary representations of 2*n-1, converting to decimal and dividing by maximal possible power of 3.
  • A224140 (program): Number of n X n 0..1 arrays with rows and antidiagonals unimodal and columns nondecreasing
  • A224141 (program): Number of n X 3 0..1 arrays with rows and antidiagonals unimodal and columns nondecreasing.
  • A224142 (program): Number of n X 4 0..1 arrays with rows and antidiagonals unimodal and columns nondecreasing.
  • A224147 (program): Number of 3 X n 0..1 arrays with rows and antidiagonals unimodal and columns nondecreasing.
  • A224195 (program): Ordered sequence of numbers of form (2^n - 1)*2^m + 1 where n >= 1, m >= 1.
  • A224212 (program): Number of nonnegative solutions to x^2 + y^2 <= n.
  • A224213 (program): Number of nonnegative solutions to x^2 + y^2 + z^2 + u^2 <= n.
  • A224216 (program): Expansion of q * f(-q,-q^7)^2 / (phi(q^2) * psi(-q)) in powers of q where phi(), psi(), f(,) are Ramanujan theta functions.
  • A224217 (program): Numbers b such that b^2 + 4*b + 9 is prime.
  • A224227 (program): a(n) = (1/50)*((15*n^2-20*n+4)*Fibonacci(n)-(5*n^2-6*n)*A000032(n)).
  • A224232 (program): a(n) = n! if n <= 3, otherwise a(n) = 2*(a(n-1) + a(n-3)) + a(n-2).
  • A224233 (program): Decimal expansion of number of inches in a meter.
  • A224234 (program): Decimal expansion of number of feet in a meter.
  • A224235 (program): Decimal expansion of number of yards in a meter.
  • A224247 (program): G.f.: Sum_{n>=1} x^n*(1+x)^d(n), where d(n) is the number of divisors of n (A000005).
  • A224251 (program): Numbers, a(n) where binomial(a(n), 5n-1) == 0 (mod 5) and binomial(a(n), k) != 0 (mod 5) for k != 5n - 1.
  • A224270 (program): Absolute values of the numerators of the third column of ( 0 followed by (mix 0 , A001803(n))/A060818(n) ) and its successive differences.
  • A224271 (program): Number of set partitions of {1,2,…,n} such that the element 1 is in an odd-sized block.
  • A224273 (program): Decimal expansion of Baxter’s four-coloring constant.
  • A224274 (program): a(n) = binomial(4*n,n)/4.
  • A224289 (program): Number of permutations of length n containing exactly 1 occurrence of 123 and 2 occurrences of 132.
  • A224292 (program): Number of permutations of length n avoiding 1234 and containing exactly 1 occurrence of 1243.
  • A224317 (program): a(n) = a(n-1) + 3 - a(n-1)!.
  • A224327 (program): Number of idempotent n X n 0..2 matrices of rank n-1.
  • A224328 (program): Number of idempotent n X n 0..3 matrices of rank n-1
  • A224329 (program): Number of idempotent n X n 0..4 matrices of rank n-1.
  • A224330 (program): Number of idempotent n X n 0..5 matrices of rank n-1.
  • A224331 (program): Number of idempotent n X n 0..6 matrices of rank n-1.
  • A224332 (program): Number of idempotent n X n 0..7 matrices of rank n-1.
  • A224333 (program): T(n,k)=Number of idempotent n X n 0..k matrices of rank n-1
  • A224334 (program): Number of idempotent 3 X 3 0..n matrices of rank 2.
  • A224335 (program): Number of idempotent 4X4 0..n matrices of rank 3.
  • A224336 (program): Number of idempotent 5X5 0..n matrices of rank 4.
  • A224337 (program): Number of idempotent 6X6 0..n matrices of rank 5.
  • A224338 (program): Number of idempotent 7 X 7 0..n matrices of rank 6.
  • A224339 (program): Absolute difference between sum of odd divisors of n^2 and sum of even divisors of n^2.
  • A224340 (program): G.f.: exp( Sum_{n>=1} A113184(n^2)*x^n/n ), where A113184(n) = difference between sum of odd divisors of n and sum of even divisors of n.
  • A224342 (program): Apparently solves the identity: find sequence B that represents the numbers of ordered compositions of n using the terms of A, and vice versa.
  • A224362 (program): Number of partitions of n into a prime and a triangular number.
  • A224363 (program): Primes p such that there are no squares between p and the prime following p.
  • A224364 (program): G.f.: exp( Sum_{n>=1} A064027(n)*x^n/n ), where A064027(n) = (-1)^n*Sum_{d|n}(-1)^d*d^2.
  • A224380 (program): Table read by antidiagonals of numbers of form (2^n -1)*2^(m+2) + 3 where n>=1, m>=1.
  • A224382 (program): Fibonacci-like numbers without positive multiples of 4: a(0) = 0, a(1) = 1, for n>=2, a(n) = a(n-1) + a(n-2) divided by maximal possible power of 4.
  • A224383 (program): Primes of the form (2^n - 1)*(2^(m+2)) + 3 where n >= 1, m >= 1.
  • A224384 (program): a(n) = 1 + 17^n.
  • A224404 (program): Number of n X 3 0..1 arrays with rows unimodal and antidiagonals nondecreasing.
  • A224410 (program): Number of 3 X n 0..1 arrays with rows unimodal and antidiagonals nondecreasing.
  • A224419 (program): Numbers n such that triangular(n) + triangular(2*n) is a square.
  • A224422 (program): Expansion of (1-x)*(1-3*x)/(1-9*x+28*x^2-35*x^3+15*x^4-x^5).
  • A224439 (program): G.f.: A(x) = exp( Sum_{n>=1} sigma(n)^(n-1) * x^n/n ).
  • A224440 (program): a(n) = sigma(n)^(n-1).
  • A224446 (program): Denominators of certain rationals approximating sqrt(3).
  • A224450 (program): Numbers that are the primitive sum of two nonzero squares in exactly one way.
  • A224454 (program): The Wiener index of the linear phenylene with n hexagons.
  • A224455 (program): The hyper-Wiener index of the linear phenylene with n hexagons.
  • A224456 (program): The Wiener index of the cyclic phenylene with n hexagons (n>=3).
  • A224459 (program): The Wiener index of the straight pentachain of n pentagonal rings (see Fig. 2.1 in the A. A. Ali et al. reference).
  • A224467 (program): Numbers n such that 27*n+1 is prime.
  • A224473 (program): (2*5^(2^n) - 1) mod 10^n: a sequence of trimorphic numbers ending in 9.
  • A224474 (program): (2*16^(5^n) - 1) mod 10^n: a sequence of trimorphic numbers ending in 1.
  • A224475 (program): (2*5^(2^n) + (10^n)/2 - 1) mod 10^n: a sequence of trimorphic numbers ending (for n > 1) in 9.
  • A224476 (program): (2*16^(5^n) + (10^n)/2 - 1) mod 10^n: a sequence of trimorphic numbers ending (for n > 1) in 1.
  • A224477 (program): (5^(2^n) + (10^n)/2) mod 10^n: a sequence of trimorphic numbers ending (for n > 1) in 5.
  • A224478 (program): (16^(5^n) + (10^n)/2 - 1) mod 10^n: a sequence of trimorphic numbers ending (for n > 1) in 5.
  • A224479 (program): a(n) = Product_{k=1..n} Product_{i=1..k-1} gcd(k,i).
  • A224481 (program): Positive integers x such that x^2 - 34 is the average of a twin prime pair.
  • A224484 (program): Numbers which are the sum of two positive cubes and divisible by 3.
  • A224486 (program): Numbers k such that 2*k+1 divides 2^k+1.
  • A224489 (program): Smallest k such that k*2*p(n)^2-1 is prime.
  • A224493 (program): Smallest k such that k*2*p(n)^2+1 is prime.
  • A224497 (program): a(n) = sqrt(floor(n/2)! * Product_{k=1..n} Product_{i=1..k-1} gcd(k,i)).
  • A224499 (program): Numbers k such that if 2*k+1 divides 2^k+1 then 2*(k+1)+1 divides 2^(k+1)+1.
  • A224500 (program): Number of ordered full binary trees with labels from a set of at most n labels.
  • A224503 (program): Smallest nontrivial prime power congruent to 1 mod n.
  • A224508 (program): a(n+2) = a(n+1) + a(n) + A*t^n, with A = 1 and t = -2.
  • A224509 (program): Expansion of (1-x)*(1-2*x)*(1-3*x)/(1-9*x+28*x^2-35*x^3+15*x^4-x^5).
  • A224512 (program): Gray code variant of A147582.
  • A224513 (program): Gray code variant of A147562.
  • A224514 (program): Expansion of (1-x)*(1-3*x)*(1-3*x+x^2)/(1-9*x+28*x^2-35*x^3+15*x^4-x^5).
  • A224516 (program): Number of solutions to x^4 - x == 0 (mod n).
  • A224519 (program): For n >= 4, a(n) = (A056899(n) - A056899(n-1))/72, where A056899 lists the primes of the form k^2 + 2.
  • A224520 (program): Numbers a(n) with property a(n) + a(n+4) = 2^(n+4) - 1 = A000225(n+4).
  • A224521 (program): Numbers a(n) with property a(n) + a(n+5) = 2^(n+5) - 1 = A000225(n+5).
  • A224525 (program): Number of idempotent 3 X 3 0..n matrices of rank 1.
  • A224534 (program): Primes numbers that are the sum of three distinct prime numbers.
  • A224535 (program): Odd numbers that are the sum of three distinct prime numbers.
  • A224541 (program): Number of doubly-surjective functions f:[n]->[3].
  • A224544 (program): Number of (n+1) X 3 0..1 matrices with each 2 X 2 subblock idempotent.
  • A224545 (program): Number of (n+1) X 4 0..1 matrices with each 2 X 2 subblock idempotent.
  • A224607 (program): a(n) = A219331(n^2).
  • A224609 (program): Smallest j such that 2*j*prime(n)^3-1 is prime.
  • A224613 (program): a(n) = sigma(6*n).
  • A224644 (program): Number of (n+2) X 3 0..1 matrices with each 3 X 3 subblock having the same population.
  • A224666 (program): Number of 4 X 4 0..n matrices with each 2 X 2 subblock idempotent.
  • A224667 (program): Number of 5 X 5 0..n matrices with each 2 X 2 subblock idempotent.
  • A224668 (program): Number of 6 X 6 0..n matrices with each 2 X 2 subblock idempotent.
  • A224669 (program): Number of (n+1) X 2 0..2 matrices with each 2 X 2 subblock idempotent.
  • A224670 (program): Number of (n+1) X 3 0..2 matrices with each 2 X 2 subblock idempotent
  • A224678 (program): L.g.f.: -log(1 - Sum_{n>=1} x^(n*(n+1)/2)) = Sum_{n>=1} a(n)*x^n/n.
  • A224680 (program): a(n) = A224678(n^2).
  • A224681 (program): G.f.: exp( Sum_{n>=1} A224678(n^2) * x^n/n ).
  • A224692 (program): Expansion of (1+5*x+7*x^2-x^3)/((1-2*x^2)*(1-x)*(1+x)).
  • A224694 (program): Numbers n such that n^2 AND n = 0, where AND is the bitwise logical AND operator.
  • A224701 (program): Table read by antidiagonals of numbers of form (2^n - 1)*2^(m+3) + 5 where n>=1, m>=1.
  • A224703 (program): Numbers divisible by the twice the number of their prime factors (counted with multiplicity), or numbers n divisible by 2*Omega(n).
  • A224705 (program): Composite numbers n divisible by Omega(n)^2 (the square of the number of their prime factors, counted with multiplicity).
  • A224708 (program): The number of unordered partitions {a,b} of n such that a and b are composite.
  • A224709 (program): The number of unordered partitions {a,b} of the even numbers 2n such that a and b are composite.
  • A224710 (program): The number of unordered partitions {a,b} of 2n-1 such that a and b are composite.
  • A224712 (program): The number of unordered partitions {a, b} of n such that a or b is composite and the other is prime.
  • A224713 (program): The number of unordered partitions {a, b} of the even numbers 2n such that a or b is composite and the other is prime.
  • A224714 (program): The number of unordered partitions {a,b} of the odd numbers 2n-1 such that one of a and b is composite and the other is prime.
  • A224715 (program): The number of unordered partitions {a,b} of prime(n) such that a or b is a nonnegative composite and the other is prime.
  • A224731 (program): b(n+1) - b(n) + n where b(n) = A095114(n).
  • A224732 (program): G.f.: exp( Sum_{n>=1} binomial(2*n,n)^n * x^n/n ).
  • A224733 (program): a(n) = binomial(2*n,n)^n.
  • A224734 (program): G.f.: exp( Sum_{n>=1} binomial(2*n,n)^2 * x^n/n ).
  • A224735 (program): G.f.: exp( Sum_{n>=1} binomial(2*n,n)^3 * x^n/n ).
  • A224736 (program): G.f.: exp( Sum_{n>=1} binomial(2*n,n)^4 * x^n/n ).
  • A224738 (program): Number of (n+1) X 2 0..1 matrices with each 2 X 2 permanent equal.
  • A224747 (program): Number of lattice paths from (0,0) to (n,0) that do not go below the x-axis and consist of steps U=(1,1), D=(1,-1) and H=(1,0), where H-steps are only allowed if y=1.
  • A224749 (program): Vauban’s sequence: a(n)=0 if n<=0, a(1)=1; thereafter a(n) = 3*a(n-1) + 6*a(n-2) + 6*a(n-3) + 6*a(n-4) + 6*a(n-5).
  • A224752 (program): a(1)=1; thereafter a(n) = smallest number m such that a(n-1)+m = (a(n-1) followed by the leading digit of m).
  • A224753 (program): a(2)=2; thereafter a(n) = smallest number m such that a(n-1)+m = (a(n-1) followed by the leading digit of m).
  • A224754 (program): a(2)=3; thereafter a(n) = smallest number m such that a(n-1)+m = (a(n-1) followed by the leading digit of m).
  • A224755 (program): a(2)=4; thereafter a(n) = smallest number m such that a(n-1)+m = (a(n-1) followed by the leading digit of m).
  • A224756 (program): a(2)=5; thereafter a(n) = smallest number m such that a(n-1)+m = (a(n-1) followed by the leading digit of m).
  • A224757 (program): a(2)=6; thereafter a(n) = smallest number m such that a(n-1)+m = (a(n-1) followed by the leading digit of m).
  • A224758 (program): a(2)=7; thereafter a(n) = smallest number m such that a(n-1)+m = (a(n-1) followed by the leading digit of m).
  • A224759 (program): a(2)=8; thereafter a(n) = smallest number m such that a(n-1)+m = (a(n-1) followed by the leading digit of m).
  • A224760 (program): a(2)=9; thereafter a(n) = smallest number m such that a(n-1)+m = (a(n-1) followed by the leading digit of m).
  • A224761 (program): a(2)=10; thereafter a(n) = smallest number m such that a(n-1)+m = (a(n-1) followed by the leading digit of m).
  • A224770 (program): Numbers that are the primitive sum of two squares in exactly two ways.
  • A224773 (program): One half of the even terms of A224771.
  • A224777 (program): Triangle with integer geometric mean sqrt(n*m) for 1 <= m <= n, and 0 if sqrt(n*m) is not integer.
  • A224778 (program): One half of the even numbers that are the sum of four nonzero squares.
  • A224779 (program): One half of the even numbers that are a primitive sum of four nonzero squares at least once.
  • A224783 (program): Denominator of Bernoulli(n,1/2) - Bernoulli(n,0).
  • A224785 (program): Expansion of (1+4*x+8*x^2-x^3)/((1-x)*(1+x)*(1-3*x^2)).
  • A224787 (program): Sum of cubes of prime factors of n (counted with multiplicity).
  • A224790 (program): a(n) = 3*9^n + 8.
  • A224796 (program): Pi*n rounded to the nearest integer is prime.
  • A224808 (program): Number of permutations (p(1), p(2), …, p(n)) satisfying -k <= p(i)-i <= r and p(i)-i not in the set I, i=1..n, with k=2, r=6, I={-1,1,2,3,4,5}.
  • A224809 (program): Number of permutations (p(1), p(2), …, p(n)) satisfying -k <= p(i)-i <= r and p(i)-i not in the set I, i=1..n, with k=2, r=4, I={-1,1,2,3}.
  • A224810 (program): Subsets of {1,2,…,n-6} without differences equal to 3 or 6.
  • A224811 (program): Number of subsets of {1,2,…,n-8} without differences equal to 2, 4, 6 or 8.
  • A224823 (program): Number of solutions to n = x + y + 3*z where x, y, z are triangular numbers.
  • A224825 (program): Expansion of psi(x) * psi(x^3)^2 in powers of x where psi() is a Ramanujan theta function.
  • A224829 (program): Numbers m, such that there is no solution m = x + y + 3*z, with triangular numbers x, y, z.
  • A224831 (program): Expansion of phi(-x^3)^2 * psi(x) / chi(-x)^2 in powers of x where phi(), psi(), chi() are Ramanujan theta functions.
  • A224833 (program): Expansion of phi(-x)^2 * chi(-x) * psi(x^3) in powers of x where phi(), psi(), chi() are Ramanujan theta functions.
  • A224837 (program): Surface area of Johnson square pyramid (rounded down) with all the edge-lengths equal to n.
  • A224854 (program): Numbers n such that 90*n + 11 and 90*n + 13 are twin prime.
  • A224855 (program): Numbers n such that 90*n + 17 and 90*n + 19 are twin primes.
  • A224856 (program): Numbers n such that 90*n + 29 and 90*n + 31 are twin primes.
  • A224857 (program): Numbers n such that 90n + 41 and 90n + 43 are twin primes.
  • A224859 (program): Numbers n such that 90*n + 47 and 90*n + 49 are twin primes.
  • A224860 (program): Numbers n such that 90*n + 59 and 90*n + 61 are twin prime.
  • A224862 (program): Numbers n such that 90*n + 71 and 90*n + 73 are twin primes.
  • A224864 (program): Numbers n such that 90*n + 77 and 90*n + 79 are twin primes.
  • A224865 (program): Numbers n such that 90*n + 89 and 90*n + 91 are twin primes.
  • A224866 (program): Numbers of the form m*rad(m)+1, where rad = A007947 (squarefree kernel).
  • A224868 (program): a(1) = greatest k such that H(k) - H(4) < 1/3 + 1/4; a(2) = greatest k such that H(k) - H(a(1)) < H(a(1)) - H(4); and for n > 2, a(n) = greatest k such that H(k) - H(a(n-1) > H(a(n-1)) - H(a(n-2)), where H = harmonic number.
  • A224869 (program): a(n) = n*( a(n-1)+1 ), initialized by a(1) = -1.
  • A224870 (program): Numbers n such that n^2 + (n+3)^2 is prime.
  • A224880 (program): a(n) = 2n + sum of divisors of n.
  • A224881 (program): Expansion of 1/(1 - 16*x)^(1/8).
  • A224882 (program): G.f.: 1/(1 - 32*x)^(1/16).
  • A224884 (program): Expansion of x / Series_Reversion(x*sqrt(1 + 4*x)).
  • A224889 (program): Numbers n such that 90n + 91 is prime.
  • A224895 (program): Let p = prime(n). Smallest odd number m > p such that m + p is semiprime.
  • A224900 (program): n!*((n+1)!)^2.
  • A224902 (program): O.g.f.: exp( Sum_{n>=1} (sigma(2*n^4) - sigma(n^4)) * x^n/n ).
  • A224903 (program): a(n) = sigma(2*n^4) - sigma(n^4).
  • A224907 (program): Numbers n such that the sum of reciprocals of even divisors of n > 1.
  • A224909 (program): a(1) = a(2) = 1; a(n) = (a(n-1) + a(n-2)) mod (n - a(n-1)).
  • A224911 (program): Greatest prime dividing A190339(n).
  • A224914 (program): Accumulation of products of all divisors of n, positive or negative.
  • A224915 (program): a(n) = Sum_{k=0..n} n XOR k where XOR is the bitwise logical exclusive-or operator.
  • A224916 (program): Expansion of chi(x)^2 / chi(-x^2)^6 in powers of x where chi() is a Ramanujan theta function.
  • A224920 (program): Fifth powers expressed in base 3.
  • A224921 (program): Number of Pythagorean triples (a, b, c) with a^2 + b^2 = c^2 and 0 < a < b < c < n.
  • A224923 (program): Sum_{i=0..n} Sum_{j=0..n} (i XOR j), where XOR is the binary logical exclusive-or operator.
  • A224924 (program): Sum_{i=0..n} Sum_{j=0..n} (i AND j), where AND is the binary logical AND operator.
  • A224946 (program): Leap years having 53 Mondays and Tuesdays.
  • A224949 (program): Leap years having 53 Thursdays and Fridays.
  • A224951 (program): Leap years having 53 Saturdays and Sundays.
  • A224966 (program): Numbers n such that n^2+sum-of-digits(n^2) is prime.
  • A224976 (program): L.g.f.: log( 1 + Sum_{n>=1} x^(n*(3*n-1)/2) + x^(n*(3*n+1)/2) ) = Sum_{n>=1} a(n)*x^n/n.
  • A224977 (program): n^2 minus sum of digits of n^2.
  • A224979 (program): Number of primes of the form p-q+1 where q is any prime < p = prime(n).
  • A224980 (program): Number of primes of the form p-q-1 where q is any prime < p = prime(n).
  • A224992 (program): Non-crossing, non-nesting, 3-colored permutations on {1,2,…,n}.
  • A224995 (program): Floor(1/f(x^(1/n))) for x = 3/2, where f computes the fractional part.
  • A224996 (program): Floor(1/f(x^(1/n))) for x = 2, where f computes the fractional part.
  • A224998 (program): Floor(1/f(x^(1/n))) for x = Pi, where f computes the fractional part.
  • A225006 (program): Number of n X n 0..1 arrays with rows unimodal and columns nondecreasing.
  • A225007 (program): Number of n X 5 0..1 arrays with rows unimodal and columns nondecreasing.
  • A225008 (program): Number of n X 6 0..1 arrays with rows unimodal and columns nondecreasing.
  • A225009 (program): Number of n X 7 0..1 arrays with rows unimodal and columns nondecreasing.
  • A225010 (program): T(n,k) = number of n X k 0..1 arrays with rows unimodal and columns nondecreasing.
  • A225011 (program): Number of 4 X n 0..1 arrays with rows unimodal and columns nondecreasing.
  • A225012 (program): Number of 5 X n 0..1 arrays with rows unimodal and columns nondecreasing.
  • A225013 (program): Number of 6Xn 0..1 arrays with rows unimodal and columns nondecreasing
  • A225014 (program): Number of 7Xn 0..1 arrays with rows unimodal and columns nondecreasing
  • A225015 (program): Number of sawtooth patterns of length 1 in all Dyck paths of semilength n.
  • A225016 (program): Decimal expansion of Pi^3/8.
  • A225017 (program): Odd part of digit sum of 5^n divided by maximal possible power of 5.
  • A225018 (program): Number of cusps in a class of degree-3n complex algebraic surfaces.
  • A225034 (program): a(n) is the number of binary words containing n 1’s and at most n 0’s that do not contain the substring 101.
  • A225043 (program): Pascal’s triangle with row n reduced modulo n+1.
  • A225050 (program): Number of shortest paths from one vertex of a cube (side = n units) to farthest vertex, along the grid on 3 surfaces meeting at another vertex.
  • A225051 (program): Numbers of the form x^3 + SumOfCubedDigits(x).
  • A225054 (program): Triangle read by rows: Eulerian numbers T(n,k) = A008292(n,k) reduced mod n+1.
  • A225055 (program): Irregular triangle which lists the three positions of 2*n-1 in A060819 in row n.
  • A225058 (program): a(4*n) = n-1. a(2*n+1) = a(4*n+2) = 2*n+1.
  • A225081 (program): Gray code variant of A048896.
  • A225091 (program): The odd part of the digit sum of 7^n.
  • A225101 (program): Numerator of (2^n - 2)/n.
  • A225107 (program): Number of (4n-3)-digit 4th powers in carryless arithmetic mod 10.
  • A225108 (program): Number of pairs (x,y) of elements x of the symmetric group S_{n-1} and y of the symmetric group S_{n} that commute. Here the symmetric group S_{n-m} is to be thought of as the subgroup of the symmetric group S_n which stabilizes n-m+1,n-m+2,…n.
  • A225116 (program): a(n) = 3^n*A_{n, 1/3}(-1) where A_{n, k}(x) are the generalized Eulerian polynomials.
  • A225117 (program): Triangle read by rows, coefficients of the generalized Eulerian polynomials A_{n, 3}(x) in descending order.
  • A225118 (program): Triangle read by rows, coefficients of the generalized Eulerian polynomials A_{n, 4}(x) in descending order.
  • A225119 (program): Decimal expansion of Integral_{x=0..Pi/2} sin(x)^(3/2) dx.
  • A225126 (program): Central terms of the triangle in A048152.
  • A225127 (program): Convolutory inverse of the nonprimes.
  • A225132 (program): Convolutory inverse of the Thue Morse sequence.
  • A225144 (program): a(n) = Sum_{i=n..2*n} i^2*(-1)^i.
  • A225145 (program): Square array read by downwards antidiagonals: T(n,k) = 1 if k mod (n+1) > 0, T(n,k) = 0 if k mod (n+1) = 0.
  • A225152 (program): Let b(k) be A036378, then a(n) is the number of b(k) terms such that 2^n < b(k) <= 2^(n+1).
  • A225180 (program): Infinite sequence M defined by the rules M = 1:X, X = 2:zip_2(X,Y), Y = 2:zip_3(M,Y,Y).
  • A225181 (program): Version of A225180 over the alphabet {0,1}.
  • A225187 (program): a(n) = gcd_{all Latin squares L of order n} n!*n/A(L), where A(L) is the order of the autotopism group of L.
  • A225190 (program): (n+2)^(n+2) mod n^n.
  • A225195 (program): Primes p such that (p+nextprime(p))/2 is a perfect square.
  • A225196 (program): Number of 6-line partitions of n (i.e., planar partitions of n with at most 6 lines).
  • A225203 (program): Table T(n,k) composed of rows equal to: n * (the characteristic function of the multiples of (n+1)), read by downwards antidiagonals.
  • A225213 (program): Triangular array read by rows. T(n,k) is the number of cycles in the digraph representation of all functions f:{1,2,…,n}->{1,2,…,n} that have length k; 1<=k<=n.
  • A225214 (program): Primes of the form (2^n - 1)*(2^(m+3)) + 5 where n >= 1, m >= 1.
  • A225215 (program): Floor of the Euclidean distance of a point on the (1, 1, 1; 1, 1, 1) 3D walk.
  • A225223 (program): Primes of the form p - 1, where p is a practical number (A005153).
  • A225230 (program): In canonical prime factorization of n: (number of distinct primes) minus (largest prime exponent).
  • A225232 (program): The number of FO3C2 moves required to restore a packet of n playing cards to its original state (order and orientation).
  • A225233 (program): Triangle read by rows: T(n, k) = (2*n + 2 - k)*k, for 0 <= k <= n.
  • A225240 (program): The squares on a chessboard that are white, counting from top left corner and down.
  • A225241 (program): Numbers n such that the sum of reciprocals of even divisors of n < 1.
  • A225319 (program): Prime numbers p such that p - (product of digits of p) is also prime.
  • A225328 (program): a(n) = A002426(n)^n, where A002426 is the central trinomial coefficients.
  • A225367 (program): Number of palindromes of length n in base 3 (A118594).
  • A225370 (program): Let f(S) = maximal m such that the string S contains two disjoint identical (scattered) substrings of length m (“twins”); a(n) = min f(S) over all binary strings of length n.
  • A225372 (program): Triangle read by rows: T(n,k) (1 <= k <= n) given by T(n, 1) = T(n,n) = 1, otherwise T(n, k) = (m*n-m*k+1)*T(n-1,k-1) + (m*k-m+1)*T(n-1,k), where m = -2.
  • A225373 (program): a(n) = 1 + Sum_{i=0..floor(n/2)} phi(n-2*i).
  • A225374 (program): Powers of 111.
  • A225375 (program): Odd numbers with exactly 2 distinct prime factors.
  • A225381 (program): Elimination order of the first person in a Josephus problem.
  • A225391 (program): Expansion of 1/(1 - x - x^2 - x^6 + x^8).
  • A225393 (program): Expansion of 1/(1 - x - x^2 + x^6 - x^8).
  • A225394 (program): Expansion of 1/(1 - x - x^2 + x^7 - x^9).
  • A225399 (program): Number of nontrivial triangular numbers dividing triangular(n).
  • A225419 (program): Triangle read by rows: T(n,k) (0 <= k <= n) = binomial(2*n+2,k).
  • A225435 (program): Numerators of convergents to the general continued fraction 1/(1 + 2/(1 + 3/(1 + 4/(1+ …)))).
  • A225436 (program): Denominators of convergents to the general continued fraction 1/(1 + 2/(1 + 3/(1 + 4/(1+ …))))
  • A225439 (program): Expansion of 3*x/((1-(1-9*x)^(1/3))*(1-9*x)^(2/3)).
  • A225461 (program): a(n) = (prime(k) + prime(k+1))/2 where k = A098015(n).
  • A225465 (program): Triangular array read by rows. T(n,k) is the number of rooted forests on {1,2,…,n} in which one tree has been specially designated that contain exactly k trees; n>=1, 1<=k<=n.
  • A225472 (program): Triangle read by rows, k!*S_3(n, k) where S_m(n, k) are the Stirling-Frobenius subset numbers of order m; n >= 0, k >= 0.
  • A225473 (program): Triangle read by rows, k!*S_4(n, k) where S_m(n, k) are the Stirling-Frobenius subset numbers of order m; n >= 0, k >= 0.
  • A225480 (program): a(n) = B2(n) * C(n) where B2(n) are generalized Bernoulli numbers and C(n) the Clausen numbers.
  • A225481 (program): a(n) = product{ p primes <= n+1 such that p divides n+1 or p-1 divides n }.
  • A225482 (program): Expansion of 1/(1 - x^3 - x^4 - x^5 + x^8).
  • A225484 (program): Expansion of 1/(1 - x^3 - x^4 - x^5 - x^6 + x^9).
  • A225486 (program): Maximal frequency depth for the partitions of n.
  • A225489 (program): Elimination order for the first person in a linear Josephus problem.
  • A225490 (program): Expansion of 1/(1 - x - x^2 + x^5 + x^6 - x^7).
  • A225491 (program): Maximal frequency depth for multisets over an alphabet of n letters.
  • A225497 (program): Total number of rooted labeled trees over all forests on {1,2,…,n} in which one tree has been specially designated.
  • A225505 (program): a(n) = triangular(a(n-1)+a(n-2)) if n > 1, else a(n) = n.
  • A225515 (program): First differences of A121347.
  • A225520 (program): The number of subsets of the set of divisors of n in which elements are pairwise coprime.
  • A225521 (program): Cumulative number of letters in first n English names of playing card denominations: ace, two, three, … jack, queen, king.
  • A225524 (program): G.f.: exp( Sum_{n>=1} (sigma(2*n) - sigma(n))*Lucas(n)*x^n/n ), where Lucas(n) = A000204(n) and sigma(n) = A000203(n) is the sum of divisors of n.
  • A225525 (program): a(n) = (sigma(2*n) - sigma(n))*Lucas(n) where Lucas(n) = A000204(n) and sigma(n) = A000203(n) is the sum of divisors of n.
  • A225528 (program): a(n) = sigma(n)*Lucas(n) where Lucas(n) = A000204(n) and sigma(n) = A000203(n) is the sum of divisors of n.
  • A225530 (program): Number of ordered pairs (i,j) with i,j >= 0, i + j = n and gcd(i,j) <= 1.
  • A225531 (program): Number of ordered pairs (i, j) with i, j >= 0, i + j <= n and gcd(i, j) <= 1.
  • A225534 (program): Numbers whose sum of cubed digits is prime.
  • A225537 (program): Inverse of the Rydberg constant in meters.
  • A225539 (program): Numbers n where 2^n and n have the same digital root.
  • A225551 (program): Longest checkmate in king and queen versus king endgame on an n X n chessboard.
  • A225553 (program): Longest checkmate in king and amazon versus king endgame on an n X n chessboard.
  • A225559 (program): The number of practical numbers <= n where the practical numbers are A005153.
  • A225561 (program): Largest number m such that 1, 2, …, m can be represented as the sum of distinct divisors of n.
  • A225564 (program): Expansion of psi(-x)^2 * f(-x^4)^6 in powers of x where psi(), f() are Ramanujan theta functions.
  • A225566 (program): The set of magic numbers for an idealized harmonic oscillator atomic nucleus with a biaxially deformed prolate ellipsoid shape and an oscillator ratio of 3:1
  • A225569 (program): Decimal expansion of Sum_{n>=0} 1/10^(3^n), a transcendental number.
  • A225573 (program): Number of trees over all forests of labeled rooted trees in which some (possibly all or none) of the trees have been specially designated.
  • A225578 (program): Sum of first (prime(n) - 1) (prime(n) - 1)th powers.
  • A225580 (program): The sum of all substrings of n (including n).
  • A225585 (program): Floor((3^n-1)/n).
  • A225586 (program): Floor((5^n-1)/n).
  • A225593 (program): The integer closest to n/e.
  • A225595 (program): Conjectured square array T(n,k) read by antidiagonals related to the existence of rectangles of size n*k in the toothpick structure of A139250.
  • A225596 (program): Sum of largest parts of all partitions of n plus n. Also, total number of parts in all partitions of n plus n.
  • A225601 (program): a(n) = A000172(n)^n, where A000172(n) = Sum_{k=0..n} binomial(n,k)^3 forms the Franel numbers.
  • A225602 (program): a(n) = A002426(n^2), where A002426 is the central trinomial coefficients.
  • A225604 (program): G.f.: exp( Sum_{n>=1} A002426(n^2) * x^n/n ), where A002426 is the central trinomial coefficients.
  • A225605 (program): (1) = least k such that 1/3 < H(k) - 1/3; a(2) = least k such that H(a(1)) - H(3) < H(k) -H(a(1)), and for n > 2, a(n) = least k such that H(a(n-1)) - H(a(n-2) > H(k) - H(a(n-1)), where H = harmonic number.
  • A225609 (program): Recurrence a(n) = 2^n*a(n-1) + a(n-2) with a(0)=0, a(1)=1.
  • A225612 (program): Partial sums of the binomial coefficients C(4*n,n).
  • A225615 (program): Partial sums of the binomial coefficients C(5*n,n).
  • A225620 (program): Indices of partitions in the table of compositions of A228351.
  • A225621 (program): Central terms of the triangle in A074911.
  • A225657 (program): Union of {6} and A000961.
  • A225658 (program): a(n) = n! + (n+1)! + 3*(n+2)!.
  • A225667 (program): Decimal expansion of 13-5*sqrt(5).
  • A225668 (program): a(n) = floor(4*log_2(n)).
  • A225679 (program): Numerators of phi(k)/k, as k runs through the squarefree numbers (A005117).
  • A225680 (program): Denominators of phi(k)/k, as k runs through the squarefree numbers (A005117).
  • A225682 (program): Triangle read by rows: T(n,k) (0 <= k <= n) = chi(k)*binomial(n,k), where chi(k) = 1,-1,0 according as k == 0,1,2 mod 3.
  • A225683 (program): Numbers divisible by their first digit squared.
  • A225686 (program): a(n) = Fibonacci(2*n^2), a “Somos-like” sequence.
  • A225688 (program): E.g.f.: sec(x)^3+(sec(x)^2*tan(x)).
  • A225689 (program): E.g.f.: sec(x)^2*tan(x)+sec(x)*tan(x)^2.
  • A225690 (program): Number of Dyck paths of semilength n avoiding the pattern U^3 D^3 U D.
  • A225692 (program): Number of Dyck paths of semilength n avoiding the pattern U^(n-1) D^(n-1).
  • A225693 (program): Alternating sum of digits of n.
  • A225697 (program): Numerators of mass formula for vacuum graphs for a phi^4 field theory.
  • A225698 (program): Denominators of mass formula for vacuum graphs for a phi^4 field theory.
  • A225699 (program): Numerators of coefficients arising from q-expansion of Integrate[eta[q^4]^8/eta[q^2]^4, q]/q where eta is the Dedekind eta function.
  • A225700 (program): Denominators of coefficients arising from q-expansion of Integrate[eta[q^4]^8/eta[q^2]^4, q]/q where eta is the Dedekind eta function.
  • A225743 (program): Triangular array: row n is least squarefree word of length n using positive integers.
  • A225748 (program): Numbers n for which the sum of the numbers in the Collatz (3x+1) iteration of n is prime.
  • A225751 (program): Number of different figures obtained by a putting two Young diagrams of partitions lambda and mu, such that |lambda| + |mu| = n on top of each other.
  • A225771 (program): Numbers that are positive integer divisors of 1 + 2*x^2 where x is a positive integer.
  • A225773 (program): The squares on a chessboard that are black, counting from top left corner and down.
  • A225785 (program): Numbers n such that triangular(n) + triangular(2*n) is a triangular number.
  • A225786 (program): Numbers k such that oblong(2*k) + oblong(k) is a square, where oblong(k) = A002378(k) = k*(k+1).
  • A225793 (program): Numbers n that can be uniquely expressed as (m + sum of digits of m) for some m.
  • A225799 (program): Sum_{k=0..n} binomial(n,k) * 10^(n-k) * Fibonacci(n+k).
  • A225804 (program): Arithmetic mean of the first n primes, rounded up.
  • A225810 (program): a(n) = (10^n)^2 + 4*(10^n) + 1.
  • A225813 (program): a(n) = (10^n)^2 + 7(10^n) + 1.
  • A225816 (program): Square array A(n,k) = (k!)^n, n>=0, k>=0, read by antidiagonals.
  • A225817 (program): Moebius function applied to divisors of n, table read by rows.
  • A225821 (program): a(n) = Product_{p | p is prime and p, p-1 both divide n}.
  • A225822 (program): Lesser of adjacent odd numbers with different parity of binary weight and both isolated from odd numbers of same parity of binary weight.
  • A225826 (program): Number of binary pattern classes in the (2,n)-rectangular grid: two patterns are in same class if one of them can be obtained by a reflection or 180-degree rotation of the other.
  • A225828 (program): Number of binary pattern classes in the (4,n)-rectangular grid: two patterns are in the same class if one of them can be obtained by a reflection or 180-degree rotation of the other.
  • A225830 (program): Number of binary pattern classes in the (6,n)-rectangular grid: two patterns are in the same class if one of them can be obtained by a reflection or 180-degree rotation of the other.
  • A225832 (program): Number of binary pattern classes in the (8,n)-rectangular grid: two patterns are in the same class if one of them can be obtained by a reflection or 180-degree rotation of the other.
  • A225836 (program): Numbers of form 2^j*(4k+1), j >= 0, k >= 1.
  • A225837 (program): Numbers of form 2^i*3^j*(6k+1), i, j, k >= 0.
  • A225838 (program): Numbers of form 2^i*3^j*(6k+5), i, j, k >= 0.
  • A225839 (program): Triangular numbers representable as triangular(m) + triangular(2m).
  • A225845 (program): Numerator of c(n) = 2^(2*n)*(2^(2*n) - 1)/(2*n)!, a coefficient used in the expansion of tan(x) as Sum_{n>=1} c(n)*|Bernoulli(2*n)|*x^(2*n-1).
  • A225846 (program): Denominator of c(n) = 2^(2*n)*(2^(2*n) - 1)/(2*n)!, a coefficient used in the expansion of tan(x) as Sum_{n>=1} c(n)*|Bernoulli(2*n)|*x^(2*n-1).
  • A225854 (program): Frequency of prime numbers between consecutive partial sums of primes.
  • A225857 (program): Numbers of form 2^i*3^j*(4k+1), i, j, k >= 0.
  • A225858 (program): Numbers of form 2^i*3^j*(4k+3), i, j, k >= 0.
  • A225865 (program): a(n) = 2^m minus (the total number of distinct subsets of length-(m-n) binary words that can appear as the factor of a word of length m, for 0 <= n < m/2).
  • A225875 (program): We write the 1 + 4*k numbers once and twice the others.
  • A225879 (program): Number of n-length words w over ternary alphabet {1,2,3} such that for every prefix z of w we have 0<=#(z,1)-#(z,2)<=2 and 0<=#(z,2)-#(z,3)<=2 and #(z,x) gives the number of occurrences of letter x in z.
  • A225883 (program): a(n) = (-1)^n * (1 - 2^n).
  • A225887 (program): a(n) = A212205(2*n + 1).
  • A225894 (program): Number of n X 2 binary arrays whose sum with another n X 2 binary array containing no more than a single 1 has rows and columns in lexicographically nondecreasing order.
  • A225901 (program): Write n in factorial base, then replace each nonzero digit d of radix k with k-d.
  • A225904 (program): Numerator of Sum_{k=1..n} 1/L(k) where L(n) is the n-th Lucas number (A000204).
  • A225918 (program): a(n) is the least k such that f(a(n-1)+1) + … + f(k) > f(a(n-2)+1) + … + f(a(n-1)) for n > 1, where f(n) = 1/(n+3) and a(1) = 1.
  • A225919 (program): a(n) is the least k such that f(a(n-1)+1) + … + f(k) > f(a(n-2)+1) + … + f(a(n-1)) for n > 1, where f(n) = 1/(n+4) and a(1) = 1.
  • A225920 (program): a(n) is the least k such that f(a(n-1)+1) + … + f(k) > f(a(n-2)+1) + … + f(a(n-1)) for n > 1, where f(n) = 1/(n+5) and a(1) = 1.
  • A225921 (program): a(n) is the least k such that f(a(n-1)+1) + … + f(k) > f(a(n-2)+1) + … + f(a(n-1)) for n > 1, where f(n) = 1/(n+6) and a(1) = 1.
  • A225922 (program): a(n) is the least k such that f(a(n-1)+1) + … + f(k) > f(a(n-2)+1) + … + f(a(n-1)) for n > 1, where f(n) = 1/(n+7) and a(1) = 1.
  • A225925 (program): G.f.: exp( Sum_{n>=1} A002129(n^2)*x^n/n ), where A002129(n) is the excess of sum of odd divisors of n over sum of even divisors of n.
  • A225928 (program): a(n) = 4*16^n + 8*4^n + 17.
  • A225948 (program): a(0) = -1; for n>0, a(n) = numerator(1/4 - 4/n^2).
  • A225949 (program): Triangle for sum of the two legs (catheti) of primitive Pythagorean triangles.
  • A225950 (program): Triangle for odd legs of primitive Pythagorean triangles.
  • A225951 (program): Triangle for perimeters of primitive Pythagorean triangles.
  • A225952 (program): Triangle read by rows, giving the even legs of primitive Pythagorean triangles, with zero entries for non-primitive triangles.
  • A225954 (program): A primitive sequence of order n = 2 generated by f(x) = x^2 - (4*x + 13) over Z/(3*5) (see below).
  • A225958 (program): O.g.f.: exp( Sum_{n>=1} (sigma(2*n^3) - sigma(n^3)) * x^n/n ).
  • A225959 (program): a(n) = sigma(2*n^3) - sigma(n^3).
  • A225972 (program): The number of binary pattern classes in the (2,n)-rectangular grid with 3 ‘1’s and (2n-3) ‘0’s: two patterns are in same class if one of them can be obtained by a reflection or 180-degree rotation of the other.
  • A225975 (program): Square root of A226008(n).
  • A226005 (program): Lexicographically earliest sequence such that (a(n), a(n+1)) runs through all the pairs of nonnegative integers exactly once, with the constraint that a(n)=0 iff n is a square.
  • A226008 (program): a(0) = 0; for n>0, a(n) = denominator(1/4 - 4/n^2).
  • A226012 (program): Number of unimodal functions f:[n]->[2n].
  • A226013 (program): Number of unimodal functions f:[n]->[2n] with f(1)<>1 and f(i)<>f(i+1).
  • A226023 (program): A142705 (numerators of 1/4-1/(4n^2)) sorted to natural order.
  • A226025 (program): Odd composite numbers that are not squares of primes.
  • A226029 (program): First differences of A182402.
  • A226031 (program): Number A(n,k) of unimodal functions f:[n]->[k*n]; square array A(n,k), n>=0, k>=0, read by antidiagonals.
  • A226033 (program): Round(n * exp(-1 - 1/(2n))), an approximation to the number of daughters to wait before picking in the sultan’s dowry problem (Better that A225593).
  • A226034 (program): Expansion of f(-x)^6 / (chi(x) * phi(-x)^6) in powers of x where phi(), chi(), f() are Ramanujan theta functions.
  • A226039 (program): Numbers k such that there exist primes p which divide k+1 and p-1 does not divide k.
  • A226041 (program): Primes generated by concatenation of three consecutive numbers divided by three.
  • A226044 (program): Period of length 8: 1, 64, 16, 64, 4, 64, 16, 64.
  • A226047 (program): Largest prime power dividing binomial(2n, n).
  • A226065 (program): Sum of all the smaller parts raised to their corresponding larger parts of the partitions of n into exactly two parts.
  • A226088 (program): a(n) is the number of the distinct quadrilaterals in a regular n-gon, which Q3 type are excluded.
  • A226089 (program): Denominators of the series a(n+1) = (a(n)+k)/(1+a(n)*k); where k=1/(n+1), a(1)=1/2.
  • A226096 (program): Squares with doubled (4*n+2)^2.
  • A226097 (program): a(n) = ((-1)^n + 2*n - 38)*(2*n - 38) + 41.
  • A226106 (program): G.f.: exp( Sum_{n>=1} A068963(n)*x^n/n ) where A068963(n) = Sum_{d|n} phi(d^3).
  • A226107 (program): Number of strict partitions of n with Cookie Monster number 2.
  • A226122 (program): Expansion of (1+2*x+x^2+x^3+2*x^4+x^5)/(1-2*x^3+x^6).
  • A226123 (program): Number of terms of the form 2^k in Collatz(3x+1) trajectory of n.
  • A226132 (program): Expansion of - c(-q) * c(q^2) / 9 in powers of q where c() is a cubic AGM theta function.
  • A226133 (program): Integers of the form (pq-1)/24 where p < q are primes.
  • A226136 (program): Positions of the positive integers in the ordering of rational numbers as generated by the rules: 1 is in S, and if nonzero x is in S, then x+1 and -1/x are in S. (See Comments.)
  • A226139 (program): Expansion of b(-q) * b(q^2) in powers of q where b() is a cubic AGM theta function.
  • A226140 (program): a(n) = Sum_{i=1..floor(n/2)} (n-i)^i.
  • A226141 (program): Sum of the squared parts of the partitions of n into exactly two parts.
  • A226156 (program): a(n) = BS(n) * W(n) where BS = Sum_{k=0..n} ((-1)^k*k!/(k+1)) S(n, k) and S(n, k) the Stirling subset numbers A048993(n, k). W(n) = Product_{ p primes <= n+1 such that p divides n+1 or p-1 divides n } = A225481(n).
  • A226162 (program): a(n) = Kronecker Symbol (-5/n), n >= 0.
  • A226164 (program): Sequence used for the quadratic irrational number belonging to the principal indefinite binary quadratic form.
  • A226165 (program): Squarefree part of A077425(n) (numbers 4*k+1, k>=0, not a square).
  • A226167 (program): Array read by antidiagonals: a(i,j) is the number of ways of labeling a tableau of shape (i,1^j) with the integers 1, 2, … i+j-2 (each label being used once) such that the first row is decreasing, and the first column has m-1 labels.
  • A226175 (program): a(n) = A068336(n+1) - 1.
  • A226177 (program): a(n) = mu(n)*d(n), where mu(n) = A008683 and d(n) = A000005.
  • A226180 (program): Denominators in Taylor series for integral of tan(x)/x.
  • A226192 (program): Expansion of phi(x^2) * psi(-x) in powers of x where phi(), psi() are Ramanujan theta functions.
  • A226194 (program): Expansion of f(-x^1, -x^7) * f(-x^3, -x^5) in powers of x where f(, ) is Ramanujan’s general theta function.
  • A226197 (program): Numbers of vectors with 2*n integers such that each element is either 1 or -1, and their sum > n.
  • A226198 (program): Floor((n-1)!/n).
  • A226199 (program): 7^n + n.
  • A226200 (program): 6^n + n.
  • A226201 (program): 8^n + n.
  • A226202 (program): 9^n + n.
  • A226203 (program): a(5n) = a(5n+3) = a(5n+4) = 2n+1, a(5n+1) = 2n-3, a(5n+2) = 2n-1.
  • A226205 (program): a(n) = F(n)^2 - F(n-1)^2 or F(n+1) * F(n-2) where F(n) = A000045(n), the Fibonacci numbers.
  • A226225 (program): Expansion of phi(q) * phi(q^8) in powers of q where phi() is a Ramanujan theta function.
  • A226226 (program): Number of alignments of n points with no singleton cycles
  • A226233 (program): Ten copies of each positive integer.
  • A226234 (program): Triangle defined by T(n,k) = binomial(n^2, k^2), for n>=0, k=0..n, as read by rows.
  • A226235 (program): Expansion of q * (chi(-q) / chi(-q^3))^12 in powers of q where chi() is a Ramanujan theta function.
  • A226237 (program): Sum of the parts in the Goldbach partitions of 2n.
  • A226238 (program): a(n) = (n^n - n)/(n - 1).
  • A226239 (program): Minimum m such that there exists an n-row subtractive triangle with distinct integers in 1..m.
  • A226240 (program): Expansion of phi(q^4) * phi(q^8) + 2 * q *phi(q^2) * psi(q^8) in powers of q where phi(), psi() are Ramanujan theta functions.
  • A226249 (program): Positions of nonpositive numbers in the ordering of the rational numbers at A226247.
  • A226250 (program): Positions of positive numbers in the ordering of the rational numbers at A226247.
  • A226251 (program): Concatenated cyclical sequence starting from Fibonacci sequence.
  • A226252 (program): Number of ways of writing n as the sum of 7 triangular numbers.
  • A226253 (program): Number of ways of writing n as the sum of 9 triangular numbers.
  • A226254 (program): Number of ways of writing n as the sum of 10 triangular numbers from A000217.
  • A226255 (program): Number of ways of writing n as the sum of 11 triangular numbers.
  • A226262 (program): Number of additive Z_2 Z_8 codes of a certain type (see Siap-Aydogdu for precise definition).
  • A226263 (program): Number of additive Z_2 Z_8 codes of a certain type (see Siap-Aydogdu for precise definition).
  • A226264 (program): Number of additive Z_2 Z_8 codes of a certain type (see Siap-Aydogdu for precise definition).
  • A226265 (program): Number of additive Z_2 Z_8 codes of a certain type (see Siap-Aydogdu for precise definition).
  • A226268 (program): Number of additive Z_2 Z_8 codes of a certain type (see Siap-Aydogdu for precise definition).
  • A226271 (program): Index of 1/n in the Fibonacci (or rabbit) ordering of the positive rationals.
  • A226274 (program): Position of 1/n in the ordering of the rationals given by application of the map t -> (1+t,-1/t), cf. A226130.
  • A226275 (program): Number of new rationals produced at the n-th iteration by applying the map t -> {t+1, -1/t} to nonzero terms, starting with S[0] = {1}.
  • A226276 (program): Period 4: repeat [8, 4, 4, 4].
  • A226279 (program): a(4n) = a(4n+2) = 2*n , a(4n+1) = a(4n+3) = 2*n-1.
  • A226280 (program): The perfect numbers produced by the aspiring numbers (A063769).
  • A226282 (program): [n/2]!*[(n+1)/2]!*C([n/2],1)*C([(n+1)/2],1).
  • A226283 (program): [n/2]!*[(n+1)/2]!*C([n/2],2)*C([(n+1)/2],2).
  • A226284 (program): [n/2]!*[(n+1)/2]!*C([n/2],3)*C([(n+1)/2],3).
  • A226289 (program): Expansion of f(-x) * phi(x^3) in powers of x where f(), phi() are Ramanujan theta functions.
  • A226292 (program): (10*n^2+4*n+(1-(-1)^n))/8.
  • A226293 (program): Class of sequences of (p-1)-tuples of reverse order of natural numbers for p = 7.
  • A226294 (program): Period 2: repeat [6, 4].
  • A226302 (program): a(n) = P_n(-1), where P_n(x) is a certain polynomial arising in the enumeration of tatami mat coverings.
  • A226308 (program): a(n) = a(n-1) + a(n-2) + 2*a(n-3) with a(0)=2, a(1)=1, a(2)=5.
  • A226309 (program): a(n) = a(n-1) + a(n-2) + a(n-3) + 2*a(n-4) with a(0)=2, a(1)=1, a(2)=5, a(3)=10.
  • A226310 (program): a(n+5) = a(n+4)+a(n+3)+a(n+2)+a(n+1)+2*a(n) with a(0)=0, a(1)=a(2)=a(3)=a(4)=1.
  • A226311 (program): a(n+5) = a(n+4)+a(n+3)+a(n+2)+a(n+1)+2*a(n) with a(0)=2, a(1)=1, a(2)=5, a(3)=10, a(4)=20.
  • A226312 (program): Sum_{k=0..n} k*binomial(n,k)^2*binomial(2*k,k).
  • A226313 (program): Number of commuting 4-tuples of elements from S_n, divided by n!.
  • A226314 (program): Triangle read by rows: T(i,j) = j+(i-j)/gcd(i,j) (1<=i<=j).
  • A226315 (program): (n^2/8+3*n/8-2)*2^n+3.
  • A226316 (program): Expansion of g.f. 1/2 + 1/(1+sqrt(1-8*x+8*x^2)).
  • A226323 (program): Number of ordered pairs (i,j) with |i| * |j| <= n and gcd(i,j) <= 1.
  • A226328 (program): a(0)=1, a(1)=-2; a(n+2) = a(n+1) + a(n) + (period 3: repeat 3, 1, -1).
  • A226333 (program): Expansion of (E_4(q) - E_4(q^5)) / 240 in powers of q where E_4 is an Eisenstein series.
  • A226341 (program): Number of nondecreasing -n..n vectors of length 2 whose dot product with some other -n..n vector equals 2
  • A226350 (program): Expansion of psi(x) * psi(-x^3) in powers of x where psi() is a Ramanujan theta function.
  • A226355 (program): Number of ordered pairs (i,j) with |i| * |j| <= n.
  • A226369 (program): Number of tilings of a 5 X n rectangle using integer-sided square tiles of area > 1.
  • A226370 (program): Number of tilings of a 6 X n rectangle using integer-sided square tiles of area > 1.
  • A226391 (program): a(n) = Sum_{k=0..n} binomial(k*n, k).
  • A226399 (program): Number of nondecreasing -n..n vectors of length 2 whose dot product with some nonincreasing -n..n vector equals 2
  • A226405 (program): Expansion of x/((1-x-x^3)*(1-x)^3).
  • A226431 (program): The number of permutations of length n in a particular geometric grid class.
  • A226432 (program): The number of simple permutations of length n in a particular geometric grid class.
  • A226433 (program): The number of permutations of length n in a particular geometric grid class.
  • A226435 (program): Number of permutations of 1..n with fewer than 2 interior elements having values lying between the values of their neighbors.
  • A226447 (program): Expansion of (1-x+x^3)/(1-x^2+2*x^3-x^4).
  • A226449 (program): a(n) = n*(5*n^2-8*n+5)/2.
  • A226450 (program): a(n) = n*(3*n^2 - 5*n + 3).
  • A226451 (program): a(n) = n*(7*n^2-12*n+7)/2.
  • A226455 (program): G.f.: exp( Sum_{n>=1} A056789(n)*x^n/n ), where A056789(n) = Sum_{k=1..n} lcm(k,n)/gcd(k,n).
  • A226457 (program): D(n,2^n), where D is the binary graph metric, as in A226456.
  • A226458 (program): G.f.: exp( Sum_{n>=1} A226459(n)*x^n/n ), where A226459(n) = Sum_{d|n} phi(d^d).
  • A226459 (program): a(n) = Sum_{d|n} phi(d^d), where phi(n) is the Euler totient function A000010(n).
  • A226470 (program): a(n) = n^2 XOR triangular(n), where XOR is the bitwise logical exclusive-or operator.
  • A226474 (program): Central terms of triangles A226463 and A226464.
  • A226478 (program): A085192(n)/2.
  • A226482 (program): Number of runs of consecutive ones and zeros in successive states of cellular automaton generated by “Rule 30”.
  • A226485 (program): Integer part of length of median to hypotenuse of primitive Pythagorean triangles sorted on hypotenuse.
  • A226488 (program): a(n) = n*(13*n - 9)/2.
  • A226489 (program): a(n) = n*(15*n-11)/2.
  • A226490 (program): a(n) = n*(19*n-15)/2.
  • A226491 (program): a(n) = n*(21*n-17)/2.
  • A226492 (program): a(n) = n*(11*n-5)/2.
  • A226493 (program): Closed walks of length n in K_4 graph.
  • A226500 (program): Triangular numbers representable as 3 * x^2.
  • A226502 (program): Let P(k) denote the k-th prime (P(1)=2, P(2)=3 …); a(n) = P(n+1)P(n+3) - P(n)P(n+2).
  • A226503 (program): Expansion of g.f. x*(1+x+x^2)/(1-x^3-x^5).
  • A226506 (program): a(n) = B(n+2)-3*B(n+1)+B(n), where B(i) are the Bell numbers A000110.
  • A226508 (program): a(n) = Sum_{i=3^n..3^(n+1)-1} i.
  • A226509 (program): Expansion of (3-2*x)/(1-x-x^3)+x/(1-x)^2+x/(1-x^2).
  • A226511 (program): 3*(5^n-3^n)/2.
  • A226514 (program): Column 3 of array in A226513.
  • A226515 (program): Row 2 of array in A226513.
  • A226523 (program): a(n) = 0 if p=2, 1 if 2 is a square mod p, -1 otherwise, where p = prime(n).
  • A226527 (program): Slowest-growing sequence of 3-almost primes (trientprimes) where 1/(tp+1) sums to 1 without actually reaching it.
  • A226534 (program): q + p - 1 mod q - p + 1 where p, q are consecutive primes.
  • A226535 (program): Expansion of b(-q) in powers of q where b() is a cubic AGM theta function.
  • A226538 (program): a(2t) = a(2t-1) + 1, a(2t+1) = a(2t) + a(2t-2) for t >= 1, with a(0) = a(1) = 1.
  • A226540 (program): Maximum of the proper divisors of the triangular numbers.
  • A226546 (program): Number of squares in all tilings of a 3 X n rectangle using integer-sided square tiles.
  • A226555 (program): Numerators of row sums of the triangular enumeration of rational numbers A226314(n,k) / A054531(n,k), 1 <= k <= n.
  • A226556 (program): Expansion of f(x, -x^4) / f(-x^2, x^3) in powers of x where f(,) is Ramanujan’s general theta function.
  • A226560 (program): exp( Sum_{n>=1} A226561(n)*x^n/n ), where A226561(n) = Sum_{d|n} d^n*phi(d).
  • A226561 (program): a(n) = Sum_{d|n} d^n * phi(d), where phi(n) is the Euler totient function A000010(n).
  • A226567 (program): Numbers n such that 2n+1 is neither a square nor a prime.
  • A226570 (program): Sum_{k=1..n} (k+1)! mod n
  • A226576 (program): Smallest number of integer-sided squares needed to tile a 3 X n rectangle.
  • A226577 (program): Smallest number of integer-sided squares needed to tile a 4 X n rectangle.
  • A226588 (program): a(n) = c({1}^n), the Cantor tuple function c applied to an n-tuple of 1’s.
  • A226590 (program): Total number of 0’s in binary expansion of all divisors of n.
  • A226595 (program): Lengths of maximal nontouching increasing paths in n X n grids.
  • A226602 (program): Number of ordered triples (i,j,k) with i*j*k = n, i,j,k >= 0 and gcd(i,j,k) <= 1.
  • A226622 (program): Expansion of phi(x^2) / f(-x) in powers of x where phi(), f() are Ramanujan theta functions.
  • A226635 (program): Expansion of psi(x^4) / f(-x) in powers of x where psi(), f() are Ramanujan theta functions.
  • A226636 (program): Numbers whose base-3 sum of digits is 3.
  • A226637 (program): Numbers m having with m+1 no common digit in decimal representations.
  • A226638 (program): Product of Pell and Lucas numbers.
  • A226639 (program): a(n) = n^4/8 + (5*n^3)/12 - n^2/8 - (5*n)/12 + 1.
  • A226649 (program): Fibonacci shuffles: a(2n) = A000071(n) and a(2n+1) = A001611(n+2).
  • A226654 (program): Decimal expansion of the 1st Lebesgue constant L1.
  • A226693 (program): Squarefree parts of A079896(n), n>= 0.
  • A226694 (program): Pell equation solutions (32*a(n))^2 - 41*(5*b(n))^2 = -1 with b(n) := A226695(n), n>=0.
  • A226695 (program): Pell equation solutions (32*b(n))^2 - 41*(5*a(n))^2 = -1 with b(n) := A226694(n), n>=0.
  • A226699 (program): Solutions x of the Pell equation x^2 - 61*y^2 = +4.
  • A226700 (program): Solutions y/(3*5*13) of the Pell equation x^2 - 61*y^2 = +4.
  • A226701 (program): Positive solutions x/(3*13) of the Pell equation x^2 - 61*y^2 = -4.
  • A226702 (program): Positive solutions y/5 of the Pell equation x^2 - 61*y^2 = -4.
  • A226705 (program): G.f.: 1 / (1 + 12*x*G(x)^4 - 16*x*G^5) where G(x) = 1 + x*G(x)^6 is the g.f. of A002295.
  • A226710 (program): Number of n X 1 (-1,0,1) arrays of determinants of 2 X 2 subblocks of some (n+1) X 2 binary array.
  • A226718 (program): n! mod tetrahedral(n), that is A000142(n) mod A000292(n).
  • A226720 (program): Complement of A122437.
  • A226721 (program): Position of 2^n in the joint ranking of all the numbers 2^j for j>=0 and 5^k for k>=1; complement of A123384.
  • A226725 (program): Denominator of the median of {1, 1/2, 1/3, …, 1/n}.
  • A226730 (program): a(n) = n! + (2*n-1)!/(n-1)!.
  • A226731 (program): a(n) = (2n - 1)!/(2n).
  • A226733 (program): G.f.: 1 / (1 + 8*x*G(x)^2 - 10*x*G(x)^3) where G(x) = 1 + x*G(x)^4 is the g.f. of A002293.
  • A226734 (program): A002110(n) mod A000217(n).
  • A226737 (program): 11^n + n.
  • A226738 (program): Row 3 of array in A226513.
  • A226739 (program): Row 4 of array in A226513.
  • A226740 (program): Row 5 of array in A226513.
  • A226741 (program): Column 4 of array in A226513.
  • A226746 (program): Numbers n such that x^2 = 1 has more than two solutions in the Gaussian integers modulo n.
  • A226751 (program): G.f.: 1 / (1 + 6*x*G(x) - 7*x*G(x)^2), where G(x) = 1 + x*G(x)^3 is the g.f. of A001764.
  • A226754 (program): Numbers of the form p*q, p and q prime with q=2*p+3.
  • A226755 (program): Numbers of the form p*q, p and q prime with q=2p-3.
  • A226756 (program): Number of elements X in the matrix ring M_2(Z_n) such that X^2 == X (mod n).
  • A226761 (program): G.f.: 1 / (1 + 12*x*G(x)^2 - 13*x*G(x)^3) where G(x) = 1 + x*G(x)^4 is the g.f. of A002293.
  • A226762 (program): Least k such that 1/k <= mean of {1, 1/2, 1/3,…, 1/n}.
  • A226763 (program): Greatest k such that 1/k >= mean{1, 1/2, 1/3,…, 1/n}.
  • A226765 (program): Decimal expansion of (13-5*sqrt(5))/2.
  • A226778 (program): Numbers having no common divisor > 1 with their reversal in decimal representation (see A043537).
  • A226780 (program): Triangular array read by rows. T(n,k) is the number of 2 tuple lists of length n that have exactly k coincidences; n >= 0, 0 <= k <= n.
  • A226781 (program): Number of 1’s in A132199 preceding the n-th Rowland prime, A137613(n).
  • A226782 (program): If n == 0 (mod 2) then a(n) = 0, otherwise a(n) = 4^(-1) in Z/nZ*.
  • A226783 (program): If n=0 (mod 5) then a(n)=0, otherwise a(n)=5^(-1) in Z/nZ*.
  • A226784 (program): If gcd(n,6) != 1 then a(n)=0, otherwise a(n)=6^(-1) in Z/nZ*.
  • A226785 (program): If n=0 (mod 7) then a(n)=0, otherwise a(n)=7^(-1) in Z/nZ*.
  • A226786 (program): If n=0 (mod 2) then a(n)=0, otherwise a(n)=8^(-1) in Z/nZ*.
  • A226787 (program): If n=0 (mod 3) then a(n)=0, otherwise a(n)=9^(-1) in Z/nZ*.
  • A226804 (program): Expansion of 1/((1-3x)(1-9x)(1-27x)(1-81x)).
  • A226805 (program): P_n(n+1) where P_n(x) is the polynomial of degree n-1 which satisfies P_n(i) = i^i for i = 1,…,n.
  • A226806 (program): Numbers of the form 2^j + 4^k, for j and k >= 0.
  • A226820 (program): Numbers of the form 2^j + 8^k, for j and k >= 0.
  • A226837 (program): E.g.f.: exp( Sum_{n>=1} x^(2*n) / n^2 ) = Sum_{n>=0} a(n)*x^(2*n)/(2*n)!.
  • A226843 (program): a(n) = prime(prime(n + 1) - 2).
  • A226845 (program): Number of n X 1 (0,1,2) arrays of permanents of 2 X 2 subblocks of some (n+1) X 2 binary array.
  • A226855 (program): a(n) = n*B(n-1) + n*(n-1)*B(n-2), where the B(i) are Bell numbers (A000110).
  • A226858 (program): Numbers n such that there are six distinct triples (k, k+n, k+2n) of squares.
  • A226860 (program): Expansion of psi(-x) * phi(-x^6) in powers of x where phi(), psi() are Ramanujan theta functions.
  • A226861 (program): Expansion of phi(x) * f(-x^3) in powers of x where phi(), f() are Ramanujan theta functions.
  • A226862 (program): Expansion of phi(x^3) * f(-x^4) in powers of x where phi(), f() are Ramanujan theta functions.
  • A226863 (program): Triangular numbers not divisible by lesser triangular numbers > 1.
  • A226864 (program): Expansion of phi(-x^3) * f(-x^4) in powers of x where phi(), f() are Ramanujan theta functions.
  • A226866 (program): Number of n X 2 (-1,0,1) arrays of determinants of 2 X 2 subblocks of some (n+1) X 3 binary array with rows and columns of the latter in lexicographically nondecreasing order.
  • A226872 (program): 1 together with even numbers n >= 2 such that 1^n + 2^n + 3^n + … + n^n == n/2 (mod n).
  • A226881 (program): Number of n-length binary words w with #(w,0) >= #(w,1) >= 1, where #(w,x) gives the number of digits x in w.
  • A226903 (program): Shiraishi numbers: a parametrized family of solutions c to the Diophantine equation a^3 + b^3 + c^3 = d^3 with d = c+1.
  • A226910 (program): a(n) = Sum_{k=0..floor(n/5)} binomial(n,5*k)*binomial(6*k,k)/(5*k+1).
  • A226914 (program): Third column of A226518.
  • A226917 (program): Number of non-sphere-homeomorphic crossing optimal 2-page book drawings of complete graph K_{2n+1}.
  • A226918 (program): Minimal number of 1X3 I-trominoes needed to prevent any further I-trominoe from being placed on an n X n grid.
  • A226931 (program): Numerator of n + Sum(binomial(n,k)*(k/n)^k*((n-k)/n)^(n-k), k=0..n).
  • A226932 (program): Numerators in expansion of 1/(1-log(1+x)).
  • A226933 (program): Denominators in expansion of 1/(1-log(1+x)).
  • A226934 (program): Numbers k such that tau(2k) | sigma(2k).
  • A226939 (program): A recursive variation of the Collatz-Fibonacci sequence: a(n) = 1 + min(a(C(n)),a(C(C(n)))) where C(n) = A006370(n), the Collatz map.
  • A226940 (program): a(0)=0; if a(n-1) is odd, a(n) = n + a(n-1), otherwise a(n) = n - a(n-1).
  • A226946 (program): Numbers that can’t be written as x^2 + x*y + y^2, with 0 <= x <= y and gcd(x,y) = 1.
  • A226949 (program): Number of twin prime pairs of the form k*n +/- 1 with k <= n.
  • A226954 (program): Numbers n such that there are seven distinct triples (k, k+n, k+2n) of squares.
  • A226956 (program): a(0)=a(1)=1, a(n+2) = a(n+1) + a(n) - A128834(n).
  • A226958 (program): a(n) = Fibonacci(n-2)*Fibonacci(n)*Fibonacci(n+2).
  • A226968 (program): Number of labeled octopi with n nodes such that each tentacle has an odd number of nodes.
  • A226969 (program): Numbers whose base-4 sum of digits is 4.
  • A226974 (program): a(n) = Sum_{k=0..floor(n/3)} binomial(n,3*k)*binomial(4*k,k)/(3*k+1).
  • A226975 (program): Decimal expansion I_1(1), the modified Bessel function of the first kind.
  • A226976 (program): Fibonacci(n)^3 + Fibonacci(n+2)^3
  • A226982 (program): a(n) = ceiling(n/2) - primepi(n).
  • A226983 (program): a(n) = ceiling(n/2) - pi(2n) + pi(n-1).
  • A226994 (program): Number of lattice paths from (0,0) to (n,n) consisting of steps U=(1,1), H=(1,0) and S=(0,1) such that the first step leaving the diagonal (if any) is an H step.
  • A226995 (program): Number of lattice paths from (0,0) to (n,n) consisting of steps U=(1,1), H=(1,0) and S=(0,1) such that the first step leaving the diagonal (if any) is an H step and the last step joining the diagonal (if any) is a S step.
  • A226996 (program): Number of lattice paths from (0,0) to (n,n) consisting of steps U=(1,1), H=(1,0) and S=(0,1) such that the first step leaving and the last step joining the diagonal (if any) is an H step.
  • A226998 (program): The number of descents over all functions f:{1,2,…,n}->{1,2,…,n}.
  • A227000 (program): Numbers n such that (n+1)^2-n^2 and (n+1)^3-n^3 are both prime.
  • A227006 (program): Numbers n such that n-1 is not squarefree or a prime divisor of n-1 is in the sequence.
  • A227007 (program): Numbers n such that n-1 is squarefree and every prime divisor of n-1 is in the sequence.
  • A227012 (program): a(n) = floor(M(g(n-1)+1, …, g(n))), where M = harmonic mean and g(n) = n^3.
  • A227013 (program): a(n) = floor(M(g(n-1)+1,..,g(n))), where M is the harmonic mean and g(n) = n^4.
  • A227015 (program): a(n) = floor(M(g(n-1)+1, …, g(n))), where M = harmonic mean and g(n) = n^3 + n^2 + n + 1.
  • A227016 (program): Floor(M(g(n-1)+1,..,g(n))), where M = harmonic mean and g(n) = n(n + 1)(n + 2)/6.
  • A227017 (program): Floor(M(g(n-1)+1,..,g(n))), where M = harmonic mean and g(n) = n(3n-1)/2 = A000326(n).
  • A227031 (program): Odd primes such that the previous prime is not the larger part of a twin prime pair.
  • A227035 (program): a(n) = Sum_{k=0..floor(n/4)} binomial(n,4*k)*binomial(5*k,k)/(4*k+1).
  • A227036 (program): Expansion of 2*(1+x^2)/((1-x)*(1-x-2*x^3)).
  • A227037 (program): Partial sums of A013999.
  • A227041 (program): Triangle of numerators of harmonic mean of n and m, 1 <= m <= n.
  • A227042 (program): Triangle of denominators of harmonic mean of n and m, 1 <= m <= n.
  • A227043 (program): Numerator of harmonic mean H(n,2), n>= 0.
  • A227044 (program): a(n) = Sum_{k>=1} k^(2*n)/(2^k).
  • A227047 (program): Expansion of x^2*(1+x^2) / ( (x^2-x+1)*(-x^2-x+1)*(1+x+x^2) ).
  • A227052 (program): a(n) = (n^2)! / (n^2-n)! = number of ways of placing n labeled balls into n^2 labeled boxes with at most one ball in each box.
  • A227053 (program): a(n) = (n^3)! / (n^3-n)! = number of ways of placing n labeled balls into n^3 labeled boxes with at most one ball in each box.
  • A227056 (program): Number of n X 2 -2..2 arrays of 2 X 2 subblock diagonal sums minus antidiagonal sums for some (n+1) X 3 binary array with rows and columns of the latter in lexicographically nondecreasing order.
  • A227062 (program): Numbers whose base-5 sum of digits is 5.
  • A227065 (program): The number of partitions of 2n into exactly two parts such that the smaller and larger parts are not both prime.
  • A227070 (program): Powers n such that the set s(n) = {k > 0 such that k^n ends with k} does not occur for smaller n.
  • A227071 (program): Let s(m) = the set of k > 0 such that k^m ends with k. Then a(n) = least m such that s(m) = s(n).
  • A227080 (program): Numbers whose base-6 sum of digits is 6.
  • A227081 (program): Row sums of A124576.
  • A227085 (program): Number of n X 2 binary arrays indicating whether each 2 X 2 subblock of a larger binary array has lexicographically increasing rows and columns, for some larger (n+1) X 3 binary array with rows and columns of the latter in lexicographically nondecreasing order.
  • A227090 (program): Numbers n such that n^2+1 with its digits reversed is prime (ignoring leading zeros).
  • A227091 (program): Number of solutions to x^2 == 1 (mod n) in Z[i]/nZ[i].
  • A227092 (program): Numbers whose base-7 sum of digits is 7.
  • A227093 (program): Decimal expansion of 1/9899.
  • A227094 (program): Binomial transform of A013999.
  • A227095 (program): Numbers whose base-8 sum of digits is 8.
  • A227104 (program): a(0)=-1, a(1)=3; a(n+2) = a(n+1) + a(n) + 2*A057078(n+1).
  • A227106 (program): Numerators of harmonic mean H(n,3), n >= 0.
  • A227107 (program): Numerators of harmonic mean H(n,4), n >= 0.
  • A227108 (program): Denominators of harmonic mean H(n,5), n >= 0.
  • A227109 (program): Numerators of harmonic mean H(n, 5), n >= 0.
  • A227111 (program): Nonnegative solutions of the Pell equation x^2 - 89*y^2 = +1. Solutions y = 53000*a(n).
  • A227116 (program): Given an equilateral triangular grid with side n, containing n(n+1)/2 points, a(n) is the minimal number of points to be removed from the grid, so that, if 3 of the remaining points are chosen, they do not form an equilateral triangle with sides parallel to the grid.
  • A227121 (program): Number of n X 2 0,1 arrays indicating 2 X 2 subblocks of some larger (n+1) X 3 binary array having a sum of zero, with rows and columns of the latter in lexicographically nondecreasing order.
  • A227127 (program): The Akiyama-Tanigawa algorithm applied to 1/(1,2,3,5,… old prime numbers). Reduced numerators of the second row.
  • A227128 (program): The twisted Euler phi-function for the non-principal Dirichlet character mod 3.
  • A227130 (program): Numbers n for which there is an even number of nonzero digits when n is written in the factorial base (A007623).
  • A227132 (program): Numbers n for which there are an odd number of nonzero digits when n is written in the factorial base (A007623).
  • A227133 (program): Given a square grid with side n consisting of n^2 cells (or points), a(n) is the maximum number of points that can be painted so that no four of the painted ones form a square with sides parallel to the grid.
  • A227139 (program): Chebyshev S-polynomial evaluated at x = 48.
  • A227140 (program): a(n) = n/gcd(n,2^5), n >= 0.
  • A227144 (program): Numbers that are congruent to {1, 2, 7, 17, 23} modulo 24.
  • A227145 (program): Numbers satisfying an infinite nested recurrence relation.
  • A227146 (program): Numbers that are congruent to {5, 11, 13, 14, 19} modulo 24.
  • A227148 (program): Numbers n for which the sum of digits is even when n is written in the factorial base (A007623).
  • A227149 (program): Numbers n for which the sum of digits is odd when n is written in the factorial base (A007623).
  • A227152 (program): Nonnegative solutions of the Pell equation x^2 - 101*y^2 = +1. Solutions x = a(n).
  • A227153 (program): Product of nonzero digits of n in factorial base.
  • A227154 (program): Product of digits+1 of n in factorial base.
  • A227157 (program): Numbers n whose factorial base representation A007623(n) doesn’t contain any nonleading zeros.
  • A227161 (program): Number of n X 2 0,1 arrays indicating 2 X 2 subblocks of some larger (n+1) X 3 binary array having a sum of one or less, with rows and columns of the latter in lexicographically nondecreasing order.
  • A227168 (program): a(n) = gcd(2*n, n*(n+1)/2)^2.
  • A227169 (program): a(n) = 3*((2*n+2)!)^2 / (n!*(n+1)!*(n+2)!*(n+3)!).
  • A227176 (program): E.g.f.: LambertW(LambertW(-x)) / LambertW(-x).
  • A227177 (program): n occurs n^2 - n + 1 times.
  • A227179 (program): After initial 0, integers from 0 to n(n-1) followed by integers from 0 to n(n+1) and so on.
  • A227180 (program): Composite numbers n such that b^(n-1) == 1 (mod n) implies b == -1 or +1 (mod n).
  • A227181 (program): Irregular table: integers from n to n^2 followed by integers from (n+1) to (n+1)^2.
  • A227182 (program): Simple self-inverse permutation of natural numbers: List each block of n^2 - n + 1 numbers from ((n-1)^3 + 2*(n-1))/3 + 1 to (n^3 + 2*n)/3 in reverse order.
  • A227183 (program): a(n) is the sum of parts of the unique unordered partition encoded in the run lengths of the binary expansion of n; row sums of A227739 for n >= 1.
  • A227184 (program): a(n) = product of parts of the unordered partition encoded with the runlengths of binary expansion of n.
  • A227185 (program): The largest part in the unordered partition encoded in the runlengths of the binary expansion of n.
  • A227187 (program): Numbers n whose factorial base representation A007623(n) contains at least one nonleading zero. (Zero is also included as a(0)).
  • A227190 (program): a(n) = n minus (product of run lengths in binary representation of n)
  • A227191 (program): a(n) = n minus (product of nonzero digits in factorial base representation of n).
  • A227192 (program): Sum of the partial sums of the run lengths of binary expansion of n, when starting scanning from the least significant end; Row sums of A227188 and A227738.
  • A227200 (program): a(n) = a(n-1) + a(n-2) - 2^(n-1) with a(0)=a(2)=0, a(1)=-a(3)=1, a(4)=-5.
  • A227203 (program): Prime(n)^2 mod (prime(n) + prime(n+1)).
  • A227209 (program): Expansion of 1/((1-x)^2*(1-2x)*(1-4x)).
  • A227234 (program): G.f.: Sum_{n>=1} x^n * (1+x)^prime(n).
  • A227235 (program): G.f.: Sum_{n>=1} x^n / (1-x)^prime(n).
  • A227236 (program): G.f.: Sum_{n>=0} x^n * (1+x)^sigma(n).
  • A227238 (program): Numbers whose base-9 sum of digits is 9.
  • A227241 (program): a(n) = sigma(n)*( 2*sigma(n)+1 ).
  • A227252 (program): Number of n X 2 binary arrays indicating whether each 2 X 2 subblock of a larger binary array has lexicographically nondecreasing rows and columns, for some larger (n+1) X 3 binary array with rows and columns of the latter in lexicographically nondecreasing order.
  • A227259 (program): Number of n X 2 0,1 arrays indicating 2 X 2 subblocks of some larger (n+1) X 3 binary array having a sum of two or less, with rows and columns of the latter in lexicographically nondecreasing order.
  • A227265 (program): Number of n X 2 0,1 arrays indicating 2 X 2 subblocks of some larger (n+1) X 3 binary array having a sum of three or less, with rows and columns of the latter in lexicographically nondecreasing order.
  • A227277 (program): G.f.: Sum_{n>=0} x^n * (1+x)^A007814(n), where A007814(n) is the exponent of the highest power of 2 dividing n.
  • A227287 (program): G.f.: Sum_{n>=0} x^(n - b(n)) * (1+x)^b(n), where b(n) = A007814(n), which is the exponent of the highest power of 2 dividing n.
  • A227291 (program): Characteristic function of squarefree numbers squared (A062503).
  • A227298 (program): The number of squares added in the n-th step of a Pythagoras tree of the 30-60-90 triangle, using the rule larger squares come first.
  • A227300 (program): Rising diagonal sums of triangle of Fibonacci polynomials (rows displayed as centered text).
  • A227308 (program): Given an equilateral triangular grid with side n consisting of n(n+1)/2 points, a(n) is the maximum number of points that can be painted so that, if any 3 of the painted ones are chosen, they do not form an equilateral triangle with sides parallel to the grid.
  • A227314 (program): Number of prime factors, with multiplicity, of sum of first n composite numbers.
  • A227316 (program): a(n) = n(n+1) if n == 0 or 1 (mod 4), otherwise a(n) = n(n+1)/2.
  • A227318 (program): G.f.: Sum_{n>=0} x^n * (1-x)^A007814(n), where A007814(n) is the exponent of the highest power of 2 dividing n.
  • A227325 (program): A000272(n+1) * A000984(n).
  • A227326 (program): a(2n) = 2a(n)+2^(2n), a(2n+1) = 2^(2n+1), a(0)=0.
  • A227327 (program): Number of non-equivalent ways to choose two points in an equilateral triangle grid of side n.
  • A227346 (program): Distance between consecutive pairs of primes differing by 6 (p, p+6).
  • A227347 (program): Number of lattice points in the closed region bounded by the graphs of y = (5/6)*x^2, x = n, and y = 0, excluding points on the x-axis.
  • A227349 (program): Product of lengths of runs of 1-bits in binary representation of n.
  • A227350 (program): Product of lengths of runs of 0-bits in binary representation of n, or 1 if no nonleading zeros present.
  • A227351 (program): Permutation of nonnegative integers: map each number by lengths of runs of zeros in its Zeckendorf expansion shifted once left to the number which has the same lengths of runs (in the same order, but alternatively of runs of 0’s and 1’s) in its binary representation.
  • A227352 (program): Permutation of nonnegative integers: map each number by lengths of runs in its binary representation to the number in whose once left-shifted Zeckendorf representation occurs the same run lengths (in the same order) as the lengths of consecutive blocks of zeros.
  • A227353 (program): Number of lattice points in the closed region bounded by the graphs of y = 3*x/5, x = n, and y = 0, excluding points on the x-axis.
  • A227354 (program): Expansion of 2 * a(q) - a(q^2) in powers of q where a() is a cubic AGM theta function.
  • A227355 (program): Product of run lengths in Zeckendorf representation of n.
  • A227356 (program): Partial sums of A129361.
  • A227357 (program): de Bruijn’s S(6,n).
  • A227361 (program): If n is even, then a(n) = n + bitsum(n), else a(n) = n - bitsum(n), where bitsum(n) is the count of binary 1’s in n, A000120.
  • A227362 (program): Distinct digits of n arranged in decreasing order.
  • A227363 (program): a(n) = n + (n-1)*(n-2) + (n-3)*(n-4)*(n-5) + (n-6)*(n-7)*(n-8)*(n-9) + … + …*(n-n).
  • A227376 (program): G.f.: 1/(1 - x - x^2 - x^3 + x^5 + x^6 + x^7).
  • A227380 (program): Doubling the first two of every four nonnegative numbers.
  • A227386 (program): a(n) = n - 1 - a(a(n-1)) - a(a(a(n-2))) - a(a(a(a(n-3)))) - a(a(a(a(a(n-4))))) - … with a(0) = 0.
  • A227391 (program): a(n) = round(3*(4/3)^n).
  • A227394 (program): The maximum value of x^4(n-x)(x-1) for x in 1..n is reached for x = a(n).
  • A227395 (program): Expansion of q^2 * phi(-q) * psi(q^16) in powers of q where phi(), psi() are Ramanujan theta functions.
  • A227396 (program): Triangle A074909(n) with the first column equal to 1 followed by -A000027(n) instead of A000012.
  • A227398 (program): Expansion of chi(x^3) / chi(x) in powers of x where chi() is a Ramanujan theta function.
  • A227400 (program): Decimal expansion of 5/(3*phi^2) where phi is the golden ratio.
  • A227402 (program): Number of unimodal functions f:[n]->[n^2].
  • A227404 (program): Total number of inversions in all permutations of order n consisting of a single cycle.
  • A227405 (program): Order of the symmetry group of the densest possible packing of N circles in a larger circle. (If there are different patterns with the same density pick the largest value of the symmetry group order.)
  • A227406 (program): Number of unimodal functions f:[n]->[2^n].
  • A227412 (program): Primes of the form n^3 + (n+1)^3 + 2.
  • A227415 (program): a(n) = (n+1)!! mod n!!.
  • A227417 (program): Integer triples a(3n-2) = n, a(3n-1) = n+4, and a(3n) = n+7.
  • A227418 (program): Array A(n,k) with all numbers m such that 3*m^2 +- 3^k is a square and their corresponding square roots, read downward by diagonals.
  • A227428 (program): Number of twos in row n of triangle A083093.
  • A227430 (program): Expansion of x^2*(1-x)^3/((1-2*x)*(1-x+x^2)*(1-3*x+3x^2)).
  • A227431 (program): Fibonacci differences triangle, T(n,k), k<=n, where column k holds the k-th difference of A000045, read by rows.
  • A227438 (program): Number of n X 2 0,1 arrays indicating 2 X 2 subblocks of some larger (n+1) X 3 binary array having two adjacent 1’s and two adjacent 0’s.
  • A227451 (program): Number whose binary expansion encodes via runlengths the partition that is at the top of the main trunk of Bulgarian solitaire game tree drawn for the deck with n(n+1)/2 cards.
  • A227453 (program): Numbers k such that the distance to the largest square less than k is a multiple of 4.
  • A227454 (program): Expansion of q * (f(q^9) / f(q))^3 in powers of q where f() is a Ramanujan theta function.
  • A227456 (program): Number of permutations i_0, i_1, …, i_n of 0, 1, …, n with i_0 = 0 and i_n = 1 such that all the n+1 numbers i_0^2+i_1, i_1^2+i_2, …, i_{n-1}^2+i_n, i_n^2+i_0 are of the form (p+1)/4 with p a prime congruent to 3 modulo 4.
  • A227464 (program): E.g.f. equals the series reversion of sin(x) / exp(x).
  • A227466 (program): E.g.f. equals the series reversion of tanh(x) / exp(x).
  • A227469 (program): a(n) = binomial((n+1)^2, n) * (2*n+1) / (n+1)^2 for n>=0.
  • A227471 (program): Position of first 0 in the binary representation of prime(n), starting the count of positions at 1 for the least significant bit.
  • A227474 (program): Denominator/27 of hypergeom([n+1/2,1],[n+3],-3).
  • A227477 (program): Exponent of the group of Lipschitz quaternions in a reduced system modulo n.
  • A227498 (program): Expansion of (1/q) * (f(q) / f(q^9))^3 in powers of q where f() is a Ramanujan theta function.
  • A227499 (program): Number of the Lipschitz quaternions in a reduced system modulo n.
  • A227501 (program): Number of non-congruent solutions of x^2 - xy + y^2 == 1 (mod n).
  • A227506 (program): Schroeder triangle sums: a(2*n-1) = A010683(2*n-2) and a(2*n) = A010683(2*n-1) - A001003(2*n-1).
  • A227512 (program): Floor(-1/n + 1/log((2n+1)/(2n-1))).
  • A227513 (program): Round(-1/n + 1/log((2n+1)/(2n-1))).
  • A227524 (program): Expansion of 1/((1-3x)(1-9x)(1-27x)).
  • A227526 (program): G.f.: Sum_{n>=0} x^n * (1+x)^A003188(n), where A003188(n) = n XOR [n/2] is the Gray code for n.
  • A227527 (program): G.f.: Sum_{n>=0} x^n * (1-x)^A003188(n), where A003188(n) = n XOR [n/2] is the Gray code for n.
  • A227540 (program): Denominator of the rationals obtained from the e.g.f. D(1,x), a Debye function.
  • A227541 (program): a(n) = floor(13*n^2/4).
  • A227542 (program): a(n) is the number of all terms preceding a(n-1) that have the same even-odd parity as a(n-1).
  • A227545 (program): The number of idempotents in the Brauer monoid on [1..n].
  • A227546 (program): n! + n^2 + 1.
  • A227547 (program): a(n) = a(n-1) + prime(n-1), with a(1)=3.
  • A227554 (program): Number of n X 2 0,1 arrays indicating 2 X 2 subblocks of some larger (n+1) X 3 binary array having nonzero determinant, with rows and columns of the latter in lexicographically nondecreasing order.
  • A227559 (program): Number of partitions of n into distinct parts with boundary size 2.
  • A227568 (program): Largest k such that a partition of n into distinct parts with boundary size k exists.
  • A227570 (program): Numerators of rationals with e.g.f. D(3,x), a Debye function.
  • A227571 (program): Denominators of rationals with e.g.f. D(3,x), a Debye function.
  • A227573 (program): Numerators of rationals with e.g.f. D(4,x), a Debye function.
  • A227582 (program): Expansion of (2+3*x+2*x^2+2*x^3+3*x^4+x^5-x^6)/(1-2*x+x^2-x^5+2*x^6-x^7).
  • A227587 (program): Expansion of (phi(-q^3)^2 / (phi(-q) * phi(-q^9)))^2 in powers of q where phi() is a Ramanujan theta function.
  • A227589 (program): Maximum label within a minimal labeling of n identical 4-sided dice yielding the most possible sums.
  • A227595 (program): Expansion of phi(-x) * psi(x^3)^2 / chi(-x^3) in powers of x where phi(), psi(), chi() are Ramanujan theta functions.
  • A227621 (program): The nearest integer of perimeter of T-square (fractal) after n-iterations, starting with a unit square.
  • A227622 (program): Primes p of the form m^2 + 27.
  • A227623 (program): Numbers n such that phi(n) + pi(n) is prime.
  • A227625 (program): Indicator sequence of primes p > 3: k = p mod 6, if k = 5 then a(n) = -1, if k = 1 then a(n) = 1 else a(n) = 0, a(2) = -1, a(3) = 1.
  • A227628 (program): Number of Lipschitz quaternions X such that X^2 == X (mod n).
  • A227635 (program): G.f.: Sum_{n>=1} x^n * (1+x)^n / (1-x^n).
  • A227637 (program): Number of n X 2 0,1 arrays indicating 2 X 2 subblocks of some larger (n+1) X 3 binary array having determinant equal to one, with rows and columns of the latter in nondecreasing lexicographic order.
  • A227653 (program): a(1) = least k such that 1/2 + 1/3 < H(k) - H(3); a(2) = least k such that H(a(1)) - H(3) < H(k) -H(a(1)), and for n > 2, a(n) = least k such that H(a(n-1)) - H(a(n-2) > H(k) - H(a(n-1)), where H = harmonic number.
  • A227665 (program): Number of lattice paths from {n}^3 to {0}^3 using steps that decrement one component by 1 such that for each point (p_1,p_2,p_3) we have abs(p_{i}-p_{i+1}) <= 1.
  • A227675 (program): Number of n X 2 0,1 arrays indicating 2 X 2 subblocks of some larger (n+1) X 3 binary array having an odd sum, with rows and columns of the latter in lexicographically nondecreasing order.
  • A227683 (program): Number of digits in n-th Mersenne number.
  • A227695 (program): Expansion of psi(x)^2 * phi(-x)^6 in powers of x where phi(), psi() are Ramanujan theta functions.
  • A227696 (program): Expansion of f(x^3)^3 / f(x) in powers of x where f() is a Ramanujan theta function.
  • A227703 (program): The Wiener index of the zig-zag polyhex nanotube TUHC_6[2n,2] defined pictorially in Fig. 1 of the Eliasi et al. reference.
  • A227704 (program): The hyper-Wiener index of the zig-zag polyhex nanotube TUHC_6[2n,2] defined pictorially in Fig. 1 of the Eliasi et al. reference.
  • A227705 (program): The Wiener index of the nanostar dendrimer defined pictorially as G(n) in the Darafsheh et al. reference.
  • A227707 (program): The terminal Wiener index of the dendrimer D_n defined pictorially in Fig. 1 of the Heydari et al. reference.
  • A227712 (program): a(n) = 9*2^n - 3*n - 5.
  • A227717 (program): Decimal expansion of the area of the quartic curve with implicit Cartesian equation x^4 + y^2 = 1 (sometimes called “elliptic lemniscate”).
  • A227719 (program): Floor(1/s(n)), where s(n) = n*log(1+1/n) - (2n-1)/(2n).
  • A227720 (program): Round(1/s(n)), where s(n) = n*log(1+1/n) - (2n-1)/(2n).
  • A227721 (program): Floor(1/s(n)), where s(n) = (2n+1)/(2n+2) - n*log((n+1)/n).
  • A227726 (program): a(n) = [x^n] (1 + x)/(1 - x)^(2*n+1).
  • A227728 (program): a(1) = greatest k such that H(k) - H(2) < 1/1 + 1/2; a(2) = greatest k such that H(k) - H(a(1)) < H(a(1)) - H(2); and for n>2, a(n) = greatest k such that H(k) - H(a(n-1) < H(a(n-1)) - H(a(n-2)), where H = harmonic number.
  • A227732 (program): O.g.f.: exp( Sum_{n>=1} (sigma(2*n)^2 - sigma(n)^2) * x^n/n ).
  • A227733 (program): a(n) = sigma(2*n)^2 - sigma(n)^2.
  • A227737 (program): n occurs as many times as there are runs in binary representation of n.
  • A227740 (program): Integers from 0 to A037834(n) followed by integers from 0 to A037834(n+1) and so on.
  • A227742 (program): Fixed points of permutation A227741.
  • A227747 (program): Number of n X 2 0,1 arrays indicating 2 X 2 subblocks of some larger (n+1) X 3 binary array having determinant equal to one.
  • A227756 (program): Primes p such that antisigma(p) = antisigma(p+1) + 12, where antisigma = A024816.
  • A227758 (program): a(n) = sigma(sigma(n)) - sigma(n) - n, where sigma(n) = A000203(n) = sum of the divisors of n.
  • A227759 (program): Numbers n such that A227758(n) = sigma(sigma(n)) - sigma(n) - n < 0, where sigma(n) = A000203(n) = sum of the divisors of n
  • A227760 (program): Numbers n such that A227758(n) = sigma(sigma(n)) - sigma(n) - n > 0, where sigma(n) = A000203(n) = sum of the divisors of n.
  • A227776 (program): a(n) = 6*n^2 + 1.
  • A227786 (program): Take squares larger than 1, subtract 3 from even squares and 2 from odd squares; a(n) = a(n-1) + A168276(n+1) (with a(1) = 1).
  • A227788 (program): Sum of indices of Fibonacci numbers in Zeckendorf representation of n, assuming the units place is Fibonacci(2).
  • A227789 (program): Sum of indices of Fibonacci numbers in Zeckendorf representation of n, assuming that the units place is Fibonacci(1).
  • A227790 (program): Difference between 3n^2 and the nearest square number.
  • A227791 (program): Central terms of the triangle in A227550.
  • A227792 (program): Expansion of (1 + 6*x + 17*x^2 - x^3 - 3*x^4)/(1 - 6*x^2 + x^4).
  • A227793 (program): Numbers whose digital sum is a multiple of 5.
  • A227804 (program): a(1) = greatest k such that H(k) - H(8) < H(8) - H(4); a(2) = greatest k such that H(k) - H(a(1)) < H(a(1)) - H(8), and for n > 2, a(n) = greatest k such that H(k) - H(a(n-1) > H(a(n-1)) - H(a(n-2)), where H = harmonic number.
  • A227805 (program): Sum of even numbers starting at 2, alternating signs.
  • A227816 (program): a(1) = greatest k such that H(k) - H(6) < H(6) - H(3); a(2) = greatest k such that H(k) - H(a(1)) < H(a(1)) - H(6), and for n > 2, a(n) = greatest k such that H(k) - H(a(n-1) > H(a(n-1)) - H(a(n-2)), where H = harmonic number.
  • A227830 (program): Denominators of coefficients in expansion of x/(exp(x)-1).
  • A227831 (program): Numerators of coefficients in Taylor series for LambertW(x).
  • A227832 (program): Sum of odd numbers starting with 1, alternating signs (beginning with plus)
  • A227833 (program): 3-adic valuation of A005130(n).
  • A227834 (program): 2^a(n) is the highest power of 2 dividing A000930(n).
  • A227835 (program): 3^a(n) is the highest power of 3 dividing A000930(n).
  • A227836 (program): 2^a(n) is the highest power of 2 dividing A214551(n).
  • A227837 (program): 3^a(n) is the highest power of 3 dividing A214551(n).
  • A227840 (program): 3^a(n) is the highest power of 3 dividing A000110(n).
  • A227841 (program): Partial sums of A014817.
  • A227842 (program): First differences of A014817.
  • A227844 (program): Lexicographically earliest sequence whose second differences are the digits of Pi.
  • A227845 (program): G.f.: Sum_{n>=0} x^n / (1-x)^(2*n+1) * [ Sum_{k=0..n} C(n,k)^2*x^k ]^2.
  • A227849 (program): a(n) = 2 * floor( 3/14 * n^2) if n even, a(n) = 2 * round( 3/14 * n^2) -1 if n odd.
  • A227858 (program): Numbers which start and end with the same digit in decimal.
  • A227861 (program): Sum i + j for integers 2^i*3^j (A033845).
  • A227863 (program): Numbers congruent to {1,49} mod 120.
  • A227868 (program): Composite numbers congruent to 7 or 23 (mod 30).
  • A227869 (program): Composite numbers congruent to 7 (mod 30).
  • A227871 (program): Sum of digits of 14^n.
  • A227872 (program): Number of odious divisors (A000069) of n.
  • A227873 (program): Sum of odious divisors of n. See A000069 for odious numbers.
  • A227874 (program): Numbers n such that tau(n+1) - tau(n) = -2, where tau(n) = the number of divisors of n (A000005).
  • A227881 (program): Sum of digits of 17^n.
  • A227896 (program): 32-beat repeating palindromic sequence: digital roots of Fibonacci numbers indexed by the set of natural numbers not divisible by 2, 3 or 5 (A007775).
  • A227897 (program): Numbers k such that k^2 + 2 is not squarefree.
  • A227902 (program): Numbers n such that triangular(n) divides binomial(2n,n).
  • A227906 (program): Coins left after packing heart patterns (fixed orientation) into n X n coins.
  • A227910 (program): The number of necklaces with n beads of white and red colors, including at least three white ones.
  • A227911 (program): Number of remainders occurring only once when dividing n by 1,2,…n.
  • A227917 (program): Number of semi-increasing binary plane trees with n vertices.
  • A227918 (program): Sum over all permutations beginning and ending with ascents, and without double ascents on n elements and each permutation contributes 2 to the power of the number of double descents.
  • A227921 (program): Odd odious numbers (A000069), all divisors of which are odious.
  • A227930 (program): Primes p such that p-1 and p+1 have an even Hamming weight.
  • A227934 (program): G.f.: Sum_{n>=0} x^n / (1-x)^(n^4).
  • A227935 (program): G.f.: Sum_{n>=0} x^n / (1-x)^(n^5).
  • A227936 (program): Triangular numbers which become primes when their rightmost digit is removed.
  • A227937 (program): Partitions of n labeled elements into subsets of two or three elements.
  • A227944 (program): Number of iterations of “take odd part of phi” (A053575) to reach 1 from n.
  • A227956 (program): Possible lengths of minimal prime number rulers.
  • A227957 (program): Number of primes that are of the form n - 2^k - k^2.
  • A227959 (program): Number of tilings using monominoes and L-trominoes in 2 X n chessboard, such that three monominoes cannot occur together in shape of L-tromino.
  • A227964 (program): Triangle where the g.f. of row n equals (1-x-x^2+x^3)^n and terms T(n,k) are read by rows n>=0, k=0..3*n.
  • A227965 (program): a(1) = least k such that 1 + 1/2 < H(k) - H(2); a(2) = least k such that H(a(1)) - 1/2 < H(k) -H(a(1)), and for n > 2, a(n) = least k such that H(a(n-1)) - H(a(n-2) > H(k) - H(a(n-1)), where H = harmonic number.
  • A227970 (program): Triangular arithmetic on half-squares: b(n)*(b(n) - 1)/2 where b(n) = floor(n^2/2).
  • A227978 (program): a(0)=1, a(1)=2; for n>1, a(n) = n*(2^n+4)/4.
  • A227982 (program): Numbers n such that sigma(n+1) - sigma(n-1) > sigma(n); where sigma(n) = A000203(n) = sum of the divisors of n.
  • A227983 (program): Numbers n such that sigma(n+1) - sigma(n-1) < sigma(n); where sigma(n) = A000203(n) = sum of the divisors of n.
  • A227990 (program): 3^a(n) is the highest power of 3 dividing prime(n)+1.
  • A227991 (program): Highest power of 3 dividing prime(n)+1.
  • A227992 (program): Numbers m such that the continuants of their binary representations defined in A072347 equal 1.
  • A227994 (program): Primes that are the sum of the squares of three integers that form an arithmetic sequence with difference 7.
  • A227995 (program): Alternate partial sums of the binomial coefficients C(4*n,n).
  • A227996 (program): Alternate partial sums of the binomial coefficients C(5*n,n).
  • A227999 (program): a(n) = (a(n-1) * a(n-5) + a(n-2) * a(n-4) + a(n-3)^2) / a(n-6), a(0) = a(1) = a(2) = a(3) = 1, a(4) = a(5) = 2.
  • A228002 (program): Alternate partial sums of binomial(2n,n)^2.
  • A228012 (program): The 2-color Rado number for the equation x_1 + x_2 + … + x_n = 2*x_0
  • A228014 (program): Numbers k whose Collatz sequence length is greater than k+1 (counting both the x/2 and the 3x+1 steps).
  • A228016 (program): a(1) = least k such that 1/1+1/2+1/3+1/4+1/5 < H(k) - H(5); a(2) = least k such that H(a(1)) - H(5) < H(k) -H(a(1)), and for n > 2, a(n) = least k such that H(a(n-1)) - H(a(n-2) > H(k) - H(a(n-1)), where H = harmonic number.
  • A228017 (program): Numbers n divisible by the sum of any k-subset of digits of n with k >= 1.
  • A228025 (program): a(1) = least k such that 1/2+1/3+1/4+1/5 < H(k) - H(5); a(2) = least k such that H(a(1)) - H(5) < H(k) -H(a(1)), and for n > 2, a(n) = least k such that H(a(n-1)) - H(a(n-2) > H(k) - H(a(n-1)), where H = harmonic number.
  • A228037 (program): Odd-indexed terms of Agoh’s congruence A046094: a(n) is conjectured to be 1 iff 2n+1 is prime.
  • A228039 (program): Thue-Morse sequence along the squares: A010060(n^2).
  • A228056 (program): Numbers of the form p * m^2, where p is prime and m > 1.
  • A228057 (program): Odd numbers of the form p * m^2, where p is prime and m > 1.
  • A228071 (program): Write n in binary and interpret as a decimal number; a(n) is this quantity minus n.
  • A228074 (program): A Fibonacci-Pascal triangle read by rows: T(n,0) = Fibonacci(n), T(n,n) = n and for n > 0: T(n,k) = T(n-1,k-1) + T(n-1,k), 0 < k < n.
  • A228075 (program): Numbers n whose 10’s complement is prime, i.e., 10^k-n, where k is the number of digits of n, is prime.
  • A228078 (program): a(n) = 2^n - Fibonacci(n) - 1.
  • A228079 (program): a(n) = round((5^n)*4 / 3^n).
  • A228080 (program): (5*n+2)!/(2*(n!)^5), n >= 0.
  • A228081 (program): a(n) = 64^n + 1.
  • A228082 (program): Numbers that are of the form k + sum of binary digits of k for some nonnegative integer k.
  • A228085 (program): a(n) = number of distinct k which satisfy n = k + wt(k), where wt(k) (A000120) gives the number of 1’s in binary representation of a nonnegative integer k.
  • A228088 (program): Numbers n for which there is a unique k which satisfies n = k + wt(k), where wt(k) (A000120) gives the number of 1’s in binary representation of nonnegative integer k.
  • A228093 (program): Primes congruent to 5 (mod 504).
  • A228102 (program): Numbers n such that sum of all primes <=n is prime.
  • A228105 (program): a(n) = 432*n^6.
  • A228119 (program): Numbers n such that n * (product of digits of n) + 1 is prime.
  • A228120 (program): a(n) = (1^2 + 1)*(2^2 + 1)*(3^2 + 1)*…*(((prime(n) - 1)/2)^2 + 1).
  • A228121 (program): Numbers n such that 3n - 4 is prime.
  • A228124 (program): Number of blocks in a Steiner Quadruple System of order A047235(n+1).
  • A228132 (program): First differences of A014311.
  • A228137 (program): Numbers that are congruent to {1, 4} mod 12.
  • A228138 (program): Number of blocks in a Steiner system S(2, 4, A228137(n+1)).
  • A228140 (program): Numbers n such that n^2 - 2 is not squarefree.
  • A228141 (program): Numbers that are congruent to {1, 5} mod 20.
  • A228142 (program): Number of blocks in a Steiner system S(2, 5, A228141(n+1)).
  • A228157 (program): Numbers n which are anagrams of n+9.
  • A228158 (program): Numbers n such that the cardinality of (natural numbers <=n with a first digit of 1) = n/2.
  • A228161 (program): Number triangle associated to Chebyshev polynomials of the second kind.
  • A228172 (program): Number of integer pairs (x,y) such that 0<=y<=x, x>0, and x^2+y^2<=n^2.
  • A228175 (program): Least positive k such that n^n * k^k + 1 is a prime, or 0 if no such k exists.
  • A228177 (program): Floor(n*(sqrt(6)+sqrt(5))).
  • A228178 (program): The number of boundary edges for all ordered trees with n edges.
  • A228180 (program): The number of single edges on the boundary of ordered trees with n edges.
  • A228183 (program): Semiprimes generated by the Euler polynomial x^2 + x + 41.
  • A228184 (program): Numbers k such that k^2 + k + 41 is semiprime.
  • A228186 (program): a(n) is the smallest natural number k such that (k+n+1)!*(k-n-2)! < 2*k!*(k-1)!.
  • A228188 (program): Smallest triangular number divisible by 10^n.
  • A228189 (program): Volume of right circular cone (rounded down) with the diameter of base and height equal to n.
  • A228190 (program): a(n) = sum_{i=1..n} prime(i) + product_{i=1..n} prime(i).
  • A228191 (program): a(n) is the smallest number m such that the m-th triangular number ends in n zeros.
  • A228192 (program): a(n) = A001850(n^2), where A001850 forms the central Delannoy numbers.
  • A228193 (program): G.f.: exp( Sum_{n>=1} A001850(n^2)*x^n/n ), where A001850 forms the central Delannoy numbers.
  • A228197 (program): Number of n-edge ordered trees with bicolored boundary edges.
  • A228207 (program): x-values in the solution to x^2 - 20y^2 = 176.
  • A228208 (program): y-values in the solution to x^2 - 20y^2 = 176.
  • A228209 (program): x-values in the solutions to x^2 - 10y^2 = 9.
  • A228210 (program): x-values in the solutions to x^2 - 5y^2 = 44.
  • A228219 (program): Number of second differences of arrays of length 4 of numbers in 0..n.
  • A228220 (program): Number of second differences of arrays of length 5 of numbers in 0..n.
  • A228221 (program): Number of second differences of arrays of length 6 of numbers in 0..n.
  • A228227 (program): Primes congruent to {7, 11} mod 16.
  • A228228 (program): Primes congruent to {3, 5, 13, 15} mod 16.
  • A228229 (program): Recurrence a(n) = n*(n + 1)*a(n-1) + 1 with a(0) = 1.
  • A228230 (program): Recurrence a(n) = 1/2*n*(n + 1)*a(n-1) + 1 with a(0) = 1.
  • A228231 (program): Number of equivalence classes in S_n under the {123, 321} {132, 231}-equivalence.
  • A228232 (program): Number of strict Gaussian primes of norm less than or equal to n in the first quadrant.
  • A228234 (program): Number of strict Gaussian primes of norm less than or equal to n in the first quadrant on or below the first diagonal.
  • A228239 (program): Smaller of corresponding digits of Pi and e.
  • A228244 (program): Primes of the form n^2+17.
  • A228245 (program): The integers occurring in the song “Ten green bottles”.
  • A228246 (program): a(1)=1; for n >= 2, a(n) = round(x), where x is the average length (not counting draws) of a first-to-n match between two chess players of equal strength.
  • A228252 (program): Determinant of the (n+1) X (n+1) matrix with (i,j)-entry equal to (i-2j)^n for all i,j = 0,…,n.
  • A228261 (program): Number of third differences of arrays of length 5 of numbers in 0..n.
  • A228272 (program): Volume of sphere (rounded down) with the diameter equal to n.
  • A228274 (program): a(n) = Sum_{d|n, n/d odd} n * d.
  • A228275 (program): A(n,k) = Sum_{i=1..k} n^i; square array A(n,k), n>=0, k>=0, read by antidiagonals.
  • A228278 (program): Number of n X 3 binary arrays with top left value 1 and no two ones adjacent horizontally, vertically or nw-se diagonally.
  • A228290 (program): a(n) = n^6 + n^5 + n^4 + n^3 + n^2 + n.
  • A228291 (program): a(n) = Sum_{k=1..7} n^k.
  • A228292 (program): a(n) = Sum_{k=1..8} n^k.
  • A228293 (program): a(n) = Sum_{k=1..9} n^k.
  • A228294 (program): a(n) = Sum_{k=1..10} n^k.
  • A228295 (program): The ‘Honeycomb’ or ‘Beehive’ sequence: a(n) = ceiling(12^(1/4)*n).
  • A228297 (program): Generalized meta-Fibonacci sequence a(n) with parameters s=0 and k=5.
  • A228298 (program): Generalized meta-Fibonacci sequence a(n) with parameters s=0 and k=7.
  • A228304 (program): a(n) = Sum_{k=0..n} C(n,k)^4*(-1)^k.
  • A228305 (program): a(1) = 3; for n >= 1, a(2*n) = 2^(n+1), a(2*n+1) = 5*2^(n-1).
  • A228306 (program): The Wiener index of the Kneser graph K(n,2) (n>=5).
  • A228307 (program): The hyper-Wiener index of the Kneser graph K(n,2) (n>=5).
  • A228310 (program): The hyper-Wiener index of the hypercube graph Q(n) (n>=2).
  • A228312 (program): Triangle read by rows: T(m,n) (1<=n<=m) is the hyper-Wiener index of the complete bipartite graph K(m,n).
  • A228317 (program): The hyper-Wiener index of the triangular graph T(n) (n >= 1).
  • A228318 (program): The Wiener index of the graph obtained by applying Mycielski’s construction to the star graph K(1,n).
  • A228319 (program): The hyper-Wiener index of the graph obtained by applying Mycielski’s construction to the star graph K(1,n).
  • A228320 (program): The Wiener index of the graph obtained by applying Mycielski’s construction to the cycle graph C(n).
  • A228321 (program): The Wiener index of the graph obtained by applying Mycielski’s construction to the path graph on n vertices (n>=2).
  • A228329 (program): a(n) = Sum_{k=0..n} (k+1)^2*T(n,k)^2 where T(n,k) is the Catalan triangle A039598.
  • A228338 (program): Third diagonal of Catalan difference table (A059346).
  • A228339 (program): Fourth differences of Catalan numbers (A000108).
  • A228340 (program): Triangle read by rows: T(n,k) = (n-1)*T(n-1,k) + T(n-2,k), with T(n,n-1)=1, T(n,n-2)=n-2, for n >= 1, 0 <= k <= n-1.
  • A228341 (program): Third diagonal (T(n,2)) of triangle in A228340.
  • A228343 (program): The number of ordered trees with bicolored single edges on the boundary.
  • A228344 (program): a(n) = floor(3*n^2/4) - 1.
  • A228347 (program): Triangle of regions and compositions of the positive integers (see Comments lines for definition).
  • A228348 (program): Triangle of regions and compositions of the positive integers (see Comments lines for definition).
  • A228352 (program): Triangle read by rows, giving antidiagonals of an array of sequences representing the number of compositions of n when there are N types of ones (the sequences in the array begin (1, N, …).
  • A228353 (program): Primes of the form 3p - 4 where p is prime.
  • A228354 (program): Indices (k) of partitions in the list of compositions of j in colexicographic order, if 1<=k<=2^(j-1), j>=1.
  • A228356 (program): The triangle associated with the family of polynomials W_n(x).
  • A228357 (program): Numbers n such that sum of all primes <=n is not prime.
  • A228358 (program): Numbers n such that 3*n - 4 is not prime.
  • A228359 (program): Numbers n whose 10’s complement is not prime, i.e., 10^k-n, where k is the number of digits of n, is not prime.
  • A228361 (program): The number of all possible covers of L-length line segment by 2-length line segments with allowed gaps < 2.
  • A228362 (program): The number of all possible covers of L-length line segment by 3-length line segments with allowed gaps < 3.
  • A228363 (program): Sorted entries of the multiplication table a*b, with a>1, b>1.
  • A228364 (program): G.f.: x^2*(x+1)^2/(x^3+x^2-1)^2.
  • A228365 (program): Inverse binomial transform of the Galois numbers G_(n)^{(3)} (A006117).
  • A228366 (program): Toothpick sequence from a diagram of compositions of the positive integers (see Comments lines for definition).
  • A228367 (program): n-th element of the ruler function plus the highest power of 2 dividing n.
  • A228368 (program): Difference between the n-th element of the ruler function and the highest power of 2 dividing n.
  • A228370 (program): Toothpick sequence from a diagram of compositions of the positive integers (see Comments lines for definition).
  • A228371 (program): First differences of A228370. Also A001511 and A006519 interleaved.
  • A228372 (program): Number of nontrivial divisors in the first n composites.
  • A228373 (program): Numbers n such that 27*n + 1 is not prime.
  • A228374 (program): Numbers n such that 2*prime(n) - prime(n+1) is not prime.
  • A228385 (program): Number of n X 3 binary arrays with top left value 1 and no two ones adjacent horizontally or vertically.
  • A228391 (program): Volume of elliptic cone (rounded down) with semi-minor axis = height = n and semi-major axis = 3*n/2.
  • A228392 (program): The number of permutations of length n sortable by 2 block transpositions.
  • A228394 (program): The number of permutations of length n sortable by 2 prefix block transpositions.
  • A228396 (program): The number of permutations of length n sortable by 2 reversals.
  • A228398 (program): The number of permutations of length n sortable by 3 prefix reversals (in the pancake sorting sense).
  • A228403 (program): The number of boundary twigs for complete binary twigs. A twig is a vertex with one edge on the boundary and only one other descendant.
  • A228404 (program): The number of complete binary trees with bicolored twigs. A twig is a vertex with one child on the boundary and the other child having no descendants.
  • A228405 (program): Pellian Array, A(n, k) with numbers m such that 2*m^2 +- 2^k is a square, and their corresponding square roots, read downward by diagonals.
  • A228406 (program): Sequences from the quartic oscillator.
  • A228409 (program): a(n) = 4*mu(n) + 5, where mu is the Moebius function (A008683).
  • A228411 (program): G.f.: ( (1 - sqrt(1-32*x)) / (16*x) )^(1/4).
  • A228423 (program): Sum of the squared primes less than or equal to n.
  • A228437 (program): Denominator of n/24.
  • A228441 (program): G.f.: Sum_{k>0} -(-x)^k / (1 + x^k).
  • A228443 (program): G.f.: Sum_{k>=0} (2*k + 1) * x^k / (1 + x^(2*k + 1)).
  • A228446 (program): a(n) = smallest prime p such that 2*n+1 = p + x*(x+1) for some positive integer x, or -1 if no such prime exists.
  • A228447 (program): Expansion of q * (psi(q^3) * psi(q^6)) / (psi(q) * phi(q)) in powers of q where phi(), psi() are Ramanujan theta functions.
  • A228448 (program): a(n) = floor(n!/3^n).
  • A228449 (program): floor(n! / 4^n).
  • A228451 (program): Recurrence: a(2n) = a(n), a(2n+1) = a(n) + 2n + 1, with a(0) = 0, a(1) = 1.
  • A228462 (program): Number of arrays of maxima of three adjacent elements of some length 7 0..n array.
  • A228463 (program): Number of arrays of maxima of three adjacent elements of some length 8 0..n array.
  • A228465 (program): Recurrence a(n) = a(n-1) + 2^n*a(n-2) with a(0)=0, a(1)=1.
  • A228467 (program): Recurrence a(n) = 2^n*a(n-1) - a(n-2) with a(0)=0, a(1)=1.
  • A228469 (program): a(n) = 6*a(n-2) + a(n-4), where a(0) = 2, a(1) = 8, a(2) = 13, a(3) = 49.
  • A228470 (program): a(n) = 6*a(n-2) + a(n-4), where a(0) = 3, a(1) = 11, a(2) = 18, a(3) = 68.
  • A228471 (program): a(n) = 6*a(n-2) + a(n-4), where a(0) = 3, a(1) = 5, a(2) = 19, a(3) = 31.
  • A228472 (program): a(n) = 6*a(n-2) + a(n-4), where a(0) = 5, a(1) = 8, a(2) = 30, a(3) = 49.
  • A228477 (program): Number of nX3 binary arrays with top left value 1 and no two ones adjacent horizontally, vertically or antidiagonally.
  • A228483 (program): a(n) = 2 - mu(n), where mu(n) is the Moebius function (A008683).
  • A228484 (program): a(n) = 2^n*(3*n)!/(n!*(2*n)!).
  • A228495 (program): Characteristic function of the odd odious numbers (A092246).
  • A228497 (program): Decimal expansion of the fourth root of 1/2.
  • A228498 (program): a(n) = sigma(n^2) + phi(n^2) - 2n^2.
  • A228501 (program): Number of n X 3 binary arrays with top left value 1 and no two ones adjacent horizontally, vertically, diagonally or antidiagonally.
  • A228502 (program): Number of n X 4 binary arrays with top left value 1 and no two ones adjacent horizontally, vertically, diagonally or antidiagonally.
  • A228509 (program): a(n) = binomial(n^2+n+1,n) * (n+1) / (n^2+n+1) for n>=0.
  • A228511 (program): a(n) = sum_{k=0}^n binomial(n,k)^2*4^k*A000108(k).
  • A228513 (program): a(n) = Sum_{k=0..n} 2^k*(n!/k!)^2.
  • A228514 (program): a(n) = Sum_{k=0..n} binomial(n,k)^2*binomial(2k,k+1).
  • A228515 (program): Nonlinear recursion: a(n) = a(n-1) + Product_{i=1..(n-1)/2} a(n-2i+1)-a(n-2i).
  • A228521 (program): x-values in the solution to the Pell equation x^2 - 29*y^2 = -1.
  • A228522 (program): y-values in the solution to the Pell equation x^2 - 29*y^2 = -1.
  • A228524 (program): Triangle read by rows: T(n,k) = total number of occurrences of parts k in the n-th section of the set of compositions (ordered partitions) of any integer >= n.
  • A228526 (program): Triangle read by rows: T(n,k) = sum of all parts of size k in all compositions (ordered partitions) of n.
  • A228527 (program): Triangle read by rows: T(n,k) is the sum of all parts of size k of the n-th section of the set of compositions ( ordered partitions) of any integer >= n.
  • A228529 (program): a(n) = prime(n*prime(n)).
  • A228537 (program): x-values in the solution to the Pell equation x^2 - 58*y^2 = -1.
  • A228538 (program): y-values in the solution to the Pell equation x^2 - 58*y^2 = -1.
  • A228546 (program): x-values in the solution to the Pell equation x^2 - 74*y^2 = -1.
  • A228547 (program): y-values in the solution to the Pell equation x^2 - 74*y^2 = -1.
  • A228553 (program): Sum of the products formed by multiplying together the smaller and larger parts of each Goldbach partition of 2n.
  • A228560 (program): Curvature of the circles (rounded down) inscribed in golden triangle arranged as spiral form.
  • A228564 (program): Largest odd divisor of n^2 + 1.
  • A228565 (program): Triangle read by rows: coefficients of descending powers of the polynomial V(n,x) = cos((2n+1)(arccos(x)/2))/cos(arccos(x)/2), n >= 0.
  • A228568 (program): a(n) = 2^n*A056236(n).
  • A228569 (program): Binomial transform of A006497.
  • A228577 (program): The number of 1-length gaps in all possible covers of n-length line by 2-length segments.
  • A228578 (program): Sum of the distinct prime factors of the squarefree semiprimes (A006881).
  • A228581 (program): The number of binary pattern classes in the (2,n)-rectangular grid with 6 ‘1’s and (2n-6) ‘0’s: two patterns are in same class if one of them can be obtained by a reflection or 180-degree rotation of the other.
  • A228583 (program): The number of binary pattern classes in the (2,n)-rectangular grid with 8 ‘1’s and (2n-8) ‘0’s: two patterns are in same class if one of them can be obtained by a reflection or 180-degree rotation of the other.
  • A228587 (program): Sum of the squares (modulo n) of the odd numbers less than n.
  • A228593 (program): a(1) = 2, a(n) = a(n-1)*prime(n-1)*prime(n), where prime(n) denotes the n-th prime number.
  • A228597 (program): The Wiener index of the graph obtained by applying Mycielski’s construction to a benzenoid consisting of a linear chain of n hexagons.
  • A228598 (program): The Wiener index of the graph obtained by applying Mycielski’s construction to the crown graph G(n) (n>=3).
  • A228600 (program): The Szeged index of the n-sunlet graph (n>=3).
  • A228602 (program): a(1) = 17, a(2) = 80, a(n) = 4*(a(n-1) + a(n-2)) for n >= 3.
  • A228603 (program): a(1) = 9, a(2) = 44, a(n) = 4*(a(n-1) + a(n-2)) (n >=3).
  • A228604 (program): The Merrifield-Simmons index of the ortho-polyphenylene chain of length n.
  • A228605 (program): The Merrifield-Simmons index of the meta-polyphenylene chain of length n.
  • A228606 (program): The Merrifield-Simmons index of the para-polyphenylene chain of length n.
  • A228609 (program): Partial sums of the cubes of the tribonacci sequence A000073.
  • A228612 (program): Number of (possibly overlapping) occurrences of the subword given by the binary expansion of n in all binary words of length n.
  • A228620 (program): a(n) = n - phi(n) + mu(n).
  • A228628 (program): 9’s complement of prime(n).
  • A228637 (program): The number triangle associated with the polynomials V_n(x)
  • A228640 (program): a(n) = Sum_{d|n} phi(d)*n^(n/d).
  • A228641 (program): Volume of torus (rounded down) with major radius = n and minor radius = n/3.
  • A228642 (program): Squares of primes mod 100.
  • A228643 (program): Triangle read by rows: T(n,1) = n * (n - 1) + 1 and for k: 1 < k <= n: T(n,k) = T(n,k-1) + T(n-1,k-1).
  • A228647 (program): a(n) = A001609(n^2) for n>=1, where g.f. of A001609 is x*(1+3*x^2)/(1-x-x^3).
  • A228648 (program): G.f.: exp( Sum_{n>=1} A001609(n^2)*x^n/n ), where the l.g.f. of A001609 is -log(1-x-x^3).
  • A228649 (program): Numbers n such that n-1, n and n+1 are all squarefree.
  • A228652 (program): Numbers m such that if an urn contains m balls, with at least one each of c colors, there is no c > 1 for which a combination of c colors exists such that it is equally probable for c balls randomly selected from the urn to all be either the same color or distinct colors.
  • A228655 (program): Number of nX3 binary arrays with top left value 1 and no two ones adjacent horizontally, diagonally or antidiagonally.
  • A228656 (program): Number of nX4 binary arrays with top left value 1 and no two ones adjacent horizontally, diagonally or antidiagonally.
  • A228661 (program): Number of 2Xn binary arrays with top left value 1 and no two ones adjacent horizontally, diagonally or antidiagonally.
  • A228662 (program): Number of 3 X n binary arrays with top left value 1 and no two ones adjacent horizontally, diagonally or antidiagonally.
  • A228678 (program): Number of nX3 binary arrays with no two ones adjacent horizontally, diagonally or antidiagonally.
  • A228679 (program): Number of nX4 binary arrays with no two ones adjacent horizontally, diagonally or antidiagonally.
  • A228684 (program): Number of 3 X n binary arrays with no two ones adjacent horizontally, diagonally or antidiagonally.
  • A228693 (program): Largest number of maximal independent sets of nodes in any tree on n nodes.
  • A228698 (program): a(n) = 8*Product{i=1..n} p(i) - 1, where p(i) = i-th odd prime.
  • A228700 (program): a(n) = 2^n*(4^n-3^(n+1)+3*2^n-1)/6.
  • A228701 (program): a(n) = 2^(n-1)*(3^n-2^(n+1)+1).
  • A228705 (program): Expansion of (1-2*x+4*x^2-2*x^3+x^4)/((1-x)^4*(1+x^2)^2).
  • A228706 (program): Expansion of (1 - 3*x + 5*x^2 - 3*x^3 + x^4)/((1-x)^4*(1+x^2)^2).
  • A228709 (program): Numbers having in decimal representation at least one pair of consecutive digits with the same parity.
  • A228715 (program): Decimal expansion of 1 - Pi/6.
  • A228718 (program): Sequence taken from Garvan’s paper (see slides 28, 29).
  • A228719 (program): Decimal expansion of 3*Pi/5.
  • A228720 (program): Number of partitions in the first n compositions of j, according with the ordering of A228525, if 1<=n<=2^(j-1).
  • A228721 (program): Decimal expansion of 7*Pi.
  • A228728 (program): a(1)=1, a(2)=2 and for n > 2, a(n) is the least integer > a(n-1) such that there is a permutation b(1), …, b(n) of a(1), …, a(n) with b(1) = a(1) and b(n) = a(n), and with the n numbers |b(1)-b(2)|, |b(2)-b(3)|, …, |b(n-1)-b(n)|, |b(n)-b(1)| pairwise distinct.
  • A228729 (program): Product of the positive squares less than or equal to n.
  • A228733 (program): Number of arrays of the median of three adjacent elements of some length n+2 0..1 array.
  • A228741 (program): Number of arrays of the median of three adjacent elements of some length-6 0..n array.
  • A228745 (program): Expansion of (phi(q)^4 + 7 * phi(-q)^4) / 8 in powers of q where phi() is a Ramanujan theta function.
  • A228746 (program): Expansion of 8 * phi(q)^4 - 7 * phi(-q)^4 in powers of q where phi() is a Ramanujan theta function.
  • A228748 (program): Pell numbers (A000129) minus Lucas numbers beginning at 2 (A000032).
  • A228750 (program): Number of n X 4 binary arrays with top left element equal to 1 and no two ones adjacent horizontally or antidiagonally.
  • A228755 (program): Number of 3 X n binary arrays with top left element equal to 1 and no two ones adjacent horizontally or antidiagonally.
  • A228763 (program): a(n) = 2^L(n) - 1, where L(n) is the n-th Lucas number (A000032).
  • A228767 (program): Second bisection of the inverse binomial transform of the rational sequence with e.g.f. (x/2)*(exp(-x)+1)/(exp(x)-1).
  • A228774 (program): Numbers n such that the digits of n, once written in base 16, are only the hexadecimal digits A to F.
  • A228777 (program): Decimal expansion of the third smallest Pisot-Vijayaraghavan number.
  • A228778 (program): a(n) = 2^Fibonacci(n) + 1.
  • A228789 (program): a(n) = 2^L(n) + 1, where L(n) is A000032(n).
  • A228791 (program): Number of n X 3 binary arrays with top left element equal to 1 and no two ones adjacent horizontally or nw-se.
  • A228797 (program): Number of 2 X n binary arrays with top left element equal to 1 and no two ones adjacent horizontally or nw-se.
  • A228808 (program): a(n) = Sum_{k=0..n} binomial(n*k, k^2).
  • A228809 (program): G.f.: exp( Sum_{n>=1} x^n/n * Sum_{k=0..n} binomial(n*k, k^2) ).
  • A228816 (program): Sum of all parts of all partitions of n that contain 1 as a part.
  • A228824 (program): Decimal expansion of 4*Pi/5.
  • A228826 (program): Delayed continued fraction of sqrt(2).
  • A228832 (program): Triangle defined by T(n,k) = binomial(n*k, k^2), for n>=0, k=0..n, as read by rows.
  • A228833 (program): a(n) = Sum_{k=0..[n/2]} binomial((n-k)*k, k^2).
  • A228836 (program): Triangle defined by T(n,k) = binomial(n^2, (n-k)*k), for n>=0, k=0..n, as read by rows.
  • A228837 (program): a(n) = Sum_{k=0..[n/2]} binomial((n-k)^2, (n-2*k)*k).
  • A228838 (program): a(n) = n * A002445(n).
  • A228840 (program): a(n) = 3^n*A228569(n).
  • A228842 (program): Binomial transform of A014448.
  • A228843 (program): a(n) = 4^n*A228842(n).
  • A228848 (program): Round(3*n^2/Pi^2).
  • A228852 (program): G.f.: exp( Sum_{n>=1} x^n/n * Sum_{k=0..n} binomial(n^2, k*(n-k))/2 ).
  • A228857 (program): Odd primes p > 3 for which 14*p+1 is also prime.
  • A228868 (program): Sum of all numbers n>=2 such that in their Fermi-Dirac representation every A050376-factor does not exceed A050376(n).
  • A228869 (program): Numbers n such that 2 * (1^n + 2^n + 3^n + … + n^n) == 0 (mod n).
  • A228871 (program): Odd numbers producing 3 out-of-order odd numbers in the Collatz (3x+1) iteration.
  • A228873 (program): a(n) = F(n) * F(n+1) * F(n+2) * F(n+3), the product of four consecutive Fibonacci numbers, A000045.
  • A228874 (program): a(n) = L(n) * L(n+1) * L(n+2) * L(n+3), the product of four consecutive Lucas numbers, A000032.
  • A228879 (program): a(n+2) = 3*a(n), starting 4,7.
  • A228887 (program): a(n) = binomial(3*n + 1,3).
  • A228888 (program): a(n) = binomial(3*n + 2, 3).
  • A228889 (program): a(n) = 3*n*(3*n + 1)*(3*n + 2).
  • A228901 (program): Column 1 of triangle A228900.
  • A228903 (program): A diagonal of triangle A228902.
  • A228906 (program): A diagonal of triangle A228904.
  • A228908 (program): Primes of the form T(n) + S(n) + C(n) + 1 where T(n), S(n) and C(n) are the n-th triangular, square and cube numbers.
  • A228909 (program): a(n) = 7^n - 6*6^n + 15*5^n - 20*4^n + 15*3^n - 6*2^n + 1.
  • A228910 (program): a(n) = 8^n - 7*7^n + 21*6^n - 35*5^n + 35*4^n - 21*3^n + 7*2^n - 1.
  • A228911 (program): a(n) = 9^n - 8*8^n + 28*7^n - 56*6^n + 70*5^n - 56*4^n + 28*3^n - 8*2^n + 1.
  • A228912 (program): a(n) = 10^n - 9*9^n + 36*8^n - 84*7^n + 126*6^n - 126*5^n + 84*4^n - 36*3^n + 9*2^n - 1.
  • A228919 (program): Numbers n such that 1^(n+1) + 2^(n+1) + … + n^(n+1) == 0 (mod n).
  • A228920 (program): Number of solutions to Sum_{i=1..n} x_i^2 == 0 (mod 4) with x_i in 0..3.
  • A228926 (program): Sum(m^(n+1), m=1…n-1) modulo n.
  • A228935 (program): a(n) = (3 - 6*n)*(-1)^n.
  • A228936 (program): Expansion of (1 + 3*x - 3*x^3 - x^4)/(1 + 2*x^2 + x^4).
  • A228938 (program): E.g.f.: (2 + exp(3*x)) / (4 - exp(3*x)).
  • A228941 (program): The n-th convergent of CF(e) is the a(n)-th convergent of DCF(e), the delayed continued fraction of e.
  • A228947 (program): a(n) = sigma(n) - phi(n) - n.
  • A228949 (program): Coins left when packing boomerangs into n X n coins.
  • A228955 (program): Table: T(n,k) = n!*binomial(n+1,2*k).
  • A228958 (program): a(n) = 1*2 + 3*4 + 5*6 + 7*8 + 9*10 + 11*12 + 13*14 + … + (up to n).
  • A228959 (program): Total sum of squared lengths of ascending runs in all permutations of [n].
  • A228960 (program): a(n) = [x^n] (1 + x + x^3 + x^4)^n.
  • A228966 (program): G.f. satisfies: A(x) = (1 + x*A(x))^2 * (1 + A(x)) / 2.
  • A228967 (program): Table read by rows; T(n,k) = 2n for k = 1, T(n,k) = 9n for k = 2.
  • A228980 (program): Number of n X 2 0..1 arrays of the median of the corresponding element, the element to the east and the element to the south in a larger (n+1) X 3 0..1 array.
  • A228987 (program): G.f. satisfies: A(x) = 1 + x*A(x)^3 + x^3*A(x)^8.
  • A229003 (program): Total sum of cubed lengths of ascending runs in all permutations of [n].
  • A229004 (program): Indices of Bell numbers divisible by 3.
  • A229013 (program): Number of arrays of median of three adjacent elements of some length-5 0..n array, with no adjacent equal elements in the latter.
  • A229014 (program): Number of arrays of median of three adjacent elements of some length 6 0..n array, with no adjacent equal elements in the latter.
  • A229020 (program): Decimal expansion of 1 - 1/(1*2) + 1/(1*2*2) - 1/(1*2*2*3) + …
  • A229022 (program): a(n) = sopf(n) + n/rad(n).
  • A229025 (program): Expansion of 1/((1-2x)(1-4x)(1-5x)(1-7x)(1-8x)).
  • A229026 (program): Expansion of 1/((1-x)*((1-5x)^2)*(1-8x)).
  • A229031 (program): Number of 5-colorings of the strong product of the complete graph K2 and the cycle graph Cn.
  • A229032 (program): Triangle T(n,k), 0 <= k <= n, read by rows, defined by T(n,k) = 4^k * C(n+1,2*k+1).
  • A229034 (program): Indices of records in A229030.
  • A229035 (program): Partial sums of A082233 (read sequentially meandering).
  • A229036 (program): G.f.: Sum_{n>=0} (3*n-1)^n * x^n / (1 + (3*n-1)*x)^n.
  • A229039 (program): G.f.: Sum_{n>=0} (n+2)^n * x^n / (1 + (n+2)*x)^n.
  • A229042 (program): Series reversion of (sqrt(1+4*x) - 1)/2 - x^2.
  • A229043 (program): Series reversion of (sqrt(1+4*x) - 1)/2 - x^3.
  • A229046 (program): G.f.: Sum_{n>=0} n! * x^n * (1+x)^n / Product_{k=1..n} (1 + k*x).
  • A229061 (program): The (n+1)-th term of the n-th differences of the prime sequence.
  • A229062 (program): 1 if n is representable as sum of two nonnegative squares, otherwise 0.
  • A229063 (program): Volume of the Johnson square pyramid (rounded down) with all the edge lengths equal to n.
  • A229065 (program): Numbers of the form 2^(p-1)+3, where p is prime.
  • A229067 (program): Sum of n-th prime and next perfect square.
  • A229078 (program): Number of ascending runs in {1,…,n}^n.
  • A229080 (program): Primes of the form T(k) + S(k) + 1 where T(k) is the k-th triangular number and S(k) is the k-th square number.
  • A229083 (program): Numbers k such that the distance between the k-th triangular number and the nearest square is at most 1.
  • A229093 (program): The clubs patterns appearing in n X n coins.
  • A229099 (program): Decimal expansion of 1 - 6/Pi^2.
  • A229109 (program): a(n) = n plus the number of its distinct prime factors.
  • A229110 (program): Sum of non-divisors of n reduced modulo n.
  • A229118 (program): Distance from the n-th triangular number to the nearest square.
  • A229125 (program): Numbers of the form p * m^2, where p is prime and m > 0: union of A228056 and A000040.
  • A229127 (program): Number of n-digit numbers containing the digit ‘0’.
  • A229131 (program): Numbers k such that the distance between the k-th triangular number and the nearest square is exactly 1.
  • A229134 (program): Square numbers that are the sum of two non-consecutive triangular numbers.
  • A229135 (program): n * (2 + 2^(2*n - 1)).
  • A229136 (program): Number of solutions to Sum_{i=1..n} x_i^2 == 1 (mod 4) with x_i in 0..3.
  • A229141 (program): Number of circular permutations i_1, …, i_n of 1, …, n such that all the n sums i_1^2+i_2, …, i_{n-1}^2+i_n, i_n^2+i_1 are among those integers m with the Jacobi symbol (m/(2n+1)) equal to 1.
  • A229143 (program): Expansion of (b(q^3) - b(q)) / 3 in powers of q where b() is a cubic AGM theta function.
  • A229144 (program): Partial sums of (Fibonacci numbers mod 3).
  • A229146 (program): a(n) = n^3*(5*n+3)/2.
  • A229147 (program): a(n) = n^4*(3*n+2).
  • A229148 (program): a(n) = n^5*(7*n+5)/2.
  • A229149 (program): a(n) = n^6*(4*n+3).
  • A229150 (program): a(n) = n^7*(9*n+7)/2.
  • A229151 (program): a(n) = n^8*(5*n+4).
  • A229152 (program): a(n) = n^9*(11*n+9)/2.
  • A229153 (program): Numbers of the form c * m^2, where m > 0 and c is composite and squarefree.
  • A229154 (program): The clubs patterns appearing in n X n coins, with rotation allowed.
  • A229157 (program): Primes of the form T(n) + C(n) - 1 where T(n) and C(n) are n-th triangular and cube numbers.
  • A229169 (program): Define a sequence of real numbers by b(1)=2, b(n+1) = b(n) + log_2(b(n)); a(n) = floor( b(n) ).
  • A229170 (program): Define a sequence of real numbers by b(1)=2, b(n+1) = b(n) + log_2(b(n)); a(n) = ceiling( b(n) ).
  • A229183 (program): a(n) = n*(n^2 + 3)/2.
  • A229204 (program): For k>0, a(3k+1) = k*(k-3), a(3k+2) = k*(k-1), a(3k+3) = k*(k-1)-1.
  • A229212 (program): Square array of numerators of t(n,k) = (1+1/(k*n))^n, read by descending antidiagonals.
  • A229213 (program): Square array of denominators of t(n,k) = (1+1/(k*n))^n, read by descending antidiagonals.
  • A229217 (program): If 1 and 2 represent the 2D vectors (1,0) and (0,1) and -1 and -2 are the negation of these vectors, then this sequence represents the Koch curve.
  • A229220 (program): a(n) = a(n-1)^2 + (-1)^n with a(1)=1.
  • A229221 (program): Numbers n such that n - (product of digits of n) is prime.
  • A229232 (program): Number of undirected circular permutations pi(1), …, pi(n) of 1, …, n with the n numbers pi(1)*pi(2)-1, pi(2)*pi(3)-1, …, pi(n-1)*pi(n)-1, pi(n)*pi(1)-1 all prime.
  • A229244 (program): Number of n-permutations such that at least one cycle has size ceiling(n/2).
  • A229253 (program): Total number of elements of nonempty subsets of divisors of n.
  • A229274 (program): Composite squarefree numbers n such that p+tau(n) divides n-sigma(n), where p are the prime factors of n, tau(n) = A000005(n) and sigma(n) = A000203(n).
  • A229277 (program): Number of ascending runs in {1,…,3}^n.
  • A229278 (program): Number of ascending runs in {1,…,4}^n.
  • A229279 (program): Number of ascending runs in {1,…,5}^n.
  • A229280 (program): Number of ascending runs in {1,…,6}^n.
  • A229281 (program): Number of ascending runs in {1,…,7}^n.
  • A229282 (program): Number of ascending runs in {1,…,8}^n.
  • A229283 (program): Number of ascending runs in {1,…,9}^n.
  • A229284 (program): Number of ascending runs in {1,…,10}^n.
  • A229294 (program): Number of solutions to x^2 + y^2 + z^2 + t^2 == n (mod 2*n) for x,y,z,t in [0, 2*n).
  • A229297 (program): Number of solutions to x^2 == n (mod 2*n) for 0 <= x < 2*n.
  • A229303 (program): Numbers n such that A031971(2*n) == n (mod 2*n).
  • A229314 (program): Number of n X 1 0..3 arrays of the median of the corresponding element, the element to the east and the element to the south in a larger (n+1) X 2 0..3 array without adjacent equal elements in the latter.
  • A229324 (program): Composite squarefree numbers n such that p + tau(n) divides n - phi(n), where p are the prime factors of n, tau(n) = A000005(n) and phi(n) = A000010(n).
  • A229335 (program): Sum of sums of elements of subsets of divisors of n.
  • A229337 (program): Sum of products of elements of nonempty subsets of divisors of n.
  • A229338 (program): Product of products of elements of subsets of divisors of n.
  • A229339 (program): GCD of all sums of n consecutive Lucas numbers.
  • A229340 (program): Euler totient function of the arithmetic derivative of n: a(n) = phi(n’), a(1) = 0.
  • A229341 (program): a(n) = tau(n’), the number of divisors of the arithmetic derivative of n.
  • A229342 (program): a(n) = sigma(n’), the sum of divisors of the arithmetic derivative of n.
  • A229343 (program): Moebius function of the arithmetic derivative of n: a(n) = mu(n’).
  • A229347 (program): a(1) = 1, for n > 1 a(n) = n*2^(omega(n)-1) where omega is A001221.
  • A229351 (program): Numerators of the ordinary convergents of continued fraction [2/1, 3/2, 4/3, 5/4,…].
  • A229354 (program): Total sum of n-th powers of parts in all partitions of 3.
  • A229355 (program): Total sum of n-th powers of parts in all partitions of 4.
  • A229356 (program): Total sum of n-th powers of parts in all partitions of 5.
  • A229357 (program): Total sum of n-th powers of parts in all partitions of 6.
  • A229366 (program): Number of n X 2 0..2 arrays avoiding 11 horizontally, 22 vertically and 00 antidiagonally.
  • A229374 (program): Number of n X 2 0..2 arrays avoiding 11 horizontally, 22 vertically and 00 diagonally or antidiagonally.
  • A229397 (program): Number of n X 3 0..2 arrays with top left element 0, horizontal differences mod 3 never 1, vertical differences mod 3 never -1, and antidiagonal differences never 0.
  • A229414 (program): Number of set partitions of {1,…,3n} into sets of size at most 3.
  • A229422 (program): Number of n X 2 0..2 arrays with horizontal differences mod 3 never 1, vertical differences mod 3 never -1, rows lexicographically nondecreasing, and columns lexicographically nonincreasing.
  • A229423 (program): Number of n X 3 0..2 arrays with horizontal differences mod 3 never 1, vertical differences mod 3 never -1, rows lexicographically nondecreasing, and columns lexicographically nonincreasing.
  • A229439 (program): Number of n X 2 0..2 arrays with horizontal differences mod 3 never 1, vertical differences mod 3 never -1, and rows and columns lexicographically nondecreasing.
  • A229440 (program): Number of n X 3 0..2 arrays with horizontal differences mod 3 never 1, vertical differences mod 3 never -1, and rows and columns lexicographically nondecreasing.
  • A229446 (program): Number of 3 X n 0..2 arrays with horizontal differences mod 3 never 1, vertical differences mod 3 never -1, and rows and columns lexicographically nondecreasing.
  • A229447 (program): Number of 4 X n 0..2 arrays with horizontal differences mod 3 never 1, vertical differences mod 3 never -1, and rows and columns lexicographically nondecreasing.
  • A229451 (program): G.f.: exp( Sum_{n>=1} (3*n)!/n!^3 * x^n/n ).
  • A229452 (program): G.f.: exp( Sum_{n>=1} (3*n)!/(3!*n!^3) * x^n/n ).
  • A229463 (program): Expansion of 1/((1-x)^2*(1-26*x)).
  • A229464 (program): Binomial transform of (2*n + 1)!.
  • A229469 (program): Numbers n such that T(n) + S(n) + 1 is prime, where T(n) and S(n) are the n-th triangular and square numbers.
  • A229470 (program): Positions of 2 in decimal expansion of 0.1231232331232332333…, whose definition is given below.
  • A229472 (program): Number of defective 4-colorings of an n X 1 0..3 array connected horizontally, antidiagonally and vertically with exactly one mistake, and colors introduced in row-major 0..3 order.
  • A229473 (program): Number of defective 4-colorings of an n X 2 0..3 array connected horizontally, antidiagonally and vertically with exactly one mistake, and colors introduced in row-major 0..3 order.
  • A229481 (program): Final digit of 1^n + 2^n + … + n^n.
  • A229489 (program): Conjecturally, possible differences between prime(k)^2 and the next prime for some k.
  • A229497 (program): Product between n-th prime and next perfect square.
  • A229504 (program): Number of defective 3-colorings of an n X 2 0..2 array connected diagonally and antidiagonally with exactly one mistake, and colors introduced in row-major 0..2 order.
  • A229505 (program): Number of defective 3-colorings of an n X 3 0..2 array connected diagonally and antidiagonally with exactly one mistake, and colors introduced in row-major 0..2 order.
  • A229506 (program): Number of defective 3-colorings of an n X 4 0..2 array connected diagonally and antidiagonally with exactly one mistake, and colors introduced in row-major 0..2 order.
  • A229514 (program): Number of n X 1 0..2 arrays of the median of the corresponding element, the element to the east and the element to the south in a larger (n+1) X 2 0..2 array without adjacent equal elements in the latter.
  • A229522 (program): Final digit (in decimal system) of (n^n)^n, i.e., (n^n)^n mod 10.
  • A229525 (program): Sum of coefficients of the transform ax^2 + (4a/k - b)x + 4a/k^2 + 2b/k + c = 0 for a,b,c = 1,-1,-1, k = 1,2,3…
  • A229526 (program): The c coefficients of the transform ax^2 + (4a/k - b)x + 4a/k^2 + 2b/k + c= 0 for a,b,c = 1,-1,-1, k = 1,2,3…
  • A229527 (program): Start with 1, skip (sum of digits of n) numbers, accept next number.
  • A229535 (program): Number of defective 3-colorings of a 2 X n 0..2 array connected horizontally, diagonally and antidiagonally with exactly one mistake, and colors introduced in row-major 0..2 order.
  • A229545 (program): Numbers n such that n + (sum of digits of n) is a palindrome.
  • A229554 (program): 7*n! + 1.
  • A229558 (program): E.g.f.: exp(x) / (2 - exp(4*x))^(1/4).
  • A229572 (program): Number of defective 4-colorings of an n X 2 0..3 array connected horizontally, vertically, diagonally and antidiagonally with exactly one mistake, and colors introduced in row-major 0..3 order.
  • A229573 (program): Number of defective 4-colorings of an n X 3 0..3 array connected horizontally, vertically, diagonally and antidiagonally with exactly one mistake, and colors introduced in row-major 0..3 order.
  • A229580 (program): Number of defective 3-colorings of an n X 2 0..2 array connected horizontally and antidiagonally with exactly one mistake, and colors introduced in row-major 0..2 order.
  • A229581 (program): Number of defective 3-colorings of an n X 3 0..2 array connected horizontally and antidiagonally with exactly one mistake, and colors introduced in row-major 0..2 order.
  • A229582 (program): Number of defective 3-colorings of an n X 4 0..2 array connected horizontally and antidiagonally with exactly one mistake, and colors introduced in row-major 0..2 order.
  • A229583 (program): Number of defective 3-colorings of an n X 5 0..2 array connected horizontally and antidiagonally with exactly one mistake, and colors introduced in row-major 0..2 order.
  • A229587 (program): Number of defective 3-colorings of a 2 X n 0..2 array connected horizontally and antidiagonally with exactly one mistake, and colors introduced in row-major 0..2 order
  • A229593 (program): Number of boomerang patterns appearing in n X n coins, rotation not allowed.
  • A229598 (program): Voids left when packing boomerangs into n X n coins.
  • A229611 (program): Expansion of 1/((1-x)^3*(1-11x))
  • A229620 (program): Incorrect version of A045949.
  • A229661 (program): Rounded percentage of primes less than 10^n.
  • A229665 (program): Number of defective 4-colorings of an nX1 0..3 array connected horizontally, antidiagonally and vertically with exactly two mistakes, and colors introduced in row-major 0..3 order
  • A229679 (program): Number of defective 3-colorings of an n X 2 0..2 array connected diagonally and antidiagonally with exactly two mistakes, and colors introduced in row-major 0..2 order.
  • A229701 (program): Squares of triangular numbers, written backwards.
  • A229702 (program): Expansion of 1/((1-x)^4*(1-6x)).
  • A229718 (program): Number of arrays of length 2 that are sums of n consecutive elements of length 2+n-1 permutations of 0..2+n-2, and no two consecutive rises or falls in the latter permutation.
  • A229726 (program): Denominator of Sum_{k=1..2n+1} 2^k/k.
  • A229727 (program): Numerator of Sum_{k=1..2n+1} 2^k/k.
  • A229732 (program): G.f.: x^4*(2 - x^2 + x^3 + x^4)/(1-x-x^2)^3.
  • A229736 (program): Expansion of x^5*(2-5*x+3*x^2-x^3)/((1-x)^2*(1-2*x)^2*(1-3*x+x^2)).
  • A229737 (program): G.f.: x^2*(1-x)*(1-4*x+4*x^2+x^3)/((1-2*x)^2*(1-3*x+x^2)).
  • A229738 (program): a(n) = p^2*(p^2+2*p-1)/2, where p = prime(n).
  • A229739 (program): a(n) = q^2*(q^2+2*q-1)/2, where q = n-th prime power A000961(n).
  • A229742 (program): a(n) = A071585(n) - A071766(n).
  • A229745 (program): a(n) = wt(n+wt(n))-wt(n), where wt(n) is the binary weight of n, A000120(n).
  • A229759 (program): Decimal expansion of (25-10*sqrt(5))/2.
  • A229760 (program): Decimal expansion of 25 - 10*sqrt(5).
  • A229762 (program): a(n) = (n XOR floor(n/2)) AND floor(n/2), where AND and XOR are bitwise logical operators.
  • A229763 (program): a(n) = (2*n) XOR n AND n, where AND and XOR are bitwise logical operators.
  • A229764 (program): Nim sequence of MARK: the game on n counters in which the legal moves are to remove 1 counter or to halve the number of counters and round down.
  • A229780 (program): Decimal expansion of (3+sqrt(5))/10.
  • A229784 (program): a(n) = (1^1^1 + 2^2^2 . . . + n^n^n) mod 10.
  • A229785 (program): Partial sums of A157129.
  • A229786 (program): Primes modulo 23.
  • A229787 (program): Primes modulo 24.
  • A229788 (program): 6*2^n - n^2 - 5*n - 6.
  • A229790 (program): Cube roots of difference of consecutive cubes, rounded.
  • A229793 (program): The expansion of R(q)^-5 in powers of q where R() is the Rogers-Ramanujan continued fraction.
  • A229795 (program): Number of 2 X 2 0..n arrays with rows and columns in lexicographically nondecreasing order.
  • A229803 (program): Domination number for rook graph HR(n) on a triangular board of hexagonal cells. The rook can move along any row of adjacent cells, in any of the three directions.
  • A229816 (program): Number of partitions of n such that if the length is k then k is not a part.
  • A229828 (program): 7*n! - 1.
  • A229829 (program): Numbers coprime to 15.
  • A229834 (program): Expansion of (1+4*x+x^2) / ((1-x)^3*(1+x)^4).
  • A229837 (program): Decimal expansion of Sum_{n>=1} 1/(n*n!).
  • A229838 (program): Consider all primitive 60-degree triangles with sides A < B < C. The sequence gives the values of A.
  • A229841 (program): Number of n X 2 0..2 arrays x(i,j) with each element horizontally or vertically next to at least one element with value 2-x(i,j).
  • A229850 (program): Number of prime factors congruent to 1 mod 3 that divide the Fermat number 2^(2^n) + 1.
  • A229852 (program): 3*h^2, where h is an odd integer not divisible by 3.
  • A229853 (program): 384*n + 1.
  • A229854 (program): Primes of the form 384*n + 1.
  • A229855 (program): 384*n + 257.
  • A229856 (program): Primes of the form 384*n + 257.
  • A229858 (program): Consider all 120-degree triangles with sides A < B < C. The sequence gives the values of A.
  • A229863 (program): The number of integer partitions P of n such that either the length k of P is not a part or P has at least one part equal to 1 (or both).
  • A229882 (program): Squarefree oblong numbers.
  • A229896 (program): Sizes of logical groups of the same integer in A229895.
  • A229903 (program): (190/99)*(100^A001651(n)-1).
  • A229906 (program): Composite numbers whose sum of digits is 19.
  • A229912 (program): a(n) = Fibonacci(n) * (2*Fibonacci(n) + 1).
  • A229935 (program): Total number of parts in all compositions of n with at least two parts in increasing order.
  • A229936 (program): Sum of all parts of all compositions of n with at least two parts in increasing order.
  • A229937 (program): Nonprime odious numbers.
  • A229938 (program): Decimal expansion of Hartree energy in Joules.
  • A229939 (program): Decimal expansion of 9*Pi/10.
  • A229943 (program): Decimal expansion of 256/243, the Pythagorean semitone.
  • A229947 (program): Primes congruent to {1, 11, 13, 17, 19, 29} mod 30.
  • A229948 (program): Decimal expansion of 2187/2048, the Pythagorean apotome.
  • A229949 (program): Number of divisors of the n-th positive quarter-square.
  • A229950 (program): Total number of toothpicks after n-th stage in a toothpick structure in which the toothpicks represent the 1’s of triangle A229940.
  • A229951 (program): Number of toothpicks added at n-th stage to the toothpick structure of A229950.
  • A229960 (program): Primes of the form n^3 - T(n) - 1 where T(n) is the n-th triangular number.
  • A229963 (program): a(n) = 11*binomial(10*n + 11, n)/(10*n + 11) .
  • A229968 (program): Numbers not divisible by 3 or 11.
  • A229973 (program): Numbers coprime to 39.
  • A229975 (program): The base 8 expansion of the number of trailing zeros of the base 8 expansion of (8^n)!.
  • A229979 (program): Numerators of interleaved A063524(n) and A002427(n)/A006955(n).
  • A229997 (program): Numerator of d(k)/d(1) + d(k-1)/d(2) + … + d(k)/d(1), where d(1),d(2),…,d(k) are the unitary divisors of n.
  • A229998 (program): Denominator of d(k)/d(1) + d(k-1)/d(2) + … + d(k)/d(1), where d(1),d(2),…,d(k) are the unitary divisors of n.
  • A230002 (program): Array of coefficients of numerator polynomials of the rational function p(n, x - 1/x), where p(n,x) is the Fibonacci polynomial defined by p(1,x) = 1, p(2,x) = x, p(n,x) = x*p(n-1,x) + p(n-2,x).
  • A230018 (program): a(n) = (9*n^3 + 5*n)/2.
  • A230024 (program): Final nonzero digit of n^n in base 16.
  • A230038 (program): Distance between n^2 and the smallest triangular number >= n^2.
  • A230039 (program): Primes p such that 2*p+1 is not prime and 2*p+3 is prime.
  • A230044 (program): Nonnegative numbers k such that k plus a perfect square is a triangular number.
  • A230048 (program): Squarefree odious numbers.
  • A230049 (program): Triangle such that the g.f. of column k equals 1/(1-x)^(k^3) for k>=0, as read by rows.
  • A230050 (program): G.f.: Sum_{n>=0} x^n / (1-x)^(n^3).
  • A230053 (program): Recurrence a(n+2) = (n+2)*a(n+1)*a(n), with a(0) = a(1) = 1.
  • A230056 (program): G.f.: Sum_{n>=0} (n+3)^n * x^n / (1 + (n+3)*x)^n.
  • A230057 (program): Expansion of (3 * phi(q^3)^4 - phi(q)^4) / 2 in powers of q where phi () is a Ramanujan theta function.
  • A230058 (program): Numbers of the form k + wt(k) for at least two distinct k, where wt(k) = A000120(k) is the binary weight of k.
  • A230059 (program): Conjectural number of irreducible zeta values of weight 2*n+1 and depth three.
  • A230060 (program): Numbers n such that the distance from n^2 to the smallest triangular number >= n^2 is itself triangular.
  • A230063 (program): Number of nX3 0..2 arrays x(i,j) with each element diagonally or antidiagonally next to at least one element with value 2-x(i,j)
  • A230064 (program): Number of nX4 0..2 arrays x(i,j) with each element diagonally or antidiagonally next to at least one element with value 2-x(i,j)
  • A230070 (program): a(n) is the number of odious integers (A000069) not exceeding n and respectively prime to n.
  • A230071 (program): Sum over all permutations without double ascents on n elements and each permutation contributes 2 raised to the power of the number of double descents.
  • A230074 (program): Period 4: repeat [1, -2, 1, 0].
  • A230075 (program): Period 8: repeat [2, 1, 0, 1, -2, -1, 0, -1].
  • A230076 (program): a(n) = (A007521(n)-1)/4.
  • A230078 (program): Complement of A138929: positive integers not of the form 2*p^k, k >= 0, p a prime (also 2).
  • A230080 (program): Sequence needed for the nonpositive powers of rho(11) = 2*cos(Pi/11) in terms of the power basis of the degree 5 number field Q(rho(11)). Coefficients of the first power.
  • A230081 (program): Sequence needed for the nonpositive powers of rho(11) = 2*cos(Pi/11) in the power basis of the degree 5 number field Q(rho(11)). Negative of the coefficients of the second power.
  • A230088 (program): Partial sums of A010062.
  • A230089 (program): If n is divisible by 4 then 4, if n is divisible by 2 then 2, otherwise n.
  • A230091 (program): Numbers of the form k + wt(k) for exactly two distinct k, where wt(k) = A000120(k) is the binary weight of k.
  • A230093 (program): Number of values of k such that k + (sum of digits of k) is n.
  • A230094 (program): Numbers that can be expressed as (m + sum of digits of m) in exactly two ways.
  • A230095 (program): Odious numbers (A000069) that are the product of exactly two distinct primes.
  • A230096 (program): Number of tilings of an n X 1 rectangle (using tiles of dimension 1 X 1 and 2 X 1) that share no tile at the same position with their mirrored image.
  • A230098 (program): a(n) = n*prime(prime(n)) - prime(n)^2.
  • A230099 (program): a(n) = n + (product of digits of n).
  • A230100 (program): Numbers that can be expressed as (m + sum of digits of m) in exactly three ways.
  • A230101 (program): a(n) = product of n and all its nonzero digits.
  • A230102 (program): a(0)=1; thereafter a(n+1) = a(n) + (product of digits of a(n)).
  • A230103 (program): Number of m such that m + (product of digits of m) equals n.
  • A230105 (program): Numbers n such that m + (product of digits of m) = n has exactly one solution m.
  • A230106 (program): Number of m such that m + (product of nonzero digits of m) equals n.
  • A230113 (program): Digital root of summed Fibonacci and Lucas digital roots indexed by numbers not divisible by 2, 3 or 5.
  • A230115 (program): Numbers n such that tau(n+1) - tau(n) = 2; where tau(n) = the number of divisors of n (A000005).
  • A230116 (program): Value of row n in triangle A166360 when seen as binary number.
  • A230120 (program): a(n) is the number of evil integers (A001969) not exceeding n and respectively prime to n.
  • A230124 (program): Squarefree evil numbers.
  • A230128 (program): The number of multinomial coefficients over partitions with value equal to 4.
  • A230135 (program): Triangle read by rows: T(n, k) = 1 if ((k mod 4 = 2) and (n mod 2 = 1)) or ((k mod 4 = 0) and (n mod 2 = 0)) else T(n, k) = 0.
  • A230137 (program): a(n)/2^n is the expected value of the maximum of the number of heads and the number of tails when n fair coins are tossed.
  • A230149 (program): The number of multinomial coefficients over partitions with value equal to 5.
  • A230151 (program): Decimal expansion of the positive real solution of the equation x^(k+1)+x^k-1=0. Case k=3.
  • A230152 (program): Decimal expansion of the positive real solution of the equation x^(k+1)+x^k-1=0. Case k=4.
  • A230153 (program): Decimal expansion of the positive real solution of the equation x^(k+1)+x^k-1=0. Case k=5.
  • A230154 (program): Decimal expansion of the positive real solution of the equation x^(k+1)+x^k-1=0. Case k=6.
  • A230155 (program): Decimal expansion of the positive real solution of the equation x^(k+1)+x^k-1=0. Case k=7.
  • A230156 (program): Decimal expansion of the positive real solution of the equation x^(k+1)+x^k-1=0. Case k=8.
  • A230157 (program): Decimal expansion of the positive real solution of the equation x^(k+1)+x^k-1=0. Case k=9.
  • A230158 (program): Decimal expansion of the positive real solution of the equation x^(k+1)+x^k-1=0. Case k=10.
  • A230159 (program): Decimal expansion of the positive real solution of the equation x^k-x-1=0. Case k=6.
  • A230160 (program): Decimal expansion of the positive real solution of the equation x^k-x-1=0. Case k=7.
  • A230161 (program): Decimal expansion of the positive real solution of the equation x^k-x-1=0. Case k=8.
  • A230162 (program): Decimal expansion of the positive real solution of the equation x^k-x-1=0. Case k=9.
  • A230163 (program): Decimal expansion of the positive real solution of the equation x^k-x-1=0. Case k=10.
  • A230179 (program): Number of n X 3 0..2 arrays x(i,j) with each element horizontally or antidiagonally next to at least one element with value 2-x(i,j).
  • A230193 (program): Numbers divisible by 3 or 11.
  • A230196 (program): Number of pairs (p,q) such that 2*p + 3*q = n and p != q.
  • A230197 (program): The number of multinomial coefficients over partitions with value equal to 7.
  • A230198 (program): The number of multinomial coefficients over partitions with value equal to 8.
  • A230201 (program): Numbers k such that sigma(phi(k)) < k.
  • A230202 (program): Primes that end in 999.
  • A230203 (program): Numbers n such that sigma(phi(n)) > n.
  • A230204 (program): Expansion of phi(-x) * f(x^3, x^5) in powers of x where phi(), f() are Ramanujan theta functions.
  • A230205 (program): Expansion of phi(-x) * f(x^1, x^7) in powers of x where phi(), f() are Ramanujan theta functions.
  • A230215 (program): Numbers divisible by 3 or 13.
  • A230216 (program): Number of binary strings of length n avoiding “squares” (that is, repeated blocks of the form xx) with |x| = 3.
  • A230225 (program): Primes p such that 2*p+1 and 2*p+3 are not prime.
  • A230227 (program): Primes p with 3*p - 10 also prime.
  • A230239 (program): Values of N for which the equation x^2 - 4*y^2 = N has integer solutions.
  • A230240 (program): Values of N for which the equation x^2 - 9*y^2 = N has integer solutions.
  • A230242 (program): Decimal expansion of (25+3*sqrt(69))/2.
  • A230245 (program): Number of n X 2 0..3 arrays x(i,j) with each element horizontally or vertically next to at least one element with value (x(i,j)+1) mod 4, and upper left element zero.
  • A230251 (program): Number of permutations of [2n+1] in which the longest increasing run has length n+1.
  • A230263 (program): Number of nonnegative integer solutions to the equation x^2 - 4*y^2 = n.
  • A230264 (program): Number of nonnegative integer solutions to the equation x^2 - 9*y^2 = n.
  • A230267 (program): Coins left after packing 5 curves coins patterns into fountain of coins base n.
  • A230269 (program): Number of n X 2 0..2 arrays x(i,j) with each element horizontally or vertically next to at least one element with value (x(i,j)+1) mod 3, and upper left element zero.
  • A230276 (program): Voids left after packing 5-curves coins patterns into fountain of coins with base n.
  • A230278 (program): Expansion of q^(-2/3) * eta(q^2)^10 / eta(q)^4 in powers of q.
  • A230279 (program): Number of nonnegative integer solutions to the equation x^2 - 16*y^2 = n.
  • A230280 (program): Expansion of q^(-1/3) * eta(q)^4 * eta(q^2)^2 in powers of q.
  • A230285 (program): a(n) = n*prime(prime(n)) - prime(n).
  • A230286 (program): a(n) = A016052(n)/3.
  • A230287 (program): First differences of A016052/3 (= A230286).
  • A230297 (program): a(n) = A010062(n) written in binary: a(n+1) = a(n) + hammingweight(a(n)) in binary.
  • A230298 (program): a(n) = A010062(n) mod 2.
  • A230300 (program): a(n) = n + wt(n-1), where wt() = A000120() is the binary weight.
  • A230301 (program): Positive numbers not of the form m + wt(m-1), m >= 1.
  • A230312 (program): Squares which cannot be written as the sum of a smaller nonzero square and twice a triangular number.
  • A230313 (program): Numbers n such that A031971(47058*n) <> n (mod 47058*n).
  • A230319 (program): Least positive k such that k! > k^n.
  • A230325 (program): (prime(n)^2 -1)*(prime(n)^2 - prime(n))/2.
  • A230328 (program): Denominator of n(n+3)/(4(n+1)(n+2)) = sum(k=1..n, 1/(k(k+1)(k+2)) ).
  • A230329 (program): Prime(prime(2*n)) - 2*prime(n).
  • A230331 (program): Number of n X 2 0..2 arrays x(i,j) with each element horizontally, vertically or antidiagonally next to at least one element with value (x(i,j)+1) mod 3, and upper left element zero.
  • A230339 (program): Numerator of Sum_{k=1..n} 1/(k(k+1)(k+2)(k+3)) = Sum_{k=1..n} 1/Pochhammer(k,4).
  • A230340 (program): Denominator of Sum_{k=1..n} 1/(k(k+1)(k+2)(k+3)) = Sum_{k=1..n} 1/Pochhammer(k,4).
  • A230341 (program): Number of permutations of [2n] in which the longest increasing run has length n.
  • A230342 (program): Number of permutations of [2n+2] in which the longest increasing run has length n+2.
  • A230343 (program): Number of permutations of [2n+3] in which the longest increasing run has length n+3.
  • A230344 (program): Number of permutations of [2n+4] in which the longest increasing run has length n+4.
  • A230345 (program): Number of permutations of [2n+5] in which the longest increasing run has length n+5.
  • A230346 (program): Number of permutations of [2n+6] in which the longest increasing run has length n+6.
  • A230347 (program): Number of permutations of [2n+7] in which the longest increasing run has length n+7.
  • A230348 (program): Number of permutations of [2n+8] in which the longest increasing run has length n+8.
  • A230366 (program): a(n) = Sum_{k=1..floor(n/2)} (k^2 mod n).
  • A230368 (program): A strong divisibility sequence associated with the algebraic integer 1 + i.
  • A230369 (program): A strong divisibility sequence associated with the algebraic integer 2 + i.
  • A230375 (program): Squarefree numbers congruent to 2 or 3 mod 4.
  • A230382 (program): Number of ascending runs of length n in the permutations of [2n].
  • A230388 (program): a(n) = binomial(11*n+1,n)/(11*n+1).
  • A230390 (program): 5*binomial(8*n+10,n)/(4*n+5).
  • A230402 (program): Integer areas of orthic triangles of integer-sided triangles.
  • A230403 (program): a(n) = the largest k such that (k+1)! divides n; the number of trailing zeros in the factorial base representation of n (A007623(n)).
  • A230404 (program): a(n) = the largest k such that (k+1)! divides 2n; the number of trailing zeros in the factorial base representation of even numbers.
  • A230405 (program): a(n) = A000217(A230404(n+1)); the first differences of A219650.
  • A230412 (program): a(n) = the number of ways to express n as a sum d1*(k1!-1) + d2*(k2!-1) + … + dj*(kj!-1), where all k’s are distinct and greater than one and each di is in range [1,ki]; the characteristic function of A219650.
  • A230413 (program): a(0)=0 and from then on, the partial sums of A230412 summed from the term a(1) onward.
  • A230414 (program): Inverse function for injection A219650.
  • A230423 (program): a(n) = smallest natural number x such that x=n+A034968(x), or zero if no such number exists.
  • A230424 (program): a(n) = largest natural number x such that x=n+A034968(x), or zero if no such number exists.
  • A230431 (program): After the first zero, integers from 0 to A219661(n)-1 followed by integers from 0 to A219661(n+1)-1, etc.
  • A230435 (program): Triangle by rows, A001047 convolved with A000079.
  • A230437 (program): Decimal expansion of (2/(3 - 2^(1/2)))^(1/4).
  • A230441 (program): Number of overpartitions of n minus the number of partitions of n.
  • A230442 (program): Expansion of q^(-1/6) * eta(q)^2 * eta(q^2) in powers of q.
  • A230445 (program): Triangle read by rows: T(n,m) = 3^m*2^(n-m)-1, the number of neighbors in an n-dimensional cubic array.
  • A230458 (program): Decimal expansion of Δν_{Cs} in unit s^{-1}; one of the seven units of the 2019 SI system.
  • A230460 (program): Prime(2*prime(n)).
  • A230462 (program): Numbers congruent to {1, 11, 13, 17, 19, or 29} mod 30.
  • A230478 (program): Smallest number divisible by all numbers from 1 to 2*n-1, but not divisible by n, or 0 if impossible.
  • A230501 (program): Floor(Sum(d(k), k=1..n)/n), where d(k) is the number of divisors of k.
  • A230515 (program): Numbers n such that n*(n+1)-1 is a Sophie Germain prime.
  • A230520 (program): Number of n X 2 0..2 arrays x(i,j) with each element horizontally, vertically, diagonally or antidiagonally next to at least one element with value (x(i,j)+1) mod 3, and upper left element zero.
  • A230535 (program): Expansion of q * (f(-q, -q^7) / f(-q^3, -q^5))^2 in powers of q where f(,) is Ramanujan’s two-variable theta function.
  • A230536 (program): Expansion of q^(-1) * f(-q^5, -q^7) / f(-q, -q^11) in powers of q where f(,) is Ramanujan’s two-variable theta function.
  • A230539 (program): a(n) = 3*n*2^(3*n-1).
  • A230540 (program): a(n) = 2*n*3^(2*n-1).
  • A230547 (program): a(n) = 3*binomial(3*n+9, n)/(n+3).
  • A230555 (program): Number of involutions avoiding 3421.
  • A230577 (program): Positive integers that have exactly 6 odd divisors.
  • A230579 (program): a(n) = 2^n mod 341.
  • A230584 (program): Either two less than a square or two more than a square.
  • A230585 (program): First terms of first rows of zigzag matrices as defined in A088961.
  • A230586 (program): a(n) = n^5 - 5*n^3 + 5*n.
  • A230588 (program): Number of nX2 0..5 arrays x(i,j) with each element horizontally or vertically next to at least one element with value (x(i,j)+1) mod 6, and upper left element zero
  • A230593 (program): a(n) = n * Sum_{q|n} 1 / q, where q are noncomposite numbers (A008578) dividing n.
  • A230594 (program): Number of ways to write n as n = x*y, where x, y = noncomposite numbers (A008578), 1 <= x <= n, 1 <= y <= n.
  • A230595 (program): Number of ways to write n as n = x*y, where x and y are primes, 1 <= x <= n, 1 <= y <= n.
  • A230600 (program): a(n) = Lucas(2^n - 1).
  • A230601 (program): a(n) = Lucas(2^n + 2).
  • A230603 (program): Generalized Fibonacci word. Binary complement of A221150.
  • A230606 (program): Numbers n such that sigma(n) = k*(n+1) for some integer k.
  • A230610 (program): Number of nX4 0..2 arrays x(i,j) with each element horizontally or antidiagonally next to at least one element with value (x(i,j)+1) mod 3, and upper left element zero
  • A230628 (program): Maximum number of colors needed to color a planar map of several empires, each empire consisting of n countries.
  • A230629 (program): a(0) = 0; thereafter a(n) = (1 + a(floor(n/2))) mod 3.
  • A230630 (program): a(1)=0; thereafter a(n) = (1 + a(floor(n/2))) mod 3.
  • A230631 (program): a(n) = n + (sum of digits in base-4 representation of n).
  • A230632 (program): Number of integers m such that m + (sum of digits in base-4 representation of m) = n.
  • A230633 (program): Numbers n such that m + (sum of digits in base-4 representation of m) = n has exactly one solution.
  • A230634 (program): Numbers n such that m + (sum of digits in base-4 representation of m) = n has exactly two solutions.
  • A230641 (program): a(n) = n + (sum of digits in base-3 representation of n).
  • A230642 (program): Number of integers m such that m + (sum of digits in base-3 representation of m) = n.
  • A230643 (program): Number of integers m such that m + (sum of digits in base-3 representation of m) = 2n.
  • A230647 (program): Number of nX3 0..2 white square subarrays x(i,j) with each element diagonally or antidiagonally next to at least one element with value 2-x(i,j)
  • A230648 (program): Number of nX4 0..2 white square subarrays x(i,j) with each element diagonally or antidiagonally next to at least one element with value 2-x(i,j)
  • A230654 (program): Numbers n such that tau(n+1) - tau(n) = 4, where tau(n) = the number of divisors of n (A000005).
  • A230658 (program): Number of nX3 0..2 black square subarrays x(i,j) with each element diagonally or antidiagonally next to at least one element with value 2-x(i,j)
  • A230664 (program): a(n) = floor(3^n/n^2).
  • A230701 (program): Number of (n+3) X (1+3) 0..2 white square subarrays x(i,j) with each element diagonally or antidiagonally next to at least one element with value (x(i,j)+1) mod 3, and upper left element zero.
  • A230709 (program): Union of even odious (cf. A128309) and evil numbers (cf. A001969).
  • A230718 (program): Smallest n-th power equal to a sum of some consecutive, immediately preceding, positive n-th powers, or 0 if none.
  • A230720 (program): Even sorting numbers, cf. A003071.
  • A230721 (program): Odd sorting numbers, cf. A003071.
  • A230724 (program): Digital sum of tribonacci numbers with a(0)=a(1)=0, a(2)=1.
  • A230725 (program): Digital sum of tribonacci numbers with a(0)=a(1)=a(2)=1.
  • A230750 (program): Number of (n+3)X(1+3) 0..2 arrays x(i,j) with each element diagonally or antidiagonally next to at least one element with value (x(i,j)+1) mod 3, and upper left element zero
  • A230772 (program): Number of primes in the half-open interval [n, 3*n/2).
  • A230774 (program): Number of primes less than first prime above square root of n.
  • A230775 (program): Smallest prime number greater than or equal to the square root of n.
  • A230779 (program): Numbers which are uniquely decomposable into a sum of two squares, the unique decomposition being with two distinct nonzero squares.
  • A230780 (program): Positive numbers without a prime factor congruent to 1 (mod 6).
  • A230799 (program): The number of distinct nonzero coefficients in the n-th cyclotomic polynomial.
  • A230800 (program): Number of n X 2 0..3 arrays x(i,j) with each element horizontally or vertically next to at least one element with value (x(i,j)+1) mod 4 and at least one element with value (x(i,j)-1) mod 4, and upper left element zero.
  • A230809 (program): Primes p of the form 60*n + 59 such that 2*p + 1 is also prime.
  • A230812 (program): Smallest squarefree side lengths of primitive integer Soddyian triangles.
  • A230813 (program): Number of n X 2 0..2 arrays x(i,j) with each element horizontally or vertically next to at least one element with value (x(i,j)+1) mod 3 and at least one element with value (x(i,j)-1) mod 3, and upper left element zero.
  • A230825 (program): Number of n X 2 0..3 arrays x(i,j) with each element horizontally, vertically or antidiagonally next to at least one element with value (x(i,j)+1) mod 4 and at least one element with value (x(i,j)-1) mod 4, no adjacent elements equal, and upper left element zero.
  • A230835 (program): Number of n X 2 0..3 arrays x(i,j) with each element horizontally, vertically or antidiagonally next to at least one element with value (x(i,j)+1) mod 4, and upper left element zero.
  • A230843 (program): Cubefree numbers which in their canonical prime factorization have mutually distinct exponents.
  • A230846 (program): 1 + A075526(n).
  • A230847 (program): a(n) = 1 + A054541(n).
  • A230849 (program): A075526 and A000012 interleaved.
  • A230850 (program): A054541 and A000012 interleaved.
  • A230851 (program): Numbers with divisors which are half odious (A000069) and half evil (A001969).
  • A230853 (program): Numbers n such that m + (sum of digits in base-3 representation of m) = n has exactly one solution.
  • A230854 (program): Numbers n such that m + (sum of digits in base-3 representation of m) = n has exactly two solutions.
  • A230855 (program): Numbers n such that m + (sum of digits in base-3 representation of m) = n has exactly three solutions.
  • A230864 (program): log2*(n) (version 3): number of iterations log_2(log_2(log_2(…(n)…))) required for the result to be <= 1.
  • A230865 (program): a(n) = n + (sum of digits in base-5 representation of n).
  • A230866 (program): Number of integers m such that m + (sum of digits in base-5 representation of m) = 2n.
  • A230871 (program): Construct a triangle as in the Comments, read nodes from left to right starting at the root and proceeding downwards.
  • A230874 (program): a(1)=1; thereafter a(n) = 2^a(ceiling(n/2)).
  • A230875 (program): a(1)=0; thereafter a(n) = 2^a(ceiling(n/2)).
  • A230877 (program): If n = Sum_{i=0..m} c(i)*2^i, c(i) = 0 or 1, then a(n) = Sum_{i=0..m} (m+1-i)*c(i).
  • A230879 (program): Number of 2-packed n X n matrices.
  • A230893 (program): Number of n X 2 0..3 arrays x(i,j) with each element horizontally or vertically next to at least one element with value (x(i,j)+1) mod 4 and at least one element with value (x(i,j)-1) mod 4, no adjacent elements equal, and upper left element zero.
  • A230900 (program): a(n) = 2^Lucas(n).
  • A230901 (program): Sturmian word: equals the limit word S(infinity) where S(0) = 0, S(1) = 1 and for n >= 1, S(n+1) = S(n)S(n)S(n)S(n-1).
  • A230904 (program): Number of n X 2 0..3 arrays x(i,j) with each element horizontally, vertically or antidiagonally next to at least one element with value (x(i,j)+1) mod 4, no adjacent elements equal, and upper left element zero.
  • A230928 (program): Number of black-square subarrays of (n+2) X (1+2) 0..3 arrays x(i,j) with each element diagonally or antidiagonally next to at least one element with value (x(i,j)+1) mod 4, no adjacent elements equal, and upper left element zero.
  • A230929 (program): Number of black-square subarrays of (n+2) X (2+2) 0..3 arrays x(i,j) with each element diagonally or antidiagonally next to at least one element with value (x(i,j)+1) mod 4, no adjacent elements equal, and upper left element zero.
  • A230960 (program): Boustrophedon transform of factorials, cf. A000142.
  • A230961 (program): Boustrophedon transform of factorials beginning with 1, cf. A000142.
  • A230970 (program): Number of (n+2) X (1+2) 0..3 arrays x(i,j) with each element diagonally or antidiagonally next to at least one element with value (x(i,j)+1) mod 4, no adjacent elements equal, and upper left element zero.
  • A230971 (program): Number of (n+2) X (2+2) 0..3 arrays x(i,j) with each element diagonally or antidiagonally next to at least one element with value (x(i,j)+1) mod 4, no adjacent elements equal, and upper left element zero.
  • A230980 (program): Number of primes <= n, starting at n=0.
  • A230981 (program): Decimal expansion of 3/(2^(1/2)).
  • A230983 (program): Number of white square subarrays of (n+1) X (2+1) binary arrays with no element equal to a strict majority of its diagonal and antidiagonal neighbors, with upper left element zero.
  • A231000 (program): Number of years after which a date can fall on the same day of the week, in the Julian calendar.
  • A231001 (program): Number of years after which an entire year can have the same calendar, in the Julian calendar.
  • A231002 (program): Number of years after which it is possible to have a date falling on same day of the week, but the entire year does not have the same calendar, in the Julian calendar.
  • A231003 (program): Number of years after which it is not possible to have a date falling on the same day of the week, in the Julian calendar.
  • A231004 (program): Number of years after which it is not possible to have the same calendar for the entire year, in the Julian calendar.
  • A231025 (program): Number of n X 2 0..2 arrays x(i,j) with each element horizontally, vertically or antidiagonally next to at least one element with value (x(i,j)+1) mod 3 and at least one element with value (x(i,j)-1) mod 3, and upper left element zero.
  • A231045 (program): Number of n X 4 0..3 arrays x(i,j) with each element horizontally, diagonally or antidiagonally next to at least one element with value (x(i,j)+1) mod 4 and at least one element with value (x(i,j)-1) mod 4, no adjacent elements equal, and upper left element zero.
  • A231057 (program): Number of n X 2 0..3 arrays x(i,j) with each element horizontally or vertically next to at least one element with value (x(i,j)+1) mod 4, no adjacent elements equal, and upper left element zero.
  • A231067 (program): Number of black square subarrays of (n+1) X (2+1) binary arrays with no element equal to a strict majority of its diagonal and antidiagonal neighbors, with upper left element zero.
  • A231087 (program): Number of perfect matchings in graph C_3 x C_{2n}
  • A231101 (program): a(n)=3*a(n-3)+a(n-2), a(0)=3, a(1)=0, a(2)=2.
  • A231103 (program): Number of n X 3 0..3 arrays x(i,j) with each element horizontally or antidiagonally next to at least one element with value (x(i,j)+1) mod 4, no adjacent elements equal, and upper left element zero.
  • A231104 (program): Number of n X 4 0..3 arrays x(i,j) with each element horizontally or antidiagonally next to at least one element with value (x(i,j)+1) mod 4, no adjacent elements equal, and upper left element zero.
  • A231122 (program): Numbers k >= 0 such that 2^k is number of ways to write n as n = x*y, where x, y = squarefree numbers, 1 <= x <= n, 1 <= y <= n, or -1 if no such k exists.
  • A231123 (program): Array T(n,k) read by antidiagonals: T(n,k) = sum(i=0…n, (-1)^(n+i) * C(n+i,2i) * n/(2i+1) * k^(2i+1) ), n>0, k>1.
  • A231147 (program): Array of coefficients of numerator polynomials of the rational function p(n, x + 1/x), where p(n,x) = (x^n - 1)/(x - 1).
  • A231149 (program): Greatest integer k such that n+1 + … + n+k <= 1 + … + n.
  • A231151 (program): Least integer k such that n+1 + … + n+k > 1 + … + n.
  • A231152 (program): Least integer k such that prime(n+1) + … + prime(n+k) > prime(1) + … + prime(n).
  • A231153 (program): Greatest integer k such that prime(n+1) + … + prime(n+k) <= prime(1) + … + prime(n).
  • A231167 (program): a(1) = a(2) = 0, for n>=3: (sum of non-divisors of n) modulo (number of non-divisors of n).
  • A231179 (program): Boustrophedon transform of nonnegative integers, cf. A001477.
  • A231181 (program): Expansion of 1/(1 - x - 4*x^2 + 3*x^3 + 3*x^4 - x^5).
  • A231182 (program): Coefficients for the nonnegative powers of rho(11) = 2*cos(Pi/11) when written in the power basis of the degree 5 number field Q(rho(11)). Coefficients for the zeroth and fourth powers.
  • A231183 (program): Coefficients of the nonnegative powers of rho(11) = 2*cos(Pi/11) when written in the power basis of the degree 5 number field Q(rho(11)). Negative of the coefficients of the first power.
  • A231184 (program): Coefficients of the nonnegative powers of rho(11) = 2*cos(Pi/11) when written in the power basis of the degree 5 number field Q(rho(11)). Negative of the coefficients of the second power.
  • A231185 (program): Coefficients of the nonnegative powers of rho(11) = 2*cos(Pi/11) when written in the power basis of the degree 5 number field Q(rho(11)). Coefficients of the third power.
  • A231187 (program): Decimal expansion of the length ratio (largest diagonal)/side in the regular 7-gon (or heptagon).
  • A231190 (program): Numerator of abs(n-8)/(2*n), n >= 1.
  • A231200 (program): Boustrophedon transform of even numbers.
  • A231203 (program): Numbers of the form (24*x + 1)*2^(y+6) with positive integers x and y.
  • A231204 (program): If n = Sum_{i=0..m} c(i)*2^i, c(i) = 0 or 1, then a(n) = (m-i)*c(i).
  • A231205 (program): Table of maximal number of guesses required to solve a Mastermind variant, read by columns.
  • A231209 (program): Smallest squarefree number k with 2^n ways to write k as k = x*y, where x, y = squarefree numbers, 1 <= x <= k, 1 <= y <= k.
  • A231211 (program): Number of permutations of [n] avoiding simultaneously consecutive patterns 123, 1432, 2431, and 3421.
  • A231213 (program): Number of (n+1) X (2+1) 0..2 arrays with no element unequal to a strict majority of its horizontal and vertical neighbors, with values 0..2 introduced in row major order.
  • A231233 (program): Triangle T(n,k) = greatest prime factor of n*k+1.
  • A231234 (program): Denominators related to A206771 and Lorentz gamma factor.
  • A231236 (program): Number of years after which it is either not possible to have a date falling on same day of the week, or the entire year can have the same calendar, in the Gregorian calendar.
  • A231237 (program): Number of years after which it is either not possible to have a date falling on same day of the week, or the entire year can have the same calendar, in the Julian calendar.
  • A231257 (program): Number of (n+1) X (2+1) 0..2 arrays with no element unequal to a strict majority of its horizontal and antidiagonal neighbors, with values 0..2 introduced in row major order.
  • A231273 (program): Numerator of zeta(4n)/(zeta(2n) * Pi^(2n)).
  • A231279 (program): a(n) = Jacobsthal(n^2), where Jacobsthal(n) = A001045(n), for n>=1.
  • A231280 (program): Number of n X 3 0..3 arrays x(i,j) with each element horizontally or antidiagonally next to at least one element with value (x(i,j)+1) mod 4, and upper left element zero.
  • A231292 (program): a(n) = Jacobsthal(n)^n, where Jacobsthal(n) = A001045(n), for n>=1.
  • A231295 (program): Number of (n+1) X (1+1) 0..2 arrays with no element unequal to a strict majority of its horizontal, vertical and antidiagonal neighbors, with values 0..2 introduced in row major order.
  • A231303 (program): Recurrence a(n) = a(n-2) + n^M for M=4, starting with a(0)=0, a(1)=1.
  • A231304 (program): Recurrence a(n) = a(n-2) + n^M for M=5, starting with a(0)=0, a(1)=1.
  • A231305 (program): Recurrence a(n) = a(n-2) + n^M for M=6, starting with a(0)=0, a(1)=1.
  • A231306 (program): Recurrence a(n) = a(n-2) + n^M for M=7, starting with a(0)=0, a(1)=1.
  • A231307 (program): Recurrence a(n) = a(n-2) + n^M for M=8, starting with a(0)=0, a(1)=1.
  • A231308 (program): Recurrence a(n) = a(n-2) + n^M for M=9, starting with a(0)=0, a(1)=1.
  • A231309 (program): Recurrence a(n) = a(n-2) + n^M for M=10, starting with a(0)=0, a(1)=1.
  • A231317 (program): Number of (n+1) X (1+1) 0..2 arrays with no element equal to a strict majority of its diagonal and antidiagonal neighbors, with values 0..2 introduced in row major order.
  • A231325 (program): Larger of corresponding digits of Pi and e.
  • A231326 (program): Primes p such that p - 2*k is also prime, where p is k-th prime.
  • A231337 (program): Number of (n+1) X (1+1) 0..3 arrays with no element unequal to a strict majority of its horizontal and vertical neighbors, with values 0..3 introduced in row major order.
  • A231344 (program): Number of morphisms in full subcategories of Set spanned by {{}, {1}, {1, 2}, …, {1, 2, …, n}}.
  • A231348 (program): Number of triangles after n-th stage in a cellular automaton based in isosceles triangles of two sizes (see Comments lines for precise definition).
  • A231349 (program): Number of triangles added at n-th stage to the structure of A231348.
  • A231350 (program): Decimal expansion of the speed c/a in SI units [meter/second], where “c” is the speed of light in vacuum and “a” is the fine-structure constant (alpha).
  • A231351 (program): a(n) = A231349(n+1)/2.
  • A231356 (program): Number of (n+1) X (1+1) 0..3 arrays with no element unequal to a strict majority of its horizontal, vertical and antidiagonal neighbors, with values 0..3 introduced in row major order.
  • A231390 (program): Number of (n+1) X (2+1) 0..2 arrays with no element unequal to a strict majority of its horizontal, diagonal and antidiagonal neighbors, with values 0..2 introduced in row major order.
  • A231404 (program): Integers n dividing the Lucas sequence u(n), where u(i) = 2*u(i-1) - 4*u(i-2) with initial conditions u(0)=0, u(1)=1.
  • A231425 (program): The Schramm triangle: T(n,k) = f(gcd(n,k)), where f = Dirichlet inverse of Euler totient.
  • A231430 (program): Number of ternary sequences which contain 000.
  • A231431 (program): Evil squares.
  • A231444 (program): Number of (n+1) X (1+1) 0..3 arrays with no element unequal to a strict majority of its horizontal and antidiagonal neighbors, with values 0..3 introduced in row major order.
  • A231458 (program): Number of (n+1) X (2+1) 0..3 arrays with no element unequal to a strict majority of its horizontal, diagonal and antidiagonal neighbors, with values 0..3 introduced in row major order.
  • A231470 (program): Largest integer less than 10, coprime to n.
  • A231471 (program): Largest integer less than 11 and coprime to n.
  • A231472 (program): Largest integer less than 12 and coprime to n.
  • A231475 (program): Largest integer less than 5 and coprime to n.
  • A231481 (program): Primes whose base-6 representation is also the base-9 representation of a prime.
  • A231482 (program): The number of nonlinear normal modes for a fully resonant Hamiltonian system with n degrees of freedom.
  • A231500 (program): a(n) = Sum_{i=0..n} wt(i)^2, where wt(i) = A000120(i).
  • A231501 (program): a(n) = Sum_{i=0..n} wt(i)^3, where wt() = A000120().
  • A231502 (program): a(n) = Sum_{i=0..n} wt(i)^4, where wt() = A000120().
  • A231503 (program): a(n) = Sum_{i=0..n} digsum_3(i)^2, where digsum_3(i) = A053735(i).
  • A231504 (program): a(n) = Sum_{i=0..n} digsum_3(i)^3, where digsum_3(i) = A053735(i).
  • A231505 (program): a(n) = Sum_{i=0..n} digsum_3(i)^4, where digsum_3(i) = A053735(i).
  • A231507 (program): a(n) is smallest number greater than a(n-1) such that a(n)+a(n-1) is composite.
  • A231509 (program): Number of n X 2 0..1 arrays with no element less than a strict majority of its horizontal, vertical, diagonal and antidiagonal neighbors.
  • A231530 (program): Real part of Product_{k=1..n} (k+i), where i is the imaginary unit.
  • A231531 (program): Imaginary part of Product_{k=1..n} (k+I).
  • A231535 (program): Decimal expansion of Pi^4/15.
  • A231550 (program): Permutation of nonnegative integers: for each bit[i] in the binary representation, except the most and the least significant bits, set bit[i] = bit[i] XOR bit[i-1], where bit[i-1] is the less significant bit, XOR is the binary logical exclusive or operator.
  • A231551 (program): Position of n in A231550.
  • A231552 (program): G.f. satisfies: A(x) = (1 + x*A(x))^2 * (1 + 2*A(x)) / 3.
  • A231553 (program): G.f. satisfies: A(x) = (1 + x*A(x))^2 * (1 + 3*A(x)) / 4.
  • A231554 (program): G.f. satisfies: A(x) = (1 + 2*x*A(x))^2 * (2 + A(x)) / 3.
  • A231556 (program): G.f. satisfies: A(x) = (1 - x*A(x))^2 * (2*A(x) - 1).
  • A231557 (program): Least positive integer k <= n such that 2^k + (n - k) is prime, or 0 if such an integer k does not exist.
  • A231559 (program): a(n) = floor( A000326(n)/2 ).
  • A231560 (program): Floor(sum_{i=2..n} 1/(i*log(i))).
  • A231562 (program): Numbers n such that A031971(8490421583559688410706771261086*n) == n (mod 8490421583559688410706771261086*n).
  • A231563 (program): a(n) = f(1)^n + … + f(n)^n (mod n) where f(i)=i if gcd(i,n)=1 and f(i)=0 otherwise.
  • A231564 (program): Numbers such that A231563(n)=0.
  • A231565 (program): Numbers such that A231563(n)>0.
  • A231589 (program): a(n) = sum_{k=1..(n-1)/2} (k^2 mod n).
  • A231600 (program): Output of a finite state automaton generating the period doubling sequence, when fed with binary representation of n, read from right to left.
  • A231601 (program): Number of permutations of [n] avoiding ascents from odd to even numbers.
  • A231607 (program): Primes p such that p + 600 is also prime.
  • A231615 (program): G.f. satisfies: A(x) = (1 - 2*x*A(x))^2 * (3*A(x) - 2).
  • A231616 (program): G.f. satisfies: A(x) = (1 - 3*x*A(x))^2 * (4*A(x) - 3).
  • A231617 (program): G.f. satisfies: A(x) = (1 - 3*x*A(x)^2) * sqrt(4*A(x)^2 - 3).
  • A231618 (program): G.f. satisfies: A(x) = (1 + 3*x*A(x))^2 * (3 + A(x)) / 4.
  • A231620 (program): a(n) = A000930(n^2), where A000930 is Narayana’s cows sequence.
  • A231621 (program): a(n) = A000930(n*(n+1)/2), where A000930 is Narayana’s cows sequence.
  • A231622 (program): (2*n+1)*a(n+1) = (4*n^2+1)*a(n) + (2*n+1)*a(n-1) with n>1, a(0)=2, a(1)=-1.
  • A231633 (program): Number of ways to write n = x + y (x, y > 0) with x^2 * y - 1 prime.
  • A231642 (program): Triangle read by rows, t(n,k) = binomial(n,k) mod n, k <= n.
  • A231643 (program): a(n) = 5*2^n + 5.
  • A231664 (program): a(n) = Sum_{i=0..n} digsum_4(i), where digsum_4(i) = A053737(i).
  • A231665 (program): a(n) = Sum_{i=0..n} digsum_4(i)^2, where digsum_4(i) = A053737(i).
  • A231666 (program): a(n) = Sum_{i=0..n} digsum_4(i)^3, where digsum_4(i) = A053737(i).
  • A231667 (program): a(n) = Sum_{i=0..n} digsum_4(i)^4, where digsum_4(i) = A053737(i).
  • A231668 (program): a(n) = Sum_{i=0..n} digsum_5(i), where digsum_5(i) = A053824(i).
  • A231669 (program): a(n) = Sum_{i=0..n} digsum_5(i)^2, where digsum_5(i) = A053824(i).
  • A231670 (program): a(n) = Sum_{i=0..n} digsum_5(i)^3, where digsum_5(i) = A053824(i).
  • A231671 (program): a(n) = Sum_{i=0..n} digsum_5(i)^4, where digsum_5(i) = A053824(i).
  • A231672 (program): a(n) = Sum_{i=0..n} digsum_6(i), where digsum_6(i) = A053827(i).
  • A231673 (program): a(n) = Sum_{i=0..n} digsum_6(i)^2, where digsum_6(i) = A053827(i).
  • A231674 (program): a(n) = Sum_{i=0..n} digsum_6(i)^3, where digsum_6(i) = A053827(i).
  • A231675 (program): a(n) = Sum_{i=0..n} digsum_6(i)^4, where digsum_6(i) = A053827(i).
  • A231676 (program): a(n) = Sum_{i=0..n} digsum_7(i), where digsum_7(i) = A053828(i).
  • A231677 (program): a(n) = Sum_{i=0..n} digsum_7(i)^2, where digsum_7(i) = A053828(i).
  • A231678 (program): a(n) = Sum_{i=0..n} digsum_7(i)^3, where digsum_7(i) = A053828(i).
  • A231679 (program): a(n) = Sum_{i=0..n} digsum_7(i)^4, where digsum_7(i) = A053828(i).
  • A231680 (program): a(n) = Sum_{i=0..n} digsum_8(i), where digsum_8(i) = A053829(i).
  • A231681 (program): a(n) = Sum_{i=0..n} digsum_8(i)^2, where digsum_8(i) = A053829(i).
  • A231682 (program): a(n) = Sum_{i=0..n} digsum_8(i)^3, where digsum_8(i) = A053829(i).
  • A231683 (program): a(n) = Sum_{i=0..n} digsum_8(i)^4, where digsum_8(i) = A053829(i).
  • A231684 (program): a(n) = Sum_{i=0..n} digsum_9(i), where digsum_9(i) = A053830(i).
  • A231685 (program): a(n) = Sum_{i=0..n} digsum_9(i)^2, where digsum_9(i) = A053830(i).
  • A231686 (program): a(n) = Sum_{i=0..n} digsum_9(i)^3, where digsum_9(i) = A053830(i).
  • A231687 (program): a(n) = Sum_{i=0..n} digsum_9(i)^4, where digsum_9(i) = A053830(i).
  • A231688 (program): a(n) = Sum_{i=0..n} digsum(i)^3, where digsum(i) = A007953(i).
  • A231689 (program): a(n) = Sum_{i=0..n} digsum(i)^4, where digsum(i) = A007953(i).
  • A231711 (program): Numbers n such that n > sigma(n) - sigma(n-1).
  • A231712 (program): a(n) = n^n + n - 1.
  • A231720 (program): a(0)=1, after which, for any n uniquely written as du*u! + … + d2*2! + d1*1! (each di in range 0..i), a(n) = (du+1)*(u+1)! + … + (d2+1)*3! + (d1+1)*2! + 1; the natural numbers with their factorial base representation (A007623) shifted left one step and each digit incremented by one, converted back to decimal.
  • A231721 (program): Partial sums of phitorials: a(n) = A001088(1)+A001088(2)+…+A001088(n).
  • A231722 (program): Partial sums of A001088 starting from its second term; a(1)=0, a(n) = A001088(2)+…+A001088(n).
  • A231754 (program): Products of distinct primes congruent to 1 modulo 4 (A002144).
  • A231756 (program): Numbers n such that reversal (n^2) plus 1 is prime.
  • A231797 (program): Number of endofunctions on [n] such that no element has a preimage of cardinality one.
  • A231810 (program): Numbers n such that p-1 does not divide n+1 for every prime divisor p of n.
  • A231813 (program): Number of iterations of A046665(n) = (greatest prime divisor of n) - (least prime divisor of n) [with A046665(1) = 0] required to reach zero.
  • A231819 (program): Least positive k such that k*n^2 - 1 is a prime, or 0 if no such k exists.
  • A231821 (program): a(n) = mu(n) + 3, where mu is the Mobius function (A008683).
  • A231833 (program): Number of n X 2 0..3 arrays with no element less than a strict majority of its horizontal and antidiagonal neighbors.
  • A231847 (program): Primes p such that p*(p+1)/2 + 1 is a prime.
  • A231864 (program): Partial sums of the second power of arithmetic derivative function A003415.
  • A231873 (program): Elements of the integer compositions sub-operad Comp of TN_2 generated by 00 and 010.
  • A231874 (program): Elements of the segmented integer compositions sub-operad SComp of TN_3 generated by 00, 01, 02.
  • A231875 (program): Elements of the triassociative sub-operad Tri of TN generated by 01, 10 and 11.
  • A231876 (program): Numbers n such that omega(n)^2 (cf. A001221) divides n.
  • A231877 (program): Numbers n such that omega(n)^2 (cf. A001221) does not divide n.
  • A231878 (program): Numbers n such that bigomega(n)^2 (cf. A001222) divides n.
  • A231879 (program): Numbers n such that bigomega(n)^2 (cf. A001222) does not divide n.
  • A231895 (program): a(n) = 2*A000111(n+1) + A000111(n).
  • A231896 (program): a(n) = 4*a(n-1) - a(n-2) with a(0) = 0, a(1) = 4.
  • A231935 (program): Greatest prime Q < 2*n such that 2*n-Q=P prime < Q starting at n=4.
  • A231946 (program): Partial sums of the third power of arithmetic derivative function A003415.
  • A231947 (program): Expansion of q^(-1/3) * a(q)^2 * c(q) / 3 in powers of q where a(), c() are cubic AGM theta functions.
  • A231950 (program): Number of (n+1)X(1+1) 0..1 arrays with every element equal to some horizontal, vertical, diagonal or antidiagonal neighbor, with top left element zero
  • A231958 (program): Numbers n dividing the Lucas sequence u(n) defined by u(i) = 2*u(i-1) - 5*u(i-2) with initial conditions u(0)=0, u(1)=1
  • A231959 (program): Numbers n dividing the Lucas sequence u(n) defined by u(i) = 3*u(i-1) - u(i-2) with initial conditions u(0)=0, u(1)=1.
  • A231960 (program): Powers of 3 together with multiples of 6.
  • A231963 (program): Concatenate n with its UPC check digit.
  • A231967 (program): Squarefree numbers (A005117) of the form p*q*r with prime factors p, q, r with q = 2*p + 1 and r = 2*q + 1.
  • A231982 (program): Decimal expansion of one deg^2 expressed in steradians (sr).
  • A231988 (program): Primes of the form triangular(p) + 1, where p is a prime.
  • A232006 (program): Triangular array read by rows: T(n,k) is the number of simple labeled graphs on vertex set {1,2,…,n} with exactly k components (all of which are trees) such that the labels {1,2,…,k} are all in distinct components (trees), n>=0, 0<=k<=n.
  • A232007 (program): Maximal number of moves needed by a knight to reach every square from a fixed position on an n X n chessboard, or -1 if it is not possible to reach every square.
  • A232011 (program): Numbers n such that (3n)^2 + 2 is prime.
  • A232012 (program): Numbers n such that p^2 + n is prime for some prime p.
  • A232015 (program): Expansion of (1-2*x)/((1+2*x)*(1-3*x)).
  • A232017 (program): Number of n X 2 0..2 arrays with no element less than a strict majority of its horizontal and antidiagonal neighbors.
  • A232031 (program): Number of (n+1) X (1+1) 0..1 arrays with every element equal to some horizontal, vertical or antidiagonal neighbor, with top left element zero.
  • A232059 (program): Number of n X 2 0..2 arrays with every 0 next to a 1 and every 1 next to a 2 horizontally or vertically, with no adjacent values equal.
  • A232077 (program): Number of (1+1) X (n+1) 0..1 arrays with every element equal to some horizontal, diagonal or antidiagonal neighbor, with top left element zero.
  • A232089 (program): Table read by rows, which consist of 1 followed by 2^k, 0 <= k < n ; n = 0,1,2,3,…
  • A232091 (program): Smallest square or promic (oblong) number greater than or equal to n.
  • A232094 (program): a(n) = A060130(A000217(n)); number of nonzero digits in factorial base representation (A007623) of 0+1+2+…+n.
  • A232095 (program): Minimal number of factorials which add to 0+1+2+…+n; a(n) = A034968(A000217(n)).
  • A232096 (program): a(n) = largest m such that m! divides 1+2+…+n; a(n) = A055881(A000217(n)).
  • A232098 (program): a(n) is the largest m such that m! divides n^2; a(n) = A055881(n^2).
  • A232114 (program): a(n) is the Manhattan distance between n and n^2 in a square spiral of positive integers with 1 at the center.
  • A232131 (program): Number of (n+1) X (2+1) 0..2 arrays with no element equal to a strict majority of its horizontal and antidiagonal neighbors, with values 0..2 introduced in row major order.
  • A232162 (program): Number of Weyl group elements, not containing an s_r factor, which contribute nonzero terms to Kostant’s weight multiplicity formula when computing the multiplicity of the zero-weight in the adjoint representation for the Lie algebra of type B and rank n.
  • A232163 (program): Cardinality of the Weyl alternation set corresponding to the zero-weight in the adjoint representation of the Lie algebra so(2n+1).
  • A232164 (program): Number of Weyl group elements, not containing an s_r factor, which contribute nonzero terms to Kostant’s weight multiplicity formula when computing the multiplicity of the zero-weight in the adjoint representation for the Lie algebra of type C and rank n.
  • A232165 (program): Cardinality of the Weyl alternation set corresponding to the zero-weight in the adjoint representation of the Lie algebra sp(2n).
  • A232172 (program): Partial sums of second arithmetic derivative of natural numbers.
  • A232175 (program): Least positive k such that n^3 + k^2 is a square, or 0 if there is no such k.
  • A232178 (program): Least k>=0 such that triangular(n) + k^2 is a square, or -1 if no such k exists.
  • A232179 (program): Least k >= 0 such that n^2 + triangular(k) is a triangular number.
  • A232180 (program): First bisection of harmonic numbers (numerators).
  • A232181 (program): First bisection of harmonic numbers (denominators).
  • A232205 (program): a(0)=1; thereafter a(n) = n*a(n-1) if n is even, otherwise a(n) = 2*n*a(n-1).
  • A232224 (program): Number of ways of arranging n chords on a circle (handshakes between 2n people across a table) with exactly 3 simple intersections.
  • A232228 (program): a(1)=1; thereafter a(n) = 2^(number of bits in binary expansion of a(n-1)) + 1 + a(n-1).
  • A232229 (program): a(1)=9; thereafter a(n) = 8*10^(n-1) + 8 + a(n-1).
  • A232230 (program): Expansion of (1 - 2*x + x^2 + x^3 + x^5) / ((1 - x)*(1 - 2*x - x^3)).
  • A232231 (program): G.f.: (1-3*x+2*x^2+2*x^4+4*x^5)/((1-x)*(1-3*x-4*x^3)).
  • A232243 (program): a(n) = wt(n^2) - wt(n), where wt(n) = A000120(n) is the binary weight function.
  • A232245 (program): Sum of the number of ones in binary representation of n and n^2.
  • A232246 (program): Central terms of triangle A110440.
  • A232250 (program): Number of (n+1) X (1+1) 0..2 arrays with every element both >= and <= some horizontal or antidiagonal neighbor.
  • A232265 (program): a(n) = 10*binomial(9*n + 10, n)/(9*n + 10).
  • A232266 (program): Triangle where T(n,k) = number of compositions of n^2 - k^2 into sums of squares for k=0..n, n>=0, as read by rows.
  • A232267 (program): Least k>=0 such that n^3 + k^2 is a square.
  • A232268 (program): Numbers n such that reversal (n^3) plus 1 is prime.
  • A232289 (program): Number of nX2 0..2 arrays with every 0 next to a 1 and every 1 next to a 2 horizontally or antidiagonally
  • A232290 (program): Number of n X 3 0..2 arrays with every 0 next to a 1 and every 1 next to a 2 horizontally or antidiagonally.
  • A232311 (program): Number of (n+1)X(3+1) 0..1 arrays with every element equal to some horizontal or antidiagonal neighbor, with top left element zero
  • A232317 (program): Number of (1+1)X(n+1) 0..1 arrays with every element equal to some horizontal or antidiagonal neighbor, with top left element zero
  • A232324 (program): n(n+1)/2 modulo sigma(n).
  • A232331 (program): Number of nX4 0..2 arrays with every 0 next to a 1 and every 1 next to a 2 horizontally or antidiagonally, with no adjacent elements equal
  • A232342 (program): A077068(n) minus A077065(n).
  • A232395 (program): (ceiling(sqrt(n^3 + n^2 + n + 1)))^2 - (n^3 + n^2 + n + 1).
  • A232397 (program): a(n) = ceiling(sqrt(n^4 + n^3 + n^2 + n + 1))^2 - (n^4 + n^3 + n^2 + n + 1).
  • A232423 (program): a(n) = ceiling(sqrt(n^4 - n^3 - n^2 + n + 1))^2 - (n^4 - n^3 - n^2 + n + 1).
  • A232436 (program): Numbers which are uniquely decomposable into x^2+xy+y^2, the unique decomposition being with two distinct nonzero x and y.
  • A232437 (program): Numbers whose square is expressible in only one way as x^2+xy+y^2, with x and y > 0.
  • A232449 (program): The palindromic Belphegor numbers: (10^(n+3)+666)*10^(n+1)+1.
  • A232472 (program): 2-Fubini numbers.
  • A232473 (program): 3-Fubini numbers.
  • A232474 (program): 4-Fubini numbers.
  • A232475 (program): Number of preferential arrangements of n labeled elements when at least k=4 elements per rank are required.
  • A232479 (program): Number of symmetric h-vectors of length n.
  • A232482 (program): The function l_5(n) arising in the enumeration of h-vectors.
  • A232485 (program): a(1) = 3; a(n+1) = a(n) + product of digits of a(n).
  • A232486 (program): a(1) = 3; thereafter a(n+1) = a(n) + product of nonzero digits of a(n).
  • A232487 (program): a(1) = 5; a(n+1) = a(n) + product of nonzero digits of a(n).
  • A232488 (program): a(1) = 7; a(n+1) = a(n) + product of nonzero digits of a(n).
  • A232493 (program): If n mod 2 = 0 then 2^n*3^(n-1)+2^(n+1)*3^(n/2-1) otherwise 2^n*3^(n-1)+2^n*3^((n-1)/2).
  • A232494 (program): If n mod 2 = 0 then 2^(n-1)*(3^n+3*3^(n/2)-2) otherwise 2^(n-1)*(3^n+5*3^((n-1)/2)-2).
  • A232495 (program): 9*n^3/2 - 21*n^2/2 + 8*n - 4.
  • A232500 (program): Oscillating orbitals over n sectors (nonpositive values indicating there exist none).
  • A232503 (program): Largest power of 2 in the Collatz (3x+1) trajectory of n.
  • A232508 (program): Number of (n+1) X (1+1) 0..2 arrays with every element next to itself plus and minus one within the range 0..2 horizontally, diagonally or antidiagonally, with no adjacent elements equal.
  • A232510 (program): Number of (n+1)X(3+1) 0..2 arrays with every element next to itself plus and minus one within the range 0..2 horizontally, diagonally or antidiagonally, with no adjacent elements equal
  • A232531 (program): Numbers n such that the equation a^2 + 2*n*b^2 = 2*c^2 + n*d^2 has no solutions in positive integers for a, b, c, d.
  • A232533 (program): a(n) = Sum_{i=1…n} Sum_{j=1..i} lcm(i,j)/i.
  • A232535 (program): Triangle T(n,k), 0 <= k <= n, read by rows defined by: T(n,k) = (binomial(2*n,2*k) + binomial(2*n+1,2*k))/2.
  • A232537 (program): Primes p of the form penta(n)-3, where penta(n) is the n-th pentagonal number.
  • A232545 (program): Number of Euler tours of the complete digraph on n vertices.
  • A232546 (program): Expansion of (1 - 12*x)^(3/2) in powers of x.
  • A232555 (program): Nonsquare numbers whose sum of proper square divisors is a square greater than 1.
  • A232560 (program): Inverse permutation of the sequence of positive integers at A232559.
  • A232567 (program): Number of non-equivalent binary n X n matrices with two nonadjacent 1’s.
  • A232580 (program): Number of binary sequences of length n that contain at least one contiguous subsequence 011.
  • A232582 (program): Number of (n+1) X (1+1) 0..2 arrays with every element next to itself plus and minus one within the range 0..2 horizontally or antidiagonally, with no adjacent elements equal.
  • A232583 (program): Number of (n+1)X(2+1) 0..2 arrays with every element next to itself plus and minus one within the range 0..2 horizontally or antidiagonally, with no adjacent elements equal
  • A232584 (program): Number of (n+1)X(3+1) 0..2 arrays with every element next to itself plus and minus one within the range 0..2 horizontally or antidiagonally, with no adjacent elements equal
  • A232590 (program): Number of (1+1)X(n+1) 0..2 arrays with every element next to itself plus and minus one within the range 0..2 horizontally or antidiagonally, with no adjacent elements equal
  • A232599 (program): Alternating sum of cubes, i.e., Sum_{k=0..n} k^p*q^k for p=3, q=-1.
  • A232600 (program): a(n) = Sum_{k=0..n} k^p*q^k, where p=1, q=-2.
  • A232601 (program): a(n) = Sum_{k=0..n} k^p*q^k for p = 2 and q = -2.
  • A232602 (program): a(n) = Sum_{k=0..n} k^p*q^k, where p=3, q=-2.
  • A232603 (program): a(n) = 2^n * Sum_{k=0..n} k^p*q^k, where p=2, q=-1/2.
  • A232604 (program): a(n) = 2^n * Sum_{k=0..n} k^p*q^k, where p=3, q=-1/2.
  • A232615 (program): Variant of the Chandra-sutra (A014701) using 3 instead of 2, and a mod argument using residues 1 and 2.
  • A232617 (program): Product of first n odd numbers plus product of first n even numbers: (2n-1)!! + (2n)!!, where k!! = A006882(k).
  • A232618 (program): a(n) = (2n)!! mod (2n-1)!! where k!! = A006882(k).
  • A232621 (program): The number of indecomposable domino tilings of the 5 X (2n) board.
  • A232623 (program): Number of partitions of 2n into parts with multiplicity <= n.
  • A232625 (program): Denominators of abs(n-8)/(2*n), n >= 1
  • A232626 (program): Degree of the algebraic number 2*sin(4*Pi/n).
  • A232628 (program): Denominators of the triangle of polynomial coefficients P(0,x)=1, 2*P(n)=(1+x)*((1+x)^(n-1)+x^(n-1)).
  • A232635 (program): Expansion of psi(x) * phi(x^2)^2 in powers of x where phi(), psi() are Ramanujan theta functions.
  • A232637 (program): Odious numbers of order 2: a(n) = A000069(A000069(n)).
  • A232639 (program): Inverse permutation of the sequence of positive integers at A232638.
  • A232641 (program): Inverse permutation of the sequence of positive integers at A232640.
  • A232643 (program): Inverse permutation of the sequence of positive integers at A232642.
  • A232646 (program): Sequence (or tree or triangle) generated by these rules: 1 is in S, and if x is in S, then 2*x and 5*x + 3 are in S, and duplicates are deleted as they occur.
  • A232665 (program): Number of compositions of 2n such that the largest multiplicity of parts equals n.
  • A232666 (program): 6-free Fibonacci numbers.
  • A232681 (program): Numbers n such that the equation a^2 + 5*n*b^2 = 5*c^2 + n*d^2 has no solutions in positive integers for a, b, c, d.
  • A232697 (program): Number of partitions of 2n into parts such that the largest multiplicity equals n.
  • A232701 (program): a(n) = (2*n-1)!! mod n!, where double factorial is A006882.
  • A232705 (program): Number of Gaussian integers z satisfying (n-1)/2 < |z| < n/2.
  • A232710 (program): Binary numbers (written in decimal) such that the sum of digits mod 2 equals the product of digits mod 2.
  • A232713 (program): Doubly pentagonal numbers: a(n) = n*(3*n-2)*(3*n-1)*(3*n+1)/8.
  • A232715 (program): Decimal expansion of the ratio of the area of a parbelos to the area of its associated arbelos: 4/(3*Pi).
  • A232719 (program): Sum_{k=1,…,2n} (-1)^k binomial(8*n,4*k).
  • A232723 (program): Sequence (or tree) generated by these rules: 0 is in S, and if x is in S, then 2*x and 1 - x are in S, and duplicates are deleted as they occur.
  • A232732 (program): a(n) = Sum_{k=0..2*n} (-1)^k * binomial(12*n,6*k).
  • A232736 (program): Decimal expansion of the imaginary part of I^(1/7), or sin(Pi/14).
  • A232741 (program): Numbers n for which the largest m such that (m-1)! divides n is a prime.
  • A232742 (program): Numbers n for which the largest m such that (m-1)! divides n is a composite.
  • A232744 (program): Numbers k for which the largest m such that m! divides k is odd.
  • A232745 (program): Numbers k for which the largest m such that m! divides k is even.
  • A232746 (program): n occurs A030124(n) times; a(n) = one less than the least k such that A005228(k) > n.
  • A232747 (program): Inverse function to Hofstadter’s A005228.
  • A232748 (program): Partial sums of the characteristic function of Hofstadter’s A030124.
  • A232749 (program): Inverse function to Hofstadter’s A030124.
  • A232765 (program): Values of y solving x^2 = floor(y^2/3 + y).
  • A232771 (program): Values of x satisfying x^2 = floor(y^2/3 + y).
  • A232779 (program): Sum of iterated logs; a(n) = 0 if n = 0; otherwise n + a(floor(log_2(n)).
  • A232801 (program): a(2n) = (3^n - 1)/2, a(2n+1) = 3^n.
  • A232803 (program): Odd primes, twice odd primes, 4, and 8.
  • A232812 (program): Decimal expansion of the surface index of a regular tetrahedron.
  • A232821 (program): a(n) = n^(n-1) - Sum_{k=1..n-1} k^(k-1).
  • A232845 (program): a(0) = 0, a(1) = 1, and for n>=2, a(n) = (n-2)*a(n-1) - (n-1)*a(n-2).
  • A232853 (program): Repeat n+1 times A091137(n).
  • A232866 (program): Positions of the nonnegative integers in the sequence (or tree) of complex numbers generated by these rules: 0 is in S, and if x is in S, then x + 1 and i*x are in S, where duplicates are deleted as they occur.
  • A232867 (program): Positions of the negative integers in the sequence (or tree) of complex numbers generated by these rules: 0 is in S, and if x is in S, then x + 1 and i*x are in S, where duplicates are deleted as they occur.
  • A232878 (program): Twin prime pairs which sum to perfect squares.
  • A232881 (program): Twin primes with digital root 5 or 7.
  • A232882 (program): Twin primes with digital root 8 or 1.
  • A232893 (program): Numbers whose sum of square divisors is a palindrome in base 10 having at least two digits.
  • A232896 (program): a(n) = 3*a(n-1) - 2*a(n-2) - a(n-3) + a(n-4), where a(1) = 1, a(2) = 3, a(3) = 5, a(4) = 8.
  • A232901 (program): Number of (n+1) X (1+1) 0..2 arrays with every element next to itself plus and minus one within the range 0..2 horizontally or antidiagonally.
  • A232921 (program): Number of 2 X n 0..2 arrays with no element x(i,j) adjacent to value 2-x(i,j) horizontally, diagonally or antidiagonally.
  • A232922 (program): Number of 3 X n 0..2 arrays with no element x(i,j) adjacent to value 2-x(i,j) horizontally, diagonally or antidiagonally.
  • A232935 (program): Number of n X 2 0..2 arrays with no element x(i,j) adjacent to value 2-x(i,j) horizontally, vertically or antidiagonally.
  • A232936 (program): Number of n X 3 0..2 arrays with no element x(i,j) adjacent to value 2-x(i,j) horizontally, vertically or antidiagonally.
  • A232950 (program): Number of n X 3 0..3 arrays with no element x(i,j) adjacent to value 3-x(i,j) horizontally, diagonally or antidiagonally, and top left element zero.
  • A232951 (program): Number of n X 4 0..3 arrays with no element x(i,j) adjacent to value 3-x(i,j) horizontally, diagonally or antidiagonally, and top left element zero.
  • A232956 (program): Number of 2 X n 0..3 arrays with no element x(i,j) adjacent to value 3-x(i,j) horizontally, diagonally or antidiagonally, and top left element zero.
  • A232969 (program): The sequence S(n,n) that enumerates a certain class of lattice paths from (0,0) to (n,n).
  • A232970 (program): Expansion of (1-3*x)/(1-5*x+3*x^2+x^3).
  • A232971 (program): G.f.: (1-5*x+3*x^2+x^3)/(1-7*x+10*x^2+x^3-x^4).
  • A232973 (program): Dziemianczuk’s array S(i,j) read by antidiagonals.
  • A232976 (program): Numerators of coefficients in expansion of Product_{k>=1} 1/(1-x^k)^(k/2).
  • A232977 (program): G.f.: Product_{k>=1} 1/(1-(4*x)^k)^(k/2).
  • A232980 (program): The Gauss factorial n_3!.
  • A232981 (program): The Gauss factorial n_5!.
  • A232982 (program): The Gauss factorial n_6!.
  • A232983 (program): The Gauss factorial n_7!.
  • A232984 (program): The Gauss factorial n_10!.
  • A232985 (program): The Gauss factorial n_11!.
  • A232990 (program): Period 5: repeat [1,0,0,1,0].
  • A232991 (program): Period 6: repeat [1, 0, 0, 0, 1, 0].
  • A232994 (program): a(n) = 6*(n - 3)*(n - 4)*2^(n-3)*n^(n-4).
  • A232995 (program): a(n) = (n - 3)^2*(n - 4)*2^n*n^(n-5).
  • A232997 (program): Number of tilings of a fortress (or Penta-Aztec-Diamond) of order n.
  • A233000 (program): Let L(n) = Fibonacci(n-1)+Fibonacci(n+1) (cf. A000045, A000032); if n is even then a(n) = (L(n)+2)^2 otherwise a(n) = L(2*n)+2.
  • A233003 (program): (n!)^2 mod Pt(n), where Pt(n) is product of first n positive triangular numbers (A000217).
  • A233004 (program): Pt(n) mod n!, where Pt(n) is product of first n positive triangular numbers (A000217).
  • A233005 (program): floor(Pt(n)/n!), where Pt(n) is product of first n positive triangular numbers (A000217).
  • A233013 (program): Number of n X 3 0..3 arrays with no element x(i,j) adjacent to value 3-x(i,j) horizontally or vertically, top left element zero, and 1 appearing before 2 in row major order.
  • A233020 (program): Number of n X 2 0..3 arrays with no element x(i,j) adjacent to value 3-x(i,j) horizontally, vertically, diagonally or antidiagonally, and top left element zero.
  • A233034 (program): Expansion of (f(-x^2) / phi(-x^3))^2 in powers of x where phi(), f() are Ramanujan theta functions.
  • A233035 (program): a(n) = n * floor(n/4).
  • A233036 (program): The maximum number of I-tetrominoes that can be packed into an n X n array of squares when rotation is allowed.
  • A233077 (program): Number of n X 3 0..3 arrays with no element x(i,j) adjacent to value 3-x(i,j) horizontally or antidiagonally, top left element zero, and 1 appearing before 2 in row major order.
  • A233078 (program): Number of n X 4 0..3 arrays with no element x(i,j) adjacent to value 3-x(i,j) horizontally or antidiagonally, top left element zero, and 1 appearing before 2 in row major order.
  • A233083 (program): Number of 2 X n 0..3 arrays with no element x(i,j) adjacent to value 3-x(i,j) horizontally or antidiagonally, top left element zero, and 1 appearing before 2 in row major order.
  • A233090 (program): Decimal expansion of sum_(n=1..infinity) (-1)^(n-1)*H(n)/n^2, where H(n) is the n-th harmonic number.
  • A233091 (program): Decimal expansion of Sum_{i>=0} 1/(2*i+1)^3.
  • A233093 (program): Number of n X 3 0..3 arrays with no element x(i,j) adjacent to value 3-x(i,j) horizontally, diagonally or antidiagonally, top left element zero, and 1 appearing before 2 in row major order.
  • A233094 (program): Number of n X 4 0..3 arrays with no element x(i,j) adjacent to value 3-x(i,j) horizontally, diagonally or antidiagonally, top left element zero, and 1 appearing before 2 in row major order.
  • A233099 (program): Number of 2 X n 0..3 arrays with no element x(i,j) adjacent to value 3-x(i,j) horizontally, diagonally or antidiagonally, top left element zero, and 1 appearing before 2 in row major order.
  • A233106 (program): Number of n X 1 0..5 arrays with no element x(i,j) adjacent to value 5-x(i,j) horizontally or vertically, top left element zero, and 1 appearing before 2 3 and 4, and 2 appearing before 3 in row major order.
  • A233107 (program): Number of n X 2 0..5 arrays with no element x(i,j) adjacent to value 5-x(i,j) horizontally or vertically, top left element zero, and 1 appearing before 2 3 and 4, and 2 appearing before 3 in row major order.
  • A233123 (program): Number of n X 2 0..5 arrays with no element x(i,j) adjacent to itself or value 5-x(i,j) horizontally or vertically, top left element zero, and 1 appearing before 2 3 and 4, and 2 appearing before 3 in row major order (unlabelled 6-colorings with no clashing color pairs).
  • A233124 (program): Number of n X 3 0..5 arrays with no element x(i,j) adjacent to itself or value 5-x(i,j) horizontally or vertically, top left element zero, and 1 appearing before 2 3 and 4, and 2 appearing before 3 in row major order (unlabelled 6-colorings with no clashing color pairs).
  • A233125 (program): Number of nX4 0..5 arrays with no element x(i,j) adjacent to itself or value 5-x(i,j) horizontally or vertically, top left element zero, and 1 appearing before 2 3 and 4, and 2 appearing before 3 in row major order (unlabelled 6-colorings with no clashing color pairs)
  • A233131 (program): Sum of remainders of n modulo all smaller composite numbers.
  • A233135 (program): Shortest (x+1,2x)-code of n.
  • A233137 (program): Reversed shortest (x+1,2x)-code of n.
  • A233139 (program): Number of tilings of a 4 X n rectangle using T and Z tetrominoes.
  • A233141 (program): Number of n X 2 0..5 arrays with no element x(i,j) adjacent to value 5-x(i,j) horizontally, antidiagonally or vertically, top left element zero, and 1 appearing before 2 3 and 4, and 2 appearing before 3 in row major order.
  • A233152 (program): Number of n X 5 0..2 arrays with no element x(i,j) adjacent to value 2-x(i,j) horizontally or antidiagonally.
  • A233153 (program): Number of n X 6 0..2 arrays with no element x(i,j) adjacent to value 2-x(i,j) horizontally or antidiagonally.
  • A233161 (program): Number of n X n 0..7 arrays with no element x(i,j) adjacent to itself or value 7-x(i,j) horizontally, diagonally, antidiagonally or vertically, top left element zero, and 1 appearing before 2 3 4 5 and 6, 2 appearing before 3 4 and 5, and 3 appearing before 4 in row major order (unlabelled 8-colorings with no clashing color pairs)
  • A233162 (program): Number of n X 1 0..7 arrays with no element x(i,j) adjacent to itself or value 7-x(i,j) horizontally, diagonally, antidiagonally or vertically, top left element zero, and 1 appearing before 2 3 4 5 and 6, 2 appearing before 3 4 and 5, and 3 appearing before 4 in row major order (unlabelled 8-colorings with no clashing color pairs).
  • A233163 (program): Number of n X 3 0..7 arrays with no element x(i,j) adjacent to itself or value 7-x(i,j) horizontally, diagonally, antidiagonally or vertically, top left element zero, and 1 appearing before 2 3 4 5 and 6, 2 appearing before 3 4 and 5, and 3 appearing before 4 in row major order (unlabelled 8-colorings with no clashing color pairs).
  • A233176 (program): Number of 3 X n 0..5 arrays with no element x(i,j) adjacent to itself or value 5-x(i,j) horizontally, diagonally or antidiagonally, top left element zero, and 1 appearing before 2 3 and 4, and 2 appearing before 3 in row major order (unlabelled 6-colorings with no clashing color pairs).
  • A233182 (program): Numbers that are not the product of a prime and a square.
  • A233196 (program): Number of n X 2 0..7 arrays with no element x(i,j) adjacent to itself or value 7-x(i,j) horizontally, antidiagonally or vertically, top left element zero, and 1 appearing before 2 3 4 5 and 6, 2 appearing before 3 4 and 5, and 3 appearing before 4 in row major order (unlabelled 8-colorings with no clashing color pairs).
  • A233203 (program): Floor(n^n / 2^n).
  • A233207 (program): Triangle T(n,k), read by rows, given by T(n+k,k)=2*k*(2*n+1).
  • A233211 (program): Number of n X 2 0..5 arrays with no element x(i,j) adjacent to value 5-x(i,j) horizontally or antidiagonally, top left element zero, and 1 appearing before 2 3 and 4, and 2 appearing before 3 in row major order.
  • A233231 (program): a(n) = 10*a(n-3) - a(n-6) + 4 for n>5, a(0)=2, a(1)=3, a(2)=5, a(3)=12, a(4)=29, a(5)=51.
  • A233247 (program): Expansion of ( 1-x^3-x^2 ) / ( (x^3-x^2-1)*(x^3+2*x^2+x-1) ).
  • A233249 (program): a(1)=0; for k >= 1, let prime(k) map to 10…0 with k-1 zeros and let prime(k)*prime(m) map to the concatenation in binary of 2^(k-1) and 2^(m-1). For n >= 2, let the prime power factorization of n be mapped to r(n). a(n) is the term in A114994 which is c-equivalent to r(n) (see there our comment).
  • A233251 (program): Number of n X 3 0..5 arrays with no element x(i,j) adjacent to itself or value 5-x(i,j) horizontally or antidiagonally, top left element zero, and 1 appearing before 2 3 and 4, and 2 appearing before 3 in row major order (unlabelled 6-colorings with no clashing color pairs).
  • A233252 (program): Number of n X 4 0..5 arrays with no element x(i,j) adjacent to itself or value 5-x(i,j) horizontally or antidiagonally, top left element zero, and 1 appearing before 2 3 and 4, and 2 appearing before 3 in row major order (unlabelled 6-colorings with no clashing color pairs).
  • A233257 (program): Number of 2 X n 0..5 arrays with no element x(i,j) adjacent to itself or value 5-x(i,j) horizontally or antidiagonally, top left element zero, and 1 appearing before 2 3 and 4, and 2 appearing before 3 in row major order (unlabelled 6-colorings with no clashing color pairs).
  • A233271 (program): a(0)=0; thereafter a(n+1) = a(n) + 1 + number of 0’s in binary representation of a(n), counted with A080791.
  • A233272 (program): a(n) = n + 1 + number of nonleading zeros in binary representation of n (A080791).
  • A233273 (program): Bisection of A233272: a(n) = A233272(2n+1).
  • A233279 (program): Permutation of nonnegative integers: a(n) = A054429(A006068(n)).
  • A233280 (program): Permutation of nonnegative integers: a(n) = A003188(A054429(n)).
  • A233284 (program): a(n) = largest m such that 1, 2, …, m divide n-th Fibonacci number; a(n) = A055874(A000045(n)).
  • A233285 (program): a(n) = largest m such that m! divides n-th Fibonacci number; a(n) = A055881(A000045(n)).
  • A233286 (program): Number of trailing zeros in the factorial base representation of n-th Fibonacci number; a(n) = A230403(A000045(n)) = A233285(n)-1.
  • A233295 (program): Riordan array ((1+x)/(1-x)^3, 2*x/(1-x)).
  • A233325 (program): (2*6^(n+1) - 7) / 5.
  • A233326 (program): a(n) = (7^(n+1) - 4) / 3.
  • A233328 (program): a(n) = (2*8^(n+1) - 9) / 7.
  • A233329 (program): Expansion of (1+4*x+x^2)/((1+x)^2*(1-x)^5).
  • A233334 (program): a(1)=1; for n>1, a(n) is the smallest number > a(n-1) such that a(1) + a(2) +…+ a(n) is a composite number.
  • A233348 (program): Numbers n such that 3*n+2 and 3*n-2 are both prime for n multiple of 5 (A008587).
  • A233388 (program): Odious numbers that are the sum of 2 consecutive odious numbers.
  • A233389 (program): Naturally embedded ternary trees having no internal node of label greater than 1.
  • A233397 (program): floor(n^n / 3^n).
  • A233398 (program): n^n mod 3^n.
  • A233402 (program): Number of (n+1) X (1+1) 0..2 arrays with row and column sums nondecreasing, and no adjacent elements equal.
  • A233411 (program): The number of length n binary words with some prefix which contains two more 1’s than 0’s or two more 0’s than 1’s.
  • A233438 (program): Primorial(n) mod compositorial(n), that is, A002110(n) mod A036691(n).
  • A233441 (program): Floor(2^n / n^3).
  • A233442 (program): 2^n mod n^3.
  • A233446 (program): a(n) = ((2n-1)^(2n+1) + (2n+1)^(2n-1))/(2n)^2 = A154682(n)/(2n)^2 for n > 0.
  • A233447 (program): Floor(compositorial(n) / n!), that is, floor(A036691(n) / A000142(n)).
  • A233449 (program): a(n) = Sum_{k=0..n} k! * 2^(n-k).
  • A233450 (program): Numbers n such that 3*T(n)+1 is a square, where T = A000217.
  • A233457 (program): Values of n for which the equation x^2 - 16*y^2 = n has integer solutions.
  • A233468 (program): The digital root of prime(n+1) minus the digital root of prime(n).
  • A233470 (program): Numerators of the expectation of the process defined by randomly moving 2n balls between bins.
  • A233471 (program): a(n) = 3^n mod n^2.
  • A233473 (program): Least k such that there are n triangular numbers between triangular(k) and k^2.
  • A233474 (program): Numbers m such that 5*T(m)-1 is a square, where T = A000217.
  • A233481 (program): Number of singletons (strong fixed points) in pair-partitions.
  • A233508 (program): Numerators of the triangle of polynomial coefficients P(0,x)=1, 2*P(n)=(1+x)*((1+x)^(n-1)+x^(n-1)). Of the first array of A133135.
  • A233511 (program): Replace the largest prime factor p>2 in n (if any) with the prime preceding p.
  • A233522 (program): Expansion of 1 / (1 - x - x^4 + x^9) in powers of x.
  • A233541 (program): a(n) = sigma(n) + phi(n) + d(n).
  • A233543 (program): Table T(n,m) = m! read by rows.
  • A233558 (program): Triangle read by rows: T(n,k) = real part mod n of (n + ki)^2, where k=1..n-1 and i is the imaginary unit.
  • A233561 (program): Products p*q of distinct primes such that (p*q - 1)/2 is prime.
  • A233562 (program): Products p*q of distinct primes such that (p*q + 1)/2 is a prime.
  • A233570 (program): Replace the smallest prime factor p in n (if any) with the prime following p.
  • A233578 (program): n >= 2 such that the denominator/6 of Bernoulli(n) is congruent to {1, 5, 7, 13 or 19} modulo 30.
  • A233581 (program): a(n) = 2*a(n-1) - 3*a(n-2) + a(n-3), a(0) = 1, a(1) = 0, a(2) = -1.
  • A233583 (program): Coefficients of the generalized continued fraction expansion e = a(1) +a(1)/(a(2) +a(2)/(a(3) +a(3)/(a(4) +a(4)/….))).
  • A233637 (program): Number of (n+1) X (1+1) 0..2 arrays with every 2 X 2 subblock having the sum of the squares of the edge differences equal to 2.
  • A233656 (program): a(n) = 3*a(n-1) - 2*(n-1), with a(0) = 1.
  • A233657 (program): a(n) = 10 * binomial(3*n+10,n)/(3*n+10).
  • A233658 (program): 7*binomial(4*n + 7, n)/(4*n + 7).
  • A233666 (program): a(n) = 2*binomial(4*n + 8, n)/(n + 2).
  • A233667 (program): a(n) = 5*binomial(4*n+10,n)/(2*n+5).
  • A233668 (program): a(n) = 6*binomial(5*n + 6,n)/(5*n + 6).
  • A233669 (program): a(n) = 7*binomial(5*n+7, n)/(5*n+7).
  • A233670 (program): Expansion of q * phi(-q^2) * psi(q^9) / (f(q^3) * phi(q^3)) in powers of q where f(), phi(), psi() are Ramanujan theta functions.
  • A233671 (program): Numbers k such that prime(k)^2 < prime(k-1)*prime(k+1).
  • A233672 (program): Expansion of psi(q) * phi(-q^18) * f(-q^6) / f(q^3)^3 in powers of q where phi(), psi(), f() are Ramanujan theta functions.
  • A233673 (program): Expansion of phi(q) * phi(q^9) / phi(q^3)^2 in powers of q where phi() is a Ramanujan theta function.
  • A233684 (program): Number of (n+1) X (1+1) 0..3 arrays with every 2 X 2 subblock having the sum of the squares of the edge differences equal to 10, and no two adjacent values equal.
  • A233693 (program): Expansion of q * psi(-q) * chi(-q^6) * psi(-q^9) / (phi(-q) * phi(-q^18)) in powers of q where phi(), psi(), chi() are Ramanujan theta functions.
  • A233698 (program): Expansion of b(q^2) * c(q^2) / (3 * b(q)^2) in powers of q where b(), c() are cubic AGM functions.
  • A233699 (program): Ideal rectangle side length for packing squares with side 1/n.
  • A233734 (program): Central terms of triangles A019538 and A090582.
  • A233736 (program): a(n) = 8*binomial(5*n + 8, n)/(5*n + 8).
  • A233737 (program): a(n) = 9*binomial(5*n+9, n)/(5*n+9).
  • A233738 (program): 2*binomial(5*n+10, n)/(n+2).
  • A233743 (program): a(n) = 7*binomial(6*n + 7, n)/(6*n + 7).
  • A233744 (program): Numbers p = a(n) such that p divided by (n-1)! is equal to the average number of elements of partition sets of n elements excluding sets with a singleton.
  • A233757 (program): Triangle read by rows: T(n,k) = (2^n-1)*2^(k-1), for n >= 1 and 1<=k<=n.
  • A233758 (program): Bisection of A006950 (the even part).
  • A233759 (program): Bisection of A006950 (the odd part).
  • A233771 (program): Number of nonpalindromic partitions of n.
  • A233774 (program): Total number of vertices in the first n rows of Sierpinski gasket, with a(0) = 1.
  • A233775 (program): Number of vertices in the n-th row of the Sierpinski gasket (cf. A047999).
  • A233776 (program): Number of grid points that are covered on the semi-infinite hexagonal grid after n-th stage in a cellular automaton in which the toothpicks are connected by their endpoints but the toothpicks placed in northwest or northeast direction are prohibited, starting with a(0) = 1.
  • A233777 (program): Number of vertices in the n-th row of the toothpick structure of A233776, with a(0) = 1.
  • A233795 (program): Number of triangular numbers between triangular(n) and n^2.
  • A233820 (program): Period 4: repeat [20, 5, 15, 10].
  • A233824 (program): A recurrent sequence in Panaitopol’s formula for pi(x), where pi(x) is the number of primes <= x.
  • A233827 (program): a(n) = 8*binomial(6*n+8,n)/(6*n+8).
  • A233828 (program): a(n) = 2*a(n-1) + 2*a(n-2) + a(n-3). a(0) = -1, a(1) = 1, a(2) = 1.
  • A233829 (program): a(n) = 3*binomial(6*n+9,n)/(2*n+3).
  • A233830 (program): a(n) = 5*binomial(6*n+10,n)/(3*n+5).
  • A233831 (program): a(n) = -2*a(n-1) -2*a(n-2) + a(n-3). a(0) = -1, a(1) = 1, a(2) = 1.
  • A233832 (program): a(n) = 2*binomial(7*n+2,n)/(7*n+2).
  • A233833 (program): a(n) = 3*binomial(7*n+3, n)/(7*n+3).
  • A233834 (program): a(n) = 5*binomial(7*n+5,n)/(7*n+5).
  • A233835 (program): a(n) = 8*binomial(7*n + 8, n)/(7*n + 8).
  • A233836 (program): Run lengths of ones and zeros in binary expansion of sqrt(2), cf. A004539.
  • A233865 (program): Numbers n such that sigma(sigma(n))+1 is prime.
  • A233868 (program): Numbers that are not the sum of two evil numbers.
  • A233904 (program): a(2n) = a(n) - n, a(2n+1) = a(n) + n, with a(0)=0.
  • A233905 (program): a(2n) = a(n), a(2n+1) = a(n) + n, with a(0)=0.
  • A233907 (program): 9*binomial(7*n+9, n)/(7*n+9).
  • A233908 (program): 10*binomial(7*n+10,n)/(7*n+10).
  • A233931 (program): a(2n) = a(n) + n, a(2n+1) = a(n), with a(0)=0.
  • A233932 (program): Irregular table read by rows: T(n,k) is the binary representation of n shifted right k times and incremented if the last bit shifted away was set.
  • A233968 (program): Number of steps between two valleys at height 0 in the infinite Dyck path in which the k-th ascending line segment has A141285(k) steps and the k-th descending line segment has A194446(k) steps, k >= 1.
  • A233969 (program): Partial sums of A006950.
  • A233973 (program): a(n) = A232221(n)/4.
  • A233982 (program): Number of (n+1) X (1+1) 0..4 arrays with every 2 X 2 subblock having the sum of the squares of the edge differences equal to 10, and no two adjacent values equal.
  • A233999 (program): Values of n such that numbers of the form x^2+n*y^2 for some integers x, y cannot have prime factor of 7 raised to an odd power.
  • A234000 (program): Numbers of the form 4^i*(8*j+1).
  • A234011 (program): The sums of 2 consecutive odious numbers (A000069).
  • A234016 (program): Partial sums of the characteristic function of A055938.
  • A234017 (program): Inverse function for injection A055938.
  • A234022 (program): a(n) = A000120(A193231(n)); number of 1-bits in blue code for n.
  • A234024 (program): Self-inverse permutation of nonnegative integers, A059893-conjugate of blue code: a(n) = A059893(A193231(A059893(n))).
  • A234025 (program): Permutation of nonnegative integers: a(n) = A054429(A193231(n)).
  • A234026 (program): Permutation of nonnegative integers: a(n) = A193231(A054429(n)).
  • A234027 (program): Self-inverse permutation of nonnegative integers, A054429-conjugate of blue code: a(n) = A054429(A193231(A054429(n))).
  • A234037 (program): The union of odious numbers with evil squares and evil numbers with odious squares.
  • A234038 (program): Smallest positive integer solution x of 9*x - 2^n*y = 1.
  • A234040 (program): a(n) = binomial(2*(n+1),n) * gcd(n,2)/(2*(n+1)).
  • A234041 (program): a(n) = binomial(n+2,2)*gcd(n,3)/3, n >= 0.
  • A234042 (program): a(n) = binomial(n+4,4)*gcd(n,5)/5.
  • A234043 (program): a(n) = binomial(5*(n+1),4)/5, with n >= 0.
  • A234044 (program): Period 7: repeat [2, -2, 1, 0, 0, 1, -2].
  • A234045 (program): Period 7: repeat [0, 0, 1, -1, -1, 1, 0].
  • A234046 (program): Period 7: repeat [0, 1, -1, 0, 0, -1, 1].
  • A234092 (program): Limit of v(m,n) as m->oo, where v(m,n) is the number of distinct terms in the n-th partition of m in Mathematica (lexicographic) ordering of the partitions of m.
  • A234093 (program): Integers of the form (p*q - 1)/2, where p and q are distinct primes.
  • A234095 (program): Primes p such that 2*p + 1 is semiprime.
  • A234096 (program): Integers of the form (p*q + 1)/2, where p and q are distinct primes.
  • A234098 (program): Primes of the form (p*q + 1)/2, where p and q are distinct primes.
  • A234099 (program): Integers of the form (p*q*r - 1)/2, where p, q, r are distinct primes.
  • A234102 (program): Integers of the form (p*q*r + 1)/2, where p, q, r are distinct primes.
  • A234105 (program): Integers of the form (p*q*r*s - 1)/2, where p, q, r, s are distinct primes.
  • A234133 (program): Number of (n+1) X (1+1) 0..3 arrays with every 2 X 2 subblock having the sum of the absolute values of all six edge and diagonal differences equal to 9.
  • A234134 (program): Number of (n+1) X (2+1) 0..3 arrays with every 2 X 2 subblock having the sum of the absolute values of all six edge and diagonal differences equal to 9.
  • A234135 (program): Number of (n+1) X (3+1) 0..3 arrays with every 2 X 2 subblock having the sum of the absolute values of all six edge and diagonal differences equal to 9.
  • A234136 (program): Number of (n+1) X (4+1) 0..3 arrays with every 2 X 2 subblock having the sum of the absolute values of all six edge and diagonal differences equal to 9.
  • A234137 (program): Number of (n+1) X (5+1) 0..3 arrays with every 2 X 2 subblock having the sum of the absolute values of all six edge and diagonal differences equal to 9.
  • A234138 (program): Number of (n+1) X (6+1) 0..3 arrays with every 2 X 2 subblock having the sum of the absolute values of all six edge and diagonal differences equal to 9.
  • A234142 (program): Numbers k such that m - triangular(k) is a triangular number (A000217), where m is the least square above triangular(k).
  • A234145 (program): a(n) = denominator of sum_(k=1..n) 1/(2*k-1)^n.
  • A234154 (program): Number of (n+1) X (1+1) 0..3 arrays with every 2 X 2 subblock having the absolute values of all six edge and diagonal differences no larger than 1.
  • A234249 (program): Number of ways to choose 4 points in an n X n X n triangular grid.
  • A234250 (program): Number of ways to choose 3 points in an n X n X n triangular grid so that they do not form a 2 X 2 X 2 triangle.
  • A234253 (program): a(n) = sum_{i=1..n} C(7+i,8)^2.
  • A234255 (program): Decimal expansion of -B(12) = 691/2730, 13th Bernoulli number without sign.
  • A234259 (program): Number of (n+1) X (1+1) 0..2 arrays with every 2 X 2 subblock having its diagonal sum differing from its antidiagonal sum by 2 (constant-stress 1 X 1 tilings).
  • A234267 (program): Expansion of (1-x)/((1-2*x)*(1-5*x+6*x^2-x^3)).
  • A234269 (program): Expansion of (1-2*x^2-sqrt(1-4*x^2-4*x^3))/(2*x*sqrt(1-4*x^2-4*x^3)).
  • A234271 (program): G.f.: (1+4*x+10*x^2+4*x^3+x^4)/(1-2*x-2*x^2-2*x^3+x^4).
  • A234272 (program): G.f.: (1+4*x+x^2)/(1-4*x+x^2).
  • A234273 (program): G.f.: (1+x+x^2+x^3)/(1-x^2-2*x^3-x^4+x^6).
  • A234275 (program): Expansion of (1+2*x+9*x^2-4*x^3)/(1-x)^2.
  • A234277 (program): a(n) = binomial(floor(n/2),4) + (ceiling(n/2)-3)*binomial(floor(n/2),3).
  • A234279 (program): Number of spanning forests of a benzenoid chain of length n.
  • A234282 (program): Number of 321-avoiding extensions of comb K_{s,2}^{alpha}.
  • A234285 (program): Positive odd numbers n such that sigma(m) - 2m is never equal to n, where sigma(.) is the sum of divisors function A000203. Conjectural.
  • A234286 (program): Positive odd numbers n such that 2m - sigma(m) is never equal to n, where sigma(.) is the sum of divisors function A000203. Conjectural.
  • A234290 (program): E.g.f. satisfies: A(x) = 1 + A(x)^3 * Integral 1/A(x) dx.
  • A234306 (program): a(n) = n + 1 - d(2n), where d(n) is the number of divisors of n.
  • A234307 (program): a(n) = Sum_{i=1..n} gcd(2*n-i, i).
  • A234312 (program): Number of tilings of a 5 X n rectangle using n pentominoes of shapes L, X.
  • A234319 (program): Smallest sum of n-th powers of k+1 consecutive positive integers that equals the sum of n-th powers of the next k consecutive integers, or -n if none.
  • A234345 (program): Smallest q such that n <= q < 2n with p, q both prime, p+q = 2n, and p <= q.
  • A234349 (program): Maximal number of points that can be placed on a triangular grid of side n so that no three points are collinear.
  • A234355 (program): Decimal expansion of B(16) = -3617/510, the 16th Bernoulli number.
  • A234357 (program): Array T(n,k) by antidiagonals: T(n,k) = n^k * Fibonacci(k).
  • A234373 (program): Row 4 of the square array A234951.
  • A234429 (program): Numbers which are the digital sum of the square of some prime.
  • A234430 (program): Decimal expansion of 36/Pi.
  • A234431 (program): Numbers that are the sum of 2 successive evil numbers (A001969).
  • A234436 (program): Number of (n+1) X (1+1) 0..2 arrays with every 2 X 2 subblock having its diagonal sum differing from its antidiagonal sum by 1 (constant-stress 1 X 1 tilings).
  • A234461 (program): a(n) = binomial(8*n+2,n)/(4*n+1).
  • A234462 (program): a(n) = 3*binomial(8*n+3,n)/(8*n+3).
  • A234463 (program): Binomial(8*n+4,n)/(2*n+1).
  • A234464 (program): 5*binomial(8*n+5, n)/(8*n+5).
  • A234465 (program): a(n) = 3*binomial(8*n+6,n)/(4*n+3).
  • A234466 (program): 7*binomial(8*n+7,n)/(8*n+7).
  • A234467 (program): a(n) = 9*binomial(8*n + 9,n)/(8*n + 9).
  • A234472 (program): Numbers that when raised to the fourth power and written backwards give squares.
  • A234483 (program): Number of (n+1) X (1+1) 0..3 arrays with every 2 X 2 subblock having its diagonal sum differing from its antidiagonal sum by 2 (constant-stress 1 X 1 tilings).
  • A234500 (program): Integers of the form (p*q*r*s + 1)/2, where p, q, r, s are distinct primes.
  • A234505 (program): 2*binomial(9*n+2,n)/(9*n+2).
  • A234506 (program): a(n) = binomial(9*n+3, n)/(3*n+1).
  • A234507 (program): 4*binomial(9*n+4,n)/(9*n+4).
  • A234508 (program): 5*binomial(9*n+5,n)/(9*n+5).
  • A234509 (program): 2*binomial(9*n+6,n)/(3*n+2).
  • A234510 (program): a(n) = 7*binomial(9*n+7,n)/(9*n+7).
  • A234513 (program): 8*binomial(9*n+8,n)/(9*n+8).
  • A234525 (program): Binomial(10*n+2,n)/(5*n+1).
  • A234526 (program): 3*binomial(10*n+3,n)/(10*n+3).
  • A234527 (program): 2*binomial(10*n+4,n)/(5*n+2).
  • A234528 (program): Binomial(10*n+5,n)/(2*n+1).
  • A234529 (program): 3*binomial(10*n+6,n)/(5*n+3).
  • A234537 (program): Number of nontrivial non-Goldbach partitions of 2n into two odd parts (with smaller part greater than 1).
  • A234538 (program): (Number of positive digits of n written in base 3) modulo 3.
  • A234568 (program): Sum_{k=0..n} (n-k)^(2*k).
  • A234570 (program): 7*binomial(10*n+7,n)/(10*n+7).
  • A234571 (program): a(n) = 4*binomial(10*n+8,n)/(5*n+4).
  • A234573 (program): 9*binomial(10*n+9,n)/(10*n+9).
  • A234575 (program): Triangle T(n,k) read by rows: T(n,k) = floor(n/k) + n mod k, with 1<=k<=n.
  • A234576 (program): Number of Weyl group elements, not containing s_1 or s_2, which contribute nonzero terms to Kostant’s weight multiplicity formula when computing the multiplicity of the zero-weight in the adjoint representation for the Lie algebra of type D and rank n.
  • A234577 (program): Let S_n = 0 followed by base-2 expansion of n, reversed; sequence is concatenation of S_0, S_1, S_2, …
  • A234586 (program): Odd-indexed terms are absolute values of differences.
  • A234587 (program): Odd-indexed terms of A234586.
  • A234589 (program): Expansion of g.f.: (1+x^6+x^7)/(1-2*x+x^6-x^7-x^8).
  • A234590 (program): Number of binary words of length n which have no 0^b 1 1 0^a 1 0 1 0^b - matches, where a=0, b=2.
  • A234597 (program): Number of Weyl group elements, not containing an s_1 factor, which contribute nonzero terms to Kostant’s weight multiplicity formula when computing the multiplicity of the zero-weight in the adjoint representation for the Lie algebra of type D and rank n.
  • A234598 (program): Cardinality of the Weyl alternation set corresponding to the zero-weight in the adjoint representation of the Lie algebra of so(2n).
  • A234600 (program): Denominators of the expectation of the process defined by randomly moving 2n balls between bins.
  • A234612 (program): Self-inverse permutation of nonnegative integers, “blue-gray” code: a(n) = A003188(A193231(n)).
  • A234613 (program): Self-inverse permutation of nonnegative integers, “gray-blue” code: a(n) = A193231(A003188(n)).
  • A234617 (program): Numbers of undirected cycles in the 2n-crossed prism graph.
  • A234638 (program): Numbers n for which sigma(sigma(n)) is odd.
  • A234639 (program): Numbers n for which sigma(sigma(sigma(n))) is odd.
  • A234640 (program): Odd numbers n for which sigma(sigma(sigma(n))) is odd.
  • A234643 (program): E.g.f.: Sum_{n>=0} Integral^n (exp(x) + 1)^n dx^n, where integral^n F(x) dx^n is the n-th integration of F(x) with no constant of integration.
  • A234645 (program): Sum of the divisors of n^3+1.
  • A234646 (program): Sum of the distinct prime divisors of n^3 + 1.
  • A234648 (program): Even sums of 2 consecutive odious numbers (A000069).
  • A234716 (program): Number of odd composite integers k, such that n-1 < k < 2n-2.
  • A234717 (program): a(n) = floor(n/(exp(1/(2*n))-1)).
  • A234740 (program): Sum of the eleventh powers of the first n primes.
  • A234779 (program): Number of (n+1) X (1+1) 0..3 arrays with no adjacent elements equal and with each 2 X 2 subblock having the number of clockwise edge increases equal to the number of counterclockwise edge increases.
  • A234787 (program): Cubes (with at least two digits) that become squares when their rightmost digit is removed.
  • A234789 (program): Number of (n+1) X (1+1) 0..3 arrays with each 2 X 2 subblock having the number of clockwise edge increases less than or equal to the number of counterclockwise edge increases.
  • A234811 (program): (6^n - 1)^n.
  • A234825 (program): Number of (n+1) X (1+1) 0..2 arrays with each 2 X 2 subblock having the number of clockwise edge increases less than or equal to the number of counterclockwise edge increases.
  • A234833 (program): Number of tilings of a box with sides 2 X 2 X 3n in R^3 by boxes of sides Tricube-V(3-dimensional dominoes).
  • A234839 (program): a(n) = Sum_{k = 0..n} (-1)^k * binomial(n,k) * binomial(2*n,k).
  • A234850 (program): Primes in A014692, i.e., of the form prime(k)-k+1, for some k.
  • A234860 (program): Sum of the divisors of n^3 - 1.
  • A234861 (program): Sum of the distinct prime divisors of n^3 - 1.
  • A234868 (program): a(n) = 2*binomial(11*n+2,n)/(11*n+2).
  • A234869 (program): 3*binomial(11*n+3,n)/(11*n+3).
  • A234870 (program): 4*binomial(11*n+4,n)/(11*n+4).
  • A234871 (program): 5*binomial(11*n+5,n)/(11*n+5).
  • A234872 (program): 6*binomial(11*n+6,n)/(11*n+6).
  • A234873 (program): 7*binomial(11*n+7,n)/(11*n+7).
  • A234875 (program): Number of (n+1) X (1+1) 0..4 arrays with every 2 X 2 subblock having its diagonal sum differing from its antidiagonal sum by 1, with no adjacent elements equal (constant-stress tilted 1 X 1 tilings).
  • A234902 (program): a(n)*Pi is the total length of irregular spiral (center points: 1, 2, 3) after n rotations.
  • A234903 (program): a(n)*Pi is the total length of irregular spiral (center points: 1, 3, 2) after n rotations.
  • A234904 (program): a(n)*Pi is the total length of irregular spiral (center points: 2, 1, 3) after n rotations.
  • A234914 (program): Number of (n+1) X (1+1) 0..4 arrays with every 2 X 2 subblock having its diagonal sum differing from its antidiagonal sum by 2, with no adjacent elements equal (constant-stress tilted 1 X 1 tilings).
  • A234933 (program): The number of binary sequences that contain at least two consecutive 1’s and contain at least two consecutive 0’s.
  • A234950 (program): Borel’s triangle read by rows: T(n,k) = Sum_{s=k..n} binomial(s,k)*C(n,s), where C(n,s) is an entry in Catalan’s triangle A009766.
  • A234957 (program): Highest power of 4 dividing n.
  • A234959 (program): Highest power of 6 dividing n.
  • A234964 (program): Numbers of the form 123…n - (n+1)
  • A234971 (program): a(n) = Sum_{k=0..n} n^k * binomial(n,k)^4.
  • A235001 (program): Odious squares.
  • A235037 (program): Number of terms of A014847 that are not greater than n.
  • A235049 (program): Subtract one from each nonzero digit in decimal representation of n.
  • A235062 (program): Odd part of n-th superfactorial (A000178).
  • A235088 (program): a(n)*Pi is the total length of irregular spiral (center points: 1, 2, 3, 4) after n rotations.
  • A235089 (program): a(n)*Pi is the total length of irregular spiral (center points: 2, 1, 3, 4) after n rotations.
  • A235113 (program): Irregular triangle read by rows: T(n,k) = number of independent vertex subsets of size k of the graph g_n obtained by attaching two pendant edges to each vertex of the complete graph K_n (0 <= k <= 2n).
  • A235115 (program): Number of independent vertex subsets of the graph obtained by attaching two pendant edges to each vertex of the star graph S_n (having n vertices; see A235114).
  • A235118 (program): Number of independent vertex subsets of the graph obtained by attaching two pendant edges to each vertex of the ladder graph L_n (L_n is the 2 X n grid graph; see A235117).
  • A235127 (program): Greatest k such that 4^k divides n.
  • A235136 (program): a(n) = (2*n - 1) * a(n-2) for n>1, a(0) = a(1) = 1.
  • A235138 (program): Sum_{k=1..n} k^phi(n) (mod n) where phi(n) = A000010(n).
  • A235151 (program): Numbers whose sum of digits is 12.
  • A235162 (program): Decimal expansion of (sqrt(33) + 1) / 2.
  • A235163 (program): Number of positive integers with n digits in which adjacent digits differ by at most 1.
  • A235204 (program): Number of integer lattice points inside the square ABCD with side length n>0 with A(0|0), B(n*sqrt(2)/2| n*sqrt(2)/2), C(0| n*sqrt(2)) and D(-n*sqrt(2)/2| n*sqrt(2)/2).
  • A235224 (program): a(0) = 0, and for n > 0, a(n) = largest k such that A002110(k-1) <= n, where A002110(k) gives the k-th primorial number.
  • A235225 (program): Numbers whose sum of digits is 14.
  • A235226 (program): Numbers whose sum of digits is 15.
  • A235227 (program): Numbers whose sum of digits is 16.
  • A235228 (program): Numbers whose sum of digits is 18.
  • A235229 (program): Numbers whose sum of digits is 20.
  • A235269 (program): floor(s*t/(s+t)), where s(n) are the squares, t(n) the triangular numbers.
  • A235282 (program): Number of (n+1) X (1+1) 0..3 arrays with every 2 X 2 subblock having its diagonal sum differing from its antidiagonal sum by 4 (constant-stress 1 X 1 tilings).
  • A235323 (program): Squared sum of the distinct prime factors of n, i.e., sopf(n)^2.
  • A235324 (program): Sum of all parts of all partitions of n into an even number of parts minus the sum of all parts of all partitions of n into an odd number of parts.
  • A235328 (program): Number of ordered pairs of endofunctions (f,g) on a set of n elements satisfying f(x) = g(f(f(x))).
  • A235331 (program): Numbers with odious squares.
  • A235332 (program): a(n) = n*(9*n + 25)/2 + 6.
  • A235336 (program): Numbers having evil number of 1’s in their binary representation.
  • A235337 (program): Number of integer lattice points inside the square ABCD with side length n>0 with A(-n*sqrt(2)/2| 0), B(n*sqrt(2)/2| 0), C(0| n*sqrt(2)/2) and D(-n*sqrt(2)/2| 0).
  • A235338 (program): 8*binomial(11*n+8,n)/(11*n+8).
  • A235339 (program): a(n) = 9*binomial(11*n+9,n)/(11*n+9).
  • A235340 (program): 10*binomial(11*n+10,n)/(11*n+10).
  • A235347 (program): Series reversion of x*(1-3*x^2)/(1-x^2) in odd-order powers.
  • A235352 (program): Series reversion of x*(1+3*x^2)/(1+x^2) in odd-power terms.
  • A235355 (program): 0 followed by the sum of (1),(2), (3,4),(5,6), (7,8,9),(10,11,12) from the natural numbers.
  • A235361 (program): Floor((n + Pi)^2).
  • A235362 (program): Decimal expansion of the cube root of 2 divided by 2.
  • A235363 (program): (1 + Sum_{k=1..m-1} k^(m-1)) (mod m), for m = 1, 3, 5, 7, 9, …
  • A235367 (program): Sum of positive even numbers up to n^2.
  • A235375 (program): Integers k such that k^2 is of form y^2 + y + x^2 + x for positive y, x.
  • A235378 (program): a(n) = (-1)^n*(n! - (-1)^n).
  • A235382 (program): a(n) = smallest number of unit squares required to enclose n units of area.
  • A235391 (program): Expansion of 2 / (2 - x / sqrt(1 - 4*x)).
  • A235394 (program): Primes whose decimal representation is a valid number in base 8 and interpreted as such is again a prime.
  • A235398 (program): Sum of digits of the cubes of prime numbers.
  • A235399 (program): Numbers which are the digital sum of the cube of some prime.
  • A235417 (program): Number of (n+1)X(1+1) 0..2 arrays with 2X2 subblock sum of squares lexicographically nondecreasing rowwise and nonincreasing columnwise
  • A235451 (program): Number of length n words on alphabet {0,1,2} of the form 0^(i)1^(j)2^(k) such that i=j or j=k.
  • A235484 (program): Square numbers n such that n^2 - n - 1 is prime.
  • A235492 (program): Median of maximal “prime gaps” in Cramer’s model with n urns
  • A235496 (program): a(n) = round(n^n/n!).
  • A235497 (program): 2n concatenated with n.
  • A235498 (program): For k in {2,3,…,9} define a sequence as follows: a(0)=0; for n>=0, a(n+1)=a(n)+1, unless a(n) ends in k, in which case a(n+1) is obtained by replacing the last digit of a(n) with the digit(s) of k^2. This is k(2).
  • A235499 (program): For k in {2,3,…,9} define a sequence as follows: a(0)=0; for n>=0, a(n+1)=a(n)+1, unless a(n) ends in k, in which case a(n+1) is obtained by replacing the last digit of a(n) with the digit(s) of k^2. This is k(3).
  • A235501 (program): Riordan array (1/(1-2*x^2), x/(1-x)).
  • A235509 (program): Decimal expansion of arccos(4/5).
  • A235510 (program): Number of (n+1) X (1+1) 0..1 arrays with the sum of each 2 X 2 subblock maximum and minimum lexicographically nondecreasing rowwise and columnwise.
  • A235526 (program): G.f. satisfies: A(x) = Sum_{n>=0} [A(x)^n (mod 3)]*x^n.
  • A235532 (program): a(n) = floor(n^2 * (4-Pi)).
  • A235534 (program): a(n) = binomial(6*n, 2*n) / (4*n + 1).
  • A235535 (program): a(n) = binomial(9*n, 3*n) / (6*n + 1).
  • A235536 (program): a(n) = binomial(8*n, 2*n) / (6*n + 1).
  • A235537 (program): Expansion of (6 + 13*x - 8*x^2 - 8*x^3 + 6*x^4)/((1 + x)^2*(1 - x)^3).
  • A235566 (program): Number of (n+1) X (1+1) 0..1 arrays with the difference of the upper and lower median value of each 2 X 2 subblock in lexicographically nondecreasing order rowwise and columnwise.
  • A235578 (program): Squareful numbers with squareful neighbors.
  • A235583 (program): Numbers not divisible by 2, 5 or 7.
  • A235593 (program): Binomial(n-1,3)+3*binomial(n-1,4)+6*binomial(n-1,5)+5*binomial(n-1,6).
  • A235596 (program): Second column of triangle in A235595.
  • A235597 (program): Squares in which each digit exceeds the previous digit by more than one.
  • A235600 (program): a(n) = n/d(n) if d(n) divides n, otherwise a(n) = n, where d(n) is the sum of the digits of n (A007953).
  • A235602 (program): a(n) = n/wt(n) if wt(n) divides n, otherwise a(n) = n, where wt(n) is the binary weight of n (A000120).
  • A235623 (program): Numbers n for which in the prime power factorization of n!, the numbers of exponents 1 and >1 are equal.
  • A235639 (program): Primes whose base-9 representation is also the base-6 representation of a prime.
  • A235643 (program): Total number of sides of a tetraflake-like fractal after n iterations, a(1) = 16 (see comments).
  • A235644 (program): Number of decompositions of 12*n into the sum of two (not necessarily distinct) twin prime pairs.
  • A235653 (program): Number of (n+1) X (1+1) 0..1 arrays with the difference of the upper median and minimum value of each 2 X 2 subblock in lexicographically nondecreasing order rowwise and columnwise.
  • A235669 (program): Sum of parts of the form 10…0 and 20…0 with nonnegative number of zeros in ternary representation of n as the corresponding numbers 3^n and 2*3^n.
  • A235684 (program): Number of compositions of n into powers of 3 and doubled powers of 3.
  • A235698 (program): a(n+1) = a(n) + (smallest digit of a(n)) + 1, a(0)=0.
  • A235699 (program): a(n+1) = a(n) + (a(n) mod 10) + 1, a(0) = 0.
  • A235700 (program): a(n+1) = a(n) + (a(n) mod 5), a(1)=1.
  • A235702 (program): Fixed points of A001175 (Pisano periods).
  • A235706 (program): (I + A132440)^3: Coefficients for normalized generalized Laguerre polynomials n!*Lag(n, 3-n, -x).
  • A235711 (program): Arithmetic derivative of quarter squares.
  • A235793 (program): Sum of all parts of all overpartitions of n.
  • A235796 (program): 2*n - 1 - sigma(n).
  • A235799 (program): a(n) = n^2 - sigma(n).
  • A235800 (program): Length of n-th vertical line segment from left to right in a diagram of a two-dimensional version of the 3x+1 (or Collatz) problem.
  • A235801 (program): Length of n-th horizontal line segment in a diagram of a two-dimensional version of the 3x+1 (or Collatz) problem.
  • A235803 (program): Rectangular array read by upward antidiagonals: A(n,k) = 1 + sqrt(k)*((1+sqrt(k))^n - (1-sqrt(k))^n)/2, n,k >= 0.
  • A235804 (program): Rectangular array read by upward antidiagonals: A(n,k) = n-2+k*2^(n-3), n>=3, k>=0.
  • A235866 (program): G-cyclic numbers: numbers n such that gcd(n,A060968(n))=1.
  • A235868 (program): Union of 2 and powers of odd primes.
  • A235872 (program): Number of solutions to the equation x^2=0 in the ring of Gaussian integers modulo n.
  • A235876 (program): Number of (n+1)X(n+1) 0..2 arrays with the minimum plus the upper median equal to the lower median plus the maximum in every 2X2 subblock
  • A235877 (program): Number of (n+1) X (1+1) 0..2 arrays with the minimum plus the upper median equal to the lower median plus the maximum in every 2 X 2 subblock.
  • A235878 (program): Number of (n+1) X (2+1) 0..2 arrays with the minimum plus the upper median equal to the lower median plus the maximum in every 2 X 2 subblock.
  • A235879 (program): Number of (n+1) X (3+1) 0..2 arrays with the minimum plus the upper median equal to the lower median plus the maximum in every 2 X 2 subblock.
  • A235880 (program): Number of (n+1) X (4+1) 0..2 arrays with the minimum plus the upper median equal to the lower median plus the maximum in every 2 X 2 subblock.
  • A235881 (program): Number of (n+1) X (5+1) 0..2 arrays with the minimum plus the upper median equal to the lower median plus the maximum in every 2 X 2 subblock.
  • A235882 (program): Number of (n+1) X (6+1) 0..2 arrays with the minimum plus the upper median equal to the lower median plus the maximum in every 2 X 2 subblock.
  • A235883 (program): Number of (n+1) X (7+1) 0..2 arrays with the minimum plus the upper median equal to the lower median plus the maximum in every 2 X 2 subblock.
  • A235885 (program): Number of (n+1)X(n+1) 0..3 arrays with the minimum plus the upper median equal to the lower median plus the maximum in every 2X2 subblock
  • A235886 (program): Number of (n+1) X (1+1) 0..3 arrays with the minimum plus the upper median equal to the lower median plus the maximum in every 2 X 2 subblock.
  • A235887 (program): Number of (n+1) X (2+1) 0..3 arrays with the minimum plus the upper median equal to the lower median plus the maximum in every 2 X 2 subblock.
  • A235888 (program): Number of (n+1) X (3+1) 0..3 arrays with the minimum plus the upper median equal to the lower median plus the maximum in every 2 X 2 subblock.
  • A235889 (program): Number of (n+1) X (4+1) 0..3 arrays with the minimum plus the upper median equal to the lower median plus the maximum in every 2 X 2 subblock.
  • A235890 (program): Number of (n+1) X (5+1) 0..3 arrays with the minimum plus the upper median equal to the lower median plus the maximum in every 2 X 2 subblock.
  • A235891 (program): Number of (n+1) X (6+1) 0..3 arrays with the minimum plus the upper median equal to the lower median plus the maximum in every 2 X 2 subblock.
  • A235892 (program): Number of (n+1) X (7+1) 0..3 arrays with the minimum plus the upper median equal to the lower median plus the maximum in every 2 X 2 subblock.
  • A235895 (program): Number of (n+1) X (1+1) 0..2 arrays with the minimum plus the maximum equal to the lower median plus the upper median in every 2 X 2 subblock.
  • A235915 (program): a(1) = 1, a(n) = a(n-1) + (digsum(a(n-1)) mod 5) + 1, digsum = A007953.
  • A235918 (program): Largest m such that 1, 2, …, m divide n^2.
  • A235921 (program): Numbers n such that smallest number not dividing n^2 (A236454) is different from smallest prime not dividing n (A053669).
  • A235933 (program): Numbers coprime to 35.
  • A235944 (program): Digital roots of squares of Lucas numbers.
  • A235945 (program): Number of partitions of n containing at least one prime.
  • A235963 (program): n appears (n+1)/(1 + (n mod 2)) times.
  • A235988 (program): Sum of the partition parts of 3n into 3 parts.
  • A235991 (program): Numbers with an odd arithmetic derivative, cf. A003415.
  • A235992 (program): Numbers with an even arithmetic derivative, cf. A003415.
  • A235996 (program): Number of length n binary words that contain at least one pair of consecutive 0’s followed by (at some point in the word) at least one pair of consecutive 1’s.
  • A236024 (program): Record values in A236022.
  • A236043 (program): Number of triangular numbers <= 10^n.
  • A236076 (program): A skewed version of triangular array A122075.
  • A236103 (program): Number of distinct partition numbers dividing n.
  • A236144 (program): a(n) = F(floor( (n+3)/2 )) * L(floor( (n+2)/2 )) where F=Fibonacci and L=Lucas numbers.
  • A236165 (program): a(n) = a(n-1) + a(n-2) + a(n-3), with a(0) = a(1) = 1, a(2) = 0.
  • A236175 (program): Prime gap pattern of compacting Eratosthenes sieve for prime(4) = 7.
  • A236182 (program): Sum of the sixth powers of the first n primes.
  • A236184 (program): Decimal expansion of 1/65537.
  • A236185 (program): Differences between terms of compacting Eratosthenes sieve for prime(4) = 7.
  • A236186 (program): Differences between terms of compacting Eratosthenes sieve for prime(5) = 11.
  • A236187 (program): Differences between terms of compacting Eratosthenes sieve for prime(6) = 13.
  • A236188 (program): Differences between terms of compacting Eratosthenes sieve for prime(7) = 17.
  • A236189 (program): Differences between terms of compacting Eratosthenes sieve for prime(8) = 19.
  • A236190 (program): Differences between terms of compacting Eratosthenes sieve for prime(9) = 23.
  • A236191 (program): a(n) = (-1)^floor( (n-1) / 3 ) * F(n), where F = Fibonacci.
  • A236192 (program): a(n) = |{0 < k < n: p = phi(k) + phi(n-k)/4 + 1, prime(p)^2 + (2*p)^2 and p^2 + (2*prime(p))^2 are all prime}|, where phi(.) is Euler’s totient function.
  • A236194 (program): a(n) = binomial(3n+1, n-1).
  • A236203 (program): Interleave A005563(n), A028347(n).
  • A236204 (program): Numbers not divisible by 2, 3 or 11.
  • A236206 (program): Numbers not divisible by 3, 5 or 7.
  • A236207 (program): Numbers not divisible by 5 or 11.
  • A236208 (program): Numbers not divisible by 2, 5 or 11.
  • A236209 (program): Sum of the seventh powers of the first n primes.
  • A236213 (program): Number of units in the imaginary quadratic field Q(sqrt(-d)), where d > 0 is the n-th squarefree number.
  • A236214 (program): Sum of the eighth powers of the first n primes.
  • A236215 (program): Sum of the ninth powers of the first n primes.
  • A236216 (program): Sum of the tenth powers of the first n primes.
  • A236217 (program): Numbers not divisible by 3, 5 or 11.
  • A236218 (program): Sum of the twelfth powers of the first n primes.
  • A236221 (program): Sum of the thirteenth powers of the first n primes.
  • A236222 (program): Sum of the fourteenth powers of the first n primes.
  • A236223 (program): Sum of the fifteenth powers of the first n primes.
  • A236224 (program): Sum of the sixteenth powers of the first n primes.
  • A236225 (program): Sum of the seventeenth powers of the first n primes.
  • A236226 (program): Sum of the eighteenth powers of the first n primes.
  • A236227 (program): Sum of the nineteenth powers of the first n primes.
  • A236257 (program): a(n) = 2*n^2 - 7*n + 9.
  • A236267 (program): a(n) = 8n^2 + 3n + 1.
  • A236283 (program): The number of orbits of triples of {1,2,…,n} under the action of the dihedral group of order 2n.
  • A236284 (program): a(n) = tau(n)^n, where tau(n) = A000005(n) = the number of divisors of n.
  • A236285 (program): a(n) = tau(n)^sigma(n), where tau(n) = A000005(n) = the number of divisors of n and sigma(n) = A000203(n) = the sum of divisors of n.
  • A236286 (program): a(n) = tau(n)^sigma(n) / tau(n)^n, where tau(n) = A000005(n) = the number of divisors of n and sigma(n) = A000203(n) = the sum of divisors of n.
  • A236287 (program): a(n) = sigma(n)^tau(n), where tau(n) = A000005(n) = the number of divisors of n and sigma(n) = A000203(n) = the sum of divisors of n.
  • A236288 (program): a(n) = sigma(n)^n / sigma(n)^tau(n), where tau(n) = A000005(n) = the number of divisors of n and sigma(n) = A000203(n) = the sum of divisors of n.
  • A236290 (program): Decimal expansion of (sqrt(33) - 1) / 2.
  • A236291 (program): Number of length n binary words that contain an even number of 0’s or exactly two 1’s.
  • A236294 (program): a(n) = max( a(n-1) + a(n-3), 2*a(n-2) ) - a(n-4), with a(0)=1, a(1)=1, a(2)=2, a(3)=3.
  • A236305 (program): The number of P-positions in the game of Nim with up to 3 piles, allowing for piles of zero, such that the number of objects in each pile does not exceed n.
  • A236310 (program): Expansion of sum(k>=0, x^((k+1)^2)/(1-x)^k ).
  • A236311 (program): Riordan array ((1-x)/(1-3*x+3*x^2), x/(1-3*x+3*x^2)).
  • A236312 (program): a(n) = floor((n + e)^2), where e is the natural logarithm base.
  • A236313 (program): Recurrence: a(2n) = 3a(n)-1, a(2n+1) = 1.
  • A236326 (program): a(n)*Pi is the total length of irregular spiral (center points: 1, 2, 3, 4, 5; pattern 1) after n rotations.
  • A236327 (program): a(n)*Pi is the total length of irregular spiral (center points: 1, 2, 3, 4, 5; pattern 2) after n rotations.
  • A236328 (program): a(n) = sigma(n,1) + sigma(n,2) + … + sigma(n,n).
  • A236331 (program): Positive integers n such that x^2 - 18xy + y^2 + n = 0 has integer solutions.
  • A236332 (program): The number of orbits of 4-tuples of the dihedral group of order 2n acting on {1,2,…,n}.
  • A236333 (program): The (n-2)-th (n>=3) triple of terms gives coefficients of double trinomial P_n(x) = ((n-2)^2*x^2 + n*x + 2)/2 (see comment).
  • A236334 (program): Cubes k such that k-2 is prime.
  • A236337 (program): Expansion of (2 - x) / ((1 - x)^2 * (1 - x^3)) in powers of x.
  • A236339 (program): Association types in 2-dimensional algebra.
  • A236340 (program): Number of length n binary words such that maximal runs of 1’s are restricted to length one or two and maximal runs of 0’s are of odd length.
  • A236343 (program): Expansion of (1 - x + 2*x^2 - x^3) / ((1 - x)^2 * (1 - x^3)) in powers of x.
  • A236348 (program): Expansion of (1 - x + 2*x^2 + x^3) / ((1 - x) * (1 - x^3)) in powers of x.
  • A236364 (program): Sum of all the middle parts in the partitions of 3n into 3 parts.
  • A236370 (program): Sum of the largest parts in the partitions of 3n into 3 parts.
  • A236376 (program): Riordan array ((1-x+x^2)/(1-x)^2, x/(1-x)^2).
  • A236384 (program): Number of non-congruent integer triangles with base length n whose apex lies on or within a space bounded by a semicircle of diameter n.
  • A236387 (program): Numbers n such that sigma(n) is an oblong number.
  • A236392 (program): G.f.: (x+x^3+x^4)/(1-x-x^3-2*x^4).
  • A236395 (program): a(n) = Fibonacci(p) mod p^2, where p = prime(n).
  • A236398 (program): Period 4: repeat 1,1,2,1.
  • A236399 (program): Left factorial !p, where p = prime(n).
  • A236403 (program): Numbers not in A236402.
  • A236407 (program): a(n) = 2*Sum_{k=0..n-1} C(n-1,k)*C(n+k,k) + n.
  • A236428 (program): a(n) = F(n+1)^2 + F(n+1)*F(n) - F(n)^2, where F = A000045.
  • A236432 (program): a(n) = (2n-1)*210; numbers which are 210 times an odd number.
  • A236435 (program): Numerator of product_{k=1..n-1} (1 + 1/prime(k)).
  • A236436 (program): Denominator of product_{k=1..n-1} (1 + 1/prime(k)).
  • A236438 (program): a(n) = n*a(n-1) + (-1)^n for n>0, a(0)=2.
  • A236453 (program): Number of length n strings on the alphabet {0,1,2} of the form 0^i 1^j 2^k such that i,j,k>=0 and if i=1 then j=k.
  • A236454 (program): Smallest number not dividing n^2.
  • A236455 (program): Number of zero digits in all representations of n in bases 2,3,…,10.
  • A236466 (program): E.g.f. A(x) satisfies A(x) = x*(2*exp(A(x)) + exp(2*A(x))).
  • A236471 (program): Riordan array ((1-x)/(1-2*x), x(1-x)/(1-2*x)^2).
  • A236475 (program): Numbers k such that k^3 + k - 1 is prime.
  • A236477 (program): Numbers k such that k^3 - k + 1 is prime.
  • A236532 (program): Triangle T(n,k) read by rows: T(n,k) = floor(n*k/(n+k)), with 1 <= k <= n.
  • A236535 (program): a(n)*Pi is the total length of irregular spiral (center points: 2, 3, 1; pattern 1) after n rotations.
  • A236538 (program): Triangle read by rows: T(n,k) = (n+1)*2^(n-2)+(k-1)*2^(n-1) for 1 <= k <= n.
  • A236556 (program): Decimal expansion of the steradian solid angle subtended by one square facet of the cuboctahedron.
  • A236563 (program): a(p^n)=p^(n+1)(p-1) if p is prime and a(nm)=lcm(a(n),a(m)) if gcd(n,m)=1.
  • A236564 (program): Difference between 2^(2n-1) and the nearest square.
  • A236576 (program): The number of tilings of a 5 X (3n) floor with 1 X 3 trominoes.
  • A236579 (program): The number of tilings of a 5 X (4n) floor with 1 X 4 tetrominoes.
  • A236580 (program): The number of tilings of a 6 X (4n) floor with 1 X 4 tetrominoes.
  • A236581 (program): The number of tilings of a 7 X (4n) floor with 1 X 4 tetrominoes.
  • A236583 (program): The number of tilings of an 8 X (3n) floor with 2 X 3 hexominoes.
  • A236584 (program): The number of tilings of a 9 X (2n) floor with 2 X 3 hexominoes.
  • A236627 (program): Number of positive integers <= sqrt(n) not dividing n.
  • A236632 (program): Sum of all divisors of all positive integers <= n minus the total number of divisors of all positive integers <= n.
  • A236652 (program): Positive integers n such that n^2 divided by the digital root of n is a square.
  • A236653 (program): Positive integers n such that n^3 divided by the digital root of n is a cube.
  • A236677 (program): a(0)=1; for n>0, a(n) = (1-a(floor(log_2(n)))) * a(n-msb(n)); characteristic function of A079599.
  • A236678 (program): Partial sums of the characteristic function of A079599.
  • A236680 (program): Dimension of the space of spinors in n-dimensional real space.
  • A236682 (program): Values of a for triples (a,b,c) of positive integers such that 1/a + 1/b + 1/c = 1/2 and a <= b <= c, listed with multiplicity.
  • A236683 (program): Values of b of triples (a,b,c) of positive integers such that 1/a + 1/b + 1/c = 1/2 and a <= b <= c. Listed with multiplicity, corresponding to solutions (a,b,c) listed in lexicographic order.
  • A236758 (program): Number of partitions of 3n into 3 parts with smallest part prime.
  • A236759 (program): Numbers n such that n^4+n-1 is prime.
  • A236761 (program): Numbers n such that n^4-n+1 is prime.
  • A236767 (program): Numbers whose square is a fourth power plus a prime.
  • A236770 (program): a(n) = n*(n + 1)*(3*n^2 + 3*n - 2)/8.
  • A236771 (program): a(n) = n + floor(n/2 + n^2/3).
  • A236772 (program): a(n) = floor( Sum_{i=1..n} n^i/i ).
  • A236773 (program): a(n) = n + floor( n^2/2 + n^3/3 ).
  • A236799 (program): Decimal expansion of 1/9998.
  • A236830 (program): Riordan array (1/(1-x*C(x)^3), x*C(x)), C(x) the g.f. of A000108.
  • A236840 (program): n minus number of runs in the binary expansion of n: a(n) = n - A005811(n).
  • A236843 (program): Triangle read by rows related to the Catalan transform of the Fibonacci numbers.
  • A236856 (program): Partial sums of A003418 starting summing from A003418(1), with a(0) = 0.
  • A236857 (program): Each n occurs the least common multiple (LCM) of {1, 2, …, n} (= A003418(n)) times.
  • A236858 (program): Irregular table where row n contains numbers from 1 to the least common multiple (LCM) of {1, 2, …, n}. Row 0 is given as a(0)=1.
  • A236864 (program): Numbers n such that the sum of the n-th powers of all symmetric 2 X 2 matrices over Z/nZ gives a nonzero matrix.
  • A236916 (program): The first “octad” is 0, 1, 2, 2, 2, 2, 3, 3; thereafter add 4 to get the next octad.
  • A236922 (program): Number of integer solutions to a^2 + b^2 + 4*c^2 + 4*d^2 = n.
  • A236923 (program): Number of integer solutions to a^2 + b^2 + c^2 + 4*d^2 = n.
  • A236924 (program): Number of integer solutions to a^2 + 2*b^2 + 2*c^2 + 4*d^2 = n.
  • A236925 (program): Number of integer solutions to a^2 + 4*b^2 + 4*c^2 + 4*d^2 = n.
  • A236934 (program): Triangle of Poupard numbers g_n(k) read by rows, n>=1, 1<=k<=2n-1.
  • A236935 (program): The infinite Seidel matrix H read by antidiagonals upwards; H = (H(n,k): n,k >= 0).
  • A236965 (program): Number of nonzero quartic residues modulo the n-th prime.
  • A236967 (program): Expansion of (1+3*x)^2/(1-3*x)^2.
  • A236999 (program): Odd part of n*(n+3)/2-1 (A034856).
  • A237037 (program): Numbers k such that (2*k)^3 + 1 is a semiprime.
  • A237040 (program): Semiprimes of the form k^3 + 1.
  • A237042 (program): UPC check digits.
  • A237046 (program): Numbers n such that sigma(n) < 2n-1.
  • A237047 (program): Number of compositions of n minus the number of overpartitions of n.
  • A237109 (program): a(n) is the numerator of 2*n / ((n+2) * (n+3)).
  • A237120 (program): Number of white areas in the graph of elementary cellular automaton with rule 150 at generation n.
  • A237128 (program): Angles n expressed in degrees such that 2*cos(n) = phi where phi is the golden ratio (A001622).
  • A237132 (program): Values of x in the solutions to x^2 - 3xy + y^2 + 11 = 0, where 0 < x < y.
  • A237133 (program): Values of x in the solutions to x^2 - 3xy + y^2 + 19 = 0, where 0 < x < y.
  • A237187 (program): Total number of possible evolutions arising from n tandem duplications of DNA.
  • A237250 (program): Values of x in the solutions to x^2 - 4xy + y^2 + 11 = 0, where 0 < x < y.
  • A237254 (program): Values of x in the solutions to x^2 - 5xy + y^2 + 5 = 0, where 0 < x < y.
  • A237255 (program): Values of x in the solutions to x^2 - 5xy + y^2 + 17 = 0, where 0 < x < y.
  • A237262 (program): Values of x in the solutions to x^2 - 8*x*y + y^2 + 11 = 0, where 0 < x < y.
  • A237268 (program): a(1)=1; for n > 1, a(n) is the smallest F(m) > F(n) such that F(n) divides F(m), where F(k) denotes the k-th Fibonacci number.
  • A237271 (program): Number of parts in the symmetric representation of sigma(n).
  • A237274 (program): a(n) = A236283(n) mod 9.
  • A237275 (program): Smallest k divisible by the n-th power of its last decimal digit > 1.
  • A237287 (program): Numbers that are not practical: positive integers n such that there exists at least one number k <= sigma(n) that is not a sum of distinct divisors of n.
  • A237341 (program): For k in {2,3,…,9} define a sequence as follows: a(0)=0; for n>=0, a(n+1)=a(n)+1, unless a(n) ends in k, in which case a(n+1) is obtained by replacing the last digit of a(n) with the digit(s) of k^2. This is k(4).
  • A237342 (program): For k in {2,3,…,9} define a sequence as follows: a(0)=0; for n>=0, a(n+1)=a(n)+1, unless a(n) ends in k, in which case a(n+1) is obtained by replacing the last digit of a(n) with the digit(s) of k^2. This is k(5).
  • A237343 (program): For k in {2,3,…,9} define a sequence as follows: a(0)=0; for n>=0, a(n+1)=a(n)+1, unless a(n) ends in k, in which case a(n+1) is obtained by replacing the last digit of a(n) with the digit(s) of k^2. This is k(6).
  • A237344 (program): For k in {2,3,…,9} define a sequence as follows: a(0)=0; for n>=0, a(n+1)=a(n)+1, unless a(n) ends in k, in which case a(n+1) is obtained by replacing the last digit of a(n) with the digit(s) of k^2. This is k(7).
  • A237347 (program): First differences of A078633.
  • A237349 (program): a(n) = Sum_{i=1..n} ( Product_{k|i} d(k) ), where d(n) = A000005(n).
  • A237353 (program): For n=g+h, a(n) is the minimum value of omega(g)+omega(h).
  • A237415 (program): For k in {2,3,…,9} define a sequence as follows: a(0)=0; for n>=0, a(n+1)=a(n)+1, unless a(n) ends in k, in which case a(n+1) is obtained by replacing the last digit of a(n) with the digit(s) of k^3. This is k(2).
  • A237416 (program): Smallest multiple of 5 beginning with n.
  • A237420 (program): If n is odd, then a(n) = 0; otherwise, a(n) = n.
  • A237424 (program): Numbers of the form (10^a + 10^b + 1)/3.
  • A237425 (program): Denominators of A164555(n)/A027642(n) + A198631(n)/A006519(n+1).
  • A237444 (program): Triangle read by rows, T(n,k) is difference of column sum and row sum of natural numbers filled in n x n square.
  • A237447 (program): Infinite square array: row 1 is the positive integers 1, 2, 3, …, and on any subsequent row n, n is moved to the front: n, 1, …, n-1, n+1, n+2, …
  • A237448 (program): Square array T(row >= 1, col >= 1): The first row, row=1, T(1,col) = col = A000027. When row > col, T(row,col) = row, otherwise (when 1 < row <= col), T(row,col) = row-1.
  • A237450 (program): Triangle read by rows, T(n,k) = !n + (k-1)*(n-1)!, with n>=1, 1<=k<=n; Position of the first n-letter permutation beginning with number k in the list of lexicographically sorted permutations A030299.
  • A237451 (program): Zero-based column index to irregular tables organized as successively larger square matrices.
  • A237452 (program): Zero-based row index to irregular tables organized as successively larger square matrices.
  • A237498 (program): Riordan array (1/(1-x-x^2), x/(1+2*x)).
  • A237500 (program): Number of binary strings of length 2n which contain the ones’ complement of each of their two halves.
  • A237514 (program): Numbers k such that 2^(k-1) < 3^(m-1) < 2^k < 3^m < 2^(k+1), for some m > 2, a(1) = 1.
  • A237516 (program): Pyramidal centered square numbers.
  • A237526 (program): a(n) = number of unit squares in the first quadrant of a disk of radius sqrt(n) centered at the origin of a square lattice.
  • A237545 (program): Odious powers of 3.
  • A237580 (program): a(n) = (2n)! - n! + 1.
  • A237587 (program): Triangle read by rows in which row n lists the first n odd squares in decreasing order.
  • A237588 (program): Sigma(n) - 2n + 1.
  • A237589 (program): Sum of first n odd noncomposite numbers.
  • A237590 (program): a(n) is the total number of regions (or parts) after n-th stage in the diagram of the symmetries of sigma described in A236104.
  • A237616 (program): a(n) = n*(n + 1)*(5*n - 4)/2.
  • A237617 (program): a(n) = n*(n + 1)*(17*n - 14)/6.
  • A237618 (program): a(n) = n*(n + 1)*(19*n - 16)/6.
  • A237619 (program): Riordan array (1/(1+x*c(x)), x*c(x)) where c(x) is the g.f. of Catalan numbers (A000108).
  • A237621 (program): Riordan array (1+x, x*(1-x)); inverse of Riordan array A237619.
  • A237622 (program): Interpolation polynomial through n points (0,1), (1,1), …, (n-2,1) and (n-1,n) evaluated at 2n, a(0)=1.
  • A237626 (program): Sum of a^2 + b^2 for all nonnegative integers a,b such that b^2-a^2 = 4n.
  • A237627 (program): Semiprimes of the form n^3 + n^2 + n + 1.
  • A237646 (program): G.f.: exp( Sum_{n>=1} A163659(n^3)*x^n/n ), where x*exp(Sum_{n>=1} A163659(n)*x^n/n) = S(x) is the g.f. of Stern’s diatomic series (A002487).
  • A237647 (program): G.f. satisfies: A(x) = (1 + x + x^2)^7 * A(x^2)^4.
  • A237649 (program): a(n) = A163659(n^3), where A163659 is the logarithmic derivative of Stern’s diatomic series (A002487).
  • A237650 (program): G.f. satisfies: A(x) = (1+x+x^2)^3 * A(x^2)^2.
  • A237654 (program): G.f.: exp( Sum_{n>=1} 5*Fibonacci(n-1)*Fibonacci(n+1) * x^n/n ).
  • A237655 (program): G.f.: exp( Sum_{n>=1} 5*Fibonacci(n-2)*Fibonacci(n+2) * x^n/n ).
  • A237660 (program): Consider the Collatz trajectory of n; if all terms except n and 1 are even then a(n) = 0, otherwise a(n) is the last odd number before 1.
  • A237664 (program): Interpolation polynomial through n+1 points (0,1), (1,1), …, (n-1,1) and (n,n) evaluated at 2n.
  • A237670 (program): Inverse Moebius transform of Catalan numbers.
  • A237684 (program): a(n) = floor(n*prime(n) / Sum_{i<=n} prime(i).
  • A237686 (program): The number of P-positions in the game of Nim with up to four piles, allowing for piles of zero, such that the total number of objects in all piles doesn’t exceed 2n.
  • A237707 (program): Number of unit cubes, aligned with a three-dimensional Cartesian mesh, completely within the first octant of a sphere centered at the origin, ordered by increasing radius.
  • A237709 (program): Number of occurrences of n-th prime power in A188666.
  • A237711 (program): The number of P-positions in the game of Nim with up to four piles, allowing for piles of zero, such that the total number of objects in all piles is 2n.
  • A237714 (program): Expansion of (1 + x)/(1 - x^2 - 2*x^5).
  • A237716 (program): 7-distance Pell sequence.
  • A237718 (program): 9-distance Pell numbers.
  • A237765 (program): Triangular array read by rows: T(n,k) = binomial(n,2)*binomial(n,k), n>=0, 0<=k<=n.
  • A237767 (program): Product of digits of n is a nonzero cube.
  • A237836 (program): Pisano period of n^2.
  • A237841 (program): Decimal expansion of Ramanujan’s AGM Continued Fraction R(2) = R_1(2,2).
  • A237872 (program): Numerator of Sum_{i=1..n} n^i/i.
  • A237873 (program): Denominator of Sum_{i=1..n} n^i/i.
  • A237881 (program): a(n) = 2-adic valuation of prime(n)+prime(n+1).
  • A237884 (program): a(n) = (n!*m)/(m!*(m+1)!) where m = floor(n/2).
  • A237886 (program): Side length of smallest square containing n dominoes with short side lengths 1, 2, …, n.
  • A237930 (program): a(n) = 3^(n+1) + (3^n-1)/2.
  • A237989 (program): Numbers m such that the numbers of primes, even positive integers and odd positive integers less than or equal to m are all odd.
  • A237990 (program): Numbers m such that the numbers of primes, even positive integers and odd positive integers less than or equal to m are all even.
  • A237991 (program): a(n) = 991*n^2 + 1.
  • A237997 (program): Number of ordered ways to achieve a score of n in American football taking into account different scoring methods.
  • A238002 (program): Count with multiplicity of prime factors of n in (n - 1)!.
  • A238005 (program): Number of partitions of n into distinct parts such that (greatest part) - (least part) = (number of parts).
  • A238006 (program): Number of strict partitions of n such that (greatest part) - (least part) > (number of parts).
  • A238007 (program): Number of strict partitions of n such that (greatest part) - (least part) >= (number of parts).
  • A238013 (program): List n copies of each k in {1,2,…,n}, for n=1,2,3,…
  • A238015 (program): Denominator of (2*n+1)!*8*Bernoulli(2*n,1/2).
  • A238055 (program): a(n) = (13*3^n-1)/2.
  • A238084 (program): The dimensions in which extremal self-dual lattices exist.
  • A238096 (program): Sum_{k=2..n} floor(n/k)*floor((tau(k)+1)/2), where tau = A000005.
  • A238103 (program): Product of composite numbers in range n+1 to 2n, exclusive of endpoints.
  • A238111 (program): Twice the large Schroeder numbers A006318.
  • A238112 (program): Expansion of g.f.: (1-5*x+2*x^2+(2*x-1)*sqrt(x^2-6*x+1))/(4*x).
  • A238113 (program): Expansion of (3 - 5*x - 3*sqrt(x^2-6*x+1))/(4*x).
  • A238115 (program): Number of states arising in matrix method for enumerating Hamiltonian cycles on 2n X 2n grid.
  • A238133 (program): Difference between A238131(n) and A238132(n).
  • A238156 (program): Triangle T(n,k), 0<=k<=n, read by rows, given by (0, 1, 0, 0, 0, 0, 0, 0, 0, …) DELTA (2, -1/2, 1/2, 0, 0, 0, 0, 0, 0, 0, …) where DELTA is the operator defined in A084938.
  • A238160 (program): A skewed version of triangular array A029653.
  • A238161 (program): Greatest common divisor of the prime factors of n, each increased by 1
  • A238162 (program): Least common multiple of the prime factors of n, each increased by 1.
  • A238170 (program): Integer part of square root of A001017: a(n) = floor(n^(9/2)).
  • A238187 (program): Gaussian norm of 1+(1+i)^n.
  • A238191 (program): Digital root of the number of partitions of n.
  • A238192 (program): In the Collatz (3x+1) iteration of n, the last odd number before 1, or 0 if there is no such number.
  • A238200 (program): Decimal expansion of the electron magnetic moment to Bohr magneton ratio, negated.
  • A238204 (program): Even numbers n such that the difference with the preceding prime is prime.
  • A238206 (program): Square array T(n,k), n>=0, k>=0, read by antidiagonals, where T(0,k) is A007494(k) and T(n,k) = 3*T(n-1,k) + 1 for n>0.
  • A238236 (program): Expansion of (1-x-x^2)/((x-1)*(x^3+3*x^2+2*x-1)).
  • A238241 (program): Riordan array (1/(1-x-x^2)^2, x/(1-x-x^2)^2).
  • A238243 (program): A recursive sequence: a(n) = Fibonacci(n)*a(n-1) + 2.
  • A238244 (program): A recursive sequence: a(n) = Fibonacci(n)*a(n-1) + 3.
  • A238246 (program): Numbers m such that A072219(m) = 3.
  • A238247 (program): Numbers m such that A072219(m) = 5.
  • A238248 (program): Numbers m such that A072219(m) = 7.
  • A238256 (program): A060308 begins with one 2, one 3, one 5, two 7’s, one 11, two 13’s, i.e., d(n) = 1, 1, 1, 2, 1, 2, 1, 2, 3, 1,… times the primes (A000040). a(n) uses this distribution with noncomposites (A008578).
  • A238257 (program): Numbers n such that n and 2n+1 use only odd decimal digits.
  • A238259 (program): Area of smallest square containing n dominoes with short side lengths 1, 2, …, n.
  • A238263 (program): a(n) is the number of ways n can be written in the form n=2^k1*p1^k2+2^k3*p2^k4, where p1 and p2 are odd prime numbers, and k1, k2, k3, k4 are nonnegative integers.
  • A238275 (program): a(n) = (4*7^n - 1)/3.
  • A238276 (program): a(n) = (9*8^n - 2)/7.
  • A238290 (program): a(n+1) = a(n) + 6 + 2*(n - 2*floor(n/2)) for n > 0, a(0) = 0.
  • A238291 (program): Final digit of real part of (n+n*i)^n.
  • A238292 (program): Final digit of imaginary part of (n+n*i)^n.
  • A238299 (program): Second convolution of A107841.
  • A238300 (program): Fourth convolution of A107841.
  • A238303 (program): Triangle T(n,k), 0<=k<=n, read by rows given by T(n,0) = 1, T(n,k) = 2 if k>0.
  • A238315 (program): An oscillating sequence: a(n) = n^2 + 2^(n-1) - 2*a(n-1), n>0, with a(1) = 1.
  • A238324 (program): a(1) = 1 and a(n+1) = if a(n) > 2*n+1 then a(n)-2*n-1 else a(n)+2*n+1.
  • A238327 (program): Recursively defined by a(0) = 1, a(n + 1) = p + 2, where p is the least prime greater than a(n).
  • A238328 (program): Sum of all the parts in the partitions of 4n into 4 parts.
  • A238329 (program): Fibonacci numbers that have no prime factors of the form 4k+1.
  • A238337 (program): Number of distinct squarefree numbers in row n of Pascal’s triangle.
  • A238339 (program): Square number array T(n,k) = (2*n^(k+1)-n-1)/(n-1), read by antidiagonals.
  • A238340 (program): Number of partitions of 4n into 4 parts.
  • A238361 (program): Number of length n binary words that contain 111 but do not contain 000 (as contiguous subwords).
  • A238363 (program): Coefficients for the commutator for the logarithm of the derivative operator [log(D),x^n D^n]=d[(xD)!/(xD-n)!]/d(xD) expanded in the operators :xD:^k.
  • A238364 (program): Numbers n such that 9*n^2+3*n-1 and 9*n^2+3*n+1 are twin primes.
  • A238366 (program): a(n) = 5*a(n-2) + 2, a(0) = 1, a(1) = 2.
  • A238371 (program): a(1)=1; for n > 1, a(n) = the number of “topped” Mongean shuffles to reorder a stack of n cards to its original order.
  • A238374 (program): Row sums of triangle in A204026.
  • A238375 (program): Row sums of triangle in A152719.
  • A238377 (program): Row sums of triangle in A204028.
  • A238379 (program): Expansion of (1 - x)/(1 - 36*x + x^2).
  • A238381 (program): Minimal number of V-trominoes needed to prevent any further V-trominoe from being placed on an n X n grid.
  • A238383 (program): Row sums of triangle in A139040.
  • A238384 (program): Triangle of numbers related to A075535.
  • A238385 (program): Shifted lower triangular matrix A238363 with a main diagonal of ones.
  • A238389 (program): Expansion of (1+x)/(1-x^2-3*x^3).
  • A238391 (program): Expansion of (1+x)/(1-x^2-3*x^5).
  • A238392 (program): Triangle read by rows: each row is an initial segment of the terms of A000123 followed by its reflection.
  • A238401 (program): Floor(sum(i/(i+1)),i=1..n).
  • A238410 (program): a(n) = floor((3(n-1)^2 + 1)/2).
  • A238411 (program): a(n) = 2*n*floor(n/2).
  • A238419 (program): a(n) = the Wiener index of the Fibonacci cube G_n.
  • A238420 (program): a(n)=the Wiener index of the Lucas cube L_n.
  • A238441 (program): Expansion of 1/Product_{n>=1} (1 - (q + q^2)^n).
  • A238443 (program): Numbers n with the property that the symmetric representation of sigma(n) has only one part. This is the same sequence as A174973.
  • A238446 (program): Let B be a nonempty and proper subset of A_n = {1,2,…,p_n-1}, where p_n is the n-th prime. Let C be the complement of B, so that the union B and C is A_n. a(n) is half the number of sums of products of elements of B and elements of C, when B runs through all such subsets of A_n.
  • A238452 (program): Second column of the extended Catalan triangle A189231.
  • A238454 (program): Difference between 2^(2*n-1) and the next larger square.
  • A238455 (program): Difference between 4^n and the nearest triangular number.
  • A238461 (program): Greatest number k such that A000009(k) <= n.
  • A238462 (program): 2-adic valuation of A052129.
  • A238464 (program): Generalized ordered Bell numbers Bo(7,n).
  • A238465 (program): Generalized ordered Bell numbers Bo(8,n).
  • A238466 (program): Generalized ordered Bell numbers Bo(9,n).
  • A238467 (program): Generalized ordered Bell numbers Bo(10,n).
  • A238468 (program): Period 7: repeat [0, 0, -1, 1, -1, 1, 0].
  • A238469 (program): Period 7: repeat [0, 1, 0, 0, 0, 0, -1].
  • A238470 (program): Period 7: repeat [0, 0, 1, 0, 0, -1, 0].
  • A238471 (program): a(n) = binomial(5n+6, 4)/5 for n >= 0.
  • A238472 (program): a(n) = binomial(5*n+7, 4)/5 for n >= 0.
  • A238473 (program): a(n) = binomial(5*n+8, 4)/5 for n >= 0.
  • A238474 (program): a(n) = (-1)^n*(n+3)!/(2*(n+1)) for n >= 0.
  • A238475 (program): Rectangular array with all start numbers Me(n, k), k >= 1, for the Collatz operation ud^(2*n), n >= 1, ending in an odd number, read by antidiagonals.
  • A238476 (program): Rectangular array with all start numbers Mo(n, k), k >= 1, for the Collatz operation ud^(2*n-1), n >= 1, ending in an odd number, read by antidiagonals.
  • A238477 (program): a(n) = 32*n - 27 for n >= 1. Second column of triangle A238475.
  • A238478 (program): Number of partitions of n whose median is a part.
  • A238479 (program): Number of partitions of n whose median is not a part.
  • A238488 (program): Number of partitions of n not containing 2*(number of parts) as a part.
  • A238495 (program): Number of partitions p of n such that min(p) + (number of parts of p) is not a part of p.
  • A238496 (program): Number of prime factors in A052129(n).
  • A238518 (program): Number of (n+1) X (1+1) 0..3 arrays with no element equal to all horizontal neighbors or equal to all vertical neighbors.
  • A238520 (program): Number of (n+1)X(3+1) 0..3 arrays with no element equal to all horizontal neighbors or equal to all vertical neighbors
  • A238524 (program): Numbers n such that the symmetric representation of sigma(n) is formed by two or more parts.
  • A238525 (program): n modulo sopfr(n), where sopfr(n) is the sum of the prime factors of n, with multiplicity.
  • A238526 (program): Record values of A238525.
  • A238528 (program): Record prime values of A238525.
  • A238531 (program): Expansion of (1 - x + x^2)^2 / (1 - x)^3 in powers of x.
  • A238532 (program): Number of distinct factorial numbers congruent to -1 (mod n).
  • A238533 (program): Number of solutions to gcd(x^2 + y^2 + z^2 + t^2 + h^2, n) = 1 with x,y,z,t,h in [0,n-1].
  • A238535 (program): Sum of divisors d of n where d > sqrt(n).
  • A238536 (program): A fourth-order linear divisibility sequence related to the Fibonacci numbers: a(n) = (1/2)*Fibonacci(3*n)*Lucas(n).
  • A238537 (program): A fourth-order linear divisibility sequence related to the Pell numbers.
  • A238538 (program): A fourth-order linear divisibility sequence: a(n) = (2^n + 1)*(2^(3*n) - 1)/ ( (2 + 1)*(2^3 - 1) ).
  • A238539 (program): A fourth-order linear divisibility sequence: a(n) := (1/9)*(2^n + (-1)^n)*(2^(3*n) - (-1)^n).
  • A238540 (program): A fourth-order linear divisibility sequence: a(n) := (3^n + 1)*(3^(3*n) - 1)/( (3 + 1)*(3^3 - 1)).
  • A238546 (program): Number of partitions p of n such that floor(n/2) is not a part of p.
  • A238549 (program): a(n) is one fourth of the total number of free ends of 4 line segments expansion at n iterations (see Comments lines for definition).
  • A238578 (program): Expansion of -(-4*x^4 + sqrt(-4*x^2-4*x+1) * (2*x^3+x^2-2*x) -12*x^3-7*x^2+2*x) / (sqrt(-4*x^2-4*x+1) * (4*x^3+8*x^2+3*x-1) - 4*x^3-8*x^2-3*x+1).
  • A238589 (program): Number of partitions p of n such that 2*min(p) is a part of p.
  • A238594 (program): Number of partitions p of n such that 2*min(p) is not a part of p.
  • A238598 (program): Largest integer k such that n >= k^2-k-1 = A165900(k).
  • A238600 (program): A sixth-order linear divisibility sequence related to the Fibonacci numbers: a(n) := (1/6)*Fibonacci(3*n)*Fibonacci(4*n)/Fibonacci(n).
  • A238602 (program): A sixth-order linear divisibility sequence related to the Pell numbers: a(n) := (1/60)*Pell(3*n)*Pell(4*n)/Pell(n).
  • A238603 (program): A sixth-order linear divisibility sequence related to A000225: a(n) := (1/105)*(2^(3*n) - 1)*(2^(4*n) - 1)/(2^n - 1).
  • A238604 (program): a(n) = Sum_{k=0..3} f(n+k)^2 where f=A130519.
  • A238605 (program): Semiprimes n such that (n+1)/4 also is a semiprime.
  • A238622 (program): Number of partitions of n such that floor(n/2) or ceiling(n/2) is a part.
  • A238623 (program): Number of partitions of n such that neither floor(n/2) nor ceiling(n/2) is a part.
  • A238628 (program): Number of partitions p of n such that n - max(p) is a part of p.
  • A238629 (program): Number of partitions p of n such that n - 2*(number of parts of p) is a part of p.
  • A238630 (program): Number of partitions of 3^n into parts that are at most 3.
  • A238631 (program): Number of partitions of 4^n into parts that are at most 4.
  • A238642 (program): n if n+1 is prime; if n+1 is composite, n multiplied by smallest prime factor of n+1.
  • A238644 (program): Number of binary words on {H,T} that end in THTH but do not contain the contiguous subsequence HTHH.
  • A238649 (program): Number of (n+2) X (3+2) 0..1 arrays with no element equal to all horizontal neighbors or equal to all vertical neighbors, and new values 0..1 introduced in row major order.
  • A238684 (program): a(1) = a(2) = 1; for n > 2, a(n) is the product of prime factors of the n-th Fibonacci number.
  • A238696 (program): a(n) = Sum_{k=0..floor(n/2)} binomial(n*(n-k), n*k).
  • A238702 (program): Sum of the smallest parts of the partitions of 4n into 4 parts.
  • A238705 (program): Number of partitions of 4n into 4 parts with smallest part = 1.
  • A238706 (program): Sum of the smallest parts of the partitions of 4n into 4 parts with smallest part greater than 1.
  • A238708 (program): Number of strict partitions of n that include a pair of consecutive integers.
  • A238717 (program): Sum_{k=0..n} C(2*k, k)^n.
  • A238720 (program): Number of nX2 0..2 arrays with no element equal to the sum modulo 3 of elements to its left or elements above it
  • A238731 (program): Riordan array ((1-2*x)/(1-3*x+x^2), x/(1-3*x+x^2)).
  • A238737 (program): a(n) = 2*n+2 - A224911(n).
  • A238738 (program): Expansion of (1 + 2*x + 2*x^2)/(1 - x - 2*x^3 + 2*x^4 + x^6 - x^7).
  • A238740 (program): a(n) = (n+2)!^2*(n+1)!/4*hypergeom([-n],[2,3,3],-1).
  • A238745 (program): a(1) = 1; for n > 1, if the first integer with the same prime signature as n is factorized into primorials as Product A002110(i)^e(i), then a(n) = Product prime(i)^e(i).
  • A238748 (program): Numbers n such that each integer that appears in the prime signature of n appears an even number of times.
  • A238755 (program): Second convolution of A065096.
  • A238761 (program): Subtriangle of the generalized ballot numbers, T(n,k) = A238762(2*k-1,2*n-1), 1<=k<=n, read by rows.
  • A238768 (program): Number of n X 1 0..3 arrays with no element equal to the sum modulo 4 of elements to its left or elements above it.
  • A238777 (program): a(n) = floor((5^n+1)/(2*3^n)).
  • A238778 (program): Sum of all primes p such that 2n - p is also a prime.
  • A238796 (program): Symmetric (0,1)-matrices of order n where the numbers of 1’s is equal to the order n.
  • A238801 (program): Triangle T(n,k), read by rows, given by T(n,k) = C(n+1, k+1)*(1-(k mod 2)).
  • A238803 (program): Number of ballot sequences of length 2n with exactly n fixed points.
  • A238806 (program): Number of n X 2 0..2 arrays with no element equal to one plus the sum of elements to its left or one plus the sum of the sum of elements above it, modulo 3.
  • A238837 (program): Numerators in the enumeration of the rationals by Czyz and Self.
  • A238845 (program): Prefix overlap between binary expansions of n and n+1.
  • A238846 (program): Expansion of (1-2*x)/(1-3*x+x^2)^2.
  • A238847 (program): Smallest k such that k*n^3 + 1 is prime.
  • A238848 (program): Smallest k such that k*n^3 - 1 is prime.
  • A238849 (program): Smallest k such that k*n^3 - 1 and k*n^3 + 1 are twin primes.
  • A238874 (program): Strictly superdiagonal compositions: compositions (p1, p2, p3, …) of n such that pi > i.
  • A238879 (program): Row sums of the triangle of generalized ballot numbers A238762.
  • A238891 (program): Largest squarefree number in row n of Pascal’s triangle.
  • A238892 (program): Index of last squarefree number in the first half of row n of Pascal’s triangle.
  • A238898 (program): Least number m such that lcm(1,2,3,…,m) = lcm(n,n+1,n+2,…,m).
  • A238906 (program): Number of (n+1) X (1+1) 0..2 arrays with no element equal to all horizontal neighbors or equal to all vertical neighbors, and new values 0..2 introduced in row major order.
  • A238908 (program): Number of (n+1) X (3+1) 0..2 arrays with no element equal to all horizontal neighbors or equal to all vertical neighbors, and new values 0..2 introduced in row major order.
  • A238913 (program): Number of self-inverse permutations p on [n] where the maximal displacement of an element equals 2.
  • A238923 (program): Number of (n+1) X (1+1) 0..3 arrays with no element greater than all horizontal neighbors or equal to all vertical neighbors.
  • A238936 (program): Powers of 6 without the digit ‘0’ in their decimal expansion.
  • A238938 (program): Powers of 2 without the digit ‘0’ in their decimal expansion.
  • A238939 (program): Powers of 3 without the digit ‘0’ in their decimal expansion.
  • A238940 (program): Powers of 4 without the digit ‘0’ in their decimal expansion.
  • A238949 (program): Degree of divisor lattice D(n).
  • A238950 (program): The number of arcs from even to odd level vertices in divisor lattice D(n).
  • A238951 (program): The number of arcs from odd to even level vertices in divisor lattice D(n).
  • A238952 (program): The size (the number of arcs) in the transitive closure of divisor lattice D(n).
  • A238963 (program): Number of divisors of A063008(n,k).
  • A238966 (program): The number of distinct primes in divisor lattice in canonical order.
  • A238970 (program): The number of nodes at even level in divisor lattice in canonical order.
  • A238971 (program): The number of nodes at odd level in divisor lattice in canonical order.
  • A238974 (program): The size (the number of arcs) in the transitive closure of divisor lattice in canonical order.
  • A238976 (program): a(n) = ((3^(n-1)-1)^2)/4.
  • A238981 (program): Sum of n-th powers of unitary divisors of n (d such that d divides n, gcd(d, n/d) = 1).
  • A238988 (program): Triangle T(n,k), read by rows, given by (1, -1, 1, 0, 0, 0, 0, 0, 0, 0, …) DELTA (1, 0, -1, 0, 0, 0, 0, 0, 0, 0, …) where DELTA is the operator defined in A084938.
  • A238999 (program): Number of partitions of n using Fibonacci numbers > 1.
  • A239005 (program): Signed version of the Seidel triangle for the Euler numbers, read by rows.
  • A239022 (program): Decimal expansion of the volume of a rhombic dodecahedron with edges of unit length.
  • A239024 (program): Number of n X 2 0..2 arrays with no element equal to the sum of elements to its left or one plus the sum of elements above it, modulo 3.
  • A239031 (program): Number of 4 X n 0..2 arrays with no element equal to the sum of elements to its left or one plus the sum of the elements above it, modulo 3.
  • A239035 (program): Product of 8 consecutive integers. a(n) = RisingFactorial(n, 8).
  • A239040 (program): Number of n X 1 0..3 arrays with no element equal to one plus the sum of elements to its left or one plus the sum of elements above it, modulo 4.
  • A239050 (program): a(n) = 4*sigma(n).
  • A239052 (program): Sum of divisors of 4*n-2.
  • A239053 (program): Sum of divisors of 4*n-1.
  • A239056 (program): Sum of the parts in the partitions of 4n into 4 parts with smallest part = 1.
  • A239057 (program): Sum of the parts in the partitions of 4n into 4 parts with smallest part equal to 1 minus the number of these partitions.
  • A239059 (program): Sum of the two smallest parts from the partitions of 4n into 4 parts with smallest part = 1.
  • A239061 (program): Number of integers x, 1 <= x <= n, such that x^x == 1 (mod n).
  • A239062 (program): Number of integers x, 1 <= x <= n, such that x^x == 0 (mod n).
  • A239065 (program): n^3*(n^4 + n^2 - 1).
  • A239069 (program): Decimal expansion of gamma - Ei(-1).
  • A239072 (program): Maximum number of cells in an n X n square grid that can be painted such that no two orthogonally adjacent cells are painted and every unpainted cell can be reached from the edge of the grid by a series of orthogonal steps to unpainted cells.
  • A239075 (program): Number of self-inverse permutations p on [n] with displacement of elements restricted by 3: |p(i)-i| <= 3.
  • A239086 (program): The sequence S = a(1), a(2), … is defined by a(1)=1, if d,e,f are consecutive digits then we do not have d < e = f, and S is always extended with the smallest integer not yet present in S.
  • A239090 (program): The sequence S = a(1), a(2), … is defined by a(1)=1, if d,e,f are consecutive digits then we do not have d >= e < f, and S is always extended with the smallest integer not yet present in S.
  • A239091 (program): Prefix overlap of dictionary consisting of binary expansions of 0 through n.
  • A239092 (program): Prefix overlap of dictionary consisting of decimal expansions of 0 through n.
  • A239094 (program): a(n) = (5*n^9 - 30*n^7 + 63*n^5 - 50*n^3 + 12*n)/360.
  • A239095 (program): a(n) = (n^7 - 21*n^3 + 20*n)/210.
  • A239101 (program): Riordan array read by rows, corresponding to array in A180562.
  • A239107 (program): Number of hybrid 4-ary trees with n internal nodes.
  • A239108 (program): Number of hybrid 5-ary trees with n internal nodes.
  • A239109 (program): Number of hybrid 6-ary trees with n internal nodes.
  • A239111 (program): Smallest Pell number (see A000129) divisible by n-th prime.
  • A239114 (program): Exponent of 2 in prime factorization (i.e., 2-adic valuation) of odd nonprimes A014076(n) + 1.
  • A239120 (program): Decimal expansion of 1/2 - Pi/8.
  • A239122 (program): Partial sums of A061019.
  • A239123 (program): a(n) = 128*n - 107 for n >= 1. Third column of triangle A238475.
  • A239124 (program): a(n) = 64*n - 11 for n >= 1. Third column of triangle A238476.
  • A239125 (program): Smallest positive integer solution x of (3^3)*x - 2^n*y = 1 for n >= 0.
  • A239126 (program): Rectangular array showing the starting values M(n, k), k >= 1, for the Collatz operation (ud)^n, n >= 1, ending in an odd number, read by antidiagonals.
  • A239127 (program): Rectangular companion array to M(n,k), given in A239126, showing the end numbers N(n, k), k >= 1, for the Collatz operation (ud)^n, n >= 1, ending in an odd number, read by antidiagonals.
  • A239128 (program): a(n) = 32*n - 1, n >= 1. Fourth column of triangle A239126, related to the Collatz problem.
  • A239129 (program): a(n) = 18*n - 1, n >= 1, the second column of triangle A239127 related to the Collatz problem.
  • A239130 (program): Smallest positive integer solution x = a(n) of (3^4)*x - 2^n*y = 1 for n >= 0.
  • A239131 (program): A sequence with period length 54; the companion of x(n) = A239130(n), the smallest positive solution of 3^4*x - 2^n*y = 1 for n >= 0.
  • A239134 (program): Smallest k such that n^k contains k as a substring in its decimal representation.
  • A239138 (program): The sequence S = a(1), a(2), … is defined by a(1)=1, if d,e,f are consecutive digits then we do not have d <= e > f, and S is always extended with the smallest integer not yet present in S.
  • A239140 (program): Number of strict partitions of n having standard deviation σ < 1.
  • A239141 (program): Number of strict partitions of n having standard deviation <= 1.
  • A239171 (program): Number of (n+1) X (1+1) 0..2 arrays with no element greater than all horizontal neighbors or equal to all vertical neighbors.
  • A239186 (program): Sum of the largest two parts in the partitions of 4n into 4 parts with smallest part equal to 1.
  • A239195 (program): Sum of the next to smallest parts in the partitions of 4n into 4 parts with smallest part = 1.
  • A239201 (program): Expansion of -(x * sqrt(5*x^2 -6*x +1) -2*x^3 +3*x^2 -x) / ((3*x^2 -4*x +1) * sqrt(5*x^2 -6*x +1) +5*x^3 -11*x^2 +7*x -1).
  • A239204 (program): Expansion of ((x-1)*sqrt(x^2-6*x+1)-x^2-4*x+1)/(8*x^3).
  • A239206 (program): a(n) is the total number of rows of circles of radius r packing into a circle of radius R, where r = R/2^n.
  • A239224 (program): Numerator of 2n/v(n)^2, where v(1) = 0, v(2) = 1, and v(n) = v(n-1)/(n-2) + v(n-2) for n >= 3; limit of 2n/v(n)^2 is Pi.
  • A239226 (program): a(n) = A000984(n) * A081085(n).
  • A239229 (program): Euler characteristic of n-holed torus: 2 - 2*n.
  • A239249 (program): Number of n X 1 0..4 arrays with no element equal to one plus the sum of elements to its left or one plus the sum of elements above it, modulo 5.
  • A239265 (program): Number of domicule tilings of a 3 X 2n grid.
  • A239275 (program): a(n) = numerator(2^n * Bernoulli(n, 1)).
  • A239278 (program): Smallest k > 1 such that n*(n+1)*…*(n+k-1) / (n+(n+1)+…+(n+k-1)) is an integer.
  • A239282 (program): a(n) = A045917(n)*prime(n).
  • A239283 (program): n^(p1) + n^(p2) + n^(p3) + … where (p1)*(p2)*(p3)*…. is the prime factorization of n (with multiplicity).
  • A239284 (program): a(n) = (15^n - (-1)^n)/16.
  • A239285 (program): a(n) = (15^n - (-2)^n)/17.
  • A239286 (program): Expansion of (x + 1)*(3*x^2 + 2*x + 1)/(x^2 + x + 1)^2.
  • A239287 (program): Triangle T(n,k), 0 <= k <= n, read by rows: T(n,k) = floor(n/2) - min(k,n-k).
  • A239288 (program): Maximal sum of x0 + x0*x1 + … + x0*x1*…*xk over all compositions x0 + … + xk = n.
  • A239289 (program): Numbers that are not the product of three (not necessarily distinct) primes.
  • A239292 (program): (sum of all odd parts of all strict partitions of n) - (sum of all even parts of all strict partitions of n); for “strict”, see Comments.
  • A239294 (program): a(n) = (15^n - (-3)^n)/18.
  • A239297 (program): Floor of first differences of Pi*10^n.
  • A239302 (program): Triangular array: T(n,k) = number of partitions x(1) > x(2) > … > x(k) of n+2 such that x(1) = x(2) + k, for n >= 1.
  • A239305 (program): Expansion of (4*x^4-5*x^3-x^2+3*x-1) / (2*x^5+3*x^4-4*x^3-3*x^2+4*x-1).
  • A239308 (program): Size of smallest set S of integers such that {0,1,2,…,n} is a subset of S-S, where S-S={abs(i-j) | i,j in S}.
  • A239310 (program): Numbers of the form A001700(n)*k, n>=1, k>=2.
  • A239322 (program): Interleave (-1)^n*(A000182(n+1) - A000364(n)), -A028296(n+1).
  • A239324 (program): Partial sums of A090431.
  • A239325 (program): a(n) = 6*n^2 + 8*n + 1.
  • A239331 (program): Square array, read by antidiagonals: column k has g.f. (1+(k-1)*x)^2/(1-x)^3.
  • A239333 (program): Number of n X 1 0..3 arrays with no element equal to one plus the sum of elements to its left or three plus the sum of elements above it, modulo 4.
  • A239341 (program): Decimal expansion of 7 + 2021/3003.
  • A239342 (program): Number of 1’s in all compositions of n into odd parts.
  • A239350 (program): Superprimorials squared.
  • A239352 (program): van Heijst’s upper bound on the number of squares inscribed by a real algebraic curve in R^2 of degree n, if the number is finite.
  • A239354 (program): Decimal expansion of 3/4 - log(2).
  • A239362 (program): Decimal expansion of Sum_{k>=1} 1/((3k-2)*(3k-1)*(3k)).
  • A239364 (program): Numbers n such that (n^2-4)/10 is a square.
  • A239365 (program): Numbers n such that 10*n^2+4 is a square.
  • A239367 (program): The bisection of A238315 that remains constant with changes in the offset of the exponent of the second term.
  • A239394 (program): Number of prime nonnegative Lipschitz quaternions having norm prime(n).
  • A239396 (program): Number of prime nonnegative Hurwitz quaternions having norm prime(n).
  • A239426 (program): 21*n^4 - 36*n^3 + 25*n^2 - 8*n + 1.
  • A239434 (program): Number of nonnegative integer solutions to the equation x^2 - 25*y^2 = n.
  • A239435 (program): Values of n for which the equation x^2 - 25*y^2 = n has integer solutions.
  • A239438 (program): Maximal number of points that can be placed on a triangular grid of side n so that there is no pair of adjacent points.
  • A239442 (program): a(n) = phi(n^7).
  • A239443 (program): a(n) = phi(n^9), where phi = A000010.
  • A239447 (program): Partial sums of A030101.
  • A239449 (program): 7*n^2 - 5*n + 1.
  • A239450 (program): Numbers m such that T(m)^2 + T(m^2) is a perfect square, where T = A000217.
  • A239452 (program): Smallest integer m > 1 such that m^n == m (mod n).
  • A239459 (program): Concatenation of n^3 and n.
  • A239460 (program): Concatenation of n^2 and n^3.
  • A239461 (program): Concatenation of n^3 and n^2.
  • A239462 (program): A239459(n) / n.
  • A239463 (program): a(n) = A239460(n) / n^2.
  • A239464 (program): A239461(n) / n^2.
  • A239466 (program): Expansion of (1 - x + x^2 + sqrt(1 + 2*x + 3*x^2 - 2*x^3 + x^4)) / 2 in powers of x.
  • A239467 (program): Number of 1-separable partitions of n; see Comments.
  • A239473 (program): Triangle read by rows: signed version of A059260: coefficients for expansion of partial sums of sequences a(n,x) in terms of their binomial transforms (1+a(.,x))^n ; Laguerre polynomial expansion of the truncated exponential.
  • A239482 (program): Number of (2,0)-separable partitions of n; see Comments.
  • A239488 (program): Expansion of 1/x-4/(-sqrt(x^2-10*x+1)-x+1)-3.
  • A239492 (program): The fifth bicycle lock sequence: a(n) is the maximum value of min{x*y, (5-x)*(n-y)} over 0 <= x <= 5, 0 <= y <= n for integers x, y.
  • A239493 (program): Number of (2,1)-separable partitions of n; see Comments.
  • A239502 (program): (Round(q^prime(n)) - 1)/prime(n), where q is the tribonacci constant (A058265).
  • A239504 (program): Number of digits in the decimal expansion of n^10 (A008454).
  • A239508 (program): Number of partitions of n into nonprime squarefree numbers, cf. A000469.
  • A239519 (program): a(n) = n + (n-1)*(n-2) + (n-3)*(n-4)*(n-5) + (n-6)*(n-7)*(n-8)*(n-9) + … + …*1.
  • A239527 (program): Numbers k^2 + (k+1)^2 that can be expressed as a sum of two squares in exactly one other way.
  • A239530 (program): Number of (n+1) X (1+1) 0..2 arrays with no element equal to all horizontal neighbors or unequal to all vertical neighbors, and new values 0..2 introduced in row major order.
  • A239532 (program): Number of (n+1) X (3+1) 0..2 arrays with no element equal to all horizontal neighbors or unequal to all vertical neighbors, and new values 0..2 introduced in row major order.
  • A239544 (program): (Round(c^prime(n)) - 1)/prime(n), where c is the tetranacci constant (A086088).
  • A239545 (program): Decimal expansion of Sum_{k>=0} (-1)^k/((2k+1)*(2k+3)*(2k+5)).
  • A239549 (program): Expansion of x/(1-8*x-12*x^2).
  • A239568 (program): Number of ways to place 2 points on a triangular grid of side n so that they are not adjacent.
  • A239569 (program): Number of ways to place 3 points on a triangular grid of side n so that no two of them are adjacent.
  • A239577 (program): Expansion of 1/((x-1)*(3*x-1)*(3*x^2+1)).
  • A239592 (program): (n^4 - n^3 + 4*n^2 + 2)/2.
  • A239594 (program): Number of n X 2 0..3 arrays with no element equal to zero plus the sum of elements to its left or one plus the sum of elements above it or one plus the sum of the elements diagonally to its northwest or one plus the sum of the elements antidiagonally to its northeast, modulo 4.
  • A239607 (program): a(n) = (1-2*n^2)^2.
  • A239608 (program): Sin( arcsin(n)- 2*arccos(n) )^2.
  • A239609 (program): Sin(arcsin(n)- 3 arccos(n))^2.
  • A239610 (program): Sin(arcsin(n) - 4 arccos(n))^2.
  • A239613 (program): a(n) = Sum_{0 < x,y,z,t <= n and gcd(x^2 + y^2 + z^2 + t^2, n)=1} gcd(x^2 + y^2 + z^2 + t^2 - 1, n).
  • A239614 (program): a(n) = A239611(n) / A079458(n).
  • A239619 (program): Base 3 sum of digits of prime(n).
  • A239632 (program): Number of parts in all palindromic compositions of n.
  • A239634 (program): Initial digits of semiprimes in decimal representation.
  • A239636 (program): Distance between the two occurrences of n-th prime in A082500.
  • A239656 (program): First differences of sphenic numbers, cf. A007304.
  • A239668 (program): Sum of the composite divisors of n^2.
  • A239669 (program): Total number of prime factors counted with multiplicity of prime(n)-1 and prime(n)+1, where prime(n) is the n-th prime.
  • A239670 (program): Expansion of 1/((1-x)*(1-81*x)).
  • A239672 (program): Product_{i=1..n} J_6(i) where J_6(i) = A069091(i).
  • A239675 (program): Least k > 0 such that p(n)+k is prime, where p(n) is the number of partitions of n.
  • A239678 (program): Least numbers k such that k*2^n+1 is a square.
  • A239679 (program): Least number k > 0 such that k*2^n+1 is a cube.
  • A239682 (program): Product_{i=1..n} A173557(i).
  • A239683 (program): Number of digits in decimal expansion of n^5.
  • A239684 (program): Number of digits in the decimal expansion of n^4.
  • A239690 (program): Base 4 sum of digits of prime(n).
  • A239691 (program): Base 5 sum of digits of prime(n).
  • A239692 (program): Base 6 sum of digits of prime(n).
  • A239693 (program): Base 7 sum of digits of prime(n).
  • A239694 (program): Base 8 sum of digits of prime(n).
  • A239695 (program): Base 9 sum of digits of prime(n).
  • A239701 (program): Least k > 0 such that q(n)+k is prime, where q(n) is the number of strict partitions of n.
  • A239708 (program): Numbers of the form m = 2^i + 2^j, where i > j >= 0, such that m - 1 is prime.
  • A239712 (program): Primes of the form m = 2^i + 2^j - 1, where i > j >= 0.
  • A239739 (program): a(n) = n*4^(2*n+1).
  • A239745 (program): a(n) = (3*2^(n+2) + n*(n+5))/2 - 6.
  • A239750 (program): Number of ordered pairs of endofunctions (f,g) on a set of n elements satisfying g(f(x)) = f(f(f(x))).
  • A239761 (program): Number of pairs of functions (f, g) on a set of n elements into itself satisfying f(g(x)) = f(x).
  • A239767 (program): Degrees of polynomial on the fermionic side of the finite generalization of identity 46 from Slater’s List.
  • A239768 (program): Number of pairs of functions (f,g) from a set of n elements into itself satisfying f(x) = f(g(f(x))).
  • A239787 (program): Numbers n such that 3n^3 - 1 is prime.
  • A239791 (program): Number of compositions of n with no consecutive 2’s.
  • A239794 (program): 5*n^2 + 4*n - 15.
  • A239796 (program): a(n) = 7*n^2 + 2*n - 15.
  • A239797 (program): Decimal expansion of square root of 3 divided by cube root of 4.
  • A239798 (program): Decimal expansion of the midsphere radius in a regular dodecahedron with unit edges.
  • A239799 (program): a(n) = gcd(Sum_{k=1…n} L(k), Product_{j=1…n} L(j)), where L(k) is the k-th Lucas number.
  • A239812 (program): Number of n X 1 0..3 arrays with no element equal to zero plus the sum of elements to its left or one plus the sum of elements above it, modulo 4.
  • A239840 (program): Number of ordered pairs of permutation functions (f,g) on n elements satisfying f(x) = f(g(g(x))).
  • A239844 (program): Number of n X 2 0..3 arrays with no element equal to one plus the sum of elements to its left or one plus the sum of elements above it or two plus the sum of the elements diagonally to its northwest, modulo 4.
  • A239851 (program): Number of n X 1 0..3 arrays with no element equal to zero plus the sum of elements to its left or zero plus the sum of elements above it or one plus the sum of the elements diagonally to its northwest or one plus the sum of the elements antidiagonally to its northeast, modulo 4.
  • A239868 (program): Sum of sigma(i) mod i for i from 1 to n.
  • A239876 (program): Partial sums of A229110, where A229110(n) = antisigma(n) mod n = A024816(n) mod n.
  • A239878 (program): Numbers n with digit_sum(n*n) + 1 = digit_sum((n+1)*(n+1)).
  • A239885 (program): a(n) = prime(n)*2^(n-2).
  • A239889 (program): From unfriendly seating arrangement problem for fat men at a circular table with n seats.
  • A239890 (program): Number of terms in consolidated series for normal reflectance of a three-layer thin film system of path length n.
  • A239904 (program): a(n) = n - wt(n) + (number of times 11 appears in binary expansion of n).
  • A239906 (program): Let cn(n,k) denote the number of times 11..1 (k 1’s) appears in the binary representation of n; a(n) = n - cn(n,1) + cn(n,2) - cn(n,3).
  • A239907 (program): Let cn(n,k) denote the number of times 11..1 (k 1’s) appears in the binary representation of n; a(n) = n - cn(n,1) + cn(n,2) - cn(n,3) + cn(n,4) - … .
  • A239909 (program): Arises from a construction of equiangular lines in complex space of dimension 2.
  • A239914 (program): Total number of preferential arrangements of 1, 2, …, n things.
  • A239926 (program): 3^(p-1)-2^(p+1) for primes p > 3.
  • A239929 (program): Numbers n with the property that the symmetric representation of sigma(n) has two parts.
  • A239930 (program): Number of distinct quarter-squares dividing n.
  • A239937 (program): Numbers k such that DigitSum(k^2) > DigitSum((k+1)^2).
  • A239942 (program): Prime(n)! - prime(n - 1)!.
  • A239967 (program): a(n) = a(n-1)*a(n-2) - a(n-3)*a(n-4), starting with 1,1,2,2.
  • A239968 (program): 0 unless n is a nonprime A018252(k) when a(n) = k.
  • A239976 (program): Positions of ones in binary representation of log(2).
  • A240001 (program): Number of 2 X n 0..3 arrays with no element equal to one plus the sum of elements to its left or two plus the sum of the elements above it or one plus the sum of the elements diagonally to its northwest, modulo 4.
  • A240022 (program): Total number of digits in palindromes with n digits.
  • A240023 (program): Product of factorials of prime divisors of n (with multiplicity).
  • A240025 (program): Characteristic function of quarter squares, cf. A002620.
  • A240052 (program): 2nd arithmetic derivative of products of 2 successive prime numbers (A006094).
  • A240053 (program): 3rd Arithmetic derivation of products of 2 successive prime numbers (A006094).
  • A240054 (program): 4th arithmetic derivative of products of 2 successive prime numbers (A006094).
  • A240056 (program): Number of partitions of n such that m(1) > m(2), where m = multiplicity.
  • A240058 (program): Number of partitions of n such that m(1) = m(3), where m = multiplicity.
  • A240059 (program): Number of partitions of n such that m(1) > m(3), where m = multiplicity.
  • A240063 (program): Number of partitions of n such that m(2) < m(3), where m = multiplicity.
  • A240064 (program): Number of partitions of n such that m(2) = m(3), where m = multiplicity.
  • A240065 (program): Number of partitions of n such that m(2) > m(3), where m = multiplicity.
  • A240068 (program): Number of prime Lipschitz quaternions having norm prime(n).
  • A240076 (program): Number of partitions of n such that m(greatest part) < m(1), where m = multiplicity.
  • A240077 (program): Number of partitions of n such that m(greatest part) <= m(1), where m = multiplicity.
  • A240078 (program): Number of partitions of n such that m(greatest part) = m(1), where m = multiplicity.
  • A240080 (program): Number of partitions of n such that m(greatest part) >= m(1), where m = multiplicity.
  • A240086 (program): a(n) = sum(p prime and divides n, phi(gcd(p, n/p))) where phi is Euler’s totient function.
  • A240088 (program): The number of ways of writing n as an ordered sum of a triangular number (A000217), a square (A000290) and a pentagonal number (A000326).
  • A240098 (program): Product of the greatest common divisors of n and k! over k=0..n-1.
  • A240114 (program): Maximal number of points that can be placed on a triangular grid of side n so that no three of them are vertices of an equilateral triangle in any orientation.
  • A240115 (program): Schoenheim lower bound L(n,4,2).
  • A240116 (program): Schoenheim lower bound L(n,5,2).
  • A240117 (program): Schoenheim lower bound L(n,6,2).
  • A240130 (program): Least prime of the form prime(n)^2 + k^2, or 0 if none.
  • A240131 (program): Least k such that prime(n)^2 + k^2 is prime, or 0 if none.
  • A240134 (program): Numerator of (n-1) * ceiling(n/2) / n.
  • A240135 (program): a(n) = composite(n)*2^(n - 3).
  • A240137 (program): Sum of n consecutive cubes starting from n^3.
  • A240165 (program): E.g.f.: exp( x*(1 + exp(2*x)) ).
  • A240171 (program): Numbers k such that k has more divisors than k-1.
  • A240172 (program): O.g.f.: Sum_{n>=0} n! * x^n * (1+x)^n.
  • A240199 (program): Area under the path specified by n-th composition.
  • A240222 (program): Rectangular array giving all start values M(n, k), k >= 1, for Collatz sequences following the pattern (udd)^(n-1) ud, n >= 1, read by antidiagonals.
  • A240223 (program): Rectangular companion array to M(n,k), given in A240222, showing the end numbers N(n, k), k >= 1, for the Collatz operation (udd)^(n-1) ud, n >= 1, read by antidiagonals.
  • A240226 (program): 4-adic value of 1/n, n >= 1.
  • A240227 (program): All even positive integers which have at least one ‘balanced’ representation as a sum of three distinct nonzero squares.
  • A240277 (program): Minimal number of people such that exactly n days are required to spread gossip.
  • A240328 (program): Inverse of 37th cyclotomic polynomial.
  • A240329 (program): Inverse of 41st cyclotomic polynomial.
  • A240330 (program): Inverse of 43rd cyclotomic polynomial.
  • A240331 (program): Inverse of 47th cyclotomic polynomial.
  • A240342 (program): Number of n X 2 0..3 arrays with no element equal to one plus the sum of elements to its left or one plus the sum of elements above it or three plus the sum of the elements diagonally to its northwest, modulo 4.
  • A240348 (program): Inverse of 53rd cyclotomic polynomial.
  • A240349 (program): Inverse of 59th cyclotomic polynomial.
  • A240350 (program): Inverse of 61st cyclotomic polynomial.
  • A240353 (program): Inverse of 68th cyclotomic polynomial.
  • A240354 (program): Inverse of 71st cyclotomic polynomial.
  • A240355 (program): Inverse of 72nd cyclotomic polynomial.
  • A240357 (program): Inverse of 74th cyclotomic polynomial.
  • A240370 (program): Positive integers n such that every element in the ring of integers modulo n can be written as the sum of two squares modulo n.
  • A240388 (program): A sequence related to the Stern sequence s(n) (A002487), defined by w(n) = s(3n)/2.
  • A240400 (program): Numbers n having a partition into distinct parts of form 3^k-2^k.
  • A240434 (program): Binomial transform of the sum of the first n even squares (A002492).
  • A240436 (program): Semiprimes of the form n^3 - 2*n.
  • A240437 (program): Number of non-palindromic n-tuples of 5 distinct elements.
  • A240438 (program): Greatest minimal difference between numbers of adjacent cells in a regular hexagonal honeycomb of order n with cells numbered from 1 through the total number of cells, the order n corresponding to the number of cells on one side of the honeycomb.
  • A240440 (program): Number of ways to place 3 points on a triangular grid of side n so that they are not vertices of an equilateral triangle of any orientation.
  • A240443 (program): Maximal number of points that can be placed on an n X n square grid so that no four of them are vertices of a square with any orientation.
  • A240445 (program): Numbers of ways to place five indistinguishable points on an n X n square grid so that no four of them are vertices of a square of any orientation.
  • A240450 (program): Greatest number of distinct numbers in the intersection of p and its conjugate, as p ranges through the partitions of n.
  • A240453 (program): Greatest prime divisors of the palindromes with an even number of digits.
  • A240454 (program): Smallest prime divisors of the palindromes with an even number of digits.
  • A240461 (program): Number of 2 X n 0..3 arrays with no element equal to one plus the sum of elements to its left or three plus the sum of the elements above it or one plus the sum of the elements diagonally to its northwest, modulo 4.
  • A240465 (program): Inverse of 76th cyclotomic polynomial.
  • A240467 (program): Inverse of 152nd cyclotomic polynomial.
  • A240468 (program): Sum of the distinct prime divisors of the palindromes having an even number of digits.
  • A240471 (program): Integer part of (n * A000005(n) / A000203(n)).
  • A240473 (program): Distance from prime(n) to the closest smaller squarefree number.
  • A240474 (program): Distance from prime(n) to the closest larger squarefree number.
  • A240478 (program): Number of n X 2 0..1 arrays with no element equal to more than two horizontal or vertical neighbors, with new values 0..1 introduced in row major order.
  • A240486 (program): Number of partitions of n containing m(1) as a part, where m denotes multiplicity.
  • A240501 (program): Given circular disks of radius r in a hexagonal lattice covered by a circular disk of radius R = r*2n, if the center of the circle is chosen at the middle between two lattice points, a(n) is the number of points at which an r-circle is tangent to the R-circle.
  • A240504 (program): Read (exponents of primes in the factorization of n!) modulo 2 and convert to decimal.
  • A240505 (program): Products of primes the squares of which are Fermi-Dirac divisors of n!
  • A240506 (program): Number of length-n gap-free words on {1,2,3}.
  • A240513 (program): Number of n X 2 0..1 arrays with no element equal to exactly two horizontal and vertical neighbors, with new values 0..1 introduced in row major order.
  • A240521 (program): a(n) = A050376(n)*A050376(n+1) where A050376(n) is the n-th number of the form p^(2^k) with p is prime and k >= 0.
  • A240522 (program): S_5 sequence in partition of integers > 1 described in A240521.
  • A240523 (program): a(n) = floor(4^n/((1+sqrt(5))/2)^(2*n)).
  • A240524 (program): S_7 sequence in partition of integers > 1 described in A240521.
  • A240525 (program): 2^(n-2)*(2^(n+4)-(-1)^n+5).
  • A240526 (program): 2^(n-2)*(2^(n+4)-(-1)^n+13).
  • A240527 (program): Indices of 7-almost prime triangular numbers.
  • A240528 (program): Indices of 8-almost prime triangular numbers.
  • A240529 (program): Indices of 9-almost prime triangular numbers.
  • A240530 (program): a(n) = 4*(2*n)! / (n!)^2.
  • A240531 (program): Numbers n such that 24*n + 19 is not prime.
  • A240533 (program): a(n) = numerators of n!/10^n.
  • A240534 (program): a(n) = denominators of n!/10^n.
  • A240536 (program): S_9 sequence in partition of integers > 1 described in A240521.
  • A240542 (program): The midpoint of the (rotated) Dyck path from (0, n) to (n, 0) defined by A237593 has coordinates (a(n), a(n)). Also a(n) is the alternating sum of the n-th row of A235791.
  • A240546 (program): a(n) = prime(n+1)^n mod prime(n).
  • A240547 (program): Number of non-congruent solutions of x^2 + y^2 + z^2 + t^2 == 0 mod n.
  • A240548 (program): Greatest prime factor of n^5 + 1.
  • A240549 (program): Greatest prime factor of n^6+1.
  • A240550 (program): Greatest prime factor of n^7+1.
  • A240552 (program): Greatest prime factor of n^9+1.
  • A240554 (program): Square array of the greatest prime factor of n^k + 1, read by antidiagonals.
  • A240558 (program): a(n) = 2^n*n!/((floor(n/2)+1)*floor(n/2)!^2).
  • A240559 (program): a(n) = -2^n*(E(n, 1/2) + E(n, 1) + (n mod 2)*2*(E(n+1, 1/2) + E(n+1, 1))), where E(n, x) are the Euler polynomials.
  • A240560 (program): a(n) = 2^n*E(n,1/2) + 2^(n+1)*E(n+1,0), where E(n,x) the Euler polynomials.
  • A240561 (program): The main diagonal in the difference table of A240559.
  • A240564 (program): A number (where A=1, B=2…) for every letter in the capitalized alphabet that does not have a curved line in the letter.
  • A240567 (program): a(n) = optimal number of tricks to throw in the game of One Round War (with n cards) in order to maximize the expected number of tricks won.
  • A240568 (program): Difference between n times the n-th prime and twice the sum of the first n primes.
  • A240571 (program): a(n) = round(n^n/n!).
  • A240572 (program): a(n) = floor(4^n/(2 + sqrt(2))^n).
  • A240574 (program): Number of partitions of n such that the number of odd parts is a part.
  • A240599 (program): Expansion of A(x) = x*B’(x)*(B(x)-x)/B(x)^2 where B(x)/x is g.f. of A027307.
  • A240603 (program): Numbers that are the sum of two successive squarefree numbers.
  • A240607 (program): a(n) = 2*a(n-2)+a(n-3)+a(n-4) for n>=4, a(n) = binomial(n,3) for n<4.
  • A240657 (program): Least k such that 2^k == -1 (mod prime(n)), or 0 if no such k exists.
  • A240658 (program): Least k such that 3^k == -1 (mod prime(n)), or 0 if no such k exists.
  • A240659 (program): Least k such that 4^k == -1 (mod prime(n)), or 0 if no such k exists.
  • A240660 (program): Least k such that 5^k == -1 (mod prime(n)), or 0 if no such k exists.
  • A240661 (program): Least k such that 6^k == -1 (mod prime(n)), or 0 if no such k exists.
  • A240663 (program): Least k such that 8^k == -1 (mod prime(n)), or 0 if no such k exists.
  • A240664 (program): Least k such that 9^k == -1 (mod prime(n)), or 0 if no such k exists.
  • A240665 (program): Least k such that 10^k == -1 (mod prime(n)), or 0 if no such k exists.
  • A240668 (program): Number of the first odd exponents in the prime power factorization of (2*n)!.
  • A240676 (program): Number of digits in the decimal expansion of n^7.
  • A240688 (program): Expansion of -(x*sqrt(-4*x^2-4*x+1)-2*x^2-3*x) / ((x+1)*sqrt(-4*x^2-4*x+1)+ 4*x^3+8*x^2+3*x-1).
  • A240689 (program): The number of values of the digit k for which prime(n)*10+k is prime.
  • A240690 (program): Number of partitions p of n such that p contains fewer 1s than its conjugate.
  • A240691 (program): Number of partitions p of n such that (# 1s in p) = (#1s in conjugate(p)).
  • A240707 (program): Sum of the middle parts in the partitions of 4n-1 into 3 parts.
  • A240708 (program): Number of decompositions of 2n into an unordered sum of two terms of A240699.
  • A240711 (program): Sum of the largest parts in the partitions of 4n into 4 parts with smallest part = 1.
  • A240712 (program): Number of decompositions of 2n into an unordered sum of two terms of A240710.
  • A240721 (program): Expansion of -(4*x+sqrt(1-8*x)-1)/(sqrt(1-8*x)*(4*x^2+x)+8*x^2-x).
  • A240722 (program): Expansion of log’((-1-sqrt(1-8*x)+sqrt(2+2*sqrt(1-8*x)+8*x))/(4*x)).
  • A240732 (program): The unique set of ten distinct positive numbers up to 35 the sum of whose reciprocals of squares is 1/2.
  • A240734 (program): Floor(6^n/(2+sqrt(5))^n).
  • A240735 (program): Floor(6^n/(3+sqrt(3))^n).
  • A240747 (program): Least number k > 0 such that n^k - (n-1)^k - … - 3^k - 2^k - 1 is prime, or 0 if no such k exists.
  • A240752 (program): First differences of digit sums of squares, cf. A004159.
  • A240754 (program): Numbers k with digit_sum(k*k) - 1 = digit_sum((k+1)*(k+1)).
  • A240769 (program): Triangle read by rows: T(1,1) = 1; T(n+1,k) = T(n,k+1), 1 <= k < n; T(n+1,n) = 2*T(n,1); T(n+1,n+1) = 2*T(n,1) - 1.
  • A240784 (program): Number of 3 X n 0..1 arrays with no element equal to fewer vertical neighbors than horizontal neighbors, with new values 0..1 introduced in row major order.
  • A240796 (program): Total number of occurrences of the pattern 1<2 in all preferential arrangements (or ordered partitions) of n elements.
  • A240797 (program): Total number of occurrences of the pattern 1=2 in all preferential arrangements (or ordered partitions) of n elements.
  • A240798 (program): Total number of occurrences of the pattern 1=2=3 in all preferential arrangements (or ordered partitions) of n elements.
  • A240799 (program): Total number of occurrences of the pattern 1=2<3 in all preferential arrangements (or ordered partitions) of n elements.
  • A240801 (program): Triangle read by rows: T(n,k) (n>=2, 0 <= k <= n-2) = number of possible topologies with n given vertices and n-k-2 Steiner points.
  • A240803 (program): a(n) = 2 + product of first n odd primes.
  • A240804 (program): a(n) = -2 + product of first n odd primes.
  • A240826 (program): Number of ways to choose three points on a centered hexagonal grid of size n.
  • A240828 (program): a(1)=a(2)=0, a(3)=2; thereafter a(n) = Sum( a(n-i-s-a(n-i-1)), i=0..k-1 ), where s=0, k=3.
  • A240836 (program): Numbers n such that n^3 = x*y*z where 2 <= x <= y <= z , n^3+1 = (x-1)*(y+1)*(z+1).
  • A240846 (program): a(0)=0, a(1)=1, a(n) = a(n-1)*12 + 13.
  • A240847 (program): a(n) = 2*a(n-1) + a(n-2) - 2*a(n-3) - a(n-4) for n>3, a(0)=a(1)=a(3)=0, a(2)=1.
  • A240848 (program): Sum of n, digitsum(n) and number of digits of n.
  • A240857 (program): Triangle read by rows: T(0,0) = 0; T(n+1,k) = T(n,k+1), 0 <= k < n; T(n+1,n) = T(n,0); T(n+1,n+1) = T(n,0)+1.
  • A240859 (program): Cubes k^3 such that k^3 + (k+1)^3 is semiprime.
  • A240860 (program): a(n) = Sum_{i=1..n} (-1)^{i+1} prime(i)^2, where prime(k) denotes the k-th prime: alternating sum of the squares of the first n primes.
  • A240871 (program): Number of partitions p of n into distinct parts such that max(p) = 3 + min(p).
  • A240876 (program): Expansion of (1 + x)^11 / (1 - x)^12.
  • A240877 (program): Sum of the denominators of the Farey series of order n (A006843).
  • A240878 (program): Numbers n such that (n^2 + 2)/3 is prime.
  • A240879 (program): Self-convolution of Sum(binomial(2*n, i), i=0..n).
  • A240880 (program): Expansion of g.f.: (-1 + sqrt(1+12*x+48*x^2)) / (6*x).
  • A240883 (program): Central terms of the triangle in A240857.
  • A240884 (program): Semiprimes of the form C(n) + T(n) where C(n) and T(n) are the n-th cube and triangular numbers.
  • A240909 (program): The sequency numbers of the 16 rows of a Hadamard-Walsh matrix of order 16.
  • A240910 (program): The sequency numbers of the 32 rows of a Hadamard-Walsh matrix, order 32.
  • A240914 (program): Semiprimes of the form S(n) + T(n) where S(n) and T(n) are the n-th square and the n-th triangular numbers.
  • A240916 (program): a(n) = 6*a(n-1) + 2*2^(n-1) - 2 for n > 2, a(0) = a(1) = 0, a(2) = 3.
  • A240917 (program): a(n) = 2*3^(2*n) - 3*3^n + 1.
  • A240920 (program): Prime numbers that occur as divisors of numbers of the form m^2 + 5.
  • A240924 (program): Digital root of squares of numbers not divisible by 2, 3 or 5.
  • A240926 (program): a(n) = 2 + L(2*n) = 2 + A005248(n), n >= 0, with the Lucas numbers (A000032).
  • A240930 (program): a(n) = n^7 - n^6.
  • A240931 (program): a(n) = n^8 - n^7.
  • A240932 (program): a(n) = n^9 - n^8.
  • A240933 (program): a(n) = n^10 - n^9.
  • A240935 (program): Decimal expansion of 3*sqrt(3)/(4*Pi).
  • A240939 (program): Least number k >= 0 such that n! + k is a perfect power.
  • A240944 (program): Number of compositions of n into square parts k^2 where there are k sorts of part k^2.
  • A240945 (program): Powers of 9 without the digit ‘0’ in their decimal expansion.
  • A240947 (program): Decimal expansion of the moment of order 1 at Pi/3 of Ls_4, where Ls_4 is a generalized log-sine integral.
  • A240951 (program): Maximum number of dividing subsets of a set of n natural numbers.
  • A240960 (program): Numbers m such that sigma(m) - phi(m) = tau(m)^omega(m), where sigma=A000203, phi=A000010, tau=A000005 and omega=A001221.
  • A240962 (program): Number of zeros in the decimal expansion of n^n.
  • A240965 (program): Decimal expansion of integral_(0..1) K(1-x^2)^3 dx, where K is the complete elliptic integral of the first kind.
  • A240975 (program): The number of distinct prime factors of n^3-1.
  • A240977 (program): Beatty sequence for cube root of Pi: a(n) = floor(n*Pi^(1/3)).
  • A240979 (program): Sum of unitary anti-divisors of n.
  • A240983 (program): Integers of the form 2^p*p^2 where p is the lesser of a pair of twin primes.
  • A240988 (program): Denominators of the (reduced) rationals (((n-1)!!)/(n!! * 2^((1 + (-1)^n)/2)))^((-1)^n), where n is a positive integer.
  • A240993 (program): A000142 (n+1) * A002109(n), a product of factorials and hyperfactorials.
  • A241008 (program): Numbers n with the property that the number of parts in the symmetric representation of sigma(n) is even, and that all parts have width 1.
  • A241013 (program): Semiprimes congruent to {1, 2, 4} mod 5.
  • A241016 (program): Triangle read by rows: T(n, k) = sum of k-th row of n X n square filled with the numbers 1 through n^2 reading across rows left-to-right.
  • A241023 (program): Central terms of the triangle in A102413.
  • A241024 (program): S_11 sequence in partition of integers > 1 described in A240521.
  • A241025 (program): S_13 sequence in partition of integers > 1 described in A240521.
  • A241029 (program): Sum of n-th powers of divisors of 22.
  • A241030 (program): Sum of n-th powers of divisors of 26.
  • A241031 (program): Sum of n-th powers of divisors of 28.
  • A241032 (program): Sum of n-th powers of divisors of 30.
  • A241038 (program): A000217(A058481(n)).
  • A241040 (program): Differences between primes having primitive root 2.
  • A241070 (program): Least number k such that k^n + (k-1)^n + … + 3^n + 2^n is prime, or 0 if no such k exists.
  • A241082 (program): a(n) = n for 1 and prime numbers. For composite numbers, first prime term in sequence starting with n and each time adding smallest prime number not a divisor of the preceding term.
  • A241083 (program): LCM of n and largest integer <= sqrt(n).
  • A241084 (program): Sum of the second largest parts of the partitions of 4n into 4 parts.
  • A241095 (program): (5^n - 1)^n.
  • A241098 (program): (4^n - 1)^n.
  • A241146 (program): Least number k such that k and n*k share at least one digit.
  • A241151 (program): Number of distinct degrees in the partition graph G(n) defined at A241150.
  • A241153 (program): Number of partitions having the maximal degree in the partition graph G(n) defined at A241150.
  • A241169 (program): Steffensen’s bracket function [n,3].
  • A241170 (program): Steffensen’s bracket function [n,n-3].
  • A241193 (program): a(n) = Sum_{k=1..n} ((3*n-k-1)/(2*n-k))*(3*n-k-2)!/((n-1)!*(n-1)!*(n-k)!).
  • A241194 (program): Numerator of phi(p-1)/(p-1), where phi is Euler’s totient function and p = prime(n).
  • A241195 (program): Denominator of phi(prime(n)-1)/(prime(n)-1), where phi is Euler’s totient function and prime(n) is the n-th prime.
  • A241199 (program): Numbers n such that 4 consecutive terms of binomial(n,k) satisfy a quadratic relation for 0 <= k <= n/2.
  • A241200 (program): For the n in A241199, the index of the first of 4 terms in binomial(n,k) that satisfy a quadratic relation.
  • A241203 (program): a(n) = floor(5^n/4^(n-1)).
  • A241204 (program): Expansion of (1 + 2*x)^2/(1 - 2*x)^2.
  • A241205 (program): Sum of x*y^2*z^3 for positive integers x,y,z with x + y + z = n.
  • A241209 (program): a(n) = E(n) - E(n+1), where E(n) are the Euler numbers A122045(n).
  • A241217 (program): Largest number that when multiplied by 7 produces an n-digit number.
  • A241219 (program): Number of ways to choose two points on a centered hexagonal grid of size n.
  • A241235 (program): a(n) = number of times n appears in A006949.
  • A241242 (program): a(n) = -2^(2*n+1)*(E(2*n+1, 1/2) + E(2*n+1, 1) + 2*(E(2*n+2, 1/2) + E(2*n+2, 1))), where E(n,x) are the Euler polynomials.
  • A241247 (program): a(n) = Sum_{k=0..n} n^k * binomial(n,k)^3.
  • A241262 (program): Array t(n,k) = binomial(n*k, n+1)/n, where n >= 1 and k >= 2, read by ascending antidiagonals.
  • A241264 (program): Numbers k such that 2*k^2 + 2*k - 41 is not a prime.
  • A241266 (program): Numbers n such that 4*n^2+2*n-1 is not prime.
  • A241269 (program): Denominators of c(n) = (n^2+n+2)/((n+1)*(n+2)*(n+3)).
  • A241271 (program): a(n) = 6*a(n-1) + 3*(2^(n-2)-1) for n > 2, a(0)=a(1)=a(2)=0.
  • A241275 (program): a(n) = 6*a(n-1) + 5*(2^(n-1)-1) for n > 0, a(0) = 0.
  • A241301 (program): Number of n X 2 0..3 arrays with no element equal to zero plus the sum of elements to its left or one plus the sum of elements above it or zero plus the sum of the elements diagonally to its northwest or zero plus the sum of the elements antidiagonally to its northeast, modulo 4.
  • A241371 (program): Number of 2 X n 0..2 arrays with no element equal to fewer vertical neighbors than horizontal neighbors, with new values 0..2 introduced in row major order.
  • A241403 (program): Numbers n such that (n^2 + 2)/3 is not prime.
  • A241404 (program): Sum of n and the sum of the factorials of its digits.
  • A241406 (program): Numbers n such that n^2 == -1 (mod 61).
  • A241407 (program): Numbers n such that n^2 == -1 (mod 73).
  • A241418 (program): First differences of Arshon’s sequence, cf. A099054.
  • A241419 (program): Number of numbers m <= n that have a prime divisor greater than sqrt(n) (i.e., A006530(m)>sqrt(n)).
  • A241422 (program): Limit-reverse of the infinite Fibonacci word A003849 with first term as initial block.
  • A241452 (program): a(n) = pg(3, n) + pg(4, n) + … + pg(n, n) where pg(m, n) is the n-th m-th-order polygonal number.
  • A241458 (program): Number of simple connected graphs g on n nodes with |Aut(g)| = 10.
  • A241460 (program): Number of simple connected graphs g on n nodes with |Aut(g)| = 14
  • A241462 (program): Number of simple connected graphs g on n nodes with |Aut(g)| = 20
  • A241467 (program): Number of simple connected graphs g on n nodes with |Aut(g)| = 120
  • A241468 (program): Number of simple connected graphs g on n nodes with |Aut(g)| = 144
  • A241469 (program): Number of simple connected graphs g on n nodes with |Aut(g)| = 240.
  • A241470 (program): Number of simple connected graphs g on n nodes with |Aut(g)| = 720
  • A241471 (program): Number of simple connected graphs g on n nodes with |Aut(g)| = 5040.
  • A241478 (program): a(n) = 4^n*(n/4 + binomial(n-1/2, -1/2)).
  • A241496 (program): Expansion of (1 + 4*x + x^2) / (1 - x^2)^3.
  • A241497 (program): q-Pell numbers with q=2.
  • A241498 (program): q-Lucas numbers with q=2.
  • A241519 (program): Denominators of b(n) = b(n-1)/2 + 1/(2*n), b(0)=0.
  • A241520 (program): Numbers n such that n^2 == -1 (mod 89).
  • A241521 (program): Numbers n such that n^2 == -1 (mod 97).
  • A241522 (program): The number of P-positions in the game of Nim with up to 4 piles, allowing for piles of zero, such that the number of objects in each pile does not exceed n.
  • A241524 (program): a(n) = 4^n*(n/4 + binomial(n+1/2, 1/2)).
  • A241526 (program): Number of different positions in which a square with side length k, 1 <= k <= n - floor(n/3), can be placed within a bi-symmetric triangle of 1 X 1 squares of height n.
  • A241527 (program): n^3 + (3^n+1)/2.
  • A241530 (program): a(n) = binomial(n,floor(n/2))*binomial(n+1,floor(n/2+1/2))*(1+floor(n/2))/(1+2*floor(n/2)).
  • A241534 (program): Number of integer arithmetic means of 2 distinct divisors of n.
  • A241539 (program): Smallest k>=1 such that the n-th semiprime + or - k are both primes, or a(n)=0 if there is no such k.
  • A241543 (program): a(n) = A241477(n, n).
  • A241554 (program): Semiprimes generated by the polynomial 2 * n^2 + 29.
  • A241557 (program): Numbers k that do not have prime anti-divisors.
  • A241560 (program): Decimal expansion of the sum of the reciprocals of the averages of the twin prime pairs.
  • A241566 (program): Number of 2-element subsets of {1,…,n} whose sum has more than 2 divisors.
  • A241571 (program): Numbers n such that 2*n+15 is not a prime.
  • A241572 (program): Numbers n such that 2*n+17 is not a prime.
  • A241573 (program): 2^p + 3 where p is prime.
  • A241575 (program): Sturmian expansion of 1/2 in base sqrt(2)-1.
  • A241576 (program): Third differences of A001521.
  • A241577 (program): n^3 + 4*n^2 - 5*n + 1.
  • A241581 (program): Row sums in triangle A241580.
  • A241587 (program): Coefficients in an expansion of the trace of the log of the adjacency operator on the infinite grid Z x Z.
  • A241590 (program): Numerators of Postnikov’s hook-length formula 2^n*(n+1)^(n-1)/n!.
  • A241591 (program): Denominators of Postnikov’s hook-length formula 2^n*(n+1)^(n-1)/n!.
  • A241596 (program): Partitions listed by alternately incrementing each part and appending a 1.
  • A241603 (program): a(n) = Sum_{d|n, d <= 5} d^2 + 5*Sum_{d|n, d>5} d.
  • A241606 (program): A linear divisibility sequence of the fourth order related to A003779.
  • A241608 (program): Number of length n+2 0..2 arrays with no consecutive three elements summing to more than 2.
  • A241657 (program): The sum of a^2 + b^2 for all nonnegative integers a,b such that b^2 - a^2 = 2*n+1.
  • A241662 (program): Numbers of the form m * 10^k where gcd(10, m) = 1 and k >= 0 and m > 0.
  • A241663 (program): Number of positive integers k less than or equal to n such that gcd(k,n) = gcd(k+1,n) = gcd(k+2,n) = gcd(k+3,n) = 1.
  • A241664 (program): Number of iterations of A058026 needed to reach either 0 or 1.
  • A241667 (program): Sum of the iterates of A058026 up to and including either 0 or 1.
  • A241672 (program): Numbers k such that A035014(k) begins with a 4.
  • A241676 (program): 2^p - 3 where p is prime.
  • A241677 (program): 2^p + 5 where p is prime.
  • A241678 (program): 2^p - 5 where p is prime.
  • A241679 (program): 2^p + 7 where p is prime.
  • A241680 (program): 2^p + 11 where p is prime.
  • A241682 (program): Total number of unit squares appearing in the Thue-Morse sequence logical matrices after n stages.
  • A241683 (program): Total number of 2 X 2 squares appearing in the Thue-Morse sequence logical matrices after n stages.
  • A241684 (program): The total number of rectangles appearing in the Thue-Morse sequence logical matrices after n stages.
  • A241685 (program): The total number of squares and rectangles appearing in the Thue-Morse sequence logical matrices after n stages.
  • A241687 (program): Numbers k such that A035014(k) begins with a 3.
  • A241710 (program): Number of simple connected graphs on n nodes with diameter 6
  • A241717 (program): The number of P-positions in the game of Nim with up to 3 piles, allowing for piles of zero, such that the number of objects in the largest pile is n.
  • A241718 (program): The number of P-positions in the game of Nim with up to 4 piles, allowing for piles of zero, such that the number of objects in the largest pile is n.
  • A241746 (program): Smallest number greater than n that CANNOT be scored using n darts on a standard dartboard.
  • A241747 (program): Triangle read by rows: T(n,k) = (4*n+3)*(4*k+3).
  • A241748 (program): a(n) = n^2 + 12.
  • A241749 (program): a(n) = n^2 + 13.
  • A241750 (program): a(n) = n^2 + 15.
  • A241751 (program): a(n) = n^2 + 16.
  • A241753 (program): Decimal expansion of sum_(n=1..infinity) (H(n)/(n+1))^2, where H(n) is the n-th harmonic number.
  • A241755 (program): A finite sum of products of binomial coefficients: Sum_(m=0..n) binomial(-1/4, m)^2*binomial(-1/4, n-m)^2 (C. C. Grosjean’s problem, numerators).
  • A241756 (program): A finite sum of products of binomial coefficients: Sum_(m=0..n) binomial(-1/4, m)^2*binomial(-1/4, n-m)^2 (C. C. Grosjean’s problem, denominators).
  • A241759 (program): Number of partitions of n into distinct parts of the form 3^k - 2^k, cf. A001047.
  • A241764 (program): Semiprimes sp such that sp-3 is also semiprime.
  • A241765 (program): a(n) = n*(n + 1)*(n + 2)*(3*n + 17)/24.
  • A241766 (program): Number of partitions of n into parts of the form 3^k - 2^k, cf. A001047.
  • A241771 (program): Number of simple connected graphs with n nodes and exactly 5 articulation points (cutpoints).
  • A241772 (program): First differences of A065094 and also arithmetic means of initial terms of A065094.
  • A241783 (program): Numbers that cannot be partitioned into distinct parts of the form 3^k - 2^k, cf. A001047.
  • A241807 (program): Numerators of c(n) = (n^2+n+2)/((n+1)*(n+2)*(n+3)) as defined in A241269.
  • A241808 (program): Numbers k such that (2*k)^3 - 3 is prime.
  • A241809 (program): Semiprimes sp such that sp+2 is a prime.
  • A241814 (program): Number of distance-regular simple connected graphs on n nodes.
  • A241816 (program): a(n) is the largest number smaller than n that can be obtained by swapping two adjacent bits in n, or n if no such number exists.
  • A241817 (program): Semiprimes sp such that sp-3 is prime.
  • A241833 (program): Greedy residue sequence of squares 2^2, 3^2, 4^2, …
  • A241834 (program): Number of terms in the greedy residue sum for n^2.
  • A241835 (program): Numbers k such that k^2 is s-greedy summable, where s is the sequence A000290 of squares.
  • A241836 (program): Squares-greedy summable squares.
  • A241847 (program): a(n) = n^2 + 17.
  • A241848 (program): a(n) = n^2 + 18.
  • A241849 (program): a(n) = n^2 + 19.
  • A241850 (program): a(n) = n^2 + 20.
  • A241851 (program): a(n) = n^2 + 21.
  • A241859 (program): 1st Arithmetic derivative of numbers with prime arithmetic derivative (A157037).
  • A241888 (program): a(n) = 2^(4*n + 1) - 1.
  • A241889 (program): a(n) = n^2 + 23.
  • A241890 (program): a(n) = n^2 + 24.
  • A241891 (program): Total number of unit squares appearing in the Thue-Morse sequence of logical matrices (1, 0 version) after n stages.
  • A241892 (program): Total number of 2 X 2 squares appearing in the Thue-Morse sequence logical matrices (1, 0 version) after n stages.
  • A241893 (program): The total number of rectangles appearing in the Thue-Morse sequence logical matrices (1, 0 version) after n stages.
  • A241894 (program): The total number of squares and rectangles appearing in the Thue-Morse sequence (1, 0 version) logical matrices after n stages.
  • A241899 (program): Numbers n equal to the sum of all the two-digit numbers formed without repetition from the digits of n.
  • A241907 (program): a(n) = floor( Catalan(2*n) / Catalan(n)^2 ).
  • A241909 (program): Self-inverse permutation of natural numbers: a(1)=1, a(p_i) = 2^i, and if n = p_i1 * p_i2 * p_i3 * … * p_{ik-1} * p_ik, where p’s are primes, with their indexes are sorted into nondescending order: i1 <= i2 <= i3 <= … <= i_{k-1} <= ik, then a(n) = 2^(i1-1) * 3^(i2-i1) * 5^(i3-i2) * … * p_k^(1+(ik-i_{k-1})). Here k = A001222(n) and ik = A061395(n).
  • A241910 (program): After a(1)=0, numbers 0 .. bigomega(n)-1, followed by numbers 0 .. bigomega(n+1)-1, etc., where bigomega(n)=A001222(n) is the number of prime factors of n (with repetition).
  • A241911 (program): After a(1)=1, numbers 1 .. bigomega(n), followed by numbers 1 .. bigomega(n+1), etc., where bigomega(n)=A001222(n) is the number of prime factors of n (with repetition).
  • A241913 (program): Complement of A241912, natural numbers not fixed by A241916.
  • A241914 (program): After a(1)=0, numbers 0 .. A061395(n)-1, followed by numbers 0 .. A061395(n+1)-1, etc.
  • A241915 (program): After a(1)=1, numbers 1 .. A061395(n), followed by numbers 1 .. A061395(n+1), etc.
  • A241916 (program): a(2^k) = 2^k, and for other numbers, if n = 2^e1 * 3^e2 * 5^e3 * … p_k^e_k, then a(n) = 2^(e_k - 1) * 3^(e_{k-1}) * … * p_{k-1}^e2 * p_k^(e1+1). Here p_k is the greatest prime factor of n (A006530), and e_k is its exponent (A071178), and the exponents e1, …, e_{k-1} >= 0.
  • A241917 (program): If n is a prime with index i, p_i, a(n) = i, (with a(1)=0), otherwise difference (i-j) of the indices of the two largest primes p_i, p_j, i >= j in the prime factorization of n: a(n) = A061395(n) - A061395(A052126(n)).
  • A241919 (program): If n is a prime power, p_i^e, a(n) = i, (with a(1)=0), otherwise difference (i-j) of the indices of the two largest distinct primes p_i, p_j, i > j in the prime factorization of n: a(n) = A061395(n) - A061395(A051119(n)).
  • A241920 (program): After a(1)=1, each n appears A061395(n) times, where A061395 gives the index of the largest prime factor of n.
  • A241929 (program): Number of inequivalent colorings of the Fano plane with n colors.
  • A241937 (program): Number of length 1+4 0..n arrays with no consecutive five elements summing to more than 2*n.
  • A241955 (program): a(n) = 2^(4*n+3) - 1.
  • A241957 (program): Rectangular array A read by upward antidiagonals in which the entry in row n and column k is defined by A(n,k) = 2^n*(2*k - 1) - 1, n,k >= 1.
  • A241958 (program): a(n) = (3*n+3)!/((4*(n+1)^2-1)*((n+1)!)^2*(n+2)!).
  • A241974 (program): a(n) is the limit of the sequence given by A241083^i, where f^[i] means iterate f i times, or 0 if the sequence diverges.
  • A241976 (program): Values of k such that k^2 + (k+3)^2 is a square.
  • A241979 (program): (0,1) sequence such that lengths of three consecutive runs are always distinct.
  • A241989 (program): Positive numbers n that are divisible by the sum of the digits of n in base 16.
  • A242002 (program): Sum_{k=1..n} (-1)^isprime(k)*2^k.
  • A242023 (program): Decimal expansion of Sum(n >= 1, (-1)^(n + 1)*24/(n*(n + 1)*(n + 2)*(n + 3)).
  • A242024 (program): Decimal expansion of Sum_{n>=1} (-1)^(n+1)*6/(n*(n+1)*(n+2)).
  • A242026 (program): Number of non-palindromic n-tuples of 4 distinct elements.
  • A242029 (program): Number of anti-divisors m <= n of n that are coprime to n.
  • A242032 (program): A sequence related to lower bounds for the number of distinct differentiable structures on spheres of the form S^(4*k-1).
  • A242034 (program): a(n)=lpf(A243937(n)-3), where lpf = least prime factor (A020639).
  • A242038 (program): Integer part of square root of A010809(n) = n^21.
  • A242043 (program): Pentagonal numbers that are also Niven numbers.
  • A242053 (program): Decimal expansion of 1/log(2)-1, the mean value of a random variable following the Gauss-Kuzmin distribution.
  • A242062 (program): Expansion of x * (1 - x^12) / ((1 - x^3) * (1 - x^4) * (1 - x^7)) in powers of x.
  • A242063 (program): Analog clock times where the minute hand is on the hour hand (in hhmm format).
  • A242073 (program): a(n) = - (a(n-1)*a(n-4) + a(n-2)*a(n-3)) / a(n-5) with a(0)=1, a(1)=a(2)=-1, a(3)=-2, a(4)=1.
  • A242082 (program): Nim sequence of game on n counters whose legal moves are removing some number of counters in A027941.
  • A242083 (program): 3^p - 2^p - 1, where p is prime.
  • A242084 (program): 5^p - 4^p - 1, where p is prime.
  • A242089 (program): Number of triples (a,b,c) with 0 < a < b < c < p and a + b + c == 0 mod p, where p = prime(n).
  • A242090 (program): Number of triples (a,b,c) with 0 < a < b < c < p and a + b + c == 0 mod p, where 2*b < p = prime(n).
  • A242091 (program): a(n) = r * (n-1)! where r is the rational number that satisfies the equation Sum_{k>=n} (-1)^(k + n)/C(k,n) = n*2^(n-1)*log(2) - r.
  • A242094 (program): Complement of A003249.
  • A242096 (program): a(n) = (n mod 2) * pi( ceiling(n/2)-1 ), where pi is the prime counting function (A000720).
  • A242097 (program): Sp = reversal of some square s where s = x^2 for x = 1,2,.. (ignoring leading zeros). Sp is in the sequence if it is semiprime.
  • A242098 (program): Numbers n such that the residue of n modulo floor(sqrt(n)) is prime.
  • A242101 (program): Number of conjugacy classes of the symmetric group S_n when conjugating only by even permutations.
  • A242107 (program): Reduced division polynomials associated with elliptic curve y^2 + x*y = x^3 - x^2 - x + 1 and multiples of point (0, 1).
  • A242108 (program): a(n) = abs(A242107(n)).
  • A242111 (program): Number of nonnegative k such that k^2+2 divides n^2+2.
  • A242112 (program): a(n) = floor((2*n+6)/(5-(-1)^n)).
  • A242114 (program): Triangle read by rows: T(n,k) = number of pairs (x,y) in {1..n}X{1..n} with gcd(x,y) = k.
  • A242118 (program): Number of unit squares that intersect the circumference of a circle of radius n centered at (0,0).
  • A242119 (program): Primes modulo 18.
  • A242120 (program): Primes modulo 20.
  • A242121 (program): Primes modulo 21.
  • A242122 (program): Primes modulo 22.
  • A242123 (program): Primes modulo 25.
  • A242124 (program): Primes modulo 26.
  • A242125 (program): Primes modulo 27.
  • A242126 (program): Primes modulo 28.
  • A242127 (program): Primes modulo 29.
  • A242135 (program): a(n) = n^3 - 2*n.
  • A242136 (program): Number of strong triangulations of a fixed square with n interior vertices.
  • A242172 (program): a(n) = 2^n*binomial((n + 1 + (n mod 2))/2, 1/2).
  • A242179 (program): T(0,0) = 1, T(n+1,2*k) = - T(n,k), T(n+1,2*k+1) = T(n,k), k=0..n, triangle read by rows.
  • A242181 (program): Numbers with four X’s in Roman numerals.
  • A242182 (program): Numbers with four C’s in Roman numerals.
  • A242187 (program): Decimal expansion of Sum_{n>=1} 1/(prime(n)*prime(n+1)*prime(n+2)): Sum of reciprocals of products of three successive primes.
  • A242189 (program): a(n) is the smallest prime number such that every number from 6 to 2n can be written as the sum of two primes less than or equal to a(n).
  • A242191 (program): Expected value of the highest die when n six-sided dice are rolled, multiplied by 6^n.
  • A242206 (program): Number of length n binary words which contain 00 and 01 and 10 and 11 as (possibly overlapping) contiguous subsequences.
  • A242215 (program): a(n) = 18*n + 5.
  • A242219 (program): Smallest a(n) in Pythagorean triple (a, b, c) such that c(n) - b(n) = n.
  • A242220 (program): Decimal expansion of (10^(1/3)-1)/2, an approximation to Euler-Mascheroni constant.
  • A242227 (program): a(n) = (2*n-1) * a(n-1) - a(n-2), a(0) = 1, a(1) = 2.
  • A242234 (program): Number of length n+3+1 0..3 arrays with every value 0..3 appearing at least once in every consecutive 3+2 elements, and new values 0..3 introduced in order.
  • A242235 (program): Number of length n+4+1 0..4 arrays with every value 0..4 appearing at least once in every consecutive 4+2 elements, and new values 0..4 introduced in order.
  • A242236 (program): Number of length n+5+1 0..5 arrays with every value 0..5 appearing at least once in every consecutive 5+2 elements, and new values 0..5 introduced in order.
  • A242237 (program): Number of length n+6+1 0..6 arrays with every value 0..6 appearing at least once in every consecutive 6+2 elements, and new values 0..6 introduced in order.
  • A242238 (program): Number of length n+7+1 0..7 arrays with every value 0..7 appearing at least once in every consecutive 7+2 elements, and new values 0..7 introduced in order.
  • A242252 (program): Start with n-th odd prime, and repeatedly subtract the greatest prime until either 0 or 1 remains. (The result is the “primes-greedy residue” of the n-th odd prime, which is “primes-greedy summable” if its residue = 0, as at A242255; see Comments.)
  • A242254 (program): Numbers k such that the k-th prime is primes-greedy summable, as defined at A242252.
  • A242255 (program): Primes-greedy summable primes, as defined at A242252.
  • A242256 (program): Primes that are not primes-greedy summable, as defined at A242252.
  • A242262 (program): Semiprimes of the form k^3 - 1.
  • A242278 (program): Number of non-palindromic n-tuples of 3 distinct elements.
  • A242284 (program): Greedy residue sequence of triangular numbers 3, 6, 10, 15, …
  • A242285 (program): Number of terms in the greedy sum for the n-th triangular number.
  • A242286 (program): Positive integers k for which the k-th triangular number is greedy-summable.
  • A242287 (program): Greedy-summable triangular numbers.
  • A242288 (program): Greedy residue sequence of tetrahedral numbers 4, 10, 20, 35, …
  • A242289 (program): Number of terms in the greedy sum for the n-th tetrahedral number.
  • A242290 (program): Positive integers k for which the k-th tetrahedral number is greedy-summable.
  • A242291 (program): Greedy-summable tetrahedral numbers.
  • A242293 (program): Greedy residue sequence of cubes 2^3, 3^3, 4^3, …
  • A242294 (program): Number of terms in the greedy sum for n^3.
  • A242295 (program): Positive integers k for which k^3 is greedy-summable.
  • A242296 (program): Greedy-summable cubes.
  • A242300 (program): a(n) = Sum_{0<=i<j<=n}L(i)*L(j), where L(k)=A000032(k) is the k-th Lucas number.
  • A242311 (program): Largest digital sum in row n of Pascal’s triangle.
  • A242312 (program): Digital roots in Pascal’s triangle, triangle read by rows, 0 <= k <= n.
  • A242313 (program): Numbers belonging to a geometric sequence whose ratio is 2 and whose first term ends in 1.
  • A242317 (program): Number of length n+2+2 0..2 arrays with every value 0..2 appearing at least once in every consecutive 2+3 elements, and new values 0..2 introduced in order.
  • A242328 (program): 5^n + 2.
  • A242329 (program): a(n) = 5^n + 4.
  • A242330 (program): Numbers k such that k^2 + 2 is a semiprime.
  • A242331 (program): Numbers k such that k^2 + 3 is a semiprime.
  • A242332 (program): Numbers k such that k^2 + 4 is a semiprime.
  • A242333 (program): Numbers k such that k^2 + 5 is a semiprime.
  • A242342 (program): a(n) = binomial(n, smallest non-divisor of n).
  • A242343 (program): Triangular numbers T such that (T+2) is semiprime.
  • A242344 (program): Triangular numbers T such that T-2 is semiprime.
  • A242349 (program): Largest power of 2 <= n^2.
  • A242357 (program): Crescendo trapezoidal.
  • A242369 (program): a(n) = P(n, 1, -2*n-1, 1-2*n)/(n+1), P the Jacobi polynomial.
  • A242371 (program): Modified eccentric connectivity index of the cycle graph with n vertices, C[n].
  • A242373 (program): Sum_{k=0..n} C(n,k) * (2*k+1)^(2*n).
  • A242374 (program): Number of digits in the decimal expansion of n^8.
  • A242376 (program): Numerators of b(n) = b(n-1)/2 + 1/(2*n), b(0)=0.
  • A242388 (program): Triangle read by rows: T(n,k) = n*2^(k-1) + 1, 1 <= k <= n.
  • A242389 (program): 2^n minus the sum of the proper divisors of n.
  • A242395 (program): Number of equilateral triangles (sides length = 1) that intersect the circumference of a circle of radius n centered at (1/2,0).
  • A242396 (program): Number of rows of equilateral triangles (sides length = 1) that intersect the circumference of a circle of radius n centered at (0,0) or (1/2,0).
  • A242398 (program): Partial sums of the number of primes separating successive pairs of twin primes.
  • A242399 (program): Write n and 3n in ternary representation and add all trits modulo 3.
  • A242400 (program): Differences between A008586 (multiples of 4) and A242399.
  • A242401 (program): Numbers that are neither triangular nor square.
  • A242405 (program): Expansion of (b(q) / b(q^2))^2 in powers of q where b() is a cubic AGM theta function.
  • A242407 (program): Numbers such that in ternary representation all pairs of adjacent digits have sums not greater than 2.
  • A242408 (program): Numbers such that in ternary representation at least one pair of adjacent digits has a sum greater than 2.
  • A242412 (program): a(n) = (2n-1)^2 + 14.
  • A242424 (program): Bulgarian solitaire operation on partition list A112798: a(1) = 1, a(n) = A000040(A001222(n)) * A064989(n).
  • A242426 (program): floor(n! / n^3).
  • A242427 (program): n! mod n^3.
  • A242429 (program): Length of longest chain of nonempty proper subsemigroups of the monoid of partial injective order-preserving functions of a chain with n elements.
  • A242436 (program): n^5 - 2n.
  • A242438 (program): a(n) is the result of factoring a(n-1) + 1 into primes, replacing each prime 2 with a 3, and taking the product of the resulting factors.
  • A242442 (program): Number of ways of writing n, a positive integer, as an unordered sum of a triangular number (A000217), an odd square (A016754) and a pentagonal number (A000326).
  • A242446 (program): a(n) = Sum_{k=1..n} C(n,k) * k^(2*n).
  • A242448 (program): Number of distinct linear polynomials b+c*x in row n of array generated as in Comments.
  • A242449 (program): a(n) = Sum_{k=0..n} C(n,k) * (2*k+1)^(2*n+1).
  • A242452 (program): Number of length n words on {1,2,3} with no more than one consecutive 1 and no more than two consecutive 2’s and no more than three consecutive 3’s.
  • A242454 (program): Triangular numbers T such that sum of digits of T is semiprime.
  • A242456 (program): Least number k such that n!/k is prime.
  • A242467 (program): Number of length n+2 0..n arrays with no three equal elements in a row and new values 0..n introduced in 0..n order
  • A242468 (program): Number of length n+2 0..5 arrays with no three equal elements in a row and new values 0..5 introduced in 0..5 order.
  • A242473 (program): Binomial(2p-1,p-1) modulo p^4, with p=prime(n).
  • A242475 (program): a(n) = 2^n + 8.
  • A242476 (program): Primes p such that p + 22 is also prime.
  • A242477 (program): Floor(3*n^2/4).
  • A242491 (program): Numbers avoiding subtractive notation when written in Roman numerals.
  • A242493 (program): a(n) is the number of not-sqrt-smooth numbers (“jagged” numbers) not exceeding n. This is the counting function of A064052.
  • A242496 (program): a(n)=sum_{j=0..n} sum_{i=0..j} F(i)*L(j), where F(n)=A000045(n) and L(n)=A000032(n).
  • A242497 (program): Sides of (Heronian) triangles where sides are consecutive integers and area is an integer.
  • A242499 (program): Number of compositions of n, where the difference between the number of odd parts and the number of even parts is 1.
  • A242500 (program): Number of compositions of n, where the difference between the number of odd parts and the number of even parts is 2.
  • A242501 (program): Number of compositions of n, where the difference between the number of odd parts and the number of even parts is 3.
  • A242502 (program): Number of compositions of n, where the difference between the number of odd parts and the number of even parts is 4.
  • A242503 (program): Number of compositions of n, where the difference between the number of odd parts and the number of even parts is 5.
  • A242504 (program): Number of compositions of n, where the difference between the number of odd parts and the number of even parts is 6.
  • A242505 (program): Number of compositions of n, where the difference between the number of odd parts and the number of even parts is 7.
  • A242506 (program): Number of compositions of n, where the difference between the number of odd parts and the number of even parts is 8.
  • A242507 (program): Number of compositions of n, where the difference between the number of odd parts and the number of even parts is 9.
  • A242508 (program): Number of compositions of n, where the difference between the number of odd parts and the number of even parts is 10.
  • A242510 (program): Number of n-length words on {1,2,3} such that the maximal blocks (runs) of 1’s have odd length, the maximal blocks of 2’s have even length and the maximal blocks of 3’s have odd length.
  • A242525 (program): Number of cyclic arrangements of S={1,2,…,n} such that the difference between any two neighbors is at most 3.
  • A242536 (program): Number of n-length words on {1,2,3,4} such that the maximal runs of identical odd integers are of odd length and the maximal runs of identical even integers are of even length.
  • A242537 (program): Number of n-length words on {1,2,3,4,5} such that the maximal runs of identical odd integers are of odd length and the maximal runs of identical even integers are of even length.
  • A242543 (program): Number of length n+3 0..2 arrays with no four elements in a row with pattern aabb (possibly a=b) and new values 0..2 introduced in 0..2 order
  • A242558 (program): a(n) = Sum_{j=0..n} Sum_{i=0..j} L(i)*F(j) where L(i)=A000032(i) and F(j)=A000045(j).
  • A242561 (program): a(0)=0; thereafter, a(n) is n multiplied by the distance of a(n-1) to the nearest prime.
  • A242563 (program): a(n) = 2*a(n-1) - a(n-3) + 2*a(n-4), a(0)=a(1)=0, a(2)=2, a(3)=3.
  • A242566 (program): Expansion of (1-sqrt(1-(2*(1-sqrt(1-4*x^2)))/x))/2.
  • A242569 (program): n!-2n.
  • A242570 (program): Multiples of 252.
  • A242578 (program): Number of length n+3 0..2 arrays with no four elements in a row with pattern aabb (with a!=b) and new values 0..2 introduced in 0..2 order.
  • A242586 (program): Expansion of 1/(2*sqrt(1-x))*(1/sqrt(1-x)+1/(sqrt(1-5*x))).
  • A242593 (program): Triangular array read by rows: T(n,k) is the number of length n words on {B,G} that contain exactly k occurrences of the contiguous substrings BGB or GBG. The substrings are allowed to overlap; n>=0, 0<=k<=max(n-2,0).
  • A242594 (program): Numbers k such that 4^k has initial digit 4.
  • A242595 (program): a(n) is the primitive period length for the sequence 2^k (mod n), k = 1, 2, …
  • A242596 (program): Numerators for partial sums of dilog(1/2).
  • A242597 (program): One half of the denominators of the partial sums of dilog(1/2).
  • A242598 (program): Triangle read by rows: T(n,k) is the coefficient A_k in the transformation of 1 + x + x^2 + … + x^n to the polynomial A_k*(x-k)^k for 0 <= k <= n.
  • A242601 (program): Integers repeated twice in a canonical order.
  • A242602 (program): Integers repeated thrice in a canonical order.
  • A242603 (program): Largest divisor of n not divisible by 7. Remove factors 7 from n.
  • A242604 (program): a(n) = (n - 1)*(n^3 + 1) = n^4 - n^3 + n - 1, for n >= 1.
  • A242609 (program): Expansion of phi(-q) * phi(q^8) in powers of q where phi() is a Ramanujan theta function.
  • A242627 (program): Number of divisors of n that are less than 10.
  • A242634 (program): G.f. A(x) satisfies A(x) = A(x^2) / (1 - x) + x / (1 - x^2).
  • A242638 (program): Number of quadrangulations of a hexagon b_1 w_3 b_2 w_1 b_3 w_2 having n inner faces and not containing the edge b_1 w_1.
  • A242640 (program): Triangle read by rows: T(s,n) (1 <= s <= n) = Sum_{d|n, d <= s} d^2 + s*Sum_{d|n, d>s} d.
  • A242643 (program): a(n) = Sum_{d|n, d <= 6} d^2 + 6*Sum_{d|n, d>6} d.
  • A242645 (program): a(n) = concatenation of decimal expansions of powers of 11 (in decreasing order).
  • A242646 (program): a(n) = concatenation of decimal expansions of powers of 11 (in increasing order).
  • A242650 (program): For any number m there is a number k such that m-k^3 is congruent mod 96 to one of these 12 numbers.
  • A242651 (program): Real part of Product_{k=0..n} (i-k), where i = sqrt(-1).
  • A242652 (program): Imaginary part of Product_{k=0..n) (i-k), where i=sqrt(-1).
  • A242653 (program): Triangle read by rows: T(n,k) = ((n+k)/2)!/k! if n,k have same parity, otherwise 0.
  • A242658 (program): a(n) = 3*n^2 - 3*n + 2.
  • A242659 (program): a(n) = n*(n^2 - 3*n + 4).
  • A242660 (program): Nonnegative numbers of the form x^2+xy-2y^2.
  • A242668 (program): Expansion of 1/(1 - 8*x + 16*x^2 + x^4 - 4*x^5).
  • A242669 (program): a(n) = n*floor(n/3).
  • A242671 (program): Decimal expansion of k2, a Diophantine approximation constant such that the area of the “critical parallelogram” (in this case a square) is 4*k2.
  • A242703 (program): Decimal expansion of sqrt(7)/2.
  • A242709 (program): Nonequivalent ways to place two different markers (e.g., a pair of Go stones, black and white) on an n X n grid.
  • A242721 (program): Decimal expansion of the positive real root of 3*x^4 - x^3 - x^2 - 2, a constant related to quasi-isometric mappings.
  • A242725 (program): Sequence with all (x, y) = (a(2m), a(2m+-1)) satisfying x|y^2+y+1 and y|x^2+1.
  • A242727 (program): Sum of the third largest parts of the partitions of 4n into 4 parts.
  • A242728 (program): Sequence a(n) with all (x,y)=(a(2m),a(2m+-1)) satisfying y|x^2+1 and x|y^2+y+1.
  • A242736 (program): Number of solutions of a^2 + b^2 congruent to -1 modulo the n-th prime.
  • A242739 (program): Semiprimes having only straight digits.
  • A242742 (program): Let k be the n-th composite number: then a(n) is the smallest base b such that b^(k-1) == 1 (mod k).
  • A242745 (program): Least k > 0 such that (k!-n!)/(k-n) is an integer.
  • A242756 (program): Semiprimes having only the curved digits.
  • A242757 (program): Partial sums of the number of integers between successive twin prime pairs.
  • A242762 (program): a(n) = -a(n-1) + a(n-3) + 5*(n-2) for n>2, a(0)=2, a(1)=3, a(2)=4.
  • A242763 (program): a(n) = 1 for n <= 7; a(n) = a(n-5) + a(n-7) for n>7.
  • A242764 (program): a(n) = floor(sqrt((2*n)^n)).
  • A242765 (program): a(1) = 2; for n>1, a(n) = product of digits of (a(n-1)^2).
  • A242766 (program): a(n) = floor(sqrt(n!+1)).
  • A242767 (program): Numbers of repetitions of terms in A242758.
  • A242771 (program): Number of integer points in a certain quadrilateral scaled by a factor of n (another version).
  • A242774 (program): a(n) = ceiling( n / 2 ) + ceiling( n / 3 ).
  • A242781 (program): Expansion of (1 - 2*x - sqrt(1-4*x))/(4*x^2 + sqrt(1-4*x)*(3*x+1) - 5*x + 1).
  • A242798 (program): Expansion of -x*d(log((1-x*(2/sqrt(3*x)) * sin((1/3) * arcsin(sqrt(27*x/4))))))/dx.
  • A242801 (program): Least number k > 1 such that (k^k+n)/(k+n) is an integer.
  • A242817 (program): a(n) = B(n,n), where B(n,x) = Sum_{k=0..n} Stirling2(n,k)*x^k are the Bell polynomials (also known as exponential polynomials or Touchard polynomials).
  • A242818 (program): a(n) = 2^floor(n/2) n! [x^n] exp(x+x^2/4), where [x^n] f(x) denotes the coefficient of x^n in the expansion of f(x).
  • A242831 (program): Triangular numbers T such that sum of the factorials of digits of T is prime.
  • A242849 (program): Triangle read by rows: T(n,k) = A060828(n)/(A060828(k) * A060828(n-k)).
  • A242850 (program): 32*n^5 - 32*n^3 + 6*n.
  • A242851 (program): 64*n^6 - 80*n^4 + 24*n^2 - 1.
  • A242852 (program): 128*n^7-192*n^5+80*n^3-8*n.
  • A242853 (program): 256*n^8 - 448*n^6 + 240*n^4 - 40*n^2 + 1.
  • A242854 (program): a(n) = 512*n^9 - 1024*n^7 + 672*n^5 - 160*n^3 + 10*n.
  • A242856 (program): Number of 2-matchings of the n X n grid graph.
  • A242874 (program): Expansion of b(q)^2 in powers of q where b() is a cubic AGM theta function.
  • A242891 (program): Beginning with a centrally symmetric ‘Sun’ configuration of 8 rhombi with rotational symmetry, number of tiles that can be added to the free edges of the tiling.
  • A242894 (program): Beginning with a central ‘Star’ configuration of a Penrose ‘Kite’ and ‘Dart’ tiling with rotational symmetry as the first step, number of tiles that can be added to the free edges of the current tiling.
  • A242911 (program): Half the number of compositions of n into exactly two different parts with equal multiplicities.
  • A242912 (program): Finite sequence where each term follows n*10^n + p, where p is an n-digit prime and 1 <= n <= 9.
  • A242926 (program): a(n) = denominator of B(0,n), where B(n,n)=0, B(n-1,n)=1/n and otherwise B(m,n)=B(m-1,n+1)-B(m-1,n).
  • A242930 (program): Primes of the form (k^2+7)/11.
  • A242936 (program): Numbers n such that n*prime(n) + (n+1)*(prime(n+1)) is semiprime.
  • A242947 (program): a(n) = n / A242926(n-1).
  • A242954 (program): a(n) = Product_{i=1..n} A234957(i).
  • A242961 (program): The smallest prime p > prime(n) such that p mod prime(n) == - 1.
  • A242962 (program): a(1) = a(2) = 0; for n >= 3: a(n) = (n*(n+1)/2) mod antisigma(n) = A000217(n) mod A024816(n).
  • A242963 (program): Numbers n such that A242962(n) = sigma(n) = A000203(n).
  • A242971 (program): Alternate n+1, 2^n.
  • A242983 (program): n/2 * (n^3 - 2*n^2 - 2*n + 5).
  • A242985 (program): a(n) = 4^n + 2^(n+1).
  • A242986 (program): a(n) = 6*(n+1)!/((3+floor(n/2))*(floor(n/2)!)^2).
  • A242992 (program): Least k>n/2, k<n, such that 2^(n-k)-1 divides 2^k-2, or 0 if no such k exists.
  • A242998 (program): Number of integers k such that R = (2^k*Q - Q - 1)/(Q + 1 - 2^k) is a prime number, when Q = A000668(n) is the n-th Mersenne prime.
  • A243004 (program): a(n) = - (a(n-1) + 1) * a(n-2) with a(1) = a(2) = 1.
  • A243005 (program): a(n) = (a(n-1) - a(n-2)) * a(n-1) / a(n-3) with a(0) = 2, a(1) = 1, a(2) = -1.
  • A243007 (program): a(n) = A084769(n)^2.
  • A243012 (program): Odd primes p such that neither p - 4 nor p + 4 is prime.
  • A243014 (program): Number of acyclic digraphs (DAGS) on n labeled nodes, where the indegree and outdegree of each node is at most 1.
  • A243019 (program): Expansion of -(2*x*sqrt(1-8*x^2)-2*x) / (16*x^3+sqrt(1-8*x^2)*(4*x^2+2*x-1)-8*x^2-2*x+1).
  • A243027 (program): Number of length n+3 0..2 arrays with no four elements in a row with pattern abba (possibly a=b) and new values 0..2 introduced in 0..2 order.
  • A243035 (program): Number of entries of length n in A240601.
  • A243036 (program): Number of entries of length n in A240602.
  • A243038 (program): Number of length n+3 0..2 arrays with no four elements in a row with pattern abab (with a!=b) and new values 0..2 introduced in 0..2 order.
  • A243054 (program): a(0)=1, and for n >= 1, a(n) = p_n * A002110(n) / 2, where p_n is the n-th prime.
  • A243055 (program): Difference between the indices of the smallest and the largest prime dividing n: If n = p_i * … * p_k, where p_i <= … <= p_k, where p_h = A000040(h), then a(n) = (k-i), a(1) = 0 by convention.
  • A243062 (program): Permutation of natural numbers, a composition of A048673 and A241909: a(n) = A241909(A048673(n)).
  • A243065 (program): Permutation of natural numbers, the odd bisection of A241909 halved; equally, a composition of A064216 and A241909: a(n) = A241909(A064216(n)).
  • A243066 (program): Permutation of natural numbers, the even bisection of A241909 incremented by one and halved; equally, a composition of A241909 and A048673: a(n) = A048673(A241909(n)).
  • A243067 (program): Integers from 0 to A000120(n)-1 followed by integers from 0 to A000120(n+1)-1 and so on, starting with n=1.
  • A243071 (program): Permutation of nonnegative integers: a(1) = 0, a(2) = 1, a(2n) = 2*a(n), a(2n+1) = 1 + 2*a(A064989(2n+1)).
  • A243074 (program): a(1) = 1, a(n) = n/p^(k-1), where p = largest prime dividing n and p^k = highest power of p dividing n.
  • A243094 (program): Cardinality of the Weyl alternation set corresponding to the zero-weight in the representation of the Lie algebra sp(2n) whose highest weight is the second fundamental weight.
  • A243099 (program): A002061 and A000217 interleaved.
  • A243101 (program): a(n) = (sum_{k=0}^{n-1}(4*k^3-1)*C(n-1,k)*C(n+k,k))/n^2, where C(m,k) denotes the binomial coefficient m!/(k!*(m-k)!).
  • A243103 (program): Product of numbers m with 2 <= m <= n whose prime divisors all divide n.
  • A243107 (program): Number of terms in a bordered skew determinant.
  • A243109 (program): a(n) is the largest number smaller than n and having the same Hamming weight as n, or n if no such number exist.
  • A243111 (program): Difference between the smallest triangular number >= n-th prime and the n-th prime.
  • A243116 (program): a(n) = Sum_{k=0..n} C(n + 2*k, 3*k) * C(3*k, 2*k).
  • A243128 (program): Squarefree numbers k such that 4k <= sum of squarefree divisors of 4k.
  • A243129 (program): a(n) = sigma(d(d(d(n)))), where d(n) is the number of divisors of n.
  • A243130 (program): 1024*n^10 - 2304*n^8 + 1792*n^6 - 560*n^4 + 60*n^2 - 1.
  • A243131 (program): a(n) = 16*n^5 - 20*n^3 + 5*n.
  • A243132 (program): 32*n^6 - 48*n^4 + 18*n^2 - 1.
  • A243133 (program): 64*n^7 - 112*n^5 + 56*n^3 - 7*n.
  • A243134 (program): 128*n^8 - 256*n^6 + 160*n^4 - 32*n^2 + 1.
  • A243135 (program): 256*n^9 - 576*n^7 + 432*n^5 - 120*n^3 + 9*n.
  • A243136 (program): 512*n^10 - 1280*n^8 + 1120*n^6 - 400*n^4 + 50*n^2 - 1.
  • A243138 (program): n^2 + 15*n + 13.
  • A243139 (program): a(n) = 2^prime(n) + prime(n).
  • A243153 (program): Larger of two consecutive primes whose difference is a semiprime.
  • A243155 (program): Larger of the two consecutive primes whose positive difference is a cube.
  • A243156 (program): G.f. satisfies: x = A(x) * (1 - A(x)) / (1 - A(x) - A(x)^3) such that A(0) = 1.
  • A243173 (program): Numbers of the form x^2+15y^2.
  • A243175 (program): Numbers of the form x^2 + xy + 7y^2.
  • A243177 (program): Numbers of the form 3x^2+2xy+3y^2.
  • A243182 (program): Numbers of the form 2x^2+2xy+5y^2.
  • A243183 (program): Primes of the form 2x^2+2xy+5y^2.
  • A243196 (program): Number of primorial numbers < 10^n.
  • A243201 (program): Odd octagonal numbers indexed by triangular numbers.
  • A243203 (program): Terms of a particular integer decomposition of N^N.
  • A243204 (program): Expansion of 2*x/((1-sqrt(1-2*(1-sqrt(1-4*x))))*sqrt(1-2*(1-sqrt(1-4*x))) * sqrt(1-4*x)).
  • A243223 (program): Number of partitions of n into positive summands in arithmetic progression with common difference 3.
  • A243224 (program): Number of odd divisors d of n such that d > 1 and d(1+d/3)/2 <= n <= 3d(d-1)/2.
  • A243225 (program): Numbers which are not the sum of positive integers in an arithmetic progression with common difference 3.
  • A243227 (program): G.f.: Sum_{n>=0} n^(2*n) * x^n / (1 + n^2*x)^n.
  • A243239 (program): a(n) = 10^n mod 97.
  • A243256 (program): Smallest distance of the n-th Fibonacci number to the set of all square integers.
  • A243271 (program): Number of graphs with n nodes that are Hamiltonian and distance-regular.
  • A243280 (program): Expansion of log’(1/2-sqrt((5*x+2*sqrt(1-4*x)-2)/x)/2).
  • A243282 (program): Partial sums of the characteristic function for A070003.
  • A243283 (program): One more than the partial sums of the characteristic function of A070003.
  • A243284 (program): a(n) = the number of distinct ways of writing such products m = k^2 * j, 0 < j <= k, (j and k natural numbers) that m is in range [1,n]; Partial sums of A102354.
  • A243285 (program): Number of integers 1 <= k <= n which are not divisible by the square of their largest noncomposite divisor.
  • A243289 (program): n minus the index of the greatest prime dividing n-th squarefree number: a(n) = n - A243290(n).
  • A243290 (program): The index of the greatest prime dividing the n-th squarefree number: a(n) = A061395(A005117(n)).
  • A243291 (program): Difference between n and the index of its largest prime factor: a(n) = n - A061395(n).
  • A243293 (program): Number of factorials < 10^n.
  • A243296 (program): Exponent of 2 in (A002110(n)/2)^2-1
  • A243302 (program): Consider a triangular Go board graph with side length n; remove i nodes and let j be the number of nodes in the largest connected subgraph remaining; then a(n) = minimum (i + j).
  • A243305 (program): a(n) = 2^phi(n)+1 = A066781(n)+1.
  • A243306 (program): 2^phi(n) - phi(n).
  • A243307 (program): a(n) = 2^phi(n) + phi(n).
  • A243308 (program): Decimal expansion of h_3, a constant related to certain evaluations of the gamma function from elliptic integrals.
  • A243310 (program): Smallest k such that both prime(k)*prime(k+1) +/- 2^n are prime, or 0 if no such k exists.
  • A243319 (program): Number of simple connected graphs with n nodes that are bipartite and distance regular.
  • A243322 (program): Number of simple connected graphs with n nodes that are distance regular and Eulerian.
  • A243328 (program): Number of simple connected graphs with n nodes that are integral and bipartite.
  • A243329 (program): Number of simple connected graphs with n nodes that are integral and distance regular.
  • A243330 (program): Number of simple connected graphs with n nodes that are integral and Eulerian.
  • A243331 (program): Number of simple connected graphs with n nodes that are integral and planar.
  • A243332 (program): Number of simple connected graphs with n nodes that are integral and triangle-free.
  • A243333 (program): Number of simple connected graphs with n nodes that are integral and K_4 free.
  • A243334 (program): Number of simple connected graphs with n nodes that are distance regular and triangle-free.
  • A243338 (program): Number of simple connected graphs with n nodes that are trees and not integral.
  • A243339 (program): Number of simple connected graphs with n nodes that are distance regular and K_4 free.
  • A243340 (program): Decimal expansion of 4*L/(3*Pi), a constant related to the asymptotic evaluation of the number of primes of the form a^2+b^4, where L is Gauss’ lemniscate constant.
  • A243348 (program): Difference between the n-th squarefree number and n: a(n) = A005117(n) - n.
  • A243349 (program): Difference between the n-th squarefree number and the index of its largest prime factor.
  • A243351 (program): Difference between 2n and the n-th squarefree number: a(n) = 2n - A005117(n).
  • A243352 (program): If n is k-th squarefree number [i.e., n = A005117(k)], a(n) = 2k-1; otherwise, when n is k-th nonsquarefree number [i.e., n = A013929(k)], a(n) = 2k.
  • A243353 (program): Permutation of natural numbers which maps between the partitions as encoded in A227739 (binary based system, zero-based) to A112798 (prime-index based system, one-based).
  • A243354 (program): Permutation of natural numbers which maps between the partitions as encoded in A112798 (prime-index based system, one-based) to A227739 (binary based system, zero-based).
  • A243359 (program): Number of steps it takes the terms in A029742 and their reversals to reach the value 9 when the smaller term is successively subtracted from the larger term.
  • A243367 (program): Primes p such that p^2+10 is prime.
  • A243383 (program): Number of length n+3 0..2 arrays with no four elements in a row with pattern abba (with a!=b) and new values 0..2 introduced in 0..2 order.
  • A243399 (program): a(0) = 1, a(1) = 19; for n > 1, a(n) = 19*a(n-1) + a(n-2).
  • A243427 (program): Floored (rational) values of sqrt(xy) such that sqrt(x) + sqrt(y) = sqrt(xy).
  • A243436 (program): Numbers n such that n^2-n-1 is semiprime.
  • A243449 (program): Primes of the form n^2 + 14.
  • A243450 (program): Primes of the form n^2 + 15.
  • A243451 (program): Primes of the form n^2 + 16.
  • A243456 (program): a(n+6) = 6*a(n+4) - 12*a(n+2) + 8*a(n), a(0)..a(5) = 8,0,9,0,8,0.
  • A243469 (program): Denominators of the rational convergents to the periodic continued fraction 1/(2 + 1/(7 + 1/(2 + 1/(7 + …)))).
  • A243470 (program): Numerators of the rational convergents to the periodic continued fraction 1/(2 + 1/(7 + 1/(2 + 1/(7 + …)))).
  • A243473 (program): a(n) = numerator(sigma(n)/n) - denominator(sigma(n)/n) where sigma(n) = sum of divisors of n.
  • A243485 (program): Sum of all the products formed by multiplying the corresponding smaller and larger parts of the Goldbach partitions of n.
  • A243499 (program): Product of parts of integer partitions as enumerated in the table A125106.
  • A243501 (program): Permutation of even numbers: a(n) = 2*A048673(n).
  • A243502 (program): Permutation of even numbers: a(n) = 2 * A064216(n).
  • A243503 (program): Sums of parts of partitions (i.e., their sizes) as ordered in the table A241918: a(n) = Sum_{i=A203623(n-1)+2..A203623(n)+1} A241918(i).
  • A243504 (program): Product of parts of integer partitions as ordered by the table A241918: a(n) = Product_{i=A203623(n-1)+2..A203623(n)+1} A241918(i).
  • A243505 (program): Permutation of natural numbers, take the odd bisection of A122111 and divide the largest prime factor out: a(n) = A052126(A122111(2n-1)).
  • A243506 (program): Permutation of natural numbers: a(n) = A048673(A122111(n)).
  • A243508 (program): Decimal expansion of the real positive root of 48x^4 + 16x^3 - 27x^2 - 18x - 3 = 0.
  • A243513 (program): Number of length n+2 0..4 arrays with no three elements in a row with pattern aba or abb (with a!=b) and new values 0..4 introduced in 0..4 order.
  • A243514 (program): Number of length n+2 0..5 arrays with no three elements in a row with pattern aba or abb (with a!=b) and new values 0..5 introduced in 0..5 order.
  • A243515 (program): Number of length n+2 0..6 arrays with no three elements in a row with pattern aba or abb (with a!=b) and new values 0..6 introduced in 0..6 order.
  • A243516 (program): Number of length n+2 0..7 arrays with no three elements in a row with pattern aba or abb (with a!=b) and new values 0..7 introduced in 0..7 order.
  • A243517 (program): Number of length n+2 0..8 arrays with no three elements in a row with pattern aba or abb (with a!=b) and new values 0..8 introduced in 0..8 order.
  • A243520 (program): Numbers that are congruent to {0, 8} mod 11.
  • A243543 (program): Smallest number whose list of divisors contains n distinct digits (in base 10).
  • A243544 (program): Primes p such that p^2 - p + 1 is semiprime.
  • A243546 (program): Number of simple connected graphs with n nodes that are distance regular and have no subgraph isomorphic to the bowtie graph.
  • A243548 (program): Number of simple connected graphs with n nodes that are integral and have no subgraph isomorphic to the bowtie graph.
  • A243554 (program): Number of simple connected graphs with n nodes that are distance-regular and have no subgraph isomorphic to bull graph.
  • A243556 (program): Number of simple connected graphs with n nodes that are integral and have no subgraph isomorphic to bull graph.
  • A243561 (program): Number of simple connected graphs with n nodes that are distance regular and have no subgraph isomorphic to diamond graph.
  • A243564 (program): Number of simple connected graphs with n nodes that are integral and have no subgraph isomorphic to diamond graph.
  • A243577 (program): Integers of the form 8k+7 that can be written as a sum of four distinct ‘almost consecutive’ squares.
  • A243578 (program): Integers n of the form 8k+7 that are sum of distinct squares of the form m, m+1, m+2, m+4, where m == 1 (mod 4).
  • A243579 (program): Integers of the form 8k+7 that can be written as a sum of four distinct squares of the form m, m+2, m+4, m+5, where m == 1 (mod 4).
  • A243580 (program): Integers of the form 8k + 7 that can be written as a sum of four distinct squares of the form m, m + 1, m + 3, m + 5, where m == 2 (mod 4).
  • A243581 (program): Integers of the form 8k + 7 that can be written as a sum of four distinct squares of the form m, m + 2, m + 3, m + 4, where m == 2 (mod 4).
  • A243585 (program): Expansion of x*log’(C(C(x)-1)-1), C(x) = (1-sqrt(1-4*x))/(2*x).
  • A243594 (program): Triangle read by rows: T(n,k) = coefficient of [x^(n-k)] in the expansion of the polynomial (x+n)^n.
  • A243597 (program): Decimal expansion of the fraction of the full solid angle subtended by a cone with the polar angle of 1 radian.
  • A243600 (program): Number of length n+2 0..3 arrays with no three elements in a row with pattern aba (with a!=b) and new values 0..3 introduced in 0..3 order.
  • A243618 (program): Table read by antidiagonals: T(n,k) is circle curvature in nested Pappus chains (see Comments for details).
  • A243624 (program): Numbers that are the sum of 2 different primes, with repetitions.
  • A243626 (program): Expansion of (1-3*x-sqrt(x^2-10*x+1))/(4*x+2).
  • A243627 (program): Primes which are the sum of two consecutive squarefree numbers.
  • A243631 (program): Square array of Narayana polynomials N_n evaluated at the integers, A(n,k) = N_n(k), n>=0, k>=0, read by antidiagonals.
  • A243632 (program): Expansion of ((1-sqrt(1-4*x))/2-sqrt(((-sqrt(1-4*x)-11)*(1-sqrt(1-4*x)))/4+1)+1)/4.
  • A243633 (program): Expansion of (4*x^3-6*x^2+4*x-1)/(5*x^3-8*x^2+5*x-1).
  • A243634 (program): Number of length n+2 0..n arrays with no three unequal elements in a row and new values 0..n introduced in 0..n order.
  • A243635 (program): Number of length n+2 0..4 arrays with no three unequal elements in a row and new values 0..4 introduced in 0..4 order.
  • A243644 (program): Expansion of x*log’(((1-sqrt(1-4*x))/2-sqrt(((-sqrt(1-4*x)-11)*(1-sqrt(1-4*x)))/4+1)+1)/4).
  • A243645 (program): Number of ways two L-tiles can be placed on an n X n square.
  • A243651 (program): Nonnegative integers of the form x^2+11y^2.
  • A243658 (program): a(0)=0; thereafter a(n) = noz(n+a(n-1)), where noz(n) = A004719(n).
  • A243659 (program): Number of Sylvester classes of 3-packed words of degree n.
  • A243660 (program): Triangle read by rows: the x = 1+q Narayana triangle at m=2.
  • A243661 (program): Triangle read by rows: the x = 1+q Narayana triangle at m=3.
  • A243662 (program): Triangle read by rows: the reversed x = 1+q Narayana triangle at m=2.
  • A243663 (program): Triangle read by rows: the reversed x = 1+q Narayana triangle at m=3.
  • A243664 (program): Number of 3-packed words of degree n.
  • A243667 (program): Number of Sylvester classes of 4-packed words of degree n.
  • A243668 (program): Number of Sylvester classes of 5-packed words of degree n.
  • A243717 (program): Number of inequivalent (mod D_4) ways to place 2 nonattacking knights on an n X n board.
  • A243722 (program): Number of length n+2 0..3 arrays with no three unequal elements in a row and no three equal elements in a row and new values 0..3 introduced in 0..3 order.
  • A243757 (program): a(n) = Product_{i=1..n} A060904(i).
  • A243758 (program): a(n) = Product_{i=1..n} A234959(i).
  • A243759 (program): Triangle T(m,k): exponent of the highest power of 3 dividing the binomial coefficient binomial(m,k).
  • A243760 (program): Expansion of (sqrt(8*x+4*sqrt(1-4*x)-3)-1)/(2*sqrt(1-4*x)-2).
  • A243762 (program): 4*n^3 + 5.
  • A243763 (program): Expansion of q * phi(q)^3 * psi(q^2)^4 in powers of q where phi(), psi() are Ramanujan theta functions.
  • A243764 (program): Expansion of -((2*sqrt(1-4*x)-2)*x)/(sqrt(8*x+4*sqrt(1-4*x)-3)-1).
  • A243786 (program): Number of graphs with n nodes that are chordal and integral.
  • A243791 (program): Number of simple connected graphs with n nodes that are Eulerian and have no subgraph isomorphic to the open-bowtie graph.
  • A243792 (program): Number of simple connected graphs with n nodes that are integral and have no subgraph isomorphic to the open-bowtie graph.
  • A243800 (program): Number of simple connected graphs on n nodes whose maximum size of an independent edge set is equal to 2.
  • A243806 (program): G.f.: exp( Integral Sum_{n>=1} (n+1)!*x^(n-1) / Product_{k=1..n} (1-k*x) dx ).
  • A243807 (program): G.f.: exp( Integral Sum_{n>=1} n!*n^(n-1)*x^(n-1) / Product_{k=1..n} (1+k*n*x) dx ).
  • A243809 (program): G.f.: exp( Integral Sum_{n>=1} n!*n^n*x^(n-1) / Product_{k=1..n} (1+k*n*x) dx ).
  • A243811 (program): Numbers n such that 2*n+3 and 2*n+5 are both prime.
  • A243813 (program): Table read by antidiagonals, T(n,k) is circle curvature (rounded down) in a variation of nested Pappus chains (see comments for details).
  • A243814 (program): Expansion of -(x*(1-sqrt((2*(1-sqrt(4*x^2+1)))/x+1)))/(1-sqrt(4*x^2+1)) - 1.
  • A243815 (program): Number of length n words on alphabet {0,1} such that the length of every maximal block of 0’s (runs) is the same.
  • A243816 (program): Expansion of (x*sqrt(4*x^2+1)-x)/(x*sqrt(-(2*sqrt(4*x^2+1)-x-2)/x) + sqrt(4*x^2+1)-x-1).
  • A243822 (program): Number of “semidivisors” of n, numbers m < n that do not divide n but divide n^e for some integer e > 1.
  • A243825 (program): Numbers n such that every divisor greater than 1 contains the digit 0.
  • A243860 (program): 2^(n+1) - (n-1)^2.
  • A243863 (program): G.f. satisfies: A(x) = 1/(1 - x*A(-x)^2).
  • A243866 (program): Table T(n,k), n>=1, k>=1, read by antidiagonals: T(n,k) = number of equivalence classes of ways of placing one 1 X 1 tile in an n X k rectangle under all symmetry operations of the rectangle.
  • A243869 (program): Expansion of x^4/[(1+x)*Product_{k=1..3} (1-k*x)].
  • A243883 (program): Numerator of circle radius r(n) at constant unit length sagitta and chord length = n.
  • A243887 (program): (p^2 - 3)/2 for odd primes p.
  • A243888 (program): Primes of the form 2*n^2+26*n+11.
  • A243889 (program): Primes of the form 2*n^2+30*n+13.
  • A243890 (program): Primes of the form 2*n^2+38*n+17.
  • A243891 (program): Primes of the form 2*n^2 + 62*n + 29.
  • A243895 (program): a(n) = prime(n^2-1).
  • A243896 (program): a(n) = prime(n^2+1).
  • A243903 (program): Numbers n such that (number of primes <= n) is greater than or equal to (number of semiprimes <= n).
  • A243905 (program): Multiplicative order of 2 modulo prime(n)^2 for n >= 2.
  • A243906 (program): (Number of semiprimes <= n) - (number of primes <= n).
  • A243907 (program): Numbers that can be expressed as n*m + (n-1)*(m-1), n = 2, 3, … , m = n, n+1, n+2, … in at least two different ways. Ordered increasingly.
  • A243910 (program): Least number k>0 such that 3^k contains exactly n different digits.
  • A243915 (program): a(n) = sigma(omega(n)).
  • A243918 (program): a(n) = Sum_{k=0..n} binomial(n,k) * (1 + 2^k)^k.
  • A243937 (program): Even numbers n>=6 for which lpf(n-1) > lpf(n-3), where lpf = least prime factor.
  • A243939 (program): Expansion of f(-q)^10 / f(-q^5)^2 in power of q where f() is a Ramanujan theta function.
  • A243943 (program): a(n) = A006442(n)^2.
  • A243944 (program): a(n) = A084768(n)^2.
  • A243945 (program): a(n) = Sum_{k=0..n} C(2*k, k)^2 * C(n+k, n-k).
  • A243946 (program): Expansion of sqrt( (1+x + sqrt(1-18*x+x^2)) / (2*(1-18*x+x^2)) ).
  • A243947 (program): Expansion of g.f. sqrt( (1+x - sqrt(1-18*x+x^2)) / (10*x*(1-18*x+x^2)) ).
  • A243948 (program): G.f.: Sum_{n>=0} x^n / (1-x)^(2*n+1) * [Sum_{k=0..n} C(n,k)^2 * x^k] * [Sum_{k=0..n} C(n,k)^2 * 2^k * x^k].
  • A243949 (program): Squares of the central Delannoy numbers: a(n) = A001850(n)^2.
  • A243953 (program): E.g.f.: exp( Sum_{n>=1} A000108(n-1)*x^n/n ), where A000108(n) = binomial(2*n,n)/(n+1) forms the Catalan numbers.
  • A243954 (program): E.g.f.: A(x) = x/Series_Reversion(x*G(x)) where G(x) = Sum_{n>=0} n^n*x^n/n!.
  • A243957 (program): Primes of the form 2*n^2+66*n+31.
  • A243963 (program): a(n) = n*4^n*(-Z(1-n, 1/4)/2 + Z(1-n, 3/4)/2 - Z(1-n, 1)*(1 - 2^(-n)))) for n > 0 and a(0) = 0, where Z(n, c) is the Hurwitz zeta function.
  • A243980 (program): Four times the sum of all divisors of all positive integers <= n.
  • A243982 (program): Number of divisors of n minus the number of parts in the symmetric representation of sigma(n).
  • A243987 (program): Triangle read by rows: T(n, k) is the number of divisors of n that are less than or equal to k for 1 <= k <= n.
  • A243989 (program): Rounded down ratio of a lune area and a unit circle one, the lune is bounded by two unit circles whose centers are separated by a distance 1/n.
  • A244003 (program): A(n,k) = k^Fibonacci(n); square array A(n,k), n>=0, k>=0, read by antidiagonals.
  • A244004 (program): a(n) = Sum_{k=0..n} binomial(n,k) * (1 + 3^k)^k.
  • A244009 (program): Decimal expansion of 1 - log(2).
  • A244035 (program): a(n) = Sum_{d|n} Sum{t|d} moebius(d/t)*binomial(3*t,t)/(3*d^2).
  • A244036 (program): a(n) = Sum_{d|n} Sum{t|d} (n/d)*moebius(d/t)*binomial(3*t,t)/(3*d^2).
  • A244037 (program): Numbers of the form x^2+14y^2.
  • A244038 (program): a(n) = 4^n*binomial(3*n/2,n).
  • A244039 (program): a(n) = 2^(2*n-1)*( binomial(3*n/2,n) + binomial((3*n-1)/2,n) ).
  • A244040 (program): Sum of digits of n in fractional base 3/2.
  • A244041 (program): Sum of digits of n written in fractional base 4/3.
  • A244042 (program): In ternary representation of n, replace 2’s with 0’s.
  • A244048 (program): Antisigma(n) minus the sum of remainders of n mod k, for k = 1,2,3,…,n.
  • A244049 (program): Sum of all proper divisors of all positive integers <= n.
  • A244050 (program): Partial sums of A243980.
  • A244056 (program): Maximum score achievable in the 2048 game on an n X n grid.
  • A244058 (program): n-th term of the ‘Reverse and Add!’ sequence starting with n.
  • A244059 (program): Initial digit of the decimal expansion of n^(n^(n^n)) or n^^4 (in Don Knuth’s up-arrow notation).
  • A244063 (program): Number of prime factors (with multiplicity) of the number of distinct prime factors of n; i.e., Omega(omega(n)).
  • A244075 (program): Numbers of nonprime digits between successive single-digit primes in the decimal expansion of e (A001113).
  • A244082 (program): a(n) = 32*n^2.
  • A244083 (program): a(n) = numerator( n^n/(2*n)! ).
  • A244084 (program): a(n) = denominator( n^n/(2*n)! ).
  • A244087 (program): Numbers n such that 4*n+3 and 8*n+7 are prime.
  • A244088 (program): Decimal expansion of 1/2+2/sqrt(13), a constant related to the asymptotic evaluation of the number of self-avoiding rook paths joining opposite corners on a 3 X n chessboard.
  • A244089 (program): Decimal expansion of sqrt((3+sqrt(13))/2), a constant related to the asymptotic evaluation of the number of self-avoiding rook paths joining opposite corners on a 3 X n chessboard.
  • A244098 (program): Total number of divisors of all the ordered prime factorizations of an integer.
  • A244116 (program): Triangle read by rows: coefficients T(n,k) of a binomial decomposition of 1 as Sum_{k=0..n} T(n,k)*binomial(n,k).
  • A244117 (program): Triangle read by rows: terms of a binomial decomposition of 1 as Sum(k=0..n)T(n,k).
  • A244118 (program): Triangle read by rows: coefficients T(n,k) of a binomial decomposition of 1 as Sum_{k=0..n} T(n,k)*binomial(n,k).
  • A244119 (program): Triangle read by rows: terms of a binomial decomposition of 1 as Sum(k=0..n)T(n,k).
  • A244120 (program): Triangle read by rows: coefficients T(n,k) of a binomial decomposition of n^n as Sum(k=0..n)T(n,k)*binomial(n,k).
  • A244121 (program): Triangle read by rows: terms T(n,k) of a binomial decomposition of n^n as Sum(k=0..n)T(n,k).
  • A244124 (program): Triangle read by rows: coefficients T(n,k) of a binomial decomposition of 2^n-1 as Sum(k=0..n)T(n,k)*binomial(n,k).
  • A244125 (program): Triangle read by rows: terms T(n,k) of a binomial decomposition of 2^n-1 as Sum(k=0..n)T(n,k).
  • A244126 (program): Triangle read by rows: coefficients T(n,k) of a binomial decomposition of 2^n-1 as Sum(k=0..n)T(n,k)*binomial(n,k).
  • A244127 (program): Triangle read by rows: terms T(n,k) of a binomial decomposition of 2^n-1 as Sum(k=0..n)T(n,k).
  • A244128 (program): Triangle read by rows: coefficients T(n,k) of a binomial decomposition of 0^(n-1) as Sum(k=0..n)T(n,k)*binomial(n,k).
  • A244129 (program): Triangle read by rows: terms of a binomial decomposition of 0^(n-1) as Sum(k=0..n)T(n,k).
  • A244130 (program): Triangle read by rows: coefficients T(n,k) of a binomial decomposition of n as Sum(k=0..n)T(n,k)*binomial(n,k).
  • A244131 (program): Triangle read by rows: terms T(n,k) of a binomial decomposition of n as Sum(k=0..n)T(n,k).
  • A244132 (program): Triangle read by rows: coefficients T(n,k) of a binomial decomposition of n as Sum(k=0..n)T(n,k)*binomial(n,k).
  • A244133 (program): Triangle read by rows: terms T(n,k) of a binomial decomposition of n as Sum(k=0..n)T(n,k).
  • A244138 (program): Triangle read by rows: coefficients T(n,k) of a binomial decomposition of n*(n-1) as Sum(k=0..n)T(n,k)*binomial(n,k).
  • A244139 (program): Triangle read by rows: terms T(n,k) of a binomial decomposition of n*(n-1) as Sum(k=0..n)T(n,k).
  • A244144 (program): Alternating sum of digits of n^n.
  • A244148 (program): The number of ways one can assign values to n arrays a_{1},…,a_{n} of increasing size (size of a_{1} is 1, size of a_{2} is 2, …, size of a_{n} is n) using the numbers 1, …, n*(n+1)/2, distinctly, such that the positions of array a_{i} can only be assigned values in the interval ((n+1)-i),… , (n*(n+1)/2-(n-i)).
  • A244149 (program): a(n) = 2*(n*Denominator(((n-1)*(n^2)+2^(n+1)-4)/(2*n))-n)/n+1.
  • A244151 (program): 0-additive sequence: start with a(1) = 2; thereafter, a(n) = smallest number not already in sequence which is not the sum of any previous two terms.
  • A244153 (program): Permutation of natural numbers, the odd bisection of A156552 halved; equally, a composition of A064216 and A156552: a(n) = A156552(A064216(n)).
  • A244154 (program): Permutation of natural numbers: a(0) = 1, a(1) = 2, a(2n) = A254049(a(n)), a(2n+1) = 3*a(n)-1; composition of A048673 and A005940.
  • A244160 (program): a(0)=0, and for n >= 1, a(n) = the largest k such that k-th Catalan number <= n.
  • A244174 (program): Number of compositions of 3n in which the minimal multiplicity of parts equals n.
  • A244189 (program): a(n) = most common final digit for a prime with n digits, or 0 if there is a tie.
  • A244191 (program): a(n) = most common final digit for a prime < 10^n, or 0 if there is a tie.
  • A244209 (program): The total number of unit circles (centered at sites of a square lattice with constant 2) intersecting a circle of radius n centered at (0,0).
  • A244210 (program): First differences of A244209.
  • A244213 (program): Inverse binomial transform of -2 followed by A000032(n+1).
  • A244214 (program): a(n) = binomial(2*c-1, c-1) (mod c^3), where c is the n-th composite.
  • A244216 (program): Numbers n that are at least twice the size the largest Catalan number less than or equal to n.
  • A244217 (program): Numbers n less than twice the largest Catalan number that is less than or equal to n.
  • A244220 (program): Binary complement of Greedy Catalan Base reduced modulo 2: a(n) = 1 - (A014418(n) modulo 2).
  • A244221 (program): Parity of Greedy Catalan Base representation for n: a(n) = A014418(n) reduced modulo 2.
  • A244224 (program): a(n) = Number of nonnegative integers 0 <= k <= n, which have an even representation in Greedy Catalan Base (A014418).
  • A244225 (program): a(n) = Number of nonnegative integers 0 <= k <= n, which have an odd representation in Greedy Catalan Base (A014418).
  • A244226 (program): Length of runs in A244221 (Greedy Catalan Base, A014418, reduced modulo 2).
  • A244229 (program): a(n) = Number of integers 0 < k <= n, which have an even representation in Greedy Catalan Base (A014418).
  • A244230 (program): a(n) is the least k such that A197433(k) >= n.
  • A244235 (program): Number of Dyck paths of semilength n having exactly one occurrence of the consecutive pattern UDDU.
  • A244239 (program): Number of partitions of n into 3 parts such that every i-th smallest part (counted with multiplicity) is different from i.
  • A244276 (program): Expansion of q^(-1/4) * eta(q)^8 * eta(q^4)^2 / eta(q^2)^5 in powers of q.
  • A244279 (program): Numerators of the n-th iteration of the alternating continued fraction of the positive integers, initiated with (1 + …).
  • A244280 (program): Denominators of the n-th iteration of the alternating continued fraction of the positive integers, initiated with (1 + …).
  • A244307 (program): Sum over each antidiagonal of A244306.
  • A244309 (program): a(n) = F(n)^3 - F(n)^2, where F(n) is the n-th Fibonacci number (A000045).
  • A244310 (program): a(n) = L(n)^3 - L(n)^2, where L(n) is the n-th Lucas number (A000032).
  • A244317 (program): n occurs A014138(n) times.
  • A244325 (program): Floor(antisigma(n) / n), where antisigma(n) = A024816(n) = the sum of the non-divisors of n that are between 1 and n.
  • A244327 (program): a(n) = floor((n*(n+1)/2) / sigma(n)) = floor(A000217(n) / A000203(n)).
  • A244328 (program): a(1) = a(2) = 0; for n >= 3: a(n) = floor((n*(n+1)/2) / antisigma(n)) = floor(A000217(n) / A024816(n)).
  • A244329 (program): Floor(antisigma(n) / sigma(n)) = floor(A024816(n) / A000203(n)).
  • A244331 (program): Number of binary digits in the high-water marks of the terms of the continued fraction of the base-2 Champernowne constant.
  • A244334 (program): Decimal expansion of 64/169, the upper bound (as given by S. Finch) of the 2-dimensional simultaneous Diophantine approximation constant.
  • A244335 (program): Decimal expansion of 1/(2*(Pi-2)), the upper bound of the 3-dimensional simultaneous Diophantine approximation constant.
  • A244339 (program): Expansion of (-2 * a(q) + 3*a(q^2) + 2*a(q^4)) / 3 in powers of q where a() is a cubic AGM theta function.
  • A244342 (program): a(n) = phi(n)*h(n) where phi() is the Euler totient function, A000010, and h() is A092089.
  • A244345 (program): Decimal expansion of xi_3 = 5*G, the volume of an ideal hyperbolic cube, where G is Gieseking’s constant.
  • A244346 (program): Decimal expansion of 56/13, the Korn constant for the sphere.
  • A244352 (program): a(n) = Pell(n)^3 - Pell(n)^2, where Pell(n) is the n-th Pell number (A000129).
  • A244360 (program): Total number of toothpicks after n-th stage in the toothpick structure of the symmetric representation of half sigma in the first octant (without the axis x and without the main diagonal).
  • A244361 (program): Number of toothpicks added at n-th stage in the toothpick structure of the symmetric representation of half sigma in the first octant (without the axis x and without the main diagonal).
  • A244362 (program): Total number of toothpicks after n-th stage in the toothpick structure of the symmetric representation of sigma in the first quadrant (without the axes x and y).
  • A244363 (program): Number of toothpicks added at n-th stage in the toothpick structure of the symmetric representation of sigma in the first quadrant (without the axis x and y).
  • A244367 (program): Main diagonal of A244580.
  • A244370 (program): Total number of toothpicks after n-th stage in the toothpick structure of the symmetric representation of sigma in the four quadrants.
  • A244371 (program): Number of toothpicks added at n-th stage in the toothpick structure of the symmetric representation of sigma in the four quadrants.
  • A244375 (program): Expansion of (a(q) + 3*a(q^2) - 4*a(q^4)) / 6 in powers of q where a() is a cubic AGM theta function.
  • A244396 (program): a(n) = Sum_{k=1, n} phi(k)*index(k, n), with phi(k) the Euler totient A000010(k) and index(k,n) the position of 1/k in the n-th row of the Farey sequence of order k, A049805(n,k).
  • A244413 (program): Exponent of highest power of 8 dividing n.
  • A244414 (program): Remove highest power of 6 from n.
  • A244415 (program): Exponent of 4 appearing in the 4-adic value of 1/n, n >= 1, given in A240226(n).
  • A244416 (program): 6-adic value of 1/n for n >= 1.
  • A244417 (program): Exponents of 6 in appearing in the 6-adic value of 1/n, n>=1 (A244416).
  • A244418 (program): Triangle read by rows T(n,m) = n*m +(n-1)*(m-1), for n >= m >= 1.
  • A244419 (program): Coefficient triangle of polynomials related to the Dirichlet kernel. Rising powers. Riordan triangle ((1+z)/(1+z^2), 2*z/(1+z^2)).
  • A244420 (program): Numerators of coefficient triangle for expansion of x^n in terms of polynomials Todd(k, x) = T(2*k+1, sqrt(x))/sqrt(x) (A084930), with the Chebyshev polynomials of the first kind (type T).
  • A244422 (program): Quasi-Riordan triangle ((2-z)/(1-z), -z^2/(1-z)). Row reversed monic Chebyshev T-polynomials without vanishing columns.
  • A244430 (program): E.g.f.: exp( Sum_{n>=1} Fibonacci(n)*x^n/n ).
  • A244432 (program): E.g.f.: exp( Sum_{n>=1} Pell(n)*x^n/n ), where Pell(n) = A000129(n).
  • A244451 (program): E.g.f.: exp( Sum_{n>=1} Fibonacci(2*n)*x^n/n ).
  • A244465 (program): Expansion of f(-x^3, -x^5) in powers of x where f() is Ramanujan’s two-variable theta function.
  • A244468 (program): E.g.f.: Sum_{n>=0} Series_Reversion( x/exp(n*x) )^n / n!.
  • A244469 (program): a(0) = 0, thereafter, a(n) = 2^(2*n-1)*( binomial((3*n-1)/2,n) - binomial(3*n/2, n)/3 ).
  • A244472 (program): 2nd-largest term in n-th row of Stern’s diatomic triangle A002487.
  • A244473 (program): 3rd-largest term in n-th row of Stern’s diatomic triangle A002487.
  • A244477 (program): a(1)=3, a(2)=2, a(3)=1; thereafter a(n) = a(n-a(n-1)) + a(n-a(n-2)).
  • A244478 (program): a(0)=2, a(1)=0, a(2)=2; thereafter a(n) = a(n-1-a(n-1))+a(n-2-a(n-2)) unless a(n-1) <= n-1 or a(n-2) <= n-2 in which case the sequence terminates.
  • A244479 (program): A244478(n)/2.
  • A244490 (program): Triangle read by rows: T(n,k) (0 <= k <= n) = Sum_{i=0..[k/2]} (-1)^i*binomial(k,2*i)*(2*i-1)!!*n^(k-2*i).
  • A244491 (program): Number of minimal idempotent generating sets for the singular part P_n \ S_n of the partition monoid P_n.
  • A244492 (program): Triangle read by rows: T(n,k) (n>=2, 0 <= k <= n-2) = n!/(2^i*i!*k!), where k=n-2i (or 0 for entries with wrong parity).
  • A244494 (program): Number of quadratic balanced Boolean functions of n variables.
  • A244497 (program): Number of magic labelings of the prism graph I X C_5 with magic sum n.
  • A244505 (program): Greater of twin primes of (40n-23,40n-21).
  • A244506 (program): Number of ways to place the maximal number of points that can be placed on a j X j X j triangular grid, j=3n-2, so that no pair of them has distance sqrt(3).
  • A244507 (program): Square roots of A244506.
  • A244509 (program): Order of GL_2(p), the general linear group over F_p, where p runs through the primes.
  • A244525 (program): Expansion of f(-x^1, -x^7) in powers of x where f(, ) is Ramanujan’s general theta function.
  • A244540 (program): Expansion of phi(q) * (phi(q) + phi(q^2)) / 2 in powers of q where phi() is a Ramanujan theta function.
  • A244543 (program): Expansion of phi(q^2) * (phi(q) + phi(q^2)) / 2 in powers of q where phi() is a Ramanujan theta function.
  • A244544 (program): Expansion of (phi(q) + phi(q^2))^2 / 4 in powers of q where phi() is a Ramanujan theta function.
  • A244553 (program): Expansion of phi(q^2) * (phi(q) - phi(q^2)) / 2 in powers of q where phi() is a Ramanujan theta function.
  • A244554 (program): Expansion of phi(q) * (phi(q) - phi(q^2)) / 2 in powers of q where phi() is a Ramanujan theta function.
  • A244576 (program): Sum of all proper divisors of all positive integers <= prime(n).
  • A244578 (program): Sum of all aliquot divisors of all positive integers <= prime(n).
  • A244579 (program): Numbers n with the property that the number of parts in the symmetric representation of sigma(n) equals the number of divisors of n.
  • A244583 (program): a(n) = sum of all divisors of all positive integers <= prime(n).
  • A244584 (program): a(n) = n OR 3.
  • A244586 (program): a(n) = n OR 4.
  • A244587 (program): a(n) = n OR 5.
  • A244588 (program): a(n) = n OR 6.
  • A244590 (program): a(n) = sum( floor(k*n/8), k=1..7 ).
  • A244591 (program): Zero followed by the terms of A032924 arranged to give the unique path to the n-th node of a complete, rooted and ordered binary tree.
  • A244593 (program): Decimal expansion of z_c = phi^5 (where phi is the golden ratio), a lattice statistics constant which is the exact value of the critical activity of the hard hexagon model.
  • A244607 (program): Numbers k such that (product of digits of k) - 1 is prime.
  • A244611 (program): Expansion of (phi(q) + phi(q^2) - phi(q^3) - phi(q^6)) / 2 in powers of q where phi() is a Ramanujan theta function.
  • A244612 (program): a(n) = 1 if n is a square, -1 if n is six times a square, 0 if n < 1.
  • A244630 (program): a(n) = 17*n^2.
  • A244631 (program): 19*n^2.
  • A244632 (program): 23*n^2.
  • A244633 (program): a(n) = 26*n^2.
  • A244634 (program): 27*n^2.
  • A244635 (program): 29*n^2.
  • A244636 (program): a(n) = 30*n^2.
  • A244642 (program): Number of nonzero cells at n-th stage in some 2D reversible second order cellular automata (see comments for precise definition).
  • A244643 (program): Number of cells with state 1 at n-th stage in some 2D reversible second order cellular automata (see comments for precise definition).
  • A244644 (program): Consider the method used by Archimedes to determine the value of Pi (A000796). This sequence denotes the number of iterations of his algorithm which would result in a difference of less than 1/10^n from that of Pi.
  • A244663 (program): Binary representation of 4^n + 2^(n+1) - 1.
  • A244664 (program): Decimal expansion of sum_(n>=1) (H(n,2)/n^2) where H(n,2) = A007406(n)/A007407(n) is the n-th harmonic number of order 2.
  • A244668 (program): Numerators of (product of divisors of n / sum of divisors of n).
  • A244669 (program): Denominators of (product of divisors of n / sum of divisors of n).
  • A244694 (program): Number of length n+4 0..2 arrays with no five consecutive elements with pattern ababa or abbba (with a!=b) and new values 0..2 introduced in 0..2 order.
  • A244725 (program): a(n) = 5*n^3.
  • A244726 (program): 6*n^3.
  • A244727 (program): a(n) = 7*n^3.
  • A244728 (program): a(n) = 9*n^3.
  • A244729 (program): 10*n^3.
  • A244730 (program): a(n) = 2*n^4.
  • A244734 (program): Numerators of the triangle T(n,k) = (n*(n+1)/2 + k + 1)/(k+1) for n >= k >= 0.
  • A244735 (program): a(n) = (prime(n) mod 5) mod 2.
  • A244736 (program): Numbers k such that (prime(k) mod 5) is even.
  • A244737 (program): Numbers k such that (prime(k) mod 5) is odd.
  • A244738 (program): a(n) = (prime(n) mod 5) mod 3.
  • A244739 (program): Numbers k such that (prime(k) mod 5) == 0 (mod 3).
  • A244741 (program): Numbers k such that (prime(k) mod 5) == 2 (mod 3).
  • A244748 (program): Numbers k such that (product of digits of k)^2 + 1 is prime.
  • A244749 (program): 0-additive sequence: a(n) is the smallest number larger than a(n-1) that is not the sum of any subset of earlier terms, starting with initial values {2, 5}.
  • A244750 (program): 0-additive sequence: a(n) is the smallest number larger than a(n-1) which is not the sum of any subset of earlier terms, with initial values {0, 2, 3, 4}.
  • A244753 (program): a(n) = Sum_{k=0..n} C(n,k) * (n + 2^k)^k.
  • A244754 (program): a(n) = Sum_{k=0..n} C(n,k) * (1 + 2^k)^(n-k).
  • A244755 (program): a(n) = Sum_{k=0..n} C(n,k) * (1 + 3^k)^(n-k).
  • A244756 (program): a(n) = Sum_{k=0..n} C(n,k) * (2 + 3^k)^(n-k).
  • A244760 (program): a(n) = Sum_{k=0..n} C(n,k) * (1 + 3^k)^(n-k) * 2^k.
  • A244762 (program): a(n) = (5*3^n-2*n-1)/4.
  • A244763 (program): Prime numbers ending in the prime number 13.
  • A244764 (program): Prime numbers ending in the prime number 17.
  • A244765 (program): Prime numbers ending in the prime number 19.
  • A244766 (program): Prime numbers ending in the prime number 23.
  • A244767 (program): Prime numbers ending in the prime number 29.
  • A244768 (program): Prime numbers ending in the prime number 37.
  • A244769 (program): Prime numbers ending in the prime number 43.
  • A244770 (program): Prime numbers ending in the prime number 47.
  • A244771 (program): Prime numbers ending in the prime number 53.
  • A244772 (program): Prime numbers ending in the prime number 59.
  • A244773 (program): Prime numbers ending in the prime number 67.
  • A244774 (program): Prime numbers ending in the prime number 73.
  • A244775 (program): Prime numbers ending in the prime number 79.
  • A244776 (program): Prime numbers ending in the prime number 83.
  • A244777 (program): Prime numbers ending in the prime number 89.
  • A244778 (program): Prime numbers ending in the prime number 97.
  • A244789 (program): Number of length 1 0..n arrays with each partial sum starting from the beginning no more than one standard deviation from its mean.
  • A244796 (program): Number of moduli m such that (prime(n) mod m) = 1.
  • A244797 (program): Number of moduli m such that (prime(n) mod m) = 2.
  • A244798 (program): Number of moduli m such that (prime(n) mod m) = 3.
  • A244799 (program): Number of moduli m such that (prime(n) mod m) is odd, where 1 <= m < prime(n).
  • A244800 (program): Number of moduli m such that (prime(n) mod m) is even, where 1 <= m < prime(n).
  • A244802 (program): The 60-degree spoke (or ray) of a hexagonal spiral of Ulam.
  • A244803 (program): The 360 degree spoke (or ray) of a hexagonal spiral of Ulam.
  • A244804 (program): The 300 degree spoke (or ray) of a hexagonal spiral of Ulam.
  • A244805 (program): The 240 degree spoke (or ray) of a hexagonal spiral of Ulam.
  • A244806 (program): The 180 degree spoke (or ray) of a hexagonal spiral of Ulam.
  • A244820 (program): E.g.f.: Sum_{n>=0} exp(n*2^n*x) * x^n/n!.
  • A244821 (program): E.g.f.: Sum_{n>=0} exp(n*3^n*x) * x^n/n!.
  • A244822 (program): E.g.f.: Sum_{n>=0} exp(n*4^n*x) * x^n/n!.
  • A244840 (program): Denominators of the triangle T(n,k) = (n*(n+1)/2+k+1)/(k+1) for n >= k >= 0.
  • A244841 (program): 4^p - 3^p - 1, where p is prime.
  • A244842 (program): a(n) = (10^n - 1)*(10^n - 10)/90.
  • A244844 (program): Decimal expansion of 2F1(1, 1/4; 5/4; -1/4), where 2F1 is a Gaussian hypergeometric function.
  • A244845 (program): Binary representation of 4^n - 2^(n+1) - 1.
  • A244847 (program): Decimal expansion of rho_c = (5-sqrt(5))/10, the asymptotic critical density for the hard hexagon model.
  • A244854 (program): Decimal expansion of Pi^2/32.
  • A244855 (program): a(n) = Fibonacci(n)^4-1.
  • A244864 (program): a(n) = binomial(n+5,5) + 4*binomial(n+4,5) + 4*binomial(n+3,5) + binomial(n+2,5).
  • A244868 (program): Number of symmetric 5 X 5 matrices of nonnegative integers with zeros on the main diagonal and every row and column adding to n.
  • A244870 (program): Number of magic labelings with magic sum n of 2nd graph shown in link.
  • A244871 (program): Number of magic labelings with magic sum n of 3rd graph shown in link.
  • A244879 (program): Number of magic labelings of the cycle-of-loops graph LOOP X C_6 having magic sum n, where LOOP is the 1-vertex, 1-loop-edge graph.
  • A244881 (program): Expansion of (1 + 26*x + 109*x^2 + 109*x^3 + 26*x^4 + x^5) / (1 - x)^8.
  • A244882 (program): Expansion of (1 + 2*x + 2*x^2) / (1 - x)^6.
  • A244884 (program): Expansion of (-2 +x^2 +x -x*sqrt(1-2*x-3*x^2))/(-1 +x -sqrt(1-2*x-3*x^2)).
  • A244885 (program): Expansion of (1-6*x+12*x^2-8*x^3+x^4)/((1-2*x)^2*(1-3*x+x^2)).
  • A244886 (program): G.f.: (1-x+sqrt(1-2*x-3*x^2))/(1-3*x+x^2+x^3+(1-x^2)*sqrt(1-2*x-3*x^2)).
  • A244887 (program): Third column of triangle in A234950.
  • A244892 (program): a(n) = a(n-a(n-1)) with initial values 5,2,5,2.
  • A244893 (program): a(n) = a(n-a(n-1)) with initial values 2,3,2.
  • A244894 (program): Composite numbers n with the property that the symmetric representation of sigma(n) has two parts.
  • A244895 (program): Period 5: repeat [0, 1, 1, -1, -1].
  • A244904 (program): Number of length 1 0..n arrays with each partial sum starting from the beginning no more than sqrt(2) standard deviations from its mean
  • A244911 (program): Table read by antidiagonals: T(n,k) = n*k + T(n-1,k) for n >=1, T(0,k) = 1.
  • A244912 (program): Sum of leading digit in representations of n in bases 2,3,…,n.
  • A244919 (program): For odd prime p, largest k such that binomial(2p-1, p-1) is congruent to 1 modulo p^k.
  • A244928 (program): Decimal expansion of Ti_2(2-sqrt(3)), where Ti_2 is the inverse tangent integral function.
  • A244953 (program): a(n) = Sum_{i=0..n} (-i mod 4).
  • A244954 (program): Smallest positive multiple of n whose base-3 representation contains only 0’s and 1’s.
  • A244955 (program): Smallest positive multiple of n whose base-4 representation contains only 0’s and 1’s.
  • A244961 (program): Decimal equivalent of the binary string generated by the n X n antidiagonal matrix read by rows.
  • A244963 (program): a(n) = sigma(n) - n * Product_{p|n, p prime} (1 + 1/p).
  • A244964 (program): Number of distinct generalized pentagonal numbers dividing n.
  • A244967 (program): A141285(n) - 1.
  • A244970 (program): Total number of regions after n-th stage in the diagram of the symmetric representation of sigma on the four quadrants.
  • A244971 (program): Number of regions in the symmetric representation of sigma(n) on the four quadrants.
  • A244973 (program): a(n) = Sum_{k=0..n} C(n,k)^2*C(2k,k)(-1)^k, where C(n,k) denotes the binomial coefficient n!/(k!(n-k)!).
  • A244974 (program): Sum of numbers m <= n whose set of prime divisors is a subset of the set of prime divisors of n.
  • A244975 (program): (7^n - 2*n - 1)/4.
  • A244976 (program): Decimal expansion of Pi/(8*sqrt(2)).
  • A244977 (program): Decimal expansion of Pi/(12*sqrt(3)).
  • A244978 (program): Decimal expansion of Pi/32.
  • A244981 (program): Permutation of natural numbers: a(n) = A122111(A102750(n)) / 2.
  • A244988 (program): a(n) = n - A244989(n).
  • A244989 (program): Partial sums of A244992: a(1) = 0, and for n >= 1, a(n) = A244992(n) + a(n-1); Inverse function for A244991.
  • A244990 (program): After 1, numbers whose greatest prime factor is a prime with an even index; n such that A061395(n) is even.
  • A244991 (program): Numbers whose greatest prime factor is a prime with an odd index; n such that A006530(n) is in A031368.
  • A244992 (program): Characteristic function for A244991: a(n) = A000035(A061395(n)).
  • A245001 (program): Number of standard Young tableaux with n cells and 3 as last value in the first row.
  • A245019 (program): Number of ordered n-tuples of positive integers, whose minimum is 0 and maximum is 4.
  • A245020 (program): Number of ordered n-tuples of positive integers, whose minimum is 0 and maximum is 5.
  • A245023 (program): Number of cases of tie (no winner) in the n-person rock-paper-scissors game.
  • A245024 (program): Even numbers n for which lpf(n-1) < lpf(n-3), where lpf = least prime factor.
  • A245031 (program): Numbers m such that 3*m+1 and 8*m+1 are both squares.
  • A245032 (program): a(n) = 27*(n - 6)^2 + 4*(n - 6)^3 = ((n - 6)^2)*(4*n + 3).
  • A245033 (program): 4*(n + 7)^3 - 27*(n + 7)^2 = (4*n +1)*(n+7)^2.
  • A245034 (program): a(n) = prime(n)^2 - 4*prime(n).
  • A245035 (program): a(n) = (prime(n) - 7)^2 * (4*prime(n) - 1).
  • A245042 (program): Primes of the form (k^2+4)/5.
  • A245045 (program): Primes of the form (k^2+2)/6.
  • A245048 (program): Primes p such that p^2 + 28 is prime.
  • A245050 (program): Number of hybrid 7-ary trees with n internal nodes.
  • A245051 (program): Number of hybrid 8-ary trees with n internal nodes.
  • A245052 (program): Number of hybrid 9-ary trees with n internal nodes.
  • A245053 (program): Number of hybrid 10-ary trees with n internal nodes.
  • A245054 (program): Number of hybrid (n+1)-ary trees with n internal nodes.
  • A245058 (program): Decimal expansion of the real part of Li_2(I), negated.
  • A245066 (program): Central terms of triangles A001497 and A001498.
  • A245067 (program): Number of three-dimensional random walks with 2n steps in the wedge region x >= y >= z, beginning and ending at the origin without crossing the wedge boundary.
  • A245070 (program): Smallest positive non-divisor of the n-th Lucas number (A000032).
  • A245071 (program): a(n) = 12n - prime(n).
  • A245076 (program): E.g.f.: Sum_{n>=0} exp(n*5^n*x) * x^n/n!.
  • A245086 (program): Central values of the n-th discrete Chebyshev polynomials of order 2n.
  • A245087 (program): Largest number such that 2^a(n) is a divisor of (n!)!.
  • A245092 (program): The even numbers (A005843) and the values of sigma function (A000203) interleaved.
  • A245093 (program): Triangle read by rows in which row n lists the first n terms of A000203.
  • A245095 (program): Triangle read by rows: T(n,k) = A006218(k)*A002865(n-k).
  • A245099 (program): Triangle read by rows: T(n,k) = A024916(k)*A002865(n-k).
  • A245112 (program): G.f. satisfies: A(x)^2 = 1 + 4*x*A(x)^5.
  • A245113 (program): G.f. satisfies: A(x)^2 = 1 + 4*x*A(x)^6.
  • A245114 (program): G.f. satisfies: A(x)^3 = 1 + 9*x*A(x)^5.
  • A245119 (program): G.f. satisfies: A(x) = 1 + x^2 + x^2*A’(x)/A(x).
  • A245135 (program): Number of length 5 0..n arrays least squares fitting to a zero slope straight line, with a single point taken as having zero slope
  • A245155 (program): E.g.f.: (cosh(3*x) + sinh(3*x)*cosh(x)) / (cosh(x) - sinh(x)*cosh(3*x)).
  • A245158 (program): Number of length n 0..3 arrays with new values introduced in order from both ends.
  • A245174 (program): Second differences of A006450.
  • A245176 (program): a(n) = 2*a(n-1)+(n-2)*a(n-2)-(n-1)*a(n-3) with initial terms (1,2,4).
  • A245178 (program): Numbers of the form (2^k+3)*2^m or (3*2^k+1)*2^m, k >= 2, m >= 0.
  • A245179 (program): Numbers of the form 2^k+3 or 3*2^k+1, k >= 2.
  • A245180 (program): A160239(n)/8.
  • A245187 (program): Trajectory of 1 under repeated applications of the morphism 0->12, 1->12, 2->00.
  • A245188 (program): Trajectory of 1 under repeated applications of the morphism 0->12, 1->13, 2->20, 3->21.
  • A245191 (program): Successive states of one-sided one-dimensional cellular automaton using Rule 90, starting with a single ON cell, converted to decimal.
  • A245194 (program): G.f.: Sum_{k>=0} t^3/((1+t)*(1+t^2)), where t=x^(2^k).
  • A245195 (program): a(n) = 2^A014081(n).
  • A245196 (program): Write n>=1 as either n=2^k-2^r with 0 <= r <= k-1, in which case a(2^k-2^r)=wt(k-r-1), or as n=2^k-2^r+j with 2 <= r <= k-1, 1 <= j < 2^r-1, in which case a(2^k-2^r+j)=a(j)*wt(k-r-1) (where wt(i) = A000120(i)).
  • A245198 (program): Decimal expansion of the Landau-Kolmogorov constant C(3,1) for derivatives in the case L_infinity(-infinity, infinity).
  • A245200 (program): Smallest positive solution to k == 0 mod 3 and k == 1 mod prime(n).
  • A245201 (program): Decimal expansion of the Landau-Kolmogorov constant C(3,1) for derivatives in the case L_infinity(0, infinity).
  • A245207 (program): a(n) = floor((n + sqrt(2))^2).
  • A245211 (program): a(n) = Sum_((d<n) | n) (d * tau(d)).
  • A245212 (program): a(n) = n * tau(n) - Sum_((d<n) | n) (d * tau(d)).
  • A245219 (program): Continued fraction expansion of the constant c in A245218; c = sup{f(n,1)}, where f(1,x) = x + 1 and thereafter f(n,x) = x + 1 if n is in A001951, else f(n,x) = 1/x.
  • A245222 (program): Continued fraction of the constant c in A245221; c = sup{f(n,1)}, where f(1,x) = x + 1 and thereafter f(n,x) = x + 1 if n is in A022838, else f(n,x) = 1/x.
  • A245231 (program): Maximum frustration of complete bipartite graph K(n,4).
  • A245232 (program): Semiprimes of the form (2*n^3+n)/3.
  • A245235 (program): Repeat 2^(n*(n+1)/2) n+1 times.
  • A245242 (program): a(n) = Sum_{k=0..n} binomial(n^2 - k^2, n*k - k^2).
  • A245243 (program): Triangle, read by rows, defined by T(n,k) = C(n^2 - k^2, n*k - k^2), for k=0..n, n>=0.
  • A245245 (program): a(n) = C(3*n^2, n^2).
  • A245265 (program): E.g.f. satisfies: A(x) = exp(x/(1-x*A(x)^4)).
  • A245268 (program): Sum of binomial(n,k) over squarefree k.
  • A245269 (program): Sum of binomial(n,k) over cubefree k.
  • A245271 (program): a(n) = floor(sqrt(F(n+2)^2 + F(n)^2)), where F(n) = A000045(n).
  • A245278 (program): Decimal expansion of k3, a Diophantine approximation constant such that the conjectured volume of the “critical parallelepiped” is 2^3*k3 (the 3-D analog of A242671).
  • A245279 (program): Decimal expansion of a1, the first of two constants associated with Djokovic’s conjecture on an integral inequality.
  • A245280 (program): Decimal expansion of a2, the second of two constants associated with Djokovic’s conjecture on an integral inequality.
  • A245282 (program): G.f.: Sum_{n>=1} Fibonacci(n+1) * x^n / (1 - x^n).
  • A245283 (program): a(n) = a(n-1) * (a(n-1) + a(n-2)) / a(n-4) with a(1) = a(2) = a(3) = a(4) = 1.
  • A245288 (program): a(n) = (4*n^2 - 2*n - 1 + (2*n^2 - 2*n + 1)*(-1)^n)/16.
  • A245294 (program): Decimal expansion of the square root of 6/5.
  • A245295 (program): Decimal expansion of the Landau-Kolmogorov constant C(4,3) for derivatives in the case L_infinity(infinity, infinity).
  • A245297 (program): Decimal expansion of the Landau-Kolmogorov constant C(5,2) for derivatives in the case L_infinity(infinity, infinity).
  • A245298 (program): Decimal expansion of the Landau-Kolmogorov constant C(5,3) for derivatives in the case L_infinity(infinity, infinity).
  • A245299 (program): Decimal expansion of the Landau-Kolmogorov constant C(5,4) for derivatives in the case L_infinity(-infinity, infinity).
  • A245300 (program): Triangle T(n,k) = (n+k)*(n+k+1)/2 + k, 0 <= k <= n, read by rows.
  • A245301 (program): a(n) = n*(7*n^2 + 15*n + 8)/6.
  • A245306 (program): a(n) = Fibonacci(n)^2+1.
  • A245317 (program): Concatenate n-th composite integer with n.
  • A245321 (program): Sum of digits of n written in fractional base 6/5.
  • A245323 (program): a(n) = F(6*n-3)*(L(2*n-1)+1), where F = A000045 are the Fibonacci and L = A000032 are the Lucas numbers.
  • A245325 (program): Numerators of an enumeration system of the reduced nonnegative rational numbers
  • A245326 (program): Denominators of an enumeration system of the reduced nonnegative rational numbers.
  • A245327 (program): Numerators in recursive bijection from positive integers to positive rationals (the bijection is f(1) = 1, f(2n) = 1/(f(n)+1), f(2n+1) = f(n)+1 .
  • A245328 (program): Denominators in recursive bijection from positive integers to positive rationals (the bijection is f(1) = 1, f(2n) = 1/(f(n)+1), f(2n+1) = f(n)+1).
  • A245329 (program): a(n) = sum_{k=0..n}C(n,k)^3*(-8)^k with C(n,k) = n!/(k!(n-k)!).
  • A245332 (program): Number of compositions of n into parts 2 and 3 with at least one 2 and one 3.
  • A245334 (program): A factorial-like triangle read by rows: T(0,0) = 1; T(n+1,0) = T(n,0)+1; T(n+1,k+1) = T(n,0)*T(n,k), k=0..n.
  • A245335 (program): Sum of digits of n in fractional base 5/4.
  • A245336 (program): Sum of digits of n written in fractional base 8/7.
  • A245337 (program): Sum of digits of n in fractional base 7/6.
  • A245338 (program): Sum of digits of n written in fractional base 9/8.
  • A245339 (program): Sum of digits of n written in fractional base 10/9.
  • A245341 (program): Sum of digits of n written in fractional base 5/2.
  • A245342 (program): Sum of digits of n written in fractional base 7/2.
  • A245343 (program): Sum of digits of n written in fractional base 5/3.
  • A245344 (program): Sum of digits of n written in fractional base 7/3.
  • A245345 (program): Sum of digits of n written in fractional base 9/2.
  • A245346 (program): Sum of digits of n in fractional base 10/3.
  • A245347 (program): Sum of digits of n written in fractional base 8/3.
  • A245349 (program): Sum of digits of n in fractional base 7/4.
  • A245350 (program): Sum of digits of n written in fractional base 9/4.
  • A245351 (program): Sum of digits of n written in fractional base 10/7.
  • A245352 (program): Sum of digits of n written in fractional base 7/5.
  • A245353 (program): Sum of digits of n written in fractional base 9/7.
  • A245354 (program): Sum of digits of n in fractional base 9/5.
  • A245355 (program): Sum of digits of n written in fractional base 8/5.
  • A245356 (program): Number of numbers whose base-4/3 expansion (see A024631) has n digits.
  • A245357 (program): Number of numbers with property that their base 5/4 expansion (see A024634) has n digits.
  • A245365 (program): Semiprimes of the form n*(3*n-1)/2.
  • A245366 (program): a(n) = 1 + a(n-1) * (a(n-2) - 1) * (a(n-3) - 1) with a(0) = 1, a(1) = 2, a(2) = 3, a(3) = 4.
  • A245367 (program): Compositions of n into parts 3, 5 and 7.
  • A245368 (program): Compositions of n into parts 3, 4 and 7.
  • A245369 (program): Number of compositions of n into parts 3, 5 and 8.
  • A245370 (program): Number of compositions of n into parts 3, 5 and 9.
  • A245380 (program): (7*n^5+5*n^3)/12.
  • A245383 (program): Numbers n whose product of decimal digits is a semiprime.
  • A245384 (program): a(n) = (1 + a(n-1)) * a(n-2) * a(n-3) with a(1) = 1, a(2) = 2, a(3) = 3.
  • A245391 (program): a(n) = 2^n*binomial(2*(n+1), n).
  • A245392 (program): Sum_{k, k|n} 2^(k-1) + Sum_{1<=k<=n, gcd(k,n)=1} 2^(k-1).
  • A245399 (program): Number of nonnegative integers with property that their base 6/5 expansion (see A024638) has n digits.
  • A245400 (program): Number of nonnegative integers with property that their base 9/8 expansion (see A024656) has n digits.
  • A245401 (program): Number of nonnegative integers with property that their base 8/7 expansion (see A024649) has n digits.
  • A245402 (program): Number of nonnegative integers with property that their base 7/6 expansion (see A024643) has n digits.
  • A245403 (program): Number of nonnegative integers with property that their base 10/9 expansion (see A024664) has n digits.
  • A245404 (program): Number of nonnegative integers with property that their base 7/2 expansion (see A024639) has n digits.
  • A245415 (program): Number of nonnegative integers with property that their base 5/2 expansion (see A024632) has n digits.
  • A245416 (program): Number of nonnegative integers with property that their base 9/2 expansion (see A024650) has n digits.
  • A245417 (program): Number of nonnegative integers with property that their base 7/3 expansion (see A024640) has n digits.
  • A245418 (program): Number of nonnegative integers with property that their base 5/3 expansion (see A024633) has n digits.
  • A245419 (program): Number of nonnegative integers with property that their base 8/3 expansion (see A024645) has n digits.
  • A245420 (program): Number of nonnegative integers with property that their base 8/5 expansion (see A024647) has n digits.
  • A245423 (program): Number of nonnegative integers with property that their base 7/5 expansion (see A024642) has n digits.
  • A245425 (program): Number of nonnegative integers with the property that their base 9/4 expansion (see A024652) has n digits.
  • A245426 (program): Number of nonnegative integers with property that their base 7/4 expansion (see A024641) has n digits.
  • A245428 (program): Number of nonnegative integers with property that their base 10/3 expansion (see A024658) has n digits.
  • A245429 (program): Number of nonnegative integers with property that their base 9/7 expansion (see A024655) has n digits.
  • A245430 (program): Number of nonnegative integers with property that their base 9/5 expansion (see A024653) has n digits.
  • A245431 (program): Number of nonnegative integers with property that their base 10/7 expansion has n digits.
  • A245432 (program): Expansion of f(-q^3, -q^5)^2 / (psi(-q) * phi(q^2)) in powers of q where phi(), psi(), f() are Ramanujan theta functions.
  • A245436 (program): Expansion of q^(-1) * (f(-q^3, -q^5) / f(-q, -q^7))^2 in powers of x where f(,) is Ramanujan’s two-variable theta function.
  • A245437 (program): Expansion of x^5/(x^6-x^4-x^2-x+1).
  • A245443 (program): Permutation of nonnegative integers: a(n) = A165199(A193231(n)).
  • A245444 (program): Permutation of nonnegative integers: a(n) = A193231(A165199(n)).
  • A245445 (program): Permutation of nonnegative integers: a(n) = A056539(A193231(n)).
  • A245446 (program): Permutation of nonnegative integers: a(n) = A193231(A056539(n)).
  • A245447 (program): Permutation of natural numbers: a(n) = A048673(A048673(n)).
  • A245448 (program): Permutation of natural numbers: a(n) = A064216(A064216(n)).
  • A245451 (program): Self-inverse permutation of nonnegative integers, A075158-conjugate of gray code: a(n) = 1 + A075157(A003188(A075158(n-1))).
  • A245455 (program): Number of minimax elements in the affine Weyl group of the Lie algebra so(2n).
  • A245466 (program): a(n) = sigma_1(1) + sigma_2(2) + sigma_3(3) + … + sigma_n-1(n-1) + sigma_n(n).
  • A245467 (program): a(n) = ( 4*n^2 - 2*n + 1 - (2*n^2 - 6*n + 1) * (-1)^n )/16.
  • A245471 (program): If n is odd, then a(n) = A065621(n+1). If n is even, then a(n) = n/2.
  • A245473 (program): Nearest integer to 2^log(n).
  • A245477 (program): Period 6: repeat [1, 1, 1, 1, 1, 2].
  • A245478 (program): Numbers n such that the n-th cyclotomic polynomial has a root mod 5.
  • A245479 (program): Numbers n such that the n-th cyclotomic polynomial has a root mod 7.
  • A245480 (program): Numbers n such that the n-th cyclotomic polynomial has a root mod 11.
  • A245484 (program): a(n) = Sum_{(d<n)|n} d*sigma(d).
  • A245485 (program): a(n) = 1 if n is a square, -1 if n is seven times a square, 0 otherwise.
  • A245486 (program): Product of the greatest prime factor of n and the greatest prime factor of n+1.
  • A245487 (program): Number of compositions of n into parts 3,4 where both parts are always present.
  • A245489 (program): a(n) = (1^n + (-2)^n + 4^n)/3.
  • A245496 (program): a(n) = n! * [x^n] (exp(x)+x)^n.
  • A245497 (program): a(n) = phi(n)^2/2, where phi(n) = A000010(n), the Euler totient function.
  • A245508 (program): Smallest double square (cf. A001105) greater than n-th prime.
  • A245524 (program): a(n) = n^2 - floor(n/2)*(-1)^n.
  • A245527 (program): Number of compositions of n into parts 4 and 5 with at least one 4 and one 5.
  • A245534 (program): a(n) = n^2 + floor(n/2)*(-1)^n.
  • A245536 (program): Write n>=1 as either n=2^k-2^r with 0 <= r <= k-1, in which case a(2^k-2^r)=k-r-1, or as n=2^k-2^r+j with 2 <= r <= k-1, 1 <= j < 2^r-1, in which case a(2^k-2^r+j)=(k-r-1)*a(j).
  • A245540 (program): Partial sums of A245180.
  • A245542 (program): Partial sums of A160239.
  • A245543 (program): First differences of A160239.
  • A245549 (program): State of one-dimensional cellular automaton ‘sigma’ (Rule 30): 000,001,010,011,100,101,110,111 -> 0,0,0,1,1,1,1,0 at generation n, regarded as a binary number.
  • A245550 (program): a(0)=0; for n >= 1, a(n) = f(n) - 2*f(floor((n-1)/2)), where f(n) = A006046(n).
  • A245551 (program): G.f.: 1/(1-2*x-3*x^2)^(5/2).
  • A245552 (program): G.f.: Sum_{n>=0} (2*n+1)*x^(n^2+n+1).
  • A245555 (program): Trajectory of 1 under the morphism 1 -> 12, 2 -> 23, 3 -> 31.
  • A245560 (program): Row sums of triangle in A144480.
  • A245561 (program): a(n) = 5^n - ( (sqrt(5)*phi)^n + (sqrt(5)/phi)^n ) + 1, where phi = golden ratio A001622.
  • A245564 (program): a(n) = Product_{i in row n of A245562} Fibonacci(i+2).
  • A245565 (program): a(n) = Product_{i in row n of A245562} Pell(i+1).
  • A245573 (program): Minimal coin changing sequence for denominations 1, 2, 5 and 10 cents.
  • A245574 (program): Minimal coin changing sequence for denominations 1, 2, 5, 10, 20 and 50 cents.
  • A245575 (program): Number of ways of writing n as the sum of two quarter-squares (cf. A002620).
  • A245578 (program): The number of permutations of {0,0,1,1,…,n-1,n-1} that begin with 0 and in which adjacent elements are adjacent mod n.
  • A245579 (program): Number of odd divisors of n multiplied by n.
  • A245580 (program): Smallest Lucas number L(m) > L(n) that is divisible by the n-th Lucas number L(n) = A000204(n).
  • A245581 (program): (5 * (1 + (-1)^(1 + n)) + 2 * n^2) / 4.
  • A245584 (program): Let f(m) put the leftmost digit of the positive integer m at its end; a(n) is the sequence of all positive integers m with f^2(m)=f(m^2).
  • A245593 (program): a(n) = (R_n)^n.
  • A245596 (program): Number of tilings of an n X 1 rectangle by tiles of dimension 1 X 1 and 2 X 1 such that every tile is next to a tile of different size.
  • A245599 (program): Numbers m with A030101(m) XOR A030109(m) = m for the binary representation of m.
  • A245611 (program): Permutation of natural numbers: a(n) = A243071(A064216(n)).
  • A245612 (program): Permutation of natural numbers: a(0) = 1, a(1) = 2, a(2n) = 3*a(n)-1, a(2n+1) = A254049(a(n)); composition of A048673 and A163511.
  • A245621 (program): Sequence of distinct least nonnegative numbers such that the average of the first n terms is a cube.
  • A245624 (program): Sequence of distinct least positive numbers such that the average of the first n terms is a cube.
  • A245626 (program): a(n)= 1 (respectively, a(n)= 3) if up to 2^n the number of A245622-terms is more (respectively, less) than the number of A245623-terms; or a(n)=0 if these numbers are equal.
  • A245627 (program): Base 10 digit sum of 11*n.
  • A245642 (program): Sum of “number of decompositions of d into ordered sums of two odd primes” over all divisors d of 2*n.
  • A245645 (program): Decimal expansion of the common value of A and B in Daniel Shanks’ “incredible identity” A = B.
  • A245650 (program): Primes in the sequence 12*n - prime(n), (A245071).
  • A245656 (program): Characteristic function of arithmetic numbers, cf. A003601.
  • A245669 (program): Expansion of q * f(q, q^5)^3 in powers of q where f() is Ramanujan’s two-variable theta function.
  • A245670 (program): Decimal expansion of 28*sqrt(3) - 48.
  • A245679 (program): a(n) = pg(n, 3) + pg(n, 4) + … + pg(n, n) where pg(n, m) is the m-th n-th-order polygonal number.
  • A245684 (program): Decimal expansion of the expected distance from a randomly selected point in the unit circle to a point on the boundary: 32/(9*Pi).
  • A245685 (program): Sigma(2p)/2, for odd primes p.
  • A245689 (program): Smallest divisor of n that is greater than the smallest prime not dividing n (A053669(n)).
  • A245699 (program): Decimal expansion of the expected distance from a randomly selected point in a 45-45-90 degree triangle of base length 1 to the vertex of the right angle: (4+sqrt(2)*log(3+2*sqrt(2)))/12.
  • A245700 (program): Decimal expansion of the expected distance from a randomly selected point in an equilateral triangle of side length 1 to a corner: (4+log(27))/12.
  • A245710 (program): Number of nonzero evil numbers <= n, see A001969.
  • A245717 (program): Triangle read by rows: T(n,k) = gcd(n,k^2), 1 <= k <= n.
  • A245738 (program): Number of compositions of n into parts 1 and 2 with both parts present.
  • A245761 (program): Numbers with a maximal multiplicative persistence of 1 in any base.
  • A245764 (program): a(n) = 2*(n^2 + 1) + n*(1 + (-1)^n).
  • A245766 (program): a(n) = 2*(n^2 + 1) - n*(1 + (-1)^n).
  • A245769 (program): a(n) = Sum_{k=0..n} C(n, k)*C(n+k, k)/(2k-1), where C(n, k) denotes the binomial coefficient n!/(k!*(n-k)!).
  • A245773 (program): a(n) = n*sigma(n) - Sum_{(d<n)|n} d*sigma(d).
  • A245779 (program): Numbers n such that (n/tau(n) - sigma(n)/n) < 1.
  • A245783 (program): Numbers n such that the hexagonal number H(n) is equal to the sum of the pentagonal numbers P(m) and P(m+1) for some m.
  • A245788 (program): n times the number of 1’s in the binary expansion of n.
  • A245789 (program): Rectangular array A read by upward antidiagonals: A(k,n) = (2^k-1)^n, n,k >= 1.
  • A245790 (program): Number of preferential arrangements of n labeled elements when at least k=5 elements per rank are required.
  • A245791 (program): Number of preferential arrangements of n labeled elements when at least k=6 elements per rank are required.
  • A245799 (program): Lucas(3*n) - Fibonacci(n).
  • A245802 (program): Numbers that are divisible by the sum of their base 8 digits.
  • A245803 (program): Numerator of the partial sum of the number of prime factors function divided by n.
  • A245804 (program): a(n) = 2*3^n - 3*2^n.
  • A245805 (program): a(n) = 12^n mod 11^n.
  • A245806 (program): 3^n + 10^n.
  • A245807 (program): a(n) = 7^n + 10^n.
  • A245809 (program): Divisors of 4620.
  • A245812 (program): Self-inverse permutation of natural numbers: a(0) = 0, a(1) = 1, and for n > 1, if A065620(n) < 0, a(n) = A065621(1+a(-(A065620(n)))), otherwise a(n) = A048724(a(A065620(n)-1)).
  • A245827 (program): Szeged index of the grid graph P_3 X P_n.
  • A245828 (program): Szeged index of the grid graph P_n X P_n.
  • A245829 (program): Szeged index of the prism graph C_n X P_2 (n >=3).
  • A245830 (program): The Szeged index of a benzenoid consisting of a linear chain of n hexagons.
  • A245831 (program): The Szeged index of the coronene/circumcoronene benzenoid H_k (see Fig. 5 of the Gutman & Klavzar reference or Fig. 5.7 of the Diudea et al. reference).
  • A245833 (program): The Szeged index of the triangle-shaped benzenoid T_k (see Fig. 5.7 of the Diudea et al. reference).
  • A245834 (program): E.g.f.: exp( x*(1 + exp(3*x)) ).
  • A245835 (program): E.g.f.: exp( x*(2 + exp(3*x)) ).
  • A245836 (program): Row sums in triangle A053398 (Kopper’s Nim values).
  • A245838 (program): Arithmetic derivative of (3*n + 1), n >= 1, (A016777)’.
  • A245839 (program): Arithmetic derivative of (3*n + 2).
  • A245852 (program): Powers of 8 without the digit ‘0’ in their decimal expansion.
  • A245853 (program): Powers of 12 without the digit ‘0’ in their decimal expansion.
  • A245864 (program): Number of length n+2 0..2 arrays with some pair in every consecutive three terms totalling exactly 2.
  • A245866 (program): Number of length n+2 0..5 arrays with some pair in every consecutive three terms totalling exactly 5.
  • A245868 (program): Number of length n+2 0..7 arrays with some pair in every consecutive three terms totalling exactly 7.
  • A245871 (program): Number of length 2+2 0..n arrays with some pair in every consecutive three terms totalling exactly n.
  • A245872 (program): Number of length 3+2 0..n arrays with some pair in every consecutive three terms totalling exactly n.
  • A245879 (program): Number of distinct fractional chromatic numbers among all connected graphs on n nodes.
  • A245884 (program): Decimal expansion of Gamma(5/2), where Gamma is Euler’s gamma function.
  • A245885 (program): Decimal expansion of Gamma(7/2), where Gamma is Euler’s gamma function.
  • A245886 (program): Decimal expansion of Gamma(-3/2), where Gamma is Euler’s gamma function.
  • A245887 (program): Decimal expansion of Gamma(-5/2), where Gamma is Euler’s gamma function.
  • A245904 (program): a(n) is the number of permutations avoiding 231 and 312 realizable on increasing strict binary trees with 2n-1 nodes.
  • A245905 (program): Zero followed by the terms of A023705 arranged to give the unique path to the n-th node of a complete, rooted and ordered ternary tree.
  • A245906 (program): Numbers of the form 4n^2 + 1 or 4n^2 + 8n + 1.
  • A245908 (program): The number of distinct prime factors of prime(n)^2-1.
  • A245909 (program): The number of distinct prime factors of prime(n)^3-1.
  • A245920 (program): Limit-reverse of the (2,1)-version of the infinite Fibonacci word A014675 with first term as initial block.
  • A245925 (program): G.f.: Sum_{n>=0} x^n*Sum_{k=0..n} (-1)^k * C(n,k)^2 * Sum_{j=0..k} C(k,j)^2 * x^j.
  • A245926 (program): Expansion of g.f. sqrt( (1-x + sqrt(1-14*x+x^2)) / (2*(1-14*x+x^2)) ).
  • A245927 (program): G.f.: sqrt( (1-x - sqrt(1-14*x+x^2)) / (6*x*(1-14*x+x^2)) ).
  • A245929 (program): G.f.: Sum_{n>=0} x^n * Sum_{k=0..n} (-1)^k * C(n,k)^2 * Sum_{j=0..k} C(k,j)^2 * (-2*x)^j.
  • A245930 (program): G.f.: 1 / AGM((1 - 3*x)^2, (1 + x)^2).
  • A245932 (program): G.f.: G’(x) / G(x) where G(x) = 1 / sqrt( AGM((1 - 3*x)^2, (1 + x)^2) ) is the g.f. of A245931.
  • A245933 (program): Limit-reverse of A006337 (the difference sequence of Beatty sequence for sqrt(2)), with first term as initial block.
  • A245936 (program): Limit-reverse of the Kolakoski sequence (A000002), with first term as initial block.
  • A245938 (program): Limit-reverse of the Thue-Morse sequence (A010060), with first term as initial block.
  • A245940 (program): (2n^7 + 4n^6 - n^5 - 4n^4 - n^3) / 24.
  • A245951 (program): Number of length 1+3 0..n arrays with some pair in every consecutive four terms totalling exactly n.
  • A245961 (program): Number of 4-cycles in the Lucas cube Lambda(n).
  • A245963 (program): Triangle read by rows: T(n,k) is the number of maximal hypercubes Q(p) in the Fibonacci cube Gamma(n) (i.e., Q(p) is an induced subgraph of Gamma(n) that is not a subgraph of a subgraph of Gamma(n) that is isomorphic to the hypercube Q(p+1)).
  • A245968 (program): The edge independence number of the Lucas cube Lambda(n).
  • A245969 (program): The average Wiener index of the set of all fibonacenes with n hexagons.
  • A245977 (program): Limit-reverse of the infinite Fibonacci word A014675 = (s(0),s(1),…) = (2,1,2,2,1,2,1,2, …) using initial block (s(2),s(3)) = (2,2).
  • A245978 (program): Index sequence for limit-reversing the infinite Fibonacci word A014675 = (s(0),s(1),…) = (2,1,2,2,1,2,1,2,…) using initial block (s(2),s(3)) = (2,2).
  • A245979 (program): First differences of A245978.
  • A245989 (program): Number of length n+2 0..2 arrays with no pair in any consecutive three terms totalling exactly 2.
  • A245990 (program): Number of length n+2 0..3 arrays with no pair in any consecutive three terms totalling exactly 3.
  • A245992 (program): Number of length n+2 0..5 arrays with no pair in any consecutive three terms totalling exactly 5
  • A245994 (program): Number of length n+2 0..7 arrays with no pair in any consecutive three terms totalling exactly 7
  • A245996 (program): Number of length 1+2 0..n arrays with no pair in any consecutive three terms totaling exactly n.
  • A245997 (program): Number of length 2+2 0..n arrays with no pair in any consecutive three terms totalling exactly n
  • A246003 (program): Floor(m^n/n) with n >= m >= 1.
  • A246004 (program): The duodecimal period of 1/n, or 0 if 1/n terminates.
  • A246009 (program): Length of Collatz cycles ‘3*n + 1’ of prime numbers.
  • A246010 (program): a(n) = floor(5*prime(n)^2 / 4).
  • A246011 (program): a(n) = Product_{i in row n of A245562} Lucas(i+1), where Lucas = A000204.
  • A246016 (program): a(n) = (-1)^A055941(n).
  • A246017 (program): Partial sums of A246016.
  • A246024 (program): A070952(n)-n.
  • A246027 (program): a(n) = n - A071049(n).
  • A246028 (program): a(n) = Product_{i in row n of A245562} Fibonacci(i+1).
  • A246029 (program): a(n) = Product_{i in row n of A245562} prime(i).
  • A246030 (program): a(n) = (5*2^(2*n)+(-2)^(n+1))/3.
  • A246035 (program): Number of odd terms in f^n, where f = (1/x+1+x)*(1/y+1+y).
  • A246036 (program): Expansion of (1+4*x)/((1+2*x)*(1-4*x)).
  • A246037 (program): Number of odd terms in f^n, where f = (1/x+1+x)*(1/y+y).
  • A246038 (program): G.f.: (1+2x)(1+2x+4x^2)/(1-3x-8x^3-8x^4).
  • A246046 (program): [Pi((n + Pi/2)/(Pi -1) - 1/2)]; complement of A062389.
  • A246057 (program): a(n) = (5*10^n - 2)/3.
  • A246058 (program): a(n) = (16*10^n-7)/9.
  • A246059 (program): (17*10^n-8)/9.
  • A246062 (program): G.f.: sqrt( (1 + sqrt(1+8*x)) / (1 + sqrt(1-8*x)) ).
  • A246065 (program): a(n) = sum_{k=0..n}C(n,k)^2*C(2k,k)/(2k-1), where C(n,k) denotes the binomial coefficient n!/(k!*(n-k)!).
  • A246074 (program): Paradigm Shift Sequence for a (-4,5) production scheme with replacement.
  • A246075 (program): Paradigm shift sequence for a (-3,5) production scheme with replacement.
  • A246080 (program): Paradigm shift sequence for (0,2) production scheme with replacement.
  • A246082 (program): Paradigm shift sequence for (0,4) production scheme with replacement.
  • A246104 (program): Least m > 0 for which (s(m), …, s(n+m-1) = (s(0), …, s(n)), the first n+1 terms of the infinite Fibonacci word A003849.
  • A246105 (program): Least m > 0 for which (s(m),…,s(n+m-1) = (s(n),…,s(0)), the reverse of the first n+1 terms of the infinite Fibonacci word A003849.
  • A246127 (program): Limiting block extension of the (2,1)-version of the infinite Fibonacci word A014675 with first term as initial block.
  • A246130 (program): Binomial(2n,n)-2 mod n.
  • A246132 (program): Binomial(2n, n) - 2 mod n^2.
  • A246133 (program): Binomial(2n, n) - 2 mod n^3.
  • A246134 (program): Binomial(2n, n) - 2 mod n^4.
  • A246138 (program): a(n) = sum(k=0..n-1, A246065(k) ) / n^2.
  • A246139 (program): 2^n + 10.
  • A246140 (program): Limiting block extension of A006337 (difference sequence of the Beatty sequence for sqrt(2)) with first term as initial block.
  • A246142 (program): Limiting block extension of A004539 (base-2 representation of sqrt(2)) with first term as initial block.
  • A246144 (program): Limiting block extension of A000002 (Kolakoski sequence) with first term as initial block.
  • A246146 (program): Limiting block extension of A010060 (Thue-Morse sequence) with first term as initial block.
  • A246159 (program): Inverse function to the injection A048724.
  • A246160 (program): Inverse function to the injection A065621.
  • A246168 (program): 2^n - 10.
  • A246170 (program): Beatty sequence for sqrt(14).
  • A246171 (program): Beatty sequence for sqrt(15).
  • A246172 (program): a(n) = (n^2+9*n-8)/2.
  • A246178 (program): Expansion of 1/(1 - 3*x + x^2)^3.
  • A246184 (program): Decimal expansion of Hermite’s constant gamma_6 = 2/3^(1/6).
  • A246260 (program): a(n) = 1 if A003961(n) is of the form 4k+1, otherwise a(n) = 0, (when A003961(n) is of the form 4k+3). [A003961 is fully multiplicative with a(p) = nextprime(p)].
  • A246261 (program): Numbers n such that A003961(n) is of the form 4k+1.
  • A246262 (program): Inverse function to injection A246261, partial sums of A246260.
  • A246263 (program): Numbers n such that A003961(n) is of the form 4k+3.
  • A246264 (program): Inverse function for injection A246263.
  • A246265 (program): Permutation of natural numbers: a(n) = (1+A048673(A246261(n)))/2.
  • A246267 (program): Permutation of natural numbers: a(n) = A048673(A246263(n))/2.
  • A246269 (program): a(1) = 1, a(p(k)) = p(k+1) mod 4 for k-th prime p(k) and a(u * v) = a(u) * a(v) for u, v > 0.
  • A246270 (program): Number of prime factors of the form 4k+3 (counted with multiplicity) in A003961(n): a(n) = A065339(A003961(n)).
  • A246277 (program): Column index of n in A246278: a(1) = 0, a(2n) = n, a(2n+1) = a(A064989(2n+1)).
  • A246281 (program): Numbers k for which A003961(k) < 2*k; Numbers n such that if n = product_{k >= 1} (p_k)^(c_k), then product_{k >= 1} (p_{k+1})^(c_k) < 2*n, where p_k indicates the k-th prime, A000040(k).
  • A246282 (program): Numbers k for which A003961(k) > 2*k; numbers n such that if n = Product_{k >= 1} (p_k)^(c_k), then Product_{k >= 1} (p_{k+1})^(c_k) > 2*n, where p_k indicates the k-th prime, A000040(k).
  • A246292 (program): Number of permutations on [n*(n+1)/2] with cycles of n distinct lengths.
  • A246294 (program): Numbers k such that sin(k) < sin(k+1) > sin(k+2).
  • A246295 (program): Numbers k such that sin(k) < sin(k+1) < sin(k+2) > sin(k+3).
  • A246296 (program): Numbers k such that sin(k) < sin(k+1) < sin(k+2) < sin(k+3) > sin(k+4).
  • A246297 (program): Numbers k such that sin(k) > sin(k+1) < sin(k+2).
  • A246298 (program): Numbers k such that sin(k) > sin(k+1) > sin(k+2) < sin(k+3).
  • A246299 (program): Numbers k such that sin(k) > sin(k+1) > sin(k+2) > sin(k+3) < sin(k+4).
  • A246300 (program): Numbers k such that cos(k) < cos(k+1) > cos(k+2).
  • A246301 (program): Numbers k such that cos(k) < cos(k+1) < cos(k+2) > cos(k+3).
  • A246302 (program): Numbers k such that cos(k) < cos(k+1) < cos(k+2) < cos(k+3) > cos(k+4).
  • A246304 (program): Numbers k such that cos(k) > cos(k+1) < cos(k+2).
  • A246305 (program): Numbers k such that cos(k) > cos(k+1) < cos(k+2) > cos(k+3).
  • A246306 (program): Numbers k such that cos(k) > cos(k+1) < cos(k+2) < cos(k+3) > cos(k+4).
  • A246313 (program): G.f.: (-1+6*x)/(1-3*x-2*x^2).
  • A246324 (program): Numbers n such that the Shephard-Todd group G_n is an exceptional spetsial irreducible reflection group acting on a complex vector space.
  • A246331 (program): Total number of ON cells at stage 2n of two-dimensional 5-neighbor outer totalistic cellular automaton defined by “Rule 465”.
  • A246336 (program): Partial sums of A151548.
  • A246339 (program): Positions of 0 in base-2 representation of 1/sqrt(2).
  • A246347 (program): Record values in A135141.
  • A246348 (program): a(1)=1, a(p_n) = 1 + a(n), a(c_n) = 1 + a(n), where p_n = n-th prime = A000040(n), c_n = n-th composite number = A002808(n); Also binary width of terms of A135141.
  • A246351 (program): Numbers n such that A048673(n) < n.
  • A246352 (program): Numbers n such that A048673(n) >= n.
  • A246353 (program): If n = Sum 2^e_i, e_i distinct, then a(n) = Position of (product prime_{e_i+1}) among squarefree numbers (A005117).
  • A246359 (program): Maximum digit in the factorial base expansion of n (A007623).
  • A246360 (program): a(1) = 1, then A007051 ((3^n)+1)/2 interleaved with A057198 (5*3^(n-1)+1)/2.
  • A246369 (program): a(1)=0, a(p_n) = a(n), a(c_n) = 1 + a(n), where p_n = n-th prime = A000040(n), c_n = n-th composite number = A002808(n); Also one less than the binary weight of terms of A135141.
  • A246370 (program): a(1)=0, a(p_n) = 1 + a(n), a(c_n) = a(n), where p_n = n-th prime = A000040(n), c_n = n-th composite number = A002808(n); Also number of nonleading 0-bits in the binary representation of A135141(n).
  • A246388 (program): Nonnegative integers k satisfying sin(k) >= 0 and sin(k+1) <= 0.
  • A246389 (program): Nonnegative integers k satisfying sin(k) >= 0 and sin(k+1) >= 0.
  • A246390 (program): Nonnegative integers k satisfying sin(k) <= 0 and sin(k+1) <= 0.
  • A246393 (program): Nonnegative integers k satisfying cos(k) >= 0 and cos(k+1) <= 0.
  • A246394 (program): Nonnegative integers k satisfying cos(k) <= 0 and cos(k+1) >= 0.
  • A246395 (program): Nonnegative integers k satisfying cos(k) >= 0 and cos(k+1) >= 0.
  • A246396 (program): Nonnegative integers k satisfying cos(k) <= 0 and cos(k+1) <= 0.
  • A246408 (program): Nonnegative integers k satisfying sec(k) < sec(k+1) > sec(k+2).
  • A246416 (program): A permutation of essentially the duplicate nonnegative numbers: a(4n) = n + 1/2 - (-1)^n/2, a(2n+1) = a(4n+2) = 2n+1.
  • A246425 (program): In the Collatz 3x+1 problem: start at an odd number 2n+1 and find the next odd number 2m+1 in the trajectory; then a(n) = m-n.
  • A246432 (program): Convolution inverse of A001700.
  • A246434 (program): Expansion of (3*x/2 - 1 - (7*x-2)/(2*sqrt(1 - 4*x)))/x.
  • A246435 (program): Length of representation of n in fractional base 3/2.
  • A246437 (program): Expansion of (1/2)*(1/(x+1)+1/(sqrt(-3*x^2-2*x+1))).
  • A246438 (program): Numbers m such that A164349(m) = 0.
  • A246439 (program): Numbers m such that A164349(m) = 1.
  • A246440 (program): Nonnegative integers k satisfying cos(k) > sec(k+1).
  • A246441 (program): Nonnegative integers k satisfying cos(k) < sec(k+1).
  • A246444 (program): Nonnegative integers k satisfying sin(k) > sec(k).
  • A246447 (program): The odd primes squared plus 1 and the composites squared minus 1.
  • A246448 (program): Numbers n such that a square will never end in the digits of n.
  • A246453 (program): Lucas numbers (A000204) of the form n^2 + 2.
  • A246456 (program): a(n) = sigma(n + sigma(n)).
  • A246459 (program): a(n) = Sum_{k=0..n} C(n,k)^2*C(2k,k)*(2k+1), where C(n,k) denotes the binomial coefficient n!/(k!*(n-k)!).
  • A246461 (program): a(n) = Sum_{k=0..n} ((2k+1)*C(n,k)*C(n+k,k))^2, where C(n,k) denotes the binomial coefficient n!/(k!*(n-k)!).
  • A246462 (program): a(n) = Sum_{k=0..n} (2k+1)*C(n,k)^2*C(n+k,k)^2, where C(n,k) denotes the binomial coefficient n!/(k!*(n-k)!).
  • A246467 (program): G.f.: 1 / AGM(1-5*x, sqrt((1-x)*(1-25*x))).
  • A246472 (program): Number of order-preserving (monotone) functions from the power set of 1 = {0} to the power set of n = {0, …, n-1}.
  • A246473 (program): Number of length n+3 0..2 arrays with no pair in any consecutive four terms totalling exactly 2.
  • A246474 (program): Number of length n+3 0..3 arrays with no pair in any consecutive four terms totalling exactly 3.
  • A246476 (program): Number of length n+3 0..5 arrays with no pair in any consecutive four terms totalling exactly 5.
  • A246478 (program): Number of length n+3 0..7 arrays with no pair in any consecutive four terms totalling exactly 7.
  • A246489 (program): The duodecimal period length of 1/(n-th prime) (0 by convention for the primes 2 and 3).
  • A246498 (program): Numerator of the harmonic mean of the first n squares.
  • A246506 (program): a(n) is the number m_0 with the property that if m >= m_0, then every graph obtained from the complete bipartite graph K_{m,m+n} by deleting two edges is chromatically unique.
  • A246507 (program): a(n) = 70*(n+1)*binomial(2*n+1,n+1)/(n+5).
  • A246508 (program): Digital root of numbers congruent to {1,7,11,13,17,19,23,29} modulo 30.
  • A246514 (program): Number of composite numbers between prime(n) and 2*prime(n) exclusive.
  • A246523 (program): Number of endofunctions on [n] whose cycle lengths are divisors of 3.
  • A246534 (program): a(n) = Sum_{k=1..n} 2^(T(k)-1), where T(k)=k(k+1)/2 are the triangular numbers A000217; for n=0 the empty sum a(0)=0.
  • A246538 (program): G.f.: Sum_{n>=0} 2^n * x^n / (1-x)^(2*n+1) * [Sum_{k=0..n} C(n,k)^2 * x^k]^2.
  • A246539 (program): G.f.: Sum_{n>=0} 3^n * x^n / (1-x)^(2*n+1) * [Sum_{k=0..n} C(n,k)^2 * x^k]^2.
  • A246540 (program): G.f.: Sum_{n>=0} 4^n * x^n / (1-x)^(2*n+1) * [Sum_{k=0..n} C(n,k)^2 * x^k]^2.
  • A246547 (program): Prime powers p^e where p is a prime and e >= 2 (prime powers without the primes or 1).
  • A246551 (program): Prime powers p^e where p is a prime and e is odd.
  • A246552 (program): 2-adic valuation of the number of involutions of n (A000085).
  • A246554 (program): Concatenation of the n-th Fibonacci number with itself.
  • A246555 (program): a(n) = A036765(n-1) if n>0, with a(0) = 1.
  • A246558 (program): Product of the digits of the n-th Fibonacci number.
  • A246574 (program): a(n) = 2*(n-1)*Catalan(n).
  • A246575 (program): Expansion of (Product_{r>=1} (1-x^r))*x^(k^2) / Product_{i=1..k} (1-x^i)^2 with k=1.
  • A246584 (program): Number of overcubic partitions of n.
  • A246585 (program): Zeroth trisection of A246584.
  • A246586 (program): First trisection of A246584.
  • A246587 (program): Second trisection of A246584.
  • A246590 (program): Even numbers whose odd part is of the form 4m+3; Numbers missing from A241816.
  • A246591 (program): Smallest number that can be obtained by swapping 2 bits in the binary expansion of n.
  • A246592 (program): Smallest number that can be obtained by swapping 2 adjacent bits in the binary expansion of n.
  • A246595 (program): Run Length Transform of squares.
  • A246596 (program): Run Length Transform of Catalan numbers A000108.
  • A246600 (program): Number of divisors d of n with property that the binary representation of d can be obtained from the binary representation of n by changing any number of 1’s to 0’s.
  • A246601 (program): Sum of divisors d of n with property that the binary representation of d can be obtained from the binary representation of n by changing any number of 1’s to 0’s.
  • A246604 (program): a(n) = Catalan(n) - n.
  • A246606 (program): Central terms of the triangle A116853.
  • A246607 (program): Expansion of e.g.f. exp(x - x^3).
  • A246631 (program): Number of integer solutions to x^2 + 2*y^2 + 2*z^2 = n.
  • A246638 (program): Sequence a(n) = 2 + 3*A001519(n+1) appearing in a certain four circle touching problem together with A246639.
  • A246639 (program): Sequence a(n) = 3 + 5*A001519(n+1) appearing in a certain three circle touching problem, together with A246638.
  • A246640 (program): Sequence a(n) = 1 + A001519(n+1) appearing in a certain touching problem for three circles and a chord, together with A246638.
  • A246641 (program): Sequence a(n) = (1 + A007805(n))/2, appearing in a certain touching problem for three circles and a chord, together with A007805.
  • A246642 (program): Sequence appearing in the curvature of a certain four circle touching problem: (-3 + 5*A007805(n))/2.
  • A246643 (program): A sequence used in the touching circle problem described in A247512.
  • A246644 (program): Decimal expansion of the real root of s^3 - s^2 + s - 1/3 = 0.
  • A246645 (program): Expansion of 1/(1 - 22*x + 81*x^2), used in A246643.
  • A246650 (program): Expansion of phi(x) * chi(-x) * psi(x^3) in powers of x where phi(), psi(), chi() are Ramanujan theta functions
  • A246653 (program): G.f.: Sum_{n>=0} x^n / (1-x^2)^(2*n+1) * [Sum_{k=0..n} C(n,k)^2 * x^k] * [Sum_{k=0..n} C(n,k)^2 * x^(2*k)].
  • A246654 (program): T(n,k) = 2*(K(n,2)*I(k,2) - (-1)^(n+k)*I(n,2)*K(k,2)), where I(n,x) and K(n,x) are Bessel functions; triangle read by rows for 0 <= k <= n.
  • A246655 (program): Prime powers: numbers of the form p^k where p is a prime and k >= 1.
  • A246658 (program): Triangle read by rows: T(n,k) = K(n,1)*I(k,1) - (-1)^(n+k)*I(n,1)* K(k,1), where I(n,x) and K(n,x) are Bessel functions; 0<=k<=n.
  • A246660 (program): Run Length Transform of factorials.
  • A246662 (program): a(n) = 2*(K(n,2)*I(4,2) - (-1)^n*I(n,2)*K(4,2)) where I(n,x) and K(n,x) are Bessel functions.
  • A246669 (program): Catalan(prime(n)).
  • A246674 (program): Run Length Transform of A000225.
  • A246692 (program): Numbers k such that k | A000129(k).
  • A246694 (program): Triangle t(n,k) = t(n,k-2) + 1 if n > 1 and 2 <= k <= n; t(0,0) = 1, t(1,0) = 1, t(1,1) = 2; if n > 1 is odd, then t(n,0) = t(n-1,n-2) + 1 and t(n,1) = t(n-1,n-1) + 1; if n > 1 is even, then t(n,0) = t(n-1,n-1) + 1 and t(n,1) = t(n-1,n-2) + 1.
  • A246695 (program): Row sums of the triangular array A246694.
  • A246696 (program): Triangle t(n,k) = t(n,k-2) + 2 if n > 1 and 2 <= k <= n; t(0,0) = 1, t(1,0) = 2, t(1,1) = 3; if n > 1 is odd, then t(n,0) = t(n-1,n-2) + 2 and t(n,1) = t(n-1,n-1) + 2; if n > 1 is even, then t(n,0) = t(n-1,n-1) + 2 and t(n,1) = t(n-1,n-2) + 2.
  • A246697 (program): Row sums of the triangular array A246696.
  • A246698 (program): Inverse of A246696 considered as a permutation of the positive integers.
  • A246705 (program): Position of first n in A246694 (read as sequence with offset changed to 1); complement of A246706.
  • A246706 (program): Position of last n in A246694 (read as a sequence, with offset changed to 1); complement of A246705.
  • A246708 (program): Decimal expansion of the sixth root of 3.
  • A246709 (program): Decimal expansion of the seventh root of 3.
  • A246710 (program): Decimal expansion of eighth root of 3.
  • A246711 (program): Decimal expansion of the tenth root of 3.
  • A246714 (program): Catalan(n) mod prime(n).
  • A246715 (program): n * Lucas(n) - (n - 1) * Lucas(n - 1).
  • A246716 (program): Positive numbers that are not the product of (exactly) two distinct primes.
  • A246722 (program): Decimal expansion of Hermite’s constant gamma_7 = 2^(6/7).
  • A246723 (program): Decimal expansion of r_1, the smallest radius for which a compact packing of the plane exists, with disks of radius 1 and r_1.
  • A246724 (program): Decimal expansion of r_2, the second smallest radius for which a compact packing of the plane exists, with disks of radius 1 and r_2.
  • A246725 (program): Decimal expansion of r_3, the third smallest radius for which a compact packing of the plane exists, with disks of radius 1 and r_3.
  • A246726 (program): Decimal expansion of r_4, the 4th smallest radius < 1 for which a compact packing of the plane exists, with disks of radius 1 and r_4.
  • A246728 (program): Decimal expansion of r_7, the 7th smallest radius < 1 for which a compact packing of the plane exists, with disks of radius 1 and r_7.
  • A246730 (program): Decimal expansion of r_9, the 9th smallest radius < 1 for which a compact packing of the plane exists, with disks of radius 1 and r_9.
  • A246732 (program): Number of length n+4 0..3 arrays with no pair in any consecutive five terms totalling exactly 3.
  • A246752 (program): Expansion of phi(-x) * chi(x) * psi(-x^3) in powers of x where phi(), psi(), chi() are Ramanujan theta functions.
  • A246760 (program): a(1) = 5; a(n) for n > 1 is the smallest prime > a(n-1) that differs from a(n-1) by a square.
  • A246763 (program): Catalan(n)^2 mod prime(n).
  • A246767 (program): a(n) = n^4 - 2n.
  • A246773 (program): Decimal expansion of ‘v’, an auxiliary constant associated with the asymptotic number of row-convex polyominoes.
  • A246780 (program): Strictly increasing terms of the sequence A246778: a(1)= A246778(1) and for n>0 a(n+1) is next term greater than a(n) after that a(n) appears in A246778 for the first time.
  • A246788 (program): Triangle read by rows: T(n,k) is the coefficient A_k in the transformation Sum_{k=0..n} (k+1)*x^k = Sum_{k=0..n} A_k*(x+2)^k.
  • A246797 (program): Triangle read by rows: T(n,k) is the coefficient A_k in the transformation Sum_{k=0..n} (k+1)*x^k = Sum_{k=0..n} A_k*(x-2)^k.
  • A246798 (program): Triangle read by rows: T(n,k) is the coefficient A_k in the transformation Sum_{k=0..n} (k+1)*x^k = Sum_{k=0..n} A_k*(x+3)^k.
  • A246799 (program): Triangle read by rows: T(n,k) is the coefficient A_k in the transformation Sum_{k=0..n} (k+1)*x^k = Sum_{k=0..n} A_k*(x-3)^k.
  • A246800 (program): Even-indexed terms of A247984, a sequence motivated by generalized quadrangles.
  • A246811 (program): Expansion of phi(x)^2 * psi(x^4) in powers of x where phi(), psi() are Ramanujan theta functions.
  • A246812 (program): G.f.: Sum_{n>=0} x^n / (1-x)^(2*n+1) * [Sum_{k=0..n} C(n,k)^2 * x^k] * [Sum_{k=0..n} C(n,k)^2 * 3^k * x^k].
  • A246815 (program): Expansion of phi(-x) * psi(-x^2)^2 in powers of x where phi(), psi() are Ramanujan theta functions.
  • A246817 (program): Possible number of trailing zeros in hyperfactorials (A002109).
  • A246830 (program): T(n,k) is the concatenation of n-k and n+k in binary; triangle T(n,k), n>=0, 0<=k<=n, read by rows.
  • A246831 (program): a(n) is the concatenation of n and 3n in binary.
  • A246832 (program): Expansion of psi(x) * psi(x^2) * phi(x^2) in powers of x where phi(), psi() are Ramanujan theta functions.
  • A246833 (program): Expansion of psi(-x)^2 * psi(x^4) in powers of x where psi() is a Ramanujan theta function.
  • A246834 (program): A(n,k) is the concatenation of n and k*n in binary; square array A(n,k), n>=0, k>=0, read by antidiagonals.
  • A246835 (program): Expansion of psi(-x)^2 * phi(x^2) in powers of x where phi(), psi() are Ramanujan theta functions.
  • A246836 (program): Expansion of phi(x) * psi(-x^2)^2 in powers of x where phi(), psi() are Ramanujan theta functions.
  • A246837 (program): Expansion of phi(x) * psi(x) * psi(x^4) in powers of x where phi(), psi() are Ramanujan theta functions.
  • A246838 (program): Expansion of f(-x^2) * f(-x^12)^2 / f(x^1, x^5) in powers of x where f() is Ramanujan theta function.
  • A246839 (program): Number of trailing zeros in A002109(n).
  • A246840 (program): G.f.: Sum_{n>=0} x^n * Sum_{k=0..n} C(n,k)^2 * x^(2*k).
  • A246846 (program): a(n) = Catalan(n) mod Fibonacci(n).
  • A246848 (program): Decimal expansion of 1/(1+sqrt(e)), a constant appearing in the computation of a limiting probability concerning the number of cycles of a given length in a random permutation.
  • A246860 (program): Expected value of trace(O)^(2n), where O is a 4 X 4 orthogonal matrix randomly selected according to Haar measure.
  • A246861 (program): G.f. satisfies: A(x) = Sum_{n>=0} x^n * Sum_{k=0..n} C(n,k)^2 * (x*A(x))^(2*k).
  • A246862 (program): Expansion of phi(x) * f(x^3, x^5) in powers of x where phi(), f() are Ramanujan theta functions.
  • A246863 (program): Expansion of phi(x) * f(x^1, x^7) in powers of x where phi(), f() are Ramanujan theta functions.
  • A246864 (program): (n^4+1) mod prime(n).
  • A246876 (program): G.f.: 1 / AGM(1-12*x, sqrt((1-4*x)*(1-36*x))).
  • A246880 (program): 6*((10^n-1)/9)*(10^(n+1))+9*(10^n-1)/9.
  • A246883 (program): G.f.: Sum_{n>=0} x^n * Sum_{k=0..n} C(n,k)^2 * x^(3*k).
  • A246884 (program): G.f.: Sum_{n>=0} x^n * Sum_{k=0..n} C(n,k)^2 * x^(4*k).
  • A246887 (program): Number of length n+4 0..3 arrays with some pair in every consecutive five terms totalling exactly 3
  • A246906 (program): G.f.: 1 / AGM(1-21*x, sqrt((1-9*x)*(1-49*x))).
  • A246908 (program): a(n) = sigma(n + sigma(n)) - sigma(n).
  • A246923 (program): G.f.: 1 / AGM(1-9*x, sqrt((1-x)*(1-81*x))).
  • A246926 (program): Expansion of phi(x)^2 * chi(x) * psi(-x^3) in powers of x where phi(), psi(), chi() are Ramanujan theta functions.
  • A246929 (program): Prime(11*n).
  • A246930 (program): Prime(12*n).
  • A246931 (program): Prime(14*n).
  • A246932 (program): a(n) = prime(15*n).
  • A246933 (program): a(n) = prime(16*n).
  • A246934 (program): The closest square to n-th prime.
  • A246943 (program): a(4n) = 4*n , a(2n+1) = 8*n+4 , a(4n+2) = 2*n+1.
  • A246953 (program): Expansion of phi(-x) * psi(x^2)^2 in powers of x where phi(), psi() are Ramanujan theta functions.
  • A246954 (program): Expansion of phi(-x) * psi(-x)^2 in powers of x where phi(), psi() are Ramanujan theta functions.
  • A246955 (program): Numbers j for which the symmetric representation of sigma(j) has two parts, each of width one.
  • A246960 (program): Directions of the lines in the (Heighway) Dragon Curve.
  • A246962 (program): Expansion of psi(-x^3) * phi(-x^2) in powers of x where phi(), psi() are Ramanujan theta functions.
  • A246963 (program): G.f. satisfies: A(x) = Sum_{n>=0} A000108(n)^2 * (x-x^2)^n, where A000108(n) = C(2*n,n)/(n+1) is the n-th Catalan number.
  • A246965 (program): Numbers n such that 19*n-(n+19) is a prime.
  • A246972 (program): (n+1)^2 concatenated with n^2.
  • A246973 (program): n^2 concatenated with (n+1)^2.
  • A246977 (program): Sequence B related to Fraenkel’s (3,2)-Wythoff’s game in Table 5 of Liu-Zhao (2014).
  • A246978 (program): Sequence B^(1) in Table 6 of Liu-Zhao (2014).
  • A246985 (program): Expansion of (1-8*x+14*x^2)/((1-2*x)*(1-3*x)*(1-6*x)).
  • A246986 (program): Expansion of (1-5*x+6*x^2-x^3)/((1-x)*(1-2*x)*(1-3*x)*(1-4*x)).
  • A246998 (program): Multiplicity of the zero at x=1 of the characteristic polynomial P_n^{C0+}.
  • A246999 (program): a(n) is the binary word s21s211s2 where s is a string of n 1’s.
  • A247000 (program): Maximal number of palindromes in a circular binary word of length n.
  • A247004 (program): Denominator of (n+4)/gcd(n, 4)^2, a 16-periodic sequence that associates A061037 with A106617.
  • A247014 (program): Number of binary centrosymmetric matrices of size n X n.
  • A247018 (program): Numbers of the form 3*z^2 + z + 3 for some integer z.
  • A247023 (program): Riordan array (1/(1-2*x), x*C(x)) where C(x) is the o.g.f. of Catalan numbers A000108.
  • A247029 (program): G.f. satisfies: A(x) = A(x)^4 - 9*x.
  • A247035 (program): Expansion of 2*(x+1)*(x^4+6*x^3+5*x^2+6*x+1)/(x^6-18*x^3+1).
  • A247049 (program): Rectangular array read upwards by columns: T = T(n,k) = number of paths from (0,0) to (n,k), where 0 >= k <= 2, consisting of segments given by the vectors (1,1), (1,2), (1,-1).
  • A247052 (program): Primes composed of only digits with line segments or both line segments and curves {1, 2, 4, 5, 7}.
  • A247060 (program): Dynamic Betting Game D(n,4,1).
  • A247061 (program): Dynamic Betting Game D(n,5,1).
  • A247062 (program): Dynamic Betting Game D(n,5,2).
  • A247063 (program): Dynamic Betting Game D(n,5,3).
  • A247064 (program): Dynamic Betting Game D(n,5,4).
  • A247065 (program): Dynamic Betting Game D(n,6,1).
  • A247074 (program): a(n) = phi(n)/(Product_{primes p dividing n } gcd(p - 1, n - 1)).
  • A247076 (program): Number of tilings of a 5 X 2n rectangle using 2n pentominoes of shape P.
  • A247082 (program): E.g.f.: (8 - 7*cosh(x)) / (13 - 12*cosh(x)).
  • A247090 (program): Eric Rowland’s generalization of A132199 as a rectangular array A read by upward antidiagonals.
  • A247092 (program): Limiting sequence obtained by taking the sequence of Mersenne numbers 2^n-1, n=1,2,…(A000225) and applying an infinite process which is described in the comments.
  • A247100 (program): The number of ways to write an n-bit binary string and then define each run of ones as an element in an equivalence relation.
  • A247102 (program): G.f.: (6*x+2)/(sqrt(-3*x^2-6*x+1)*(4*x^2+4*x))-(2*x+1)/(2*x^2+2*x).
  • A247107 (program): a(0) = 0, a(n) = previous term + repunit of length of previous term for n > 0.
  • A247108 (program): Complementary Aitken’s array: triangle of numbers {a(n,k), n >= 0, 0<=k<=n} read by rows, defined by a(0,0)=1, a(n,0)=-a(n-1,n-1), a(n,k)=a(n,k-1)+a(n-1,k-1).
  • A247110 (program): n + reversal of digits of n, when n is not palindromic
  • A247112 (program): Floor of sums of the cubes of the non-integer square roots of n, as partitioned by the integer roots: floor( sum( j from n^2+1 to (n+1)^2-1, j^(3/2) ) ).
  • A247115 (program): Denominator of the harmonic mean of the first n heptagonal numbers.
  • A247121 (program): Number of tilings of a 5 X 2n rectangle using 2n pentominoes of shapes P, U.
  • A247128 (program): Positive numbers that are congruent to {0,5,9,13,17} mod 22.
  • A247133 (program): Expansion of f(-x, -x^11) in powers of x where f() is a Ramanujan theta function
  • A247139 (program): The number of tiling of a triangular shape T_n with n rectangles identifying all tilings which use the same rectangular shapes.
  • A247146 (program): As a binary numeral, the bit 2^(m-1) of a(n) is 1 iff m is a proper divisor of n.
  • A247155 (program): 31n^2 + 1
  • A247157 (program): Greatest number of colors possible for interval edge-colorings of the complete graph K_{2n}.
  • A247159 (program): Sum of divisors of even semiprimes.
  • A247160 (program): Dynamic Betting Game D(n,4,3).
  • A247161 (program): Dynamic Betting Game D(n,4,2).
  • A247162 (program): G.f. 1-(2*x^3)/(-sqrt(-3*x^4-4*x^3-2*x^2+1)-x^2+1).
  • A247172 (program): Expansion of -1-(sqrt(x^4+4*x^3-2*x^2-4*x+1)-x^2-2*x-1)/(4*x).
  • A247173 (program): Expansion of g.f. (-1)/(2*x^2+2*x) +(-2*x^3-3*x^2+1) / (sqrt(x^4+4*x^3-2*x^2-4*x+1)*(2*x^2+2*x)).
  • A247179 (program): Floor of area enclosed in the interior of n unit circles arranged in a circle.
  • A247180 (program): Numbers with nonrepeating smallest prime factor.
  • A247181 (program): Total domination number of the n-hypercube graph.
  • A247188 (program): a(0) = 0. a(n) is the number of repeating sums in the collection of all sums of any k elements in [a(0), … a(n-1)] chosen without replacement for 2 <= k <= n.
  • A247193 (program): a(n) = gcd(n!, Fibonacci(n)).
  • A247194 (program): a(n) = ceiling(Pi*n^3).
  • A247209 (program): Number of terms in generalized Swinnerton-Dyer polynomials.
  • A247215 (program): Integers k such that 3k+1 and 6k+1 are both squares.
  • A247223 (program): Expansion of f(-x^5, -x^7) in powers of x where f() is a Ramanujan theta function.
  • A247238 (program): a(n) = Stirling2(2*n+1, n).
  • A247247 (program): Triangular numbers that are the sum of 2 consecutive terms of A130518.
  • A247248 (program): a(n) is the least k such that n divides 2^k + k.
  • A247249 (program): a(n) = (2*n-1)*a(n-1) + (n-1)*a(n-2) with a(0) = a(1) = 1.
  • A247257 (program): The number of octic characters modulo n.
  • A247272 (program): Odd numbers n containing 256 as the highest power of 2 in their Collatz (3x+1) iteration.
  • A247281 (program): 4^n -(-1)^n.
  • A247283 (program): Positions of subrecords in A048673.
  • A247284 (program): Subrecords in A048673: maximum value between two consecutive records in A048673.
  • A247287 (program): Number of weak peaks in all Motzkin paths of length n. A weak peak of a Motzkin path is a vertex on the top of a hump. A hump is an upstep followed by 0 or more flatsteps followed by a downstep. For example, the Motzkin path u*duu*h*h*dd, where u=(1,1), h=(1,0), d(1,-1), has 4 weak peaks (shown by the stars).
  • A247296 (program): Number of uhd and uHd in all weighted lattice paths B(n).
  • A247300 (program): Number of h- and H-steps at level 0 in all lattice paths in B(n).
  • A247303 (program): Convolution of A010059(n) with itself.
  • A247304 (program): Expected value of trace(O)^(2n), where O is a 5 X 5 orthogonal matrix randomly selected according to Haar measure.
  • A247309 (program): Rectangular array read upwards by columns: T = T(n,k) = number of paths from (0,1) to (n,k), where 0 <= k <= 2, consisting of segments given by the vectors (1,1), (1,0), (1,-1), (1,-2).
  • A247311 (program): Rectangular array read upwards by columns: T = T(n,k) = number of paths from (0,1) to (n,k), where 0 <= k <= 2, consisting of segments given by the vectors (1,1), (1,0), (1,-1).
  • A247313 (program): a(n) = 5*a(n-1) - 2^n for n>0, a(0)=1.
  • A247322 (program): Number of paths from (0,0) to the line x = n, each consisting of segments given by the vectors (1,1), (1,2), (1,-1), with vertices (i,k) satisfying 0 <= k <= 3.
  • A247323 (program): Number of paths from (0,0) to (n,0), with vertices (i,k) satisfying 0 <= k <= 3, consisting of segments given by the vectors (1,1), (1,2), (1,-1).
  • A247325 (program): Number of paths from (0,0) to (n,2), with vertices (i,k) satisfying 0 <= k <= 3, consisting of segments given by the vectors (1,1), (1,2), (1,-1).
  • A247326 (program): Number of paths from (0,0) to (n,3), with vertices (i,k) satisfying 0 <= k <= 3, consisting of segments given by the vectors (1,1), (1,2), (1,-1).
  • A247327 (program): Triangle read by rows: T(n,k) = sum of k-th row of n X n square filled with odd numbers 1 through 2*n^2-1 reading across rows left-to-right.
  • A247328 (program): Odd deficient numbers.
  • A247335 (program): The curvature of touching circles inscribed in a special way in the larger segment of circle of radius 10/9 divided by a chord of length 4/3.
  • A247339 (program): a(n) is the least number k such that the greatest prime divisor of k^2+1 is the smallest prime divisor of n^2+1.
  • A247340 (program): Numbers n such that each prime divisor of the semiprime n^2+1 is also a divisor of a^2+1 and b^2+1 respectively for some a, b < n.
  • A247343 (program): Moebius transform applied four times to sequence 1,0,0,0,….
  • A247346 (program): Odd numbers n containing 1024 as the highest power of 2 in their Collatz (3x+1) iteration.
  • A247350 (program): Numbers x such that 8*x^3 - 8*x^2 + 4*x + 1 is prime.
  • A247353 (program): Number of paths from (0,1) to the line x = n, each consisting of segments given by the vectors (1,1), (1,2), (1,-1), with vertices (i,k) satisfying 0 <= k <= 3.
  • A247354 (program): Number of paths from (0,1) to (n,0), with vertices (i,k) satisfying 0 <= k <= 3, consisting of segments given by the vectors (1,1), (1,2), (1,-1).
  • A247355 (program): Number of paths from (0,1) to (n,2), with vertices (i,k) satisfying 0 <= k <= 3, consisting of segments given by the vectors (1,1), (1,2), (1,-1).
  • A247364 (program): Riordan array (f(x), (f(x)-1)/f(x)) where f(x) = (1 + x - sqrt(1 - 2x - 3x^2))/(2*x).
  • A247365 (program): Central terms of triangles A102472 and A102473.
  • A247366 (program): Integer parts of sqrt(2)^i * sqrt(3)^j with i,j >= 0, in natural order.
  • A247367 (program): Number of ways to write n as a sum of a square and a nonsquare.
  • A247368 (program): a(n) = (a(n-1) * a(n-3) - (-1)^n * a(n-2)^2) / a(n-4) with a(0) = 0, a(1) = … = a(4) = 1.
  • A247374 (program): Number of button presses required to try every combination of a binary combination lock with n number buttons.
  • A247375 (program): Numbers m such that floor(m/2) is a square.
  • A247380 (program): First differences of A117495.
  • A247386 (program): Sum of the major index over all standard Young tableaux with n cells.
  • A247395 (program): The smallest numbers of every class in a classification of positive numbers (see comment).
  • A247396 (program): Number of even numbers in classes of classification of the positive numbers defined in comment in A247395.
  • A247397 (program): Numbers n such that when n unit-diameter circles are arranged non-overlapping in the plane, and those circles are then enclosed in a rectangle, the area of the rectangle must be at least n.
  • A247416 (program): Number of friezes of type B_n.
  • A247418 (program): a(n) = Sum_{i=1..n} mu(i)*(-1)^(i+1).
  • A247419 (program): a(2n) = A003256(n); a(2n-1) = A003256(n) - 1.
  • A247425 (program): A005206(A003259(n)).
  • A247426 (program): Complement of A247425.
  • A247427 (program): 2n - m, where m is the largest integer such that A003249(m) <= n.
  • A247428 (program): Complement of A247427.
  • A247429 (program): A247427(n) for n in A003249; A247427(n) - 1 for other n.
  • A247430 (program): Complement of A247429.
  • A247431 (program): The largest integer m such that A001950(m) < A003231(n).
  • A247432 (program): Complement of A247431.
  • A247446 (program): Decimal expansion of Pi*sqrt(3)/16.
  • A247452 (program): a(n)=3^n*Bell(n).
  • A247453 (program): T(n,k) = binomial(n,k)*A000111(n-k)*(-1)^(n-k), 0 <= k <= n.
  • A247473 (program): Numbers of the form 2^k (k>=0) that are a sum of divisors of n for some n.
  • A247485 (program): Integer part of 2*sqrt(prime(n)) + 1.
  • A247487 (program): Expansion of (2 + x + x^2 + x^3 - x^4 - 2*x^5 - 4*x^6 - 8*x^7) / (1 - x^4 + 16*x^8) in powers of x.
  • A247490 (program): Square array read by antidiagonals: A(k, n) = (-1)^(n+1)* hypergeom([k, -n+1], [], 1) for n>0 and A(k,0) = 0 (n>=0, k>=1).
  • A247491 (program): Number of crossing partitions of {1,2,…,n} that contain no singletons.
  • A247492 (program): Triangle read by rows: T(n, k) = binomial(k-1, n-k)*(n+1)/(n+1-k), 0 <= k <= n.
  • A247494 (program): Number of crossing partitions of {1,2,…,n} that contain singletons.
  • A247495 (program): Generalized Motzkin numbers: Square array read by descending antidiagonals, T(n, k) = k!*x^k, n>=0, k>=0.
  • A247496 (program): a(n) = n!*x^n, n>=0, main diagonal of A247495.
  • A247498 (program): Generalized Euler numbers: Square array read by descending antidiagonals, T(n, k) = k!*[x^k] exp(n*x)*sech(x), n>=0, k>=0.
  • A247499 (program): a(n) = hypergeom([1, -n, -n-1], [2], 1).
  • A247500 (program): Triangle read by rows: T(n, k) = n!*binomial(n + 1, k)/(k + 1)!, 0 <= k <= n.
  • A247503 (program): Completely multiplicative with a(prime(n)) = prime(n)^(n mod 2).
  • A247507 (program): Square array read by ascending antidiagonals, n>=0, k>=0. Row n is the expansion of (1-n*x-sqrt(n^2*x^2-2*n*x-4*x+1))/(2*x).
  • A247513 (program): Number of elements in the set {(x,y,z): 1<=x,y,z<=n, gcd(x,y,z)=1, lcm(x,y,z)=n}.
  • A247514 (program): Where 2*floor(sqrt(prime(n))) = floor(2*sqrt(prime(n))).
  • A247515 (program): Where 2*floor(sqrt(prime(n))) < floor(2*sqrt(prime(n))).
  • A247516 (program): Card{(x,y,z,t): 1<=x,y,z,t<=n, gcd(x,y,z,t)=1, lcm(x,y,z,t)=n}.
  • A247518 (program): a(n) = a(n-1) * (11*a(n-1) - 16*a(n-2)) / (a(n-1) + 10*a(n-2)) with a(1) = 1, a(2) = 2.
  • A247519 (program): Numbers k such that d(r,k) = 0 and d(s,k) = 0, where d(x,k) = k-th binary digit of x, r = {golden ratio}, s = {(golden ratio)/2}, and { } = fractional part.
  • A247520 (program): Numbers k such that d(r,k) = 0 and d(s,k) = 1, where d(x,k) = k-th binary digit of x, r = {golden ratio}, s = {(golden ratio)/2}, and { } = fractional part.
  • A247521 (program): Numbers k such that d(r,k) = 1 and d(s,k) = 0, where d(x,k) = k-th binary digit of x, r = {golden ratio}, s = {(golden ratio)/2}, and { } = fractional part.
  • A247522 (program): Numbers k such that d(r,k) = 1 and d(s,k) = 1, where d(x,k) = k-th binary digit of x, r = {golden ratio}, s = {(golden ratio)/2}, and { } = fractional part.
  • A247523 (program): Numbers k such that d(r,k) = d(s,k), where d(x,k) = k-th binary digit of x, r = {golden ratio}, s = {(golden ratio)/2}, and { } = fractional part.
  • A247524 (program): Numbers k such that d(r,k) != d(s,k), where d(x,k) = k-th binary digit of x, r = {golden ratio}, s = {(golden ratio)/2}, and { } = fractional part.
  • A247525 (program): a(n) = 5 * a(n-1) - 2 * a(n-1)^2 / a(n-2), with a(0) = 1, a(1) = 2.
  • A247526 (program): a(n) = L(n+1) * L(n) * L(n-1) * L(n-2) / 6, where L(n) = Lucas numbers (A000032).
  • A247527 (program): Number of length n+3 0..2 arrays with some disjoint pairs in every consecutive four terms having the same sum.
  • A247528 (program): Number of length n+3 0..3 arrays with some disjoint pairs in every consecutive four terms having the same sum.
  • A247534 (program): Number of length 2+3 0..n arrays with some disjoint pairs in every consecutive four terms having the same sum.
  • A247540 (program): a(n) = 2*a(n-1) - 3*a(n-1)^2 / a(n-2), with a(0) = a(1) = 1.
  • A247541 (program): a(n) = 7*n^2 + 1.
  • A247550 (program): Number of 1 up, 1 down, 2 up, 1 down, 3 up, 1 down, … permutations of [n].
  • A247555 (program): A permutation of the nonnegative numbers: a(4n) = 8n, a(4n+1) = 2n + 1, a(4n+2) = 4n + 2, a(4n+3) = 8n + 4.
  • A247560 (program): a(n) = 3*a(n-1) - 4*a(n-2) with a(0) = a(1) = 1.
  • A247563 (program): a(n) = 3*a(n-1) - 4*a(n-2) with a(0) = 2, a(1) = 3.
  • A247564 (program): a(n) = 3*a(n-2) - 4*a(n-4) with a(0) = 2, a(1) = 1, a(2) = 3, a(3) = 1.
  • A247565 (program): a(n) = 5*a(n-1) - 10*a(n-2) + 8*a(n-3) with a(0) = 2, a(1) = a(2) = 3.
  • A247584 (program): a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + 3*a(n-5) with a(0) = a(1) = a(2) = a(3) = a(4) = 1.
  • A247586 (program): Number of acute triangles with integer sides less than or equal to n.
  • A247588 (program): Number of integer-sided acute triangles with largest side n.
  • A247594 (program): a(n) = a(n-1) + a(n-2) + 3*a(n-3) with a(0) = 1, a(1) = 2, a(2) = 5.
  • A247595 (program): a(n) = 4*a(n-1) - 4*a(n-2) + 4*a(n-3) with a(0) = 1, a(1) = 3, a(2) = 10.
  • A247599 (program): Number of ways of writing n as a sum: n = 2^0*k(0)^3 + 2^1*k(1)^3 + 2^2*k(2)^3 + … where the k’s are nonnegative integers.
  • A247608 (program): a(n) = Sum_{k=0..3} binomial(6,k)*binomial(n,k).
  • A247609 (program): a(n) = Sum_{k=0..4} binomial(8,k)*binomial(n,k).
  • A247610 (program): a(n) = Sum_{k=0..5} binomial(10,k)*binomial(n,k).
  • A247611 (program): a(n) = Sum{k=0..6} binomial(12,k)*binomial(n,k).
  • A247612 (program): a(n) = Sum_{k=0..7} binomial(14,k)*binomial(n,k).
  • A247613 (program): a(n) = Sum_{k=0..8} binomial(16,k)*binomial(n,k).
  • A247614 (program): a(n) = Sum_{k=0..9} binomial(18,k)*binomial(n,k).
  • A247615 (program): a(n) = Sum_{k=0..10} binomial(20,k)*binomial(n,k).
  • A247617 (program): a(4n) = n + 1/2 - (-1)^n/2 + (-1)^n, a(2n+1) = 2*n + 5, a(4n+2) = 2*n + 3.
  • A247618 (program): Start with a single square; at n-th generation add a square at each expandable vertex; a(n) is the sum of all label values at n-th generation. (See comment for construction rules.)
  • A247619 (program): Start with a single pentagon; at n-th generation add a pentagon at each expandable vertex; a(n) is the sum of all label values at n-th generation. (See comment for construction rules.)
  • A247620 (program): Start with a single hexagon; at n-th generation add a hexagon at each expandable vertex; a(n) is the sum of all label values at n-th generation. (See comment for construction rules.)
  • A247623 (program): Number of paths from (0,0) to the line x = n, each segment given by a vector (1,1), (1,-1), or (2,0), not crossing the x-axis, and including no horizontal segment on the x-axis.
  • A247630 (program): Number of paths from (0,0) to the line x = n, each segment given by a vector (1,1), (1,-1), or (2,0), not crossing the x-axis, and including no horizontal segment on the x-axis.
  • A247631 (program): Numbers k such that d(r,k) = 0 and d(s,k) = 0, where d(x,k) = k-th binary digit of x, r = {sqrt(2)}, s = {sqrt(8)}, and { } = fractional part.
  • A247632 (program): Numbers k such that d(r,k) = 0 and d(s,k) = 1, where d(x,k) = k-th binary digit of x, r = {sqrt(2)}, s = {sqrt(8)}, and { } = fractional part.
  • A247633 (program): Numbers k such that d(r,k) = 1 and d(s,k) = 0, where d(x,k) = k-th binary digit of x, r = {sqrt(2)}, s = {sqrt(8)}, and { } = fractional part.
  • A247634 (program): Numbers k such that d(r,k) = 1 and d(s,k) = 1, where d(x,k) = k-th binary digit of x, r = {sqrt(2)}, s = {sqrt(8)}, and { } = fractional part.
  • A247635 (program): Numbers k such that d(r,k) = d(s,k), where d(x,k) = k-th binary digit of x, r = {sqrt(2)}, s = {sqrt(8), and { } = fractional part.
  • A247636 (program): Numbers k such that d(r,k) != d(s,k), where d(x,k) = k-th binary digit of x, r = {sqrt(2)}, s = {sqrt(8)}, and { } = fractional part.
  • A247640 (program): Number of ON cells after n generations of “Odd-Rule” cellular automaton on hexagonal lattice based on 6-celled neighborhood.
  • A247643 (program): a(n) = ( 10*n*(n+1)+(2*n+1)*(-1)^n+7 )/8.
  • A247644 (program): Triangle formed from the odd-numbered rows of A088855.
  • A247647 (program): Binary numbers that begin and end with 1 and do not contain two adjacent zeros.
  • A247648 (program): Numbers whose binary expansion begins and ends with 1 and does not contain two adjacent zeros.
  • A247658 (program): Partial sums of the sequence of (primes omitting A247657).
  • A247666 (program): Number of ON cells after n generations of “Odd-Rule” cellular automaton on hexagonal lattice based on 7-celled neighborhood.
  • A247676 (program): Odd composite numbers congruent to 2 modulo 9.
  • A247678 (program): Odd composite numbers congruent to 4 modulo 9.
  • A247679 (program): Composite numbers congruent to 17 modulo 18.
  • A247681 (program): Odd nonprimes congruent to 1 modulo 9.
  • A247682 (program): Odd composite numbers congruent to 5 modulo 9.
  • A247683 (program): Odd composite numbers congruent to 7 modulo 9.
  • A247684 (program): Decimal expansion of the integral over the first quadrant (x>0, y>0) of sqrt(x^2 + x*y + y^2)*exp(-x-y) dx dy.
  • A247687 (program): Numbers m with the property that the symmetric representation of sigma(m) has three parts of width one.
  • A247714 (program): Position of A036561(n) in sequence A003586.
  • A247719 (program): Decimal expansion of Integral_{t=0..Pi/2} sqrt(tan(t)) dt.
  • A247720 (program): Number of length n+3 0..2 arrays with no disjoint pairs in any consecutive four terms having the same sum
  • A247727 (program): Number of length 1+3 0..n arrays with no disjoint pairs in any consecutive four terms having the same sum.
  • A247778 (program): Least k such that e - (1 + 1/k)^k < 1/n.
  • A247779 (program): Numbers k such that A247778(k+1) - A247778(k) = 1.
  • A247780 (program): Numbers k such that A247778(k+1) - A247778(k) = 2.
  • A247784 (program): a(n) = floor(1/(e - (1 + 1/n)^n)).
  • A247785 (program): Numbers k such that A247784(k+1) = A247784(k).
  • A247786 (program): Numbers k such that A247784(k+1) - A247784(k) = 1.
  • A247787 (program): Sum of divisors of 2*prime(n)-1.
  • A247792 (program): a(n) = 9*n^2 + 1.
  • A247795 (program): Irregular triangle read by rows in which row n lists the parities of the divisors of n.
  • A247798 (program): n-th positive integer relatively prime to 2*n - 1.
  • A247815 (program): Number of primes in n-th row of triangle A077581.
  • A247817 (program): Sum(4^k, k=2..n).
  • A247820 (program): Numbers n such that sigma(2n-1) is a prime p.
  • A247827 (program): Least prime factor of A247676.
  • A247840 (program): Sum(6^k, k=2..n).
  • A247841 (program): a(n) = Sum_{k=2..n} 8^k.
  • A247842 (program): Sum(9^k, k=2..n).
  • A247844 (program): Decimal expansion of the value of the continued fraction [1; 1, 2, 3, 4, 5, …].
  • A247847 (program): Decimal expansion of m = (1-1/e^2)/2, one of Renyi’s parking constants.
  • A247848 (program): Decimal expansion of m_2 = (2-1/e)/4, one of Renyi’s parking constants, the mean car density in case “monomer with nearest neighbor exclusion” for the 2 x infinity strip.
  • A247850 (program): The 5th Hermite Polynomial evaluated at n: H_5(n) = 32*n^5 - 160*n^3 + 120*n.
  • A247851 (program): The 6th Hermite Polynomial evaluated at n: H_6(n) = 64*n^6-480*n^4+720*n^2-120.
  • A247852 (program): The 7th Hermite Polynomial evaluated at n: H_7(n) = 128*n^7 -1344*n^5 + 3360*n^3 - 1680*n.
  • A247853 (program): The 8th Hermite Polynomial evaluated at n: H_8(n) = 256*n^8-3584*n^6+13440*n^4-13440*n^2+1680.
  • A247854 (program): The 9th Hermite Polynomial evaluated at n: H_9(n) = 512*n^9 - 9216*n^7 + 48384*n^5 - 80640*n^3 + 30240*n.
  • A247855 (program): The 10th Hermite Polynomial evaluated at n: H_10(n) = 1024*n^10 - 23040*n^8 + 161280*n^6 - 403200*n^4 + 302400*n^2 - 30240.
  • A247859 (program): The product of the first n Catalan numbers and 2^(n^2).
  • A247870 (program): Least prime factor of odd numbers congruent to 4 modulo 9.
  • A247871 (program): Least prime factor of A247679
  • A247875 (program): Numbers that are even or whose binary expansions contain one or more pairs of adjacent zeros when odd.
  • A247876 (program): Least prime factor of A247682
  • A247877 (program): Least prime factor of A247683
  • A247881 (program): Numbers of the form x^2 + 13y^2.
  • A247892 (program): Number of nonprimes in n-th row of triangle A077581.
  • A247894 (program): Integer part of square root of A010807: a(n) = floor(sqrt(n^19)).
  • A247897 (program): First differences of A247676
  • A247898 (program): First differences of A247678
  • A247899 (program): First differences of A247679
  • A247900 (program): First differences of A247681.
  • A247901 (program): First differences of A247682
  • A247902 (program): First differences of A247683
  • A247903 (program): Start with a single square; at n-th generation add a square at each expandable vertex (this is the “vertex to side” version); a(n) is the sum of all label values at n-th generation. (See comment for construction rules.)
  • A247904 (program): Start with a single pentagon; at n-th generation add a pentagon at each expandable vertex (this is the “vertex to side” version); a(n) is the sum of all label values at n-th generation. (See comment for construction rules.)
  • A247905 (program): Start with a single hexagon; at n-th generation add a hexagon at each expandable vertex (this is the “vertex to side” version); a(n) is the sum of all label values at n-th generation. (See comment for construction rules.)
  • A247907 (program): Expansion of (1 + x) / ((1 - x^4) * (1 - x - x^5)) in powers of x.
  • A247917 (program): Expansion of 1 / (1 + x - x^3) in powers of x.
  • A247918 (program): Expansion of (1 + x) / ((1 - x^4) * (1 + x^4 - x^5)) in powers of x.
  • A247919 (program): Expansion of 1 / (1 + x^4 - x^5) in powers of x.
  • A247920 (program): Expansion of 1 / (1 + x + x^2 - x^5) in powers of x.
  • A247936 (program): Riordan array ((1-2x)/(1-3x), 2x).
  • A247951 (program): a(n) = Product_{i=1..n} sigma_2(i).
  • A247954 (program): a(n) = sigma(sigma(2n-1)).
  • A247964 (program): Beatty sequence for e^(1/3): a(n)=floor(n*(e^(1/3)))
  • A247968 (program): a(n) = least k such that (k!*e^k)/(sqrt(2*Pi)*k^(k+1/2)) - 1 < 1/2^n.
  • A247970 (program): a(n) is the smallest k such that prime(k+i) (mod 6) takes successively the values 5,1,5,1… for i = 0, 1,…,n-1 ending with 1 or 5.
  • A247971 (program): Least k such that 4*k/v(2*k)^2 - Pi < 1/n, where the sequence v is defined in Comments.
  • A247973 (program): Least k such that Pi - (4*k+2)/v(2*k+2)^2 < 1/n, where the sequence v is defined in Comments.
  • A247974 (program): Numbers k such that A247973(k+1) = A247973(k).
  • A247976 (program): Triangle read by rows: T(n,k) generated by m-gon expansions in the case of odd m with “vertex to vertex” version or even m with “vertex to side” version. (See comment for details.)
  • A247983 (program): Least number k such that log(2) - sum{1/(h*2^h), h=1..k} < 1/2^n.
  • A247984 (program): Constant terms of congruences derived from a permutation polynomial motivated by generalized quadrangles.
  • A247985 (program): Least number k such that product{(k^2 + h)/(k^2 - h), h = 1..k} - e < 1/n.
  • A247986 (program): Numbers k such that A247985(k+1) - A247985(k) = 2.
  • A247987 (program): Numbers k such that A247985(k+1) - A247985(k) = 3.
  • A248003 (program): a(n) = (sum of totatives of n ) / (2^(omega(n)-1)); a(n) = A023896(n) / A007875(n).
  • A248034 (program): a(n+1) gives the number of occurrences of the last digit of a(n) so far, up to and including a(n), with a(0)=0.
  • A248038 (program): 3n concatenated with itself.
  • A248045 (program): (2*(n-1))! * (2*n-1)! / (n * (n-1)!^3).
  • A248048 (program): Numerator of u(n) where u(n) = (u(n-1) + u(n-2)) * (u(n-2) + u(n-3)) / u(n-4) with u(0) = -1, u(1) = u(2) = u(3) = 1.
  • A248049 (program): a(n) = (a(n-1) + a(n-2)) * (a(n-2) + a(n-3)) / a(n-4) with a(0) = 2, a(1) = a(2) = a(3) = 1.
  • A248056 (program): Positions of 0,0 in the Thue-Morse sequence (A010060).
  • A248057 (program): Positions of 1,1 in the Thue-Morse sequence (A010060).
  • A248076 (program): Partial sums of the sum of the 5th powers of the divisors of n: Sum_{i=1..n} sigma_5(i).
  • A248078 (program): a(1) = 1; a(n+1) = a(n) + product of digits of a(n) + sum of digits of a(n).
  • A248086 (program): Sum of the eccentricities of all vertices in the Lucas cube Lambda(n).
  • A248087 (program): Number of n-derangements that have an odd number of 2-cycles.
  • A248088 (program): a(n) = Sum_{k=0..floor(n/4)} binomial(n-3k, k)*(-3)^(3k)*4^(n-4k).
  • A248089 (program): a(n) = Sum_{k=0..floor(n/4)} binomial(n-k, 3k)*(-3)^(3k)*4^(n-4k).
  • A248092 (program): Triangle read by rows: T(n,k) is the largest inversion number of the n-permutations having k cycles.
  • A248098 (program): a(n) = 1 + a(n-1) + a(n-2) + a(n-3) if n>=4; a(1) = a(2) = a(3) = 1.
  • A248100 (program): Number of ordered trees with n edges such that non-leaf vertices at even levels have outdegree 1 and those at odd levels have outdegree 2.
  • A248101 (program): Completely multiplicative with a(prime(n)) = prime(n)^((n+1) mod 2).
  • A248103 (program): Least k such that ((2k+1)/(2k-1))^k < 1/(2n^2).
  • A248104 (program): Positions of 0,1,0 in the Thue-Morse sequence (A010060).
  • A248105 (program): Positions of 1,0,1 in the Thue-Morse sequence (A010060).
  • A248109 (program): Integer part of square root of A010811(n) = n^23.
  • A248121 (program): a(n) = floor(1 / (1/n - Pi^2/6 + Sum_{h=1..n} 1/h^2)).
  • A248126 (program): n squared with each digit repeated.
  • A248132 (program): Integer part of square root of A010813(n) = n^25.
  • A248150 (program): Numbers whose sum of divisors (A000203) is divisible by 4.
  • A248151 (program): Numbers n such that the sum of the divisors of n is not divisible by 4.
  • A248152 (program): a(n) = 48 * 4^n * (2*n-1)!! * (2*n+3)!! / ((n+2)! * (n+4)!).
  • A248155 (program): Expansion of (1 + x - x^2)/((1 + x)*(1 + 2*x)).
  • A248156 (program): Inverse Riordan triangle of A106513: Riordan ((1 - 2*x^2 )/(1 + x), x/(1+x)).
  • A248157 (program): Expansion of (1 - 2*x^2)/(1 + x)^2. First column of Riordan triangle A248156.
  • A248158 (program): Expansion of (1 - 2*x^2)/(1 + x)^3. Second column of Riordan triangle A248156.
  • A248159 (program): Expansion of (1 - 2*x^2)/(1 + x)^4. Third column of Riordan triangle A248156.
  • A248160 (program): Expansion of (1 - 2*x^2)/(1 + x)^5. Fourth column of Riordan triangle A248156.
  • A248161 (program): Expansion of (2-x+x^2)/((1+x)*(1-3*x+x^2)).
  • A248163 (program): Chebyshev’s S polynomials (A049310) evaluated at 34/3 and multiplied by powers of 3 (A000244).
  • A248167 (program): G.f.: 1 / AGM(1-33*x, sqrt((1-9*x)*(1-121*x))).
  • A248168 (program): G.f.: 1/sqrt((1-3*x)*(1-11*x)).
  • A248170 (program): Nonnegative integer whose square is the closest square to prime(n).
  • A248174 (program): 2-adic order of the tribonacci sequence.
  • A248178 (program): Least k such that r - sum{1/F(n), h = 1..k} < 1/2^(n+1), where F(n) = A000045 (Fibonacci numbers) and r = sum{1/F(n), h = 1..infinity}.
  • A248179 (program): Decimal expansion of (2/27)*(9 + 2*sqrt(3)*Pi).
  • A248180 (program): Least k such that r - sum{1/C(2h+1,h), h = 0..k} < 1/2^n, where r = (2/27)*(9 + 2*sqrt(3)*Pi).
  • A248181 (program): Decimal expansion of Sum_{h >= 0} 1/binomial(h, floor(h/2)).
  • A248182 (program): Least k such that r - sum{1/C(h,[h/2]}, h = 0..k} < 1/2^n, where r = sum{1/C(h,[h/2]}, h = 0..infinity}.
  • A248183 (program): Least k such that 1/4 - sum{1/(h*(h+1)*(h+2))}, h = 1..k} < 1/n^2.
  • A248184 (program): Numbers k such that A248183(k+1) = A248183(k).
  • A248185 (program): Numbers k such that A248183(k+1) = A248183(k) + 1.
  • A248186 (program): Least k such that 1/18 - sum{1/(h*(h+1)*(h+2)*(h+3))}, h = 1..k} < 1/n^3.
  • A248187 (program): Numbers k such that A248186(k+1) = A248186(k).
  • A248188 (program): Numbers k such that A248186(k+1) = A248186(k) + 1.
  • A248193 (program): G.f.: Sum_{n>=0} x^n * Sum_{k=0..n} C(n,k)^2 * x^(5*k).
  • A248195 (program): Numbers k such that A248180(k+1) = A248180(k).
  • A248196 (program): Numbers k such that A248180(k+1) = A248180(k) + 1.
  • A248198 (program): a(n) = ceiling(n^3*(Pi/2)).
  • A248205 (program): Indices of centered octagonal numbers (A016754) that are also pentagonal numbers (A000326).
  • A248211 (program): First differences of omega(n), the number of distinct prime factors function (A001221).
  • A248216 (program): a(n) = 6^n - 2^n.
  • A248217 (program): a(n) = 8^n - 2^n.
  • A248221 (program): Numbers m such that 52*m + 1 is prime.
  • A248223 (program): Decimal expansion of (4/45)*Pi^3.
  • A248225 (program): a(n) = 6^n - 3^n.
  • A248226 (program): a(n) = 10^n - 3^n.
  • A248227 (program): Least k such that zeta(4) - sum{1/h^4, h = 1..k} < 1/n^3.
  • A248228 (program): Numbers k such that A248227(k+1) = A248227(k).
  • A248229 (program): Numbers k such that A248227(k+1) = A248227(k) + 1.
  • A248230 (program): a(n) = floor(1/(zeta(4) - Sum_{h=1..n} 1/h^4)).
  • A248231 (program): Least k such that zeta(5) - sum{1/h^5, h = 1..k} < 1/n^4.
  • A248232 (program): Numbers k such that A248231(k+1) = A248231(k).
  • A248233 (program): Numbers k such that A248231(k+1) = A248231(k) + 1.
  • A248324 (program): Square array read by antidiagonals downwards: super Patalan numbers of order 3.
  • A248325 (program): Square array read by antidiagonals downwards: super Patalan numbers of order 4.
  • A248333 (program): Number of unit squares enclosed by n lattice points in and along the first quadrant of the coordinate plane starting from (0,0) and moving along each square gnomon starting on the y-axis and ending on the x-axis.
  • A248334 (program): The subsequence of A246885 having even values.
  • A248337 (program): 6^n - 4^n.
  • A248338 (program): 10^n - 4^n.
  • A248339 (program): a(n) = 22*n+19.
  • A248340 (program): 10^n - 5^n.
  • A248341 (program): 10^n - 7^n.
  • A248343 (program): 10^n - 8^n.
  • A248345 (program): Signed version of A094953.
  • A248348 (program): a(n) = number of polynomials a_k*x^k + … + a_1*x + a_0 with k > 0, integer coefficients, only distinct integer roots, and a_0 = p^n (p is a prime).
  • A248363 (program): Decimal expansion of Gaussian gravitational constant in the astronomical system of units.
  • A248365 (program): 4n concatenated with itself.
  • A248373 (program): Partial sums of primes of form n^2 + (n+1)^2 + (n+2)^2 (A027864).
  • A248374 (program): The integer partition a(n) (compare A194602) has only the non-one addends n+1 and 2.
  • A248375 (program): a(n) = floor(9*n/8).
  • A248380 (program): a(n) = 1 if first player in Sylver coinage game can force a win by choosing n as the first number, otherwise a(n) = 2.
  • A248422 (program): Even integers concatenated with themselves.
  • A248423 (program): Multiples of 4 with digits backwards.
  • A248425 (program): Number of “squares” (repeated identical blocks) in the n-th Fibonacci word.
  • A248427 (program): Circumference of the (n,n)-knight graph.
  • A248428 (program): Number of length n+2 0..3 arrays with every three consecutive terms having the sum of some two elements equal to twice the third.
  • A248429 (program): Number of length n+2 0..4 arrays with every three consecutive terms having the sum of some two elements equal to twice the third.
  • A248434 (program): Number of length three 0..n arrays with the sum of two elements equal to twice the third.
  • A248462 (program): Number of length 1+2 0..n arrays with no three consecutive terms having the sum of any two elements equal to twice the third.
  • A248469 (program): Floor((2*n^2)/e).
  • A248474 (program): Numbers congruent to 13 or 17 mod 30.
  • A248479 (program): a(1) = 1, a(2) = 3, and from then on alternatively subtract and multiply two previous terms.
  • A248499 (program): Numbers m that are coprime to A059995(m): floor(m/10).
  • A248500 (program): Numbers m that are not coprime to A059995(m): floor(m/10).
  • A248505 (program): Alternating the subtraction and multiplication of two previous terms, starting with 3, 2.
  • A248514 (program): Fractal sequence of the dispersion of the “odious numbers”.
  • A248515 (program): Least number k such that 1 - k*sin(1/k) < 1/n^2.
  • A248516 (program): n^2+1 divided by its largest prime factor.
  • A248517 (program): Number of odd divisors > 1 in the numbers 1 through n, counted with multiplicity.
  • A248522 (program): Beatty sequence for 1/(1-exp(-1/3)): a(n) = floor(n/(1-exp(-1/3))).
  • A248527 (program): Numbers n such that the smallest prime divisor of n^2+1 is 13.
  • A248528 (program): Numbers n such that the smallest prime divisor of n^2+1 is 17.
  • A248533 (program): Number of length n+3 0..4 arrays with every four consecutive terms having the sum of some three elements equal to three times the fourth.
  • A248556 (program): Concatenate (3n-2,3n-1,3n).
  • A248558 (program): Squares of the digits of the decimal expansion of e.
  • A248559 (program): Least k such that log(2) - sum{1/(h*2^h), h = 1..k} < 1/3^n.
  • A248560 (program): Numbers k such that A248559(k+1) = A248559(k) + 1.
  • A248561 (program): Numbers k such that A248559(k+1) = A248559(k) + 2.
  • A248565 (program): Least k such that log(4/3) - sum{1/(h*4^h), h = 1..k} < 1/8^n.
  • A248566 (program): Numbers k such that A248565(k+1) = A248565(k) + 1.
  • A248567 (program): Numbers k such that A248565(k+1) = A248565(k) + 2.
  • A248572 (program): a(n) = 29*n + 1.
  • A248574 (program): a(n) = A027306(n) + A027306(n-1) for n > 0; a(0) = 1.
  • A248575 (program): Rounded sums of the non-integer cube roots of n, as partitioned by the integer roots: round[sum(j from n^3+1 to (n+1)^3-1, j^(1/3))].
  • A248577 (program): Product of the number of divisors of n and the number of distinct prime divisors of n; i.e., tau(n) * omega(n).
  • A248583 (program): The least number m == 1 (mod 6) that is divisible by prime(n).
  • A248586 (program): a(n)= Sum_{i=0..n} C(n,i)*C(2i,i)^2.
  • A248591 (program): Numerators of the (simplified) rationals n*2^(n - 1)/(n - 1)! .
  • A248592 (program): Denominators of the (simplified) rational numbers n*2^(n - 1)/(n - 1)! .
  • A248593 (program): Least positive integer m such that m + n divides F(m), where F(m) is the m-th Fibonacci number given by A000045.
  • A248598 (program): a(n) = (2*n+23)*n*(n-1), a coefficient appearing in the formula a(n)*Pi/324+n+1 giving the average number of regions into which n random planes divide the cube.
  • A248604 (program): Numbers a(n) which are the minimum number of moves needed in a variation of the tower of Hanoi with 4 towers and n disks.
  • A248605 (program): Partitions into parts of the form k(3k plus or minus 1)/2 (in other words: 1,2,5,7,12,15,…) with a set of frequencies which has no binary carry.
  • A248619 (program): a(n) = (n*(n+1))^4.
  • A248620 (program): Lesser of twin primes of (29n + 1, 29n + 3).
  • A248621 (program): Floor of sums of the squares of the non-integer cube roots of n, as partitioned by the integer roots: floor[sum(j from n^3+1 to (n+1)^3-1, j^(2/3))].
  • A248643 (program): a(n) = phi(2^n) - phi(n^2), with Euler’s totient function phi = A000010.
  • A248646 (program): Expansion of x*(5+x+x^2)/(1-2*x).
  • A248658 (program): G.f.: Sum_{n>=0} x^n * Sum_{k=0..n} binomial(n,k)^3 * x^(2*k).
  • A248663 (program): a(1) = 0; a(A000040(n)) = 2^(n-1), and a(n*m) = a(n) XOR a(m).
  • A248666 (program): Greatest common divisor of the coefficients of the polynomial p(n,x) defined in Comments.
  • A248667 (program): Numbers k for which coefficients of the polynomial p(k,x) defined in Comments are relatively prime.
  • A248668 (program): Sum of the numbers in the n-th row of the array at A248664.
  • A248671 (program): Number of subgroups of the dihedral group Dn that are intersections of some maximal subgroups.
  • A248674 (program): Decimal expansion of the solution to the Lane-Emden equation for a sphere of polytropic index n = 4.
  • A248675 (program): Decimal expansion of r = sum_{n >= 0} floor(n/2)!/n!.
  • A248682 (program): Decimal expansion of Sum_{n >= 0} (floor(n/2)!)^2/n!.
  • A248692 (program): Fully multiplicative with a(prime(i)) = 2^i; If n = product_{k >= 1} (p_k)^(c_k) where p_k is k-th prime A000040(k) and c_k >= 0 then a(n) = product_{k >= 1} 2^(k*c_k).
  • A248697 (program): Primes of the form k+(k+3)^2 where k is a nonnegative integer.
  • A248698 (program): Floor of sums of the non-integer fourth roots of n, as partitioned by the integer roots: floor[sum(j from n^4+1 to (n+1)^4-1, j^(1/4))].
  • A248699 (program): Expansion of (2 + x + 5*x^2 + 3*x^3 + 3*x^4 + x^5) / ((1 - x^3) * (1 - x^4)) in powers of x.
  • A248707 (program): f(3n)/(f(n-1)*f(n)*f(n+1)), where f(k) = k!.
  • A248708 (program): f(4n+2)/(f(n-1)*f(n)*f(n+1)*f(n+2)), where f(k) = k!.
  • A248709 (program): f(5n)/(f(n-2)*f(n-1)*f(n)*f(n+1)*f(n+2)), where f(k) = k!.
  • A248720 (program): a(n) = (n*(n+1))^5.
  • A248739 (program): a(n) = 29*n + ceiling(n/29).
  • A248740 (program): a(n) = Fibonacci(n) mod 1000.
  • A248742 (program): Numbers of the form x^2+1 with at most two prime factors.
  • A248744 (program): Number of different ways one can attack all squares on an n X n chessboard with n rooks.
  • A248746 (program): a(n) is the index k of the greatest prime divisor A002313(k) of n^2 + 1.
  • A248749 (program): Decimal expansion of limit of the real part of f(1+i,n), where f(x,0) = 1 and f(x,n) = x + 1/f(x,n-1).
  • A248750 (program): Decimal expansion of limit of the imaginary part of f(1+i,n), where f(x,0) = 1 and f(x,n) = x + 1/f(x,n-1).
  • A248751 (program): Decimal expansion of limit of the real part of f(1-i,n)/f(1-i,n+1), where f(x,n) is the n-th Fibonacci polynomial.
  • A248752 (program): Decimal expansion of limit of the imaginary part of f(1-i,n)/f(1-i,n+1), where f(x,n) is the n-th Fibonacci polynomial.
  • A248758 (program): Ceiling(n*Pi^(1/3)).
  • A248762 (program): Greatest cube that divides n!.
  • A248763 (program): Greatest k such that k^3 divides n!
  • A248764 (program): Greatest 4th power integer that divides n!
  • A248765 (program): Greatest k such that k^4 divides n!
  • A248766 (program): Greatest 4th-power-free divisor of n!
  • A248767 (program): Greatest 5th power integer that divides n!.
  • A248769 (program): Greatest 5th-power-free divisor of n!.
  • A248770 (program): Greatest 6th power integer that divides n!.
  • A248771 (program): Greatest k such that k^6 divides n!
  • A248772 (program): Greatest 6th-power-free divisor of n!.
  • A248773 (program): Greatest 7th power integer that divides n!.
  • A248774 (program): Greatest k such that k^7 divides n!
  • A248775 (program): Greatest 7th-power-free divisor of n!.
  • A248776 (program): Greatest 8th power integer that divides n!
  • A248777 (program): Greatest k such that k^8 divides n!
  • A248778 (program): Greatest 8th-power-free divisor of n!.
  • A248780 (program): Number of cubes that divide n!
  • A248781 (program): Number of integers k^4 that divide n!
  • A248786 (program): a(n) = 29*n + floor(n/29) + 0^n - 0^(n mod 29).
  • A248788 (program): Decimal expansion of (2-sqrt(e))^2, the mean fraction of guests without a napkin in Conway’s napkin problem.
  • A248792 (program): Numbers n such that sigma(n) - 1 is a prime p.
  • A248793 (program): Sigma(n) - 1 for n such that sigma(n) - 1 is prime.
  • A248800 (program): a(n) = (2*n^2 + 3 + (-1)^n)/2.
  • A248801 (program): Number of sets of nonzero squares with sum <= n
  • A248803 (program): Decimal expansion of the square root of 101.
  • A248806 (program): Number of 2’s separating successive 1’s in the Kolakoski sequence A000002.
  • A248808 (program): Irregular triangle read by rows: row n gives golden ratio base representation of Fibonacci number F_n.
  • A248810 (program): Signed version of A164984.
  • A248811 (program): Triangle read by rows: T(n,k) is the coefficient A_k in the transformation of 1 + x + x^2 + … + x^n to the polynomial A_k*(x+3)^k for 0 <= k <= n.
  • A248812 (program): Repeated terms of (2n)! (A010050).
  • A248814 (program): a(n) = (6n)!/(6!^n).
  • A248825 (program): a(n) = n^2 + 1 - (-1)^n.
  • A248826 (program): Triangle read by rows: T(n,k) is the coefficient A_k in the transformation of 1 + x + x^2 + … + x^n to the polynomial A_k*(x+k)^k for 0 <= k <= n.
  • A248827 (program): Row sums of A187783 and A089759.
  • A248828 (program): Number of 2n-length words, either empty or beginning with the first character of an n-ary alphabet, that can be built by repeatedly inserting doublets into the initially empty word.
  • A248829 (program): Triangle read by rows: T(n,k) is the coefficient A_k in the transformation of 1 + x + x^2 + … + x^n to the polynomial A_k*(x+2k)^k for 0 <= k <= n .
  • A248830 (program): Triangle read by rows: T(n,k) is the coefficient A_k in the transformation of 1 + x + x^2 + … + x^n to the polynomial A_k*(x-2k)^k for 0 <= k <= n.
  • A248833 (program): The curvature of touching circles inscribed in a special way in the larger segment of circle of radius 1/6 divided by a chord of length sqrt(8/75).
  • A248835 (program): a(n) = n + A033677(n), where A033677(n) is the smallest divisor of n >= sqrt(n).
  • A248836 (program): Number of length n arrays x(i), i=1..n with x(i) in 0..i and no value appearing more than 2 times
  • A248844 (program): Triangle read by rows: T(m,n) = number of ways of distributing n distinguishable balls into m distinguishable bins of size 2 where empty bins are permitted (m >= 1, 1 <= n <= 2m).
  • A248848 (program): Norm of coefficients in the expansion of 1/(1 - 3*x - I*x^2), where I^2=-1.
  • A248851 (program): a(n) = ( 2*n*(2*n^2 + 9*n + 14) + (-1)^n - 1 )/16.
  • A248866 (program): Discrete Heilbronn Triangle Problem: a(n) is twice the maximal area of the smallest triangle defined by three vertices that are a subset of n points on an n X n square lattice.
  • A248868 (program): Exponents n that make k! < k^n < (k+1)! hold true for some integer k > 1, in increasing order by k, then n (if applicable).
  • A248875 (program): First n elements of the Kolakoski sequence read as a ternary number.
  • A248877 (program): a(1) = 23, a(2) = 71, a(n) = 3*a(n-1) - 2*a(n-2) for n>2.
  • A248880 (program): Number of tilings of an n X 1 rectangle by tiles of dimension 1 X 1 and 2 X 1 such that every tile shares an equal-length edge with a tile of the same size.
  • A248882 (program): Expansion of Product_{k>=1} (1+x^k)^(k^3).
  • A248883 (program): Expansion of Product_{k>=1} (1+x^k)^(k^4).
  • A248884 (program): Expansion of Product_{k>=1} (1+x^k)^(k^5).
  • A248886 (program): Expansion of f(-x, -x) * f(x^2, x^4) in powers of x where f(, ) is Ramanujan’s general theta function.
  • A248897 (program): Decimal expansion of Sum_{i >= 0} (i!)^2/(2*i+1)!.
  • A248909 (program): Completely multiplicative with a(p) = p if p = 6k+1 and a(p) = 1 otherwise.
  • A248910 (program): Numbers with no zeros in base-6 representation.
  • A248914 (program): Decimal expansion of L = integral_{0..1} 1/(1-2t^2/3) dt, an auxiliary constant associated with one of the integral inequalities studied by David Boyd.
  • A248917 (program): a(n) = 2^n * n^2 + 1.
  • A248924 (program): Sequence derived from arithmetic relations between powers of phi (A001622): a(n) = phi^n - (-1)^n * (n - phi^-n).
  • A248928 (program): Interleave (2*n+2)^2 with (2*n+3)^2, both listed n+1 times.
  • A248955 (program): Number of polynomials a_k*x^k + … + a_1*x + n with k > 0, integer coefficients and distinct positive integer roots and positive integers n.
  • A248956 (program): Number of polynomials a_k*x^k + … + a_1*x + a_0 with k > 0, integer coefficients and only non-multiple positive integer roots and a_0 = p^n (p is a prime).
  • A248971 (program): Triangular array read by rows. T(n,k)=C(k,2)+C(n-k,2),n>=2,1<=k<=floor(n/2).
  • A248974 (program): Floor( 1/(n*sinh(1/n) + n*sin(1/n) - 2) ).
  • A248977 (program): Triangle read by rows: T(n,k) is the coefficient A_k in the transformation of 1 + x + x^2 + … + x^n to the polynomial A_k*(x+3k)^k for 0 <= k <= n.
  • A248978 (program): Triangle read by rows: T(n,k) is the coefficient A_k in the transformation of 1 + x + x^2 + … + x^n to the polynomial A_k*(x-3k)^k for 0 <= k <= n.
  • A249013 (program): a(n) = floor( (n-1) * (n+4) / 10 ).
  • A249014 (program): A double binomial sum.
  • A249015 (program): A binomial convolution.
  • A249020 (program): a(n) = floor( n * (n+5) / 10) + 1.
  • A249031 (program): The non-anti-Fibonacci numbers: numbers not in A075326.
  • A249032 (program): First differences of A075326.
  • A249034 (program): Odd numbers missing from A171947.
  • A249036 (program): a(1)=1, a(2)=2; thereafter a(n) = a(n-1-(number of even terms so far)) + a(n-1-(number of odd terms so far)).
  • A249037 (program): Number of even terms in first n terms of A249036.
  • A249038 (program): Number of odd terms in first n terms of A249036.
  • A249043 (program): a(1) = 42; a(n+1) = a(n) + sum of decimal digits of a(n).
  • A249051 (program): The smallest integer > 1 of exactly n consecutive integers divisible respectively by the first n natural numbers (A000027), or 0 if no such number exists.
  • A249059 (program): Row sums of the triangular array at A249057.
  • A249060 (program): Column 1 of the triangular array at A249057.
  • A249061 (program): a(n) is the least number of successive numbers 1, 2, 3, … which when added to n produce a prime number.
  • A249062 (program): A double binomial sum.
  • A249066 (program): a(n) is the number of new prime distinct divisors of n^2+1 not already present in m^2+1 for all m < n.
  • A249071 (program): a(n) = A004001(2*n) - n, where A004001 is Hofstadter-Conway $10000 sequence.
  • A249075 (program): Sum of the numbers in row n of the array at A249074.
  • A249076 (program): a(n) = (n*(n+1))^6.
  • A249079 (program): a(n) = 29*n + floor( n/29 ) + 0^( 1-floor( (14+(n mod 29))/29 ) ).
  • A249095 (program): Triangle read by rows: interleaving successive pairs of rows of Pascal’s triangle.
  • A249096 (program): {2*h^2, h >=1} union {3*k^2, k >=1}, in increasing order.
  • A249098 (program): Position of n^6 in the ordered union of {h^6, h >=1} and {3*k^6, k >=1}.
  • A249099 (program): Position of 3*n^6 in the ordered union of {h^6, h >=1} and {3*k^6, k >=1}.
  • A249101 (program): p(n,1), where p(n,x) is defined in Comments; sum of numbers in row n of the array at A249100.
  • A249102 (program): Numbers with no 1’s in base-7 expansion.
  • A249112 (program): Second smallest k > 0 such that n+(1+2+…+k) is prime.
  • A249113 (program): Take n and successively add 1, 2, …, a(n) until reaching a prime for the third time.
  • A249114 (program): Take the counting numbers and continue adding 1, 2, …, a(n) until one reaches a fourth prime.
  • A249115 (program): Floor(r*n), where r = (5 - sqrt(5))/2; the Beatty complement of A003231.
  • A249117 (program): Position of n^6 in the ordered union of {h^6, h >= 1} and {32*k^6, k >= 1}.
  • A249118 (program): Position of 32n^6 in the ordered union of {h^6, h >=1} and {32*k^6, k >=1}.
  • A249119 (program): Decimal expansion of Product_{k >= 0} 1+1/(2^(2^k)+1).
  • A249121 (program): a(n) = n - (sum of digits of n) - (product of digits of n).
  • A249122 (program): a(n) = floor(n / lpf(n^2 + 1)) where lpf(n^2 + 1) is the smallest prime divisor of n^2 + 1.
  • A249123 (program): Position of n^6 in the ordered union of {h^6, h >= 1} and {2*k^6, k >= 1}.
  • A249124 (program): Position of 2*n^6 in the ordered union of {h^6, h >= 1} and {2*k^6, k >= 1}.
  • A249127 (program): a(n) = n * floor(3*n/2).
  • A249131 (program): p(1,n), where the polynomial p(n,x) is defined in Comments; sum of the numbers in row n of the triangular array at A249130.
  • A249133 (program): Triangle read by rows: interleaving successive pairs of rows of Sierpiński’s triangle.
  • A249135 (program): Product of the n-th digit of Pi, the n-th digit of e and the n-th digit of the golden ratio phi.
  • A249139 (program): Triangular array read by rows: row n gives the coefficients of the polynomial p(n,x) defined in Comments.
  • A249140 (program): To obtain a(n), write the n-th composite number as a product of primes, subtract 1 from each prime and multiply.
  • A249142 (program): Let k be the difference between the smallest square >= n and n. Sequence gives difference between the smallest square >= k and k.
  • A249152 (program): Exponent of 2 in the hyperfactorials: a(n) = A007814(A002109(n)).
  • A249153 (program): Exponent of 2 in the hyperfactorial of 2n: a(n) = A007814(A002109(2n)).
  • A249154 (program): (n+1) times the number of 1’s in the binary expansion of n.
  • A249160 (program): Smallest number of iterations k such that A068527^(k)(n)=A068527^(k+1)(n).
  • A249164 (program): Numbers n such that the triangular number T(n) is equal to the sum of the pentagonal numbers P(m) and P(m+1) for some m.
  • A249165 (program): Number of cds-sortable permutations in S_n. That is, number of permutations for which application of some sequence of context directed swaps (“cds” operations) terminates in the identity.
  • A249166 (program): Odd integers concatenated with themselves.
  • A249169 (program): Fibonacci 16-step numbers, a(n) = a(n-1) + a(n-2) + … + a(n-16).
  • A249181 (program): a(n) = A057137(n)^2 where A057137 = 0,1,12,123,…,123…90,…
  • A249183 (program): a(n) = row n of triangle A249133, concatenated.
  • A249184 (program): A249183 seen as binary numbers.
  • A249190 (program): Number of length n+6 0..1 arrays with no seven consecutive terms having four times the sum of any three elements equal to three times the sum of the remaining four.
  • A249205 (program): Decimal expansion of the logarithmic capacity of the unit disk.
  • A249221 (program): Expansion of x*(1+5*x-2*x^3)/(1-6*x^2+2*x^4).
  • A249222 (program): Expansion of x*(1+5*x-5*x^3)/(1-6*x^2+5*x^4).
  • A249224 (program): Lpf (n(n+11)/2): least prime dividing n(n+11)/2.
  • A249226 (program): Denominators of constants A(a) related to the asymptotic LCM of arithmetic progressions a*n+b (a and b coprime).
  • A249227 (program): Number of length n+5 0..2 arrays with no six consecutive terms having two times the sum of any two elements equal to the sum of the remaining four
  • A249243 (program): Floor(1/((1 + 1/n)^(n + 1)) - e).
  • A249245 (program): Numbers k such that A249243(k+1) = A249243(k) + 1.
  • A249250 (program): Triangular array: row n gives the coefficients of the polynomial p(n,x) defined in Comments.
  • A249251 (program): Triangular array: row n gives the coefficients of the polynomial p(n,x) defined in Comments.
  • A249252 (program): Triangular array: row n gives the coefficients of the polynomial p(n,x) defined in Comments.
  • A249303 (program): Triangular array: row n gives the coefficients of the polynomial p(n,x) defined in Comments.
  • A249304 (program): Number of zeros in row n of triangle A249133.
  • A249306 (program): Denominators A027642(n) of Bernoulli numbers except for a(4*k+5)=2 instead of 1.
  • A249308 (program): Central terms of triangle A249307.
  • A249310 (program): Expansion of x*(1+7*x-6*x^3)/(1-8*x^2+6*x^4).
  • A249311 (program): Expansion of x*(1+9*x-8*x^3)/(1-10*x^2+8*x^4).
  • A249312 (program): Expansion of x*(1+11*x-10*x^3)/(1-12*x^2+10*x^4).
  • A249313 (program): Expansion of x*(1+13*x-12*x^3)/(1-14*x^2+12*x^4).
  • A249332 (program): a(n) = Sum_{k=0..2*n} binomial(2*n, k)^4.
  • A249333 (program): Number of regions formed by extending the sides of a regular n-gon.
  • A249343 (program): The exponent of the highest power of 3 dividing the product of the elements on the n-th row of Pascal’s triangle (A001142(n)).
  • A249344 (program): A(n,k) = exponent of the largest power of n-th prime which divides k, square array read by antidiagonals.
  • A249345 (program): The exponent of the highest power of 5 dividing the product of the elements on the n-th row of Pascal’s triangle.
  • A249347 (program): The exponent of the highest power of 7 dividing the product of the elements on the n-th row of Pascal’s triangle.
  • A249348 (program): a(n) = (A001147(n+1)^2-1)/8, where A001147(n+1) = 3*5*…*(2n+1).
  • A249349 (program): (A001147(n+1)-1)/2, equals the index of A249348(n) within the triangular numbers A000217.
  • A249352 (program): (A007559(n+1)^2-1)/9, where A007559(n) = 1*4*7*…*(3n-2).
  • A249353 (program): a(n) = phi(n) + sigma(sigma(n)).
  • A249354 (program): a(n) = n*(3*n^2 + 3*n + 1).
  • A249355 (program): Remainder of n!+2 divided by n+2
  • A249356 (program): 8*A200975(n)-7 where A200975 are the numbers on the diagonals in Ulam’s spiral.
  • A249367 (program): Numbers of the form 2n^2 or 3n^2.
  • A249370 (program): Numbers p*m^2, where p is an odd prime and m >= 1, arranged in increasing order.
  • A249407 (program): Numbers not in A249406.
  • A249419 (program): Least prime p>=prime(n) such that p + 2 == 0 (mod prime(n)).
  • A249420 (program): Least number m>1 such that m*prime(n)-2 is prime.
  • A249424 (program): Odd integers n such that A249151(n) = (n-1)/2.
  • A249428 (program): Numbers n such that A249151(2n+1) = n.
  • A249435 (program): a(1) = 0, after which one less than prime powers p^m with exponent m >= 2.
  • A249446 (program): Numbers n such that 2*(n^2-1) - 1 and 2*(n^2-1) + 1 are primes.
  • A249450 (program): Alternate Fibonacci numbers - 2.
  • A249452 (program): Numbers n such that A249441(n) = 3.
  • A249453 (program): a(0) = 4; for n>0, a(n) = a(n-1) + 2^n - 3.
  • A249454 (program): E.g.f. exp(x*(sqrt(4*x^2+1)+2*x)).
  • A249455 (program): Decimal expansion of 2/sqrt(e), a constant appearing in the expression of the asymptotic expected volume V(d) of the convex hull of randomly selected n(d) vertices (with replacement) of a d-dimensional unit cube.
  • A249457 (program): The numerator of curvatures of touching circles inscribed in a special way in the larger segment of a unit circle divided by a chord of length sqrt(84)5.
  • A249458 (program): The numerators of curvatures of touching circles inscribed in a special way in the smaller segment of unit circle divided by a chord of length sqrt(84)/5.
  • A249459 (program): a(n) = Sum_{k=0..n} k^(2*n).
  • A249460 (program): Number of proper colorings of the cube with at most n colors under rotational symmetry.
  • A249483 (program): Squares (A000290) which are also centered triangular numbers (A005448).
  • A249486 (program): Nonprime numbers n such that sigma(n) + n is prime.
  • A249512 (program): Expansion of 1/(1-x*sqrt(4*x^2+1)-2*x^2).
  • A249513 (program): Expansion of -(4*x*sqrt(4*x^2+1)+8*x^2+1)/((2*x^2-1)*sqrt(4*x^2+1) +4*x^3+x).
  • A249517 (program): Numbers n for which the digital sum A007953(n) and the digital product A007954(n) both contain the same distinct digits as the number n.
  • A249519 (program): Expansion of 4*x/(16*x+(sqrt(2)*sqrt(sqrt(1-16*x)+1)-1)*sqrt(1-16*x)-1).
  • A249522 (program): Decimal expansion of the expected product of two sides of a random Gaussian triangle in three dimensions.
  • A249538 (program): Decimal expansion of 3*sqrt(Pi), the average perimeter of a random Gaussian triangle in two dimensions.
  • A249545 (program): a(n) = number of representations of A020670(n) as x^2 + 7*y^2.
  • A249546 (program): Speed of light in km/h.
  • A249547 (program): a(n) = (10*n^2+8*n-1+(-1)^n)/8.
  • A249564 (program): E.g.f.: Sum_{n>=0} exp(x*n*(n+1)/2).
  • A249572 (program): Least positive integer whose decimal digits divide the plane into n+1 regions. Equivalently, least positive integer with n holes in its decimal digits.
  • A249576 (program): List of triples (r,s,t): the matrix M = [[1,4,4][1,3,2][1,2,1]] is raised to successive powers, then (r,s,t) are the square roots of M[3,1], M[1,1], M[1,3] respectively.
  • A249577 (program): List of triples (r,s,t): the matrix M = [[1,4,4][1,3,2][1,2,1]] is raised to successive negative powers, then (r,s,t) are the square roots of M[3,1], M[1,1], M[1,3] respectively.
  • A249578 (program): List of triples (r,s,t): the matrix M = [[4,12,9][2,7,6][1,4,4]] is raised to successive powers, then (r,s,t) are the square roots of M[3,1], M[1,1], M[1,3] respectively.
  • A249586 (program): Sum of the first n^3 cubes.
  • A249596 (program): Analog of A097717 in base 2.
  • A249600 (program): Decimal expansion of 1/phi + 1/phi^3 + 1/phi^5, where phi is the Golden Ratio.
  • A249601 (program): Decimal expansion of 1/phi + 1/phi^3 + 1/phi^5 + 1/phi^7, where phi is the Golden Ratio.
  • A249604 (program): a(n) = Sum_{i=1..n} Fibonacci(i)*10^(i-1).
  • A249605 (program): Dissectible numbers in the sense of Gunjikar and Kaprekar.
  • A249606 (program): Primes of the form 2k^2 + k + 2.
  • A249608 (program): Expansion of e.g.f.: exp(x) * BesselI(0, 2*x) * BesselI(0, 2*sqrt(2)*x).
  • A249624 (program): Numbers n such that the sum of n and the least prime>n (A151800(n)) is prime.
  • A249629 (program): Number of strings of length n over a 4-letter alphabet that begin with a nontrivial palindrome.
  • A249632 (program): Triangular array read by rows. T(n,k) is the number of labeled trees with black and white nodes having exactly k black nodes, n>=0, 0<=k<=n.
  • A249664 (program): In the n-th row of Pascal’s triangle, an odious entry is replaced by 1, an evil entry is replaced by 0 and the n-th row is converted to decimal.
  • A249666 (program): Numbers n such that the sum of n and the largest prime<n (A151799(n)) is prime.
  • A249670 (program): a(n) = A017665(n)*A017666(n).
  • A249674 (program): a(n) = 30*n.
  • A249679 (program): Terms of A007504 divisible by 3.
  • A249688 (program): a(n) = n-th Ramanujan number A000594(n), squared.
  • A249691 (program): a(n) = binomial(3*n,n)*(5*n+2)/(2*n+1).
  • A249693 (program): a(4n) = 3*n+1, a(2n+1) = 3*n+2, a(4n+2) = 3*n.
  • A249708 (program): Number of length 2+3 0..n arrays with every four consecutive terms having the maximum of some two terms equal to the minimum of the remaining two terms.
  • A249719 (program): Complement of A051382.
  • A249720 (program): a(n) = 2 * A249719(n).
  • A249721 (program): Numbers whose base-3 representation consists entirely of 0’s and 2’s, except possibly for a single pair of adjacent 1’s among them.
  • A249725 (program): Inverse permutation to A135764.
  • A249727 (program): Start with a(1) = 1; then numbers 1 .. primepi(2), followed by numbers 1 .. primepi(3), and then numbers 1 .. primepi(4), …, etc, where A000720 gives primepi.
  • A249728 (program): After a(1) = 1 each n appears A000720(n) times.
  • A249732 (program): Number of (not necessarily distinct) multiples of 4 on row n of Pascal’s triangle.
  • A249733 (program): Number of (not necessarily distinct) multiples of 9 on row n of Pascal’s triangle.
  • A249734 (program): Even bisection of A003961: Replace in 2n each prime factor p(k) with prime p(k+1).
  • A249735 (program): Odd bisection of A003961: Replace in 2n-1 each prime factor p(k) with prime p(k+1).
  • A249736 (program): Triangular numbers modulo 30.
  • A249739 (program): The smallest prime whose square divides n, 1 if n is squarefree.
  • A249740 (program): The largest prime whose square divides n, 1 if n is squarefree.
  • A249743 (program): Main diagonal of square arrays A114881 and A249741.
  • A249745 (program): Permutation of natural numbers: a(n) = (1 + A064989(A007310(n))) / 2.
  • A249746 (program): Permutation of natural numbers: a(n) = A126760(A249735(n)) = A249824(A064216(n)).
  • A249755 (program): Triangular array of coefficients of polynomials p(n,x) = (x + 1)*p(n-1,x) + (n + 1)*x, p(0,x) = 1.
  • A249756 (program): Triangular array of coefficients of polynomials p(n,x) = (x + 1)*p(n-1,x) + n*x, p(0,x) = 1.
  • A249757 (program): Triangular array of coefficients of polynomials p(n,x) = (x + 1)*p(n-1,x) + 2*n*x, p(0,x) = 1.
  • A249767 (program): a(n) = mu(n) + omega(n).
  • A249769 (program): Sequence of distinct least positive numbers such that the average of the first n terms is a factorial.
  • A249772 (program): Period of the senary (base-6) representation of 1/n, or 0 if 1/n terminates.
  • A249784 (program): Number of divisors of n^(n^n).
  • A249807 (program): a(0) = 1; afterwards a(n) is the smallest positive square that added to all previous terms produces a prime.
  • A249823 (program): Permutation of natural numbers: a(n) = A246277(A084967(n)).
  • A249824 (program): Permutation of natural numbers: a(n) = A078898(A003961(A003961(2*n))).
  • A249827 (program): Row 3 of A246278: replace in 2n each prime factor p(k) with prime p(k+2).
  • A249845 (program): Number of length 1+4 0..n arrays with no five consecutive terms having the maximum of any two terms equal to the minimum of the remaining three terms.
  • A249852 (program): a(n) is the total number of pentagons on the left or the right of the vertical symmetry axis of a pentagon expansion (vertex to vertex) after n iterations.
  • A249859 (program): Least common multiple of n + 2 and n - 2.
  • A249860 (program): a(n) = Least common multiple of n + 3 and n - 3.
  • A249862 (program): A special solution of X(n)^2 - 280*Y(n)^2 = 3^(2*n), n >= 0; here the X member.
  • A249863 (program): Chebyshev S polynomial (A049310) evaluated at x = 26/7 and multiplied by powers of 7 (A000420).
  • A249864 (program): A special solution of X(n)^2 - 120*Y(n)^2 = 7^(2*n), n >= 0. The present sequence gives the X values.
  • A249866 (program): Characteristic triangle for primitive Pythagorean triples.
  • A249869 (program): Triangle giving the area of primitive Pythagorean triangles, with zero entries for non-primitive triangles.
  • A249884 (program): Number of length 1+6 0..n arrays with no seven consecutive terms having the maximum of any three terms equal to the minimum of the remaining four terms.
  • A249891 (program): G.f.: Sum_{n>=0} x^n / (1+x)^(2*n+1) * [Sum_{k=0..n} C(n,k)^2 * x^k] * [Sum_{k=0..n} C(n,k)^2 * (-x)^k].
  • A249892 (program): G.f.: Sum_{n>=0} x^n / (1 - n*x - n^2*x^2).
  • A249901 (program): a(n) = mu(n) + bigomega(n).
  • A249904 (program): a(n) = mu(n) + sigma(n) - n.
  • A249908 (program): G.f. (1-x)/(2*sqrt(5*x^2 + 2*x + 1)) - 1/2.
  • A249910 (program): Digital root of A003500(n).
  • A249911 (program): 60-gonal (hexacontagonal) numbers: a(n) = n(29n - 28).
  • A249914 (program): Number of partitions of 4n with equal sums of odd and even parts.
  • A249916 (program): a(n) = 4*(n - 1) - a(n-3), n >= 3, a(0) = a(1) = 1, a(2) = 5.
  • A249919 (program): Number of LCD (liquid-crystal display) segments needed to display n in binary.
  • A249922 (program): E.g.f. satisfies: A(x) = x + 4*A(x)^5/5.
  • A249924 (program): G.f. A(x) satisfies: x = A(x) - 3*A(x)^2 + A(x)^3.
  • A249925 (program): G.f. satisfies: A(x) = 1 + 2*x*A(x) + 5*x^2*A(x)^2.
  • A249938 (program): E.g.f.: Sum_{n>=0} exp(n^2*x) / 2^(n+1).
  • A249939 (program): E.g.f.: 1/(5 - 4*cosh(x)).
  • A249940 (program): E.g.f.: 1 + Sum_{n>=1} 2*exp(n^2*x) / 2^n.
  • A249941 (program): E.g.f.: Sum_{n>=0} exp(n^3*x) / 2^(n+1).
  • A249944 (program): Numerator of fraction equal to the finite continued fraction [2,7,1,8,2,…] (first n digits of e).
  • A249945 (program): a(n) = n! + 3^n.
  • A249946 (program): G.f.: Sum_{n>=0} x^n/(1-x)^(3*n) * Sum_{k=0..n} C(n,k)^2 * x^k.
  • A249947 (program): Number of available orbitals at increasing subshells in multi-electron atoms.
  • A249950 (program): Numerator of the harmonic mean of the first n cubes.
  • A249961 (program): Number of length 1+5 0..n arrays with no six consecutive terms having the maximum of any two terms equal to the minimum of the remaining four terms.
  • A249983 (program): Number of length 3+1 0..2*n arrays with the sum of the absolute values of adjacent differences equal to 3*n.
  • A249991 (program): Start with the natural numbers, reverse the order in each pair, skip one number, reverse the order in each triple, skip one number, and so on.
  • A249992 (program): Expansion of 1/((1+x)*(1+2*x)*(1-3*x)).
  • A249993 (program): Expansion of 1/((1+x)*(1+2*x)*(1-4*x)).
  • A249994 (program): Expansion of 1/((1-2*x)*(1+3*x)*(1-4*x)).
  • A249995 (program): Expansion of 1/((1+2*x)*(1-3*x)*(1-4*x)).
  • A249996 (program): Expansion of 1/((1+2*x)*(1+3*x)*(1-4*x)).
  • A249997 (program): Expansion of 1/((1-x)*(1+3*x)*(1-4*x)).
  • A249998 (program): Expansion of 1/((1+x)*(1+3*x)*(1-4*x)).

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