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): Trian