List of integer sequences with links to LODA programs.

  • A249999 (program): Expansion of 1/((1-x)^2(1-2x)(1-3x)).
  • A250000 (program): Peaceable coexisting armies of queens: the maximum number m such that m white queens and m black queens can coexist on an n X n chessboard without attacking each other.
  • A250015 (program): Number of length 1+5 0..n arrays with no six consecutive terms having the maximum of any three terms equal to the minimum of the remaining three terms.
  • A250024 (program): 40n - 21.
  • A250069 (program): a(n) = n^2 mod gpf(n^2 + 1) where gpf(k) is the greatest prime dividing k.
  • A250082 (program): Number of length 1+5 0..n arrays with every six consecutive terms having the maximum of some two terms equal to the minimum of the remaining four terms.
  • A250108 (program): n(n-1)/2 mod 2 + n(n-1)/2 - n*( (n-1) mod 2 ).
  • A250120 (program): Coordination sequence for planar net 3.3.3.3.6 (also called the fsz net).
  • A250121 (program): Crystal ball sequence for planar net 3.3.3.3.6.
  • A250130 (program): Numerator of the harmonic mean of the first n primes.
  • A250141 (program): Number of length 2+2 0..n arrays with the medians of every three consecutive terms nondecreasing.
  • A250162 (program): Number of length n+1 0..3 arrays with the sum of adjacent differences multiplied by some arrangement of +-1 equal to zero.
  • A250212 (program): Second partial sums of seventh powers (A001015).
  • A250230 (program): Number of length 3+1 0..n arrays with the sum of the cubes of adjacent differences multiplied by some arrangement of +-1 equal to zero.
  • A250257 (program): Least nonnegative integer whose decimal digits divide the plane into n regions.
  • A250309 (program): a(n) = a(n-1)*(1 + a(n-1)/a(n-3)), with a(0) = a(1) = a(2) = 1.
  • A250337 (program): Number of length 1+5 0..n arrays with every six consecutive terms having the maximum of some three terms equal to the minimum of the remaining three terms.
  • A250352 (program): Number of length 3 arrays x(i), i=1..3 with x(i) in i..i+n and no value appearing more than 2 times.
  • A250353 (program): Number of length 4 arrays x(i), i=1..4 with x(i) in i..i+n and no value appearing more than 2 times.
  • A250354 (program): Number of length 5 arrays x(i), i=1..5 with x(i) in i..i+n and no value appearing more than 2 times.
  • A250362 (program): Number of length 4 arrays x(i), i=1..4 with x(i) in i..i+n and no value appearing more than 3 times.
  • A250363 (program): Number of length 5 arrays x(i), i=1..5 with x(i) in i..i+n and no value appearing more than 3 times.
  • A250388 (program): Number of length 2+3 0..n arrays with no four consecutive terms having the maximum of any two terms equal to the minimum of the remaining two terms.
  • A250427 (program): Number of (n+1)X(3+1) 0..1 arrays with nondecreasing sum of every two consecutive values in every row and column
  • A250429 (program): Number of (n+1)X(5+1) 0..1 arrays with nondecreasing sum of every two consecutive values in every row and column
  • A250461 (program): Number of (n+1)X(1+1) 0..1 arrays with nondecreasing min(x(i,j),x(i,j-1)) in the i direction and nondecreasing min(x(i,j),x(i-1,j)) in the j direction.
  • A250480 (program): a(1) = 0, and for n > 1: if n is a prime, a(n) = n, otherwise a(n) = A020639(n) - 1, where A020639(n) gives the least prime dividing n.
  • A250554 (program): Number of length n+2 0..1 arrays with the sum of second differences multiplied by some arrangement of +-1 equal to zero.
  • A250576 (program): Number of (n+1) X (1+1) 0..1 arrays with nondecreasing max(x(i,j),x(i,j-1)) in the i direction and nondecreasing min(x(i,j),x(i-1,j)) in the j direction.
  • A250605 (program): Number of (n+1) X (2+1) 0..1 arrays with nondecreasing x(i,j)-x(i,j-1) in the i direction and nondecreasing x(i,j)-x(i-1,j) in the j direction.
  • A250606 (program): Number of (n+1) X (3+1) 0..1 arrays with nondecreasing x(i,j)-x(i,j-1) in the i direction and nondecreasing x(i,j)-x(i-1,j) in the j direction.
  • A250653 (program): Number of (n+1)X(5+1) 0..1 arrays with nondecreasing x(i,j)-x(i,j-1) in the i direction and nondecreasing min(x(i,j),x(i-1,j)) in the j direction
  • A250654 (program): Number of (n+1) X (6+1) 0..1 arrays with nondecreasing x(i,j)-x(i,j-1) in the i direction and nondecreasing min(x(i,j),x(i-1,j)) in the j direction.
  • A250655 (program): Number of (n+1) X (7+1) 0..1 arrays with nondecreasing x(i,j)-x(i,j-1) in the i direction and nondecreasing min(x(i,j),x(i-1,j)) in the j direction.
  • A250657 (program): Number of (3+1)X(n+1) 0..1 arrays with nondecreasing x(i,j)-x(i,j-1) in the i direction and nondecreasing min(x(i,j),x(i-1,j)) in the j direction
  • A250658 (program): Number of (4+1) X (n+1) 0..1 arrays with nondecreasing x(i,j)-x(i,j-1) in the i direction and nondecreasing min(x(i,j),x(i-1,j)) in the j direction.
  • A250659 (program): Number of (5+1) X (n+1) 0..1 arrays with nondecreasing x(i,j)-x(i,j-1) in the i direction and nondecreasing min(x(i,j),x(i-1,j)) in the j direction.
  • A250660 (program): Number of (6+1) X (n+1) 0..1 arrays with nondecreasing x(i,j)-x(i,j-1) in the i direction and nondecreasing min(x(i,j),x(i-1,j)) in the j direction.
  • A250661 (program): Number of (7+1) X (n+1) 0..1 arrays with nondecreasing x(i,j)-x(i,j-1) in the i direction and nondecreasing min(x(i,j),x(i-1,j)) in the j direction.
  • A250723 (program): Number of (n+1) X (2+1) 0..1 arrays with nondecreasing x(i,j)+x(i,j-1) in the i direction and nondecreasing min(x(i,j),x(i-1,j)) in the j direction.
  • A250730 (program): Number of (1+1)X(n+1) 0..1 arrays with nondecreasing x(i,j)+x(i,j-1) in the i direction and nondecreasing min(x(i,j),x(i-1,j)) in the j direction
  • A250737 (program): Number of (n+1) X (3+1) 0..1 arrays with nondecreasing x(i,j)-x(i,j-1) in the i direction and nonincreasing x(i,j)-x(i-1,j) in the j direction.
  • A250738 (program): Number of (n+1) X (4+1) 0..1 arrays with nondecreasing x(i,j)-x(i,j-1) in the i direction and nonincreasing x(i,j)-x(i-1,j) in the j direction.
  • A250739 (program): Number of (n+1) X (5+1) 0..1 arrays with nondecreasing x(i,j)-x(i,j-1) in the i direction and nonincreasing x(i,j)-x(i-1,j) in the j direction.
  • A250740 (program): Number of (n+1) X (6+1) 0..1 arrays with nondecreasing x(i,j)-x(i,j-1) in the i direction and nonincreasing x(i,j)-x(i-1,j) in the j direction.
  • A250741 (program): Number of (n+1) X (7+1) 0..1 arrays with nondecreasing x(i,j)-x(i,j-1) in the i direction and nonincreasing x(i,j)-x(i-1,j) in the j direction.
  • A250749 (program): Number of (n+1) X (2+1) 0..2 arrays with nondecreasing x(i,j)-x(i,j-1) in the i direction and nondecreasing x(i,j)+x(i-1,j) in the j direction.
  • A250750 (program): Number of (n+1) X (3+1) 0..2 arrays with nondecreasing x(i,j)-x(i,j-1) in the i direction and nondecreasing x(i,j)+x(i-1,j) in the j direction.
  • A250751 (program): Number of (n+1) X (4+1) 0..2 arrays with nondecreasing x(i,j)-x(i,j-1) in the i direction and nondecreasing x(i,j)+x(i-1,j) in the j direction.
  • A250753 (program): Number of (n+1) X (6+1) 0..2 arrays with nondecreasing x(i,j)-x(i,j-1) in the i direction and nondecreasing x(i,j)+x(i-1,j) in the j direction.
  • A250754 (program): Number of (n+1) X (7+1) 0..2 arrays with nondecreasing x(i,j)-x(i,j-1) in the i direction and nondecreasing x(i,j)+x(i-1,j) in the j direction.
  • A250756 (program): Number of (1+1) X (n+1) 0..2 arrays with nondecreasing x(i,j)-x(i,j-1) in the i direction and nondecreasing x(i,j)+x(i-1,j) in the j direction.
  • A250757 (program): Number of (2+1) X (n+1) 0..2 arrays with nondecreasing x(i,j)-x(i,j-1) in the i direction and nondecreasing x(i,j)+x(i-1,j) in the j direction.
  • A250758 (program): Number of (3+1) X (n+1) 0..2 arrays with nondecreasing x(i,j)-x(i,j-1) in the i direction and nondecreasing x(i,j)+x(i-1,j) in the j direction.
  • A250759 (program): Number of (4+1) X (n+1) 0..2 arrays with nondecreasing x(i,j)-x(i,j-1) in the i direction and nondecreasing x(i,j)+x(i-1,j) in the j direction.
  • A250760 (program): Number of (5+1) X (n+1) 0..2 arrays with nondecreasing x(i,j)-x(i,j-1) in the i direction and nondecreasing x(i,j)+x(i-1,j) in the j direction.
  • A250761 (program): Number of (6+1) X (n+1) 0..2 arrays with nondecreasing x(i,j)-x(i,j-1) in the i direction and nondecreasing x(i,j)+x(i-1,j) in the j direction.
  • A250762 (program): Number of (7+1) X (n+1) 0..2 arrays with nondecreasing x(i,j)-x(i,j-1) in the i direction and nondecreasing x(i,j)+x(i-1,j) in the j direction.
  • A250764 (program): Number of (n+1) X (3+1) 0..1 arrays with nondecreasing x(i,j)-x(i,j-1) in the i direction and nondecreasing absolute value of x(i,j)-x(i-1,j) in the j direction.
  • A250765 (program): Number of (n+1) X (4+1) 0..1 arrays with nondecreasing x(i,j)-x(i,j-1) in the i direction and nondecreasing absolute value of x(i,j)-x(i-1,j) in the j direction.
  • A250766 (program): Number of (n+1) X (5+1) 0..1 arrays with nondecreasing x(i,j)-x(i,j-1) in the i direction and nondecreasing absolute value of x(i,j)-x(i-1,j) in the j direction.
  • A250767 (program): Number of (n+1) X (6+1) 0..1 arrays with nondecreasing x(i,j)-x(i,j-1) in the i direction and nondecreasing absolute value of x(i,j)-x(i-1,j) in the j direction.
  • A250768 (program): Number of (n+1) X (7+1) 0..1 arrays with nondecreasing x(i,j)-x(i,j-1) in the i direction and nondecreasing absolute value of x(i,j)-x(i-1,j) in the j direction.
  • A250770 (program): Number of (2+1) X (n+1) 0..1 arrays with nondecreasing x(i,j)-x(i,j-1) in the i direction and nondecreasing absolute value of x(i,j)-x(i-1,j) in the j direction.
  • A250771 (program): Number of (3+1) X (n+1) 0..1 arrays with nondecreasing x(i,j)-x(i,j-1) in the i direction and nondecreasing absolute value of x(i,j)-x(i-1,j) in the j direction.
  • A250772 (program): Number of (4+1) X (n+1) 0..1 arrays with nondecreasing x(i,j)-x(i,j-1) in the i direction and nondecreasing absolute value of x(i,j)-x(i-1,j) in the j direction.
  • A250777 (program): Number of (n+1) X (2+1) 0..1 arrays with nondecreasing x(i,j)+x(i,j-1) in the i direction and nondecreasing absolute value of x(i,j)-x(i-1,j) in the j direction.
  • A250778 (program): Number of (n+1) X (3+1) 0..1 arrays with nondecreasing x(i,j)+x(i,j-1) in the i direction and nondecreasing absolute value of x(i,j)-x(i-1,j) in the j direction.
  • A250806 (program): Number of (n+1) X (2+1) 0..2 arrays with nondecreasing x(i,j)-x(i,j-1) in the i direction and nondecreasing min(x(i,j),x(i-1,j)) in the j direction.
  • A250807 (program): Number of (n+1) X (3+1) 0..2 arrays with nondecreasing x(i,j)-x(i,j-1) in the i direction and nondecreasing min(x(i,j),x(i-1,j)) in the j direction.
  • A250813 (program): Number of (1+1) X (n+1) 0..2 arrays with nondecreasing x(i,j)-x(i,j-1) in the i direction and nondecreasing min(x(i,j),x(i-1,j)) in the j direction.
  • A250814 (program): Number of (2+1) X (n+1) 0..2 arrays with nondecreasing x(i,j)-x(i,j-1) in the i direction and nondecreasing min(x(i,j),x(i-1,j)) in the j direction.
  • A250820 (program): Number of (n+2)X(1+2) 0..1 arrays with nondecreasing maximum minus minimum of every three consecutive values in every row and column
  • A250870 (program): Number of (n+1) X (1+1) 0..3 arrays with nondecreasing x(i,j)-x(i,j-1) in the i direction and nondecreasing x(i,j)+x(i-1,j) in the j direction.
  • A250878 (program): Number of (1+1) X (n+1) 0..3 arrays with nondecreasing x(i,j)-x(i,j-1) in the i direction and nondecreasing x(i,j)+x(i-1,j) in the j direction.
  • A250879 (program): Number of (2+1) X (n+1) 0..3 arrays with nondecreasing x(i,j)-x(i,j-1) in the i direction and nondecreasing x(i,j)+x(i-1,j) in the j direction.
  • A251091 (program): a(n) = n^2 / gcd(n+2, 4).
  • A251260 (program): Expansion of (1 + 2*x + x^2 + x^3) / ((1 - x^2)^2 * (1 - x^3) * (1 - x^4)) in powers of x.
  • A251269 (program): Number of (2+1) X (n+1) 0..1 arrays with no 2 X 2 subblock having x11-x00 less than x10-x01.
  • A251418 (program): Floor((n^2+7n-23)/14).
  • A251420 (program): Decimal expansion of Fisher’s percolation exponent in two dimensions, 187/91.
  • A251421 (program): Number of length n+2 0..1 arrays with the sum of the maximum minus twice the median plus the minimum of adjacent triples multiplied by some arrangement of +-1 equal to zero.
  • A251599 (program): Centers of rows of the triangular array formed by the natural numbers.
  • A251601 (program): Numbers n such that hexagonal numbers H(n) and H(n+1) sum to another hexagonal number.
  • A251602 (program): Numbers n such that hexagonal number H(n) is the sum of two consecutive hexagonal numbers.
  • A251610 (program): Determinants of the spiral knots S(4,k,(1,1,1)).
  • A251624 (program): Numbers n such that the octagonal numbers N(n), N(n+1) and N(n+2) sum to another octagonal number.
  • A251625 (program): Numbers n such that the octagonal number N(n) is the sum of three consecutive octagonal numbers.
  • A251630 (program): Column sums of the n X n square array filled with numbers from 1 to n^2, row by row, from left to right.
  • A251635 (program): Riordan array (1-2x,x), inverse of Riordan array (1/(1-2x), x) = A130321.
  • A251657 (program): a(n) = (2^n + 3)^n.
  • A251701 (program): a(n) = 3^n + n^2.
  • A251730 (program): Numbers n such that the sum of the triangular numbers T(n) and T(n+1) is equal to the sum of two pentagonal numbers P(m) and P(m+1) for some m.
  • A251743 (program): Pairs of nodes in a complete binary tree that are at an absolute height difference of less than 2 from each other.
  • A251754 (program): Digital root of A027444(n) = n + n^2 + n^3, n>=1. Repeat(3, 5, 3, 3, 2, 6, 3, 8, 9).
  • A251755 (program): Digital root of n + n^2.
  • A251758 (program): Let n>=2 be a positive integer with divisors 1 = d_1 < d_2 < … < d_k = n, and s = d_1d_2 + d_2d_3 + … + d_(k-1)*d_k. The sequence lists the values a(n) = floor(n^2/s).
  • A251780 (program): Digital root of A069778(n-1) = n^3 - n^2 + 1, n >= 1. Repeat(1, 6, 3, 7, 6, 6, 4, 6, 9).
  • A251867 (program): Numbers n such that n^2 + (n+1)^2 is equal to the sum of the hexagonal numbers H(m) and H(m+1) for some m.
  • A251914 (program): Numbers n such that the sum of the triangular numbers T(n) and T(n+1) is equal to the pentagonal number P(m) for some m.
  • A251924 (program): Numbers n such that the sum of the triangular numbers T(n) and T(n+1) is equal to a hexagonal number H(m) for some m.
  • A251936 (program): Number of length 2+2 0..n arrays with the sum of the maximum minus the median of adjacent triples multiplied by some arrangement of +-1 equal to zero.
  • A251963 (program): Numbers n such that the sum of the triangular numbers T(n) and T(n+1) is equal to an octagonal number N(m) for some m.
  • A251990 (program): Numbers n such that the sum of the hexagonal numbers H(n) and H(n+1) is equal to the sum of the pentagonal numbers P(m) and P(m+1) for some m.
  • A251991 (program): Numbers n such that the sum of the pentagonal numbers P(n) and P(n+1) is equal to the sum of the hexagonal numbers H(m) and H(m+1) for some m.
  • A252003 (program): Numbers n such that the sum of the octagonal numbers N(n) and N(n+1) is equal to the sum of the pentagonal numbers P(m) and P(m+1) for some m.
  • A252004 (program): Numbers n such that the sum of the pentagonal numbers P(n) and P(n+1) is equal to the sum of the octagonal numbers N(m) and N(m+1) for some m.
  • A252096 (program): Largest prime divisor of n^2+1 - smallest prime divisor of n^2+1.
  • A252178 (program): Number of length 2+2 0..n arrays with the sum of the maximum minus the minimum of adjacent triples multiplied by some arrangement of +-1 equal to zero.
  • A252233 (program): Characteristic function for the integers that are the product of an odd number of primes each with multiplicity one.
  • A252488 (program): Binary sequence starting with 1 and with run lengths given by the ruler sequence A001511.
  • A252489 (program): Index of the largest prime which divides n(n+1).
  • A252735 (program): a(1) = 0; for n > 1: a(2n) = a(n), a(2n+1) = 1 + a(A064989(n)).
  • A252736 (program): a(1) = a(2) = 0; for n > 2: a(2n) = 1 + a(n), a(2n+1) = a(A064989(2n+1)).
  • A252742 (program): Characteristic function of A246282: if A003961(n) > 2n, then a(n) = 1, otherwise 0 (when A003961(n) < 2n) [where A003961(n) shifts the prime factorization of n one step towards larger primes].
  • A252748 (program): a(n) = A003961(n) - 2*n.
  • A252749 (program): Partial sums of A252748: a(0) = 0, a(n) = A252748(n) + a(n-1).
  • A252814 (program): Number of n X 2 nonnegative integer arrays with upper left 0 and every value within 2 of its city block distance from the upper left and every value increasing by 0 or 1 with every step right or down.
  • A252870 (program): Number of n X 2 nonnegative integer arrays with upper left 0 and lower right n+2-4 and value increasing by 0 or 1 with every step right or down.
  • A252932 (program): Number of n X 2 nonnegative integer arrays with upper left 0 and every value within 3 of its king move distance from the upper left and every value increasing by 0 or 1 with every step right, diagonally se or down.
  • A252994 (program): Multiples of 26.
  • A253012 (program): a(n) = ceiling( (n+1) * (n+2) / 12).
  • A253068 (program): The subsequence A253066(2^n-1).
  • A253103 (program): A001045(n)^3.
  • A253122 (program): Number of length n+2 0..1 arrays with the sum of medians of adjacent triples multiplied by some arrangement of +-1 equal to zero.
  • A253130 (program): Number of length 2+2 0..n arrays with the sum of medians of adjacent triples multiplied by some arrangement of +-1 equal to zero.
  • A253145 (program): Triangular numbers (A000217) omitting the term 1.
  • A253175 (program): Indices of hexagonal numbers (A000384) which are also centered hexagonal numbers (A003215).
  • A253186 (program): Number of connected unlabeled loopless multigraphs with 3 vertices and n edges.
  • A253195 (program): Numbers congruent to 5 or 8 mod 9.
  • A253197 (program): a(n) = a(n-1) + a(n-2) + (1 - (-1)^(a(n-1) + a(n-2))) with a(0) = 0, a(1) = 1.
  • A253203 (program): The least square larger than n with same parity as n.
  • A253208 (program): a(n) = 4^n + 3.
  • A253209 (program): a(n) = 6^n + 5.
  • A253210 (program): a(n) = 7^n + 6.
  • A253211 (program): a(n) = 8^n + 7.
  • A253212 (program): a(n) = 9^n + 8.
  • A253213 (program): a(n) = 10^n + 9.
  • A253262 (program): Expansion of (x + x^2 + x^3) / (1 - x + x^2 - x^3 + x^4) in powers of x.
  • A253285 (program): a(n) = RF(n+1,3)*C(n+2,n-1), where RF(a,n) is the rising factorial.
  • A253298 (program): Digital root for the following sequences, F(4n)/F(4); F(12n)/F(12); F(20*n)/F(20), where the pattern increases by 8, ad infinitum, with the Fibonacci numbers F = A000045.
  • A253368 (program): a(n) = F(12*n)/(12^2) with the Fibonacci numbers F = A000045.
  • A253430 (program): Number of (n+1) X (3+1) 0..1 arrays with every 2 X 2 subblock diagonal minus antidiagonal sum nondecreasing horizontally, vertically and ne-to-sw antidiagonally.
  • A253431 (program): Number of (n+1) X (4+1) 0..1 arrays with every 2 X 2 subblock diagonal minus antidiagonal sum nondecreasing horizontally, vertically and ne-to-sw antidiagonally.
  • A253432 (program): Number of (n+1) X (5+1) 0..1 arrays with every 2 X 2 subblock diagonal minus antidiagonal sum nondecreasing horizontally, vertically and ne-to-sw antidiagonally.
  • A253433 (program): Number of (n+1) X (6+1) 0..1 arrays with every 2 X 2 subblock diagonal minus antidiagonal sum nondecreasing horizontally, vertically and ne-to-sw antidiagonally.
  • A253434 (program): Number of (n+1) X (7+1) 0..1 arrays with every 2 X 2 subblock diagonal minus antidiagonal sum nondecreasing horizontally, vertically and ne-to-sw antidiagonally.
  • A253437 (program): Number of (3+1) X (n+1) 0..1 arrays with every 2 X 2 subblock diagonal minus antidiagonal sum nondecreasing horizontally, vertically and ne-to-sw antidiagonally.
  • A253445 (program): a(n) = concatenation of n^2 with itself.
  • A253447 (program): Indices of centered octagonal numbers (A016754) which are also centered heptagonal numbers (A069099).
  • A253458 (program): Indices of centered heptagonal numbers (A069099) which are also centered hexagonal numbers (A003215).
  • A253470 (program): Indices of centered triangular numbers (A005448) which are also centered pentagonal numbers (A005891).
  • A253472 (program): Square Pairs: Numbers n such that 1, 2, …, 2n can be partitioned into n pairs, where each pair adds up to a perfect square.
  • A253475 (program): Indices of centered square numbers (A001844) which are also centered hexagonal numbers (A003215).
  • A253487 (program): Number of lattice paths of 2*n+2 steps in the first quadrant from (0,0) to (n,n).
  • A253503 (program): Number of (n+2) X (1+2) 0..1 arrays with every 2 X 2 and 3 X 3 subblock diagonal maximum minus antidiagonal minimum nondecreasing horizontally and vertically.
  • A253513 (program): The characteristic function of the multiples of eight.
  • A253514 (program): Centered heptagonal numbers (A069099) which are also centered octagonal numbers (A016754).
  • A253515 (program): Count down from 2k to 1, then from 2(k+1) to 1 and so on.
  • A253546 (program): Centered hexagonal numbers (A003215) which are also centered heptagonal numbers (A069099).
  • A253560 (program): Multiply n by its largest prime factor: a(n) = A006530(n) * n.
  • A253570 (program): Maximum number of circles of radius 1 that can be packed into a regular n-gon with side length 2 (conjectured).
  • A253580 (program): A fractal tree, read by rows: for n > 1: T(n,0) = T(n-1,0)+2, T(n,2n) = T(n-1,0)+3, and for k=1..2n-1: T(n,k) = T(n-1,k-1).
  • A253608 (program): The binary representation of a(n) is the concatenation of n and the binary complement of n, A035327(n).
  • A253621 (program): Indices of centered heptagonal numbers (A069099) which are also centered pentagonal numbers (A005891).
  • A253622 (program): Centered heptagonal numbers (A069099) which are also centered pentagonal numbers (A005891).
  • A253636 (program): Second partial sums of eighth powers (A001016).
  • A253637 (program): Second partial sums of ninth powers (A001017).
  • A253641 (program): Largest integer b such that n=a^b for some integer a; a(0)=a(1)=1 by convention.
  • A253654 (program): Indices of pentagonal numbers (A000326) which are also centered pentagonal numbers (A005891).
  • A253655 (program): Number of monic irreducible polynomials of degree 6 over GF(prime(n)).
  • A253671 (program): a(n) = floor(A000111(n+1)/A000111(n)).
  • A253679 (program): Numbers a(n) that are the starting terms in the sum of an odd number of consecutive cubes equal to a square.
  • A253707 (program): Numbers M(n) which are the number of terms in the sums of consecutive cubed integers equaling a squared integer, b^3 + (b+1)^3 + … + (b+M-1)^3 = c^2, for a first term b(n) being an odd squared integer (A016754).
  • A253710 (program): Second partial sums of tenth powers (A008454).
  • A253712 (program): Second partial sums of 12th powers (A008456).
  • A253718 (program): Number h such that (h,0) is n steps from (0,0), where steps are as follows: (x,y)->(x-r, y) if r > 0, and (x,y)->(y, r/3) otherwise, where r = x mod 3.
  • A253724 (program): Numbers c(n) whose squares are equal to the sums of a number M(n) of consecutive cubed integers b^3 + (b+1)^3 + … + (b+M-1)^3 = c^2, starting at b(n) (A002593) for M(n) being twice a squared integer (A001105).
  • A253725 (program): Integer squares c^2 that are equal to the sums of a number M(n) of consecutive cubed integers b^3 + (b+1)^3 + … + (b+M-1)^3 = c^2, starting at b(n) (A002593) for M(n) being twice a squared integer (A001105).
  • A253769 (program): Sum of number of divisors of all positive integers <= prime(n).
  • A253786 (program): a(3n) = 0, a(3n+1) = 0, a(3n+2) = 1 + a(n+1).
  • A253811 (program): Part of the y solutions of the Pell equation x^2 - 2*y^2 = +7.
  • A253826 (program): Indices of centered octagonal numbers (A016754) which are also triangular numbers (A000217).
  • A253878 (program): Indices of triangular numbers (A000217) which are also centered heptagonal numbers (A069099).
  • A253880 (program): Triangular numbers (A000217) that are also centered heptagonal numbers (A069099).
  • A253885 (program): Permutation of even numbers: a(n) = A003961(n+1) - 1.
  • A253887 (program): Row index of n in A191450: a(3n) = 2n, a(3n+1) = 2n+1, a(3n+2) = a(n+1).
  • A253893 (program): a(1) = 0, for n > 1, a(n) = 1 + a(A253889(n)).
  • A253894 (program): a(1) = 1, for n > 1, a(n) = 1 + a(A253889(n)).
  • A253900 (program): a(n) is the number of squares of the form x^2 + x + n^2 for 0 <= x <= n^2.
  • A253902 (program): Write numbers 1, then 2^2 down to 1, then 3^2 down to 1, then 4^2 down to 1 and so on.
  • A253903 (program): The characteristic function of square pyramidal numbers.
  • A253909 (program): 1 together with the positive squares.
  • A253942 (program): a(n) = 3*binomial(n+1, 5).
  • A253943 (program): a(n) = 3*binomial(n+1,6).
  • A253944 (program): a(n) = 3*binomial(n+1,7).
  • A253945 (program): a(n) = 6*binomial(n+1,5).
  • A253946 (program): a(n) = 6*binomial(n+1, 6).
  • A253947 (program): a(n) = 6*binomial(n+1,7).
  • A254006 (program): a(0) = 1, a(n) = 3*a(n-2) if n mod 2 = 0, otherwise a(n) = 0.
  • A254028 (program): a(n) = 2^(n+1) + 3^n + 3.
  • A254029 (program): Positive solutions of Monkey and Coconut Problem for the classic case (5 sailors, 1 coconut to the monkey): a(n) = 15625*n - 4 for n >= 1.
  • A254044 (program): a(1) = 1, for n>1: a(n) = a(A253889(n)) + (1 if n is of the form 3n or 3n+1, otherwise 0).
  • A254045 (program): a(1) = 0, for n > 1: a(n) = a(A253889(n)) + floor((n modulo 3)/2).
  • A254046 (program): Column index of n in A191450: a(3n) = 1, a(3n+1) = 1, a(3n+2) = 1 + a(n+1).
  • A254049 (program): Odd bisection of A048673: a(n) = A048673(2*n-1).
  • A254050 (program): Permutation of odd numbers: a(n) = (2*(A249745(n))) - 1 = A064989(A007310(n)).
  • A254065 (program): Vulgar fractions whose denominators are numbers ending with nine, the case 1/19.
  • A254132 (program): a(0)=1 and a(1)=2, then each term is x + y + x*y where x and y are the 2 last terms.
  • A254142 (program): a(n) = (9n+10)binomial(n+9,9)/10.
  • A254322 (program): E.g.f.: (1-11*x)^(-10/11).
  • A254340 (program): Sum of the distinct prime factors of n plus n+1: a(n) = A008472(n) + n + 1.
  • A254362 (program): a(n) = 3*2^n + 3^n + 6.
  • A254365 (program): a(n) = 2^(n+2) + 3^n + 10.
  • A254368 (program): a(n) = 5*2^n + 3^n + 15.
  • A254371 (program): Sum of cubes of the first n even numbers (A016743).
  • A254373 (program): Digital roots of centered square numbers (A001844).
  • A254374 (program): Digital roots of centered pentagonal numbers (A005891).
  • A254375 (program): Digital roots of centered heptagonal numbers (A069099).
  • A254377 (program): Characteristic function of A230709: a(n) = 1 if n is either evil (A001969) or even odious (A128309), otherwise 0 (when n is odd odious).
  • A254378 (program): Run lengths of A228495 (Characteristic function of the odd odious numbers).
  • A254379 (program): Characteristic function of the even odious numbers (A128309).
  • A254381 (program): a(n) = 3^n(2n + 1)!/n!.
  • A254398 (program): Final digits of A237424 in decimal representation.
  • A254407 (program): a(n) = n(n+1)(11*n +10)/6.
  • A254408 (program): a(n) = 2n^2binomial(2*n,n)^2, a closed form for a double binomial sum involving absolute values.
  • A254460 (program): a(n) is the number of predecessors of the all-ones state of the binary cellular automaton on the n X n grid graph with edges joining diagonal neighbors as well as vertical and horizontal neighbors, whose local rule is f(i,j) = sum of the state at vertex (i,j) and the states at all of its neighbors mod 2.
  • A254469 (program): Sixth partial sums of cubes (A000578).
  • A254473 (program): 24-hedral numbers: a(n) = (2n + 1)(8n^2 + 14n + 7).
  • A254474 (program): 30-gonal numbers: a(n) = n(14n-13).
  • A254527 (program): Total number of points on a sphere when both poles are on an x by x grid where x=8*n+1.
  • A254528 (program): Number of decimal digits in the integer part of e^n.
  • A254594 (program): Expansion of 1 / ((1 - x^2)^2 * (1 - x^3) * (1 - x^4)) in powers of x.
  • A254601 (program): Numbers of n-length words on alphabet 0,1,…,6 with no subwords ii, where i is from 0,1,2 .
  • A254614 (program): Union of odd odious (A092246) and evil (A001969) numbers.
  • A254619 (program): a(n) = 4^n(2n + 1)!/n!.
  • A254620 (program): a(n) = 9^n(2n + 1)!/n!.
  • A254626 (program): Indices of triangular numbers (A000217) that are also centered pentagonal numbers (A005891).
  • A254627 (program): Indices of centered pentagonal numbers (A005891) that are also triangular numbers (A000217).
  • A254628 (program): Triangular numbers (A000217) that are also centered pentagonal numbers (A005891).
  • A254640 (program): Third partial sums of sixth powers (A001014).
  • A254641 (program): Third partial sums of seventh powers (A001015).
  • A254642 (program): Third partial sums of eighth powers (A001016).
  • A254643 (program): Third partial sums of ninth powers (A001017).
  • A254651 (program): Characteristic function of A254614, numbers that are either odd or evil (or both).
  • A254653 (program): Indices of centered heptagonal numbers (A069099) which are also pentagonal numbers (A000326).
  • A254663 (program): Numbers of n-length words on alphabet 0,1,…,7 with no subwords ii, where i is from 0,1,…,5 .
  • A254667 (program): The nonnegative numbers with 2 instead of 1.
  • A254681 (program): Fifth partial sums of fourth powers (A000583).
  • A254710 (program): Indices of centered square numbers (A001844) which are also pentagonal numbers (A000326).
  • A254711 (program): Pentagonal numbers (A000326) which are also centered square numbers (A001844).
  • A254729 (program): Number of numbers j + ksqrt(2) of length n, where the length is the least number of steps to reach 0, the allowable steps being x -> x + 1 and x -> xsqrt(2).
  • A254732 (program): a(n) is the least k > n such that n divides k^2.
  • A254745 (program): Chebyshev polynomials of the second kind, U(n,x)^2, evaluated at x = sqrt(3)/2.
  • A254749 (program): 1-gonal pyramidal numbers.
  • A254757 (program): Part of the positive proper solutions x of the Pell equation x^2 - 2*y^2 = - 7^2 based on the fundamental solution (x0, y0)= (-1, 5).
  • A254758 (program): Part of the positive proper solutions x of the Pell equation x^2 - 2*y^2 = - 7^2 based on the fundamental solution (x0, y0)= (1, 5).
  • A254759 (program): Part of the positive proper solutions y of the Pell equation x^2 - 2*y^2 = - 7^2 based on the fundamental solution (x0, y0)= (1, 5).
  • A254782 (program): Indices of centered hexagonal numbers (A003215) which are also centered pentagonal numbers (A005891).
  • A254828 (program): Number of length 1 1..(n+1) arrays with every leading partial sum divisible by 2, 3 or 5.
  • A254865 (program): a(n) = Product_ k = 1+n-floor(n/3) .. n k.
  • A254866 (program): a(n) = (n!!)^n.
  • A254869 (program): Seventh partial sums of cubes (A000578).
  • A254874 (program): a(n) = floor((10n^3 + 63n^2 + 126*n + 89) / 72).
  • A254875 (program): a(n) = floor((10n^3 + 57n^2 + 102*n + 72) / 72).
  • A254948 (program): Number of length 1 1..(n+1) arrays with every leading partial sum divisible by 2, 3, 5, 7 or 11
  • A254962 (program): Indices of hexagonal numbers (A000384) that are also centered pentagonal numbers (A005891).
  • A254963 (program): a(n) = n(11n + 3)/2.
  • A255000 (program): Prime(n + d(n)), with d(n) = prime(n+1) - prime(n), for n >= 1.
  • A255043 (program): a(n) = (5*9^n - 1)/2.
  • A255047 (program): 1 together with the positive terms of A000225.
  • A255070 (program): (1/2)*(n minus number of runs in the binary expansion of n): a(n) = (n - A005811(n)) / 2 = A236840(n)/2.
  • A255072 (program): Number of steps to reach 0 starting with n and using the iterated process: x -> x - (number of runs in binary representation of x).
  • A255108 (program): Number of length n+1 0..2 arrays with at most one downstep in every n consecutive neighbor pairs.
  • A255138 (program): a(n) = (1 + 2^n(3 + 2(-1)^n))/3.
  • A255165 (program): a(n) = Sum_ k=2..n floor(log(n)/log(k)), n >= 1.
  • A255175 (program): Expansion of phi(-x) / (1 - x)^2 in powers of x where phi() is a Ramanujan theta function.
  • A255176 (program): a(n) = H_n(2,2) where H_n is the n-th hyperoperator.
  • A255177 (program): Second differences of seventh powers (A001015).
  • A255178 (program): Second differences of eighth powers (A001016).
  • A255184 (program): 25-gonal numbers: a(n) = n(23n-21)/2.
  • A255185 (program): 26-gonal numbers: a(n) = n(12n-11).
  • A255186 (program): 27-gonal numbers: a(n) = n(25n-23)/2.
  • A255187 (program): 29-gonal numbers: a(n) = n(27n-25)/2.
  • A255201 (program): Number of prime factors of n^2.
  • A255211 (program): a(n) = n(n+1)(7*n+2)/6.
  • A255221 (program): Number of (n+2) X (1+2) 0..1 arrays with no 3 x 3 subblock diagonal sum 0 and no antidiagonal sum 0 and no row sum 2 and no column sum 2.
  • A255222 (program): Number of (n+2) X (2+2) 0..1 arrays with no 3 x 3 subblock diagonal sum 0 and no antidiagonal sum 0 and no row sum 2 and no column sum 2.
  • A255223 (program): Number of (n+2)X(3+2) 0..1 arrays with no 3x3 subblock diagonal sum 0 and no antidiagonal sum 0 and no row sum 2 and no column sum 2
  • A255224 (program): Number of (n+2)X(4+2) 0..1 arrays with no 3x3 subblock diagonal sum 0 and no antidiagonal sum 0 and no row sum 2 and no column sum 2
  • A255225 (program): Number of (n+2)X(5+2) 0..1 arrays with no 3x3 subblock diagonal sum 0 and no antidiagonal sum 0 and no row sum 2 and no column sum 2
  • A255226 (program): Number of (n+2)X(6+2) 0..1 arrays with no 3x3 subblock diagonal sum 0 and no antidiagonal sum 0 and no row sum 2 and no column sum 2
  • A255227 (program): Number of (n+2)X(7+2) 0..1 arrays with no 3x3 subblock diagonal sum 0 and no antidiagonal sum 0 and no row sum 2 and no column sum 2
  • A255236 (program): All positive solutions x of the second class of the Pell equation x^2 - 2*y^2 = -7.
  • A255264 (program): Total number of ON cells in the “Ulam-Warburton” two-dimensional cellular automaton of A147562 after A048645(n) generations.
  • A255270 (program): Integer part of fourth root of n.
  • A255308 (program): Number of times log_2 can be applied to n until the result is not a power of 2. Here log_2 means the base-2 logarithm.
  • A255309 (program): Number of times log_2 can be applied to n until the result is either 1 or not a power of 2. Here log_2 means the base-2 logarithm.
  • A255361 (program): Number of ways n can be represented as x*y+x+y where x>=y>1.
  • A255368 (program): a(n) = -(-1)^n * 2 * n / 3 if n divisible by 3, a(n) = -(-1)^n * n otherwise.
  • A255413 (program): Row 3 of Ludic array A255127: a(n) = A007310((5*n)-3).
  • A255414 (program): Row 4 of Ludic array A255127.
  • A255433 (program): a(n) = Product_ k=0..n (k^3+1).
  • A255434 (program): Product_ k=0..n (k^4+1).
  • A255435 (program): Product_ k=0..n (k^5+1).
  • A255459 (program): a(n) = A255458(2^n-1).
  • A255463 (program): a(n) = 34^n-23^n.
  • A255465 (program): a(n) = A255464(2^n-1).
  • A255471 (program): a(n) = A255470(2^n-1).
  • A255490 (program): The subsequence A247649(2^n-1).
  • A255499 (program): a(n) = (n^4 + 2*n^3 - n^2)/2.
  • A255527 (program): Where records occur in A255437.
  • A255563 (program): a(n) = -3 * n/4 if n divisible by 4, a(n) = -(-1)^n * n otherwise.
  • A255606 (program): Integer part of the area of a hexagon with side length n.
  • A255645 (program): Partial sums of A134660.
  • A255680 (program): a(n) = n(n mod 3)(n mod 5).
  • A255687 (program): a(n) = n(n + 1)(7*n + 11)/6.
  • A255738 (program): a(1) = 1; for n > 1, a(n) = 1*0^ A000120(n-1) - 1 .
  • A255743 (program): a(1) = 1; for n > 1, a(n) = 9*8^ A000120(n-1)-1 .
  • A255744 (program): a(1) = 1; for n > 1, a(n) = 10*9^(A000120(n-1)-1).
  • A255745 (program): a(1) = 1; for n > 1, a(n) = 11*10^ A000120(n-1)-1 .
  • A255748 (program): Total number of ON states after n generations of cellular automaton based on triangles in a 60-degree wedge (see Comments lines for definition).
  • A255764 (program): Partial sums of A255743.
  • A255765 (program): Partial sums of A255744.
  • A255766 (program): Partial sums of A255745.
  • A255770 (program): Number of distinct prime factors of A220161(n).
  • A255771 (program): Number of distinct prime factors of A220294(n).
  • A255817 (program): Parity of A000788, which is the total number of ones in 0..n in binary.
  • A255824 (program): a(n) = n for n < 4; a(4n) = a(n); if every 4th term (a(4), a(8), a(12),…) is deleted, this gives back the original sequence.
  • A255825 (program): A self-generating sequence: a(n) = n for n < 5; a(5n) = a(n); if every 5th term (a(5), a(10), a(15),…) is deleted, this gives back the original sequence.
  • A255827 (program): a(n) = n for n < 7; a(7n) = a(n); if every 7th term (a(7), a(14), a(21),…) is deleted, this gives back the original sequence.
  • A255829 (program): a(n) = n for n < 9; a(9n) = a(n); if every 9th term (a(9), a(18), a(27),…) is deleted, this gives back the original sequence.
  • A255840 (program): a(n) = (4n^2 - 4n + 1 - (-1)^n)/2.
  • A255842 (program): a(n) = 2*n^2 + 12.
  • A255843 (program): a(n) = 2*n^2 + 4.
  • A255844 (program): a(n) = 2*n^2 + 6.
  • A255845 (program): a(n) = 2*n^2 + 10.
  • A255846 (program): a(n) = 2*n^2 + 14.
  • A255847 (program): a(n) = 2*n^2 + 16.
  • A255848 (program): a(n) = 2*n^2 + 18.
  • A255849 (program): Characteristic function of pentagonal numbers.
  • A255873 (program): The first nonzero digit of n/7.
  • A255875 (program): a(n) = Fibonacci(n+2) + n - 2.
  • A255876 (program): a(n) = (4n^2 + 4n - 3 - 3*(-1)^n)/2.
  • A255877 (program): a(n) = (2n-2)^3 +(2n-2) - 1.
  • A255887 (program): a(n) = 1 if the n-th prime is the sum of three squares, otherwise a(n) = 0.
  • A255910 (program): Decimal expansion of 16/9.
  • A255919 (program): Gray code of Fibonacci(n).
  • A255932 (program): a(n) is the denominator of Gamma(n+1/2)^2/(2nPi), the value of an integral with sinh in the denominator.
  • A255977 (program): The number of numbers j+k*r <= n, where r = golden ratio and j and k are nonnegative integers.
  • A255978 (program): a(n) = a(n-1) + a(n-2) + (1 + (-1)^(a(n-1) + a(n-2))) with a(0)=0, a(1)=1.
  • A255993 (program): Number of length n+2 0..1 arrays with at most one downstep in every n consecutive neighbor pairs.
  • A255994 (program): Number of length n+3 0..1 arrays with at most one downstep in every n consecutive neighbor pairs.
  • A255995 (program): Number of length n+4 0..1 arrays with at most one downstep in every n consecutive neighbor pairs.
  • A255996 (program): Number of length n+5 0..1 arrays with at most one downstep in every n consecutive neighbor pairs.
  • A256008 (program): Self-inverse permutation of positive integers: 4k+1 is swapped with 4k+3, and 4k+2 with 4k+4.
  • A256019 (program): a(n) = Sum_ i=1..n-1 (i^3 * a(i)), a(1)=1.
  • A256020 (program): a(n) = Sum_ i=1..n-1 (i^4 * a(i)), a(1)=1.
  • A256031 (program): Number of irreducible idempotents in partial Brauer monoid PB_n.
  • A256077 (program): Repeat 2^d times the repunit A002275(d); d = 1, 2, 3…
  • A256078 (program): Write n in binary, exchange digits ‘0’ <-> ‘1’.
  • A256079 (program): Increase each (decimal) digit of n by 1, with carry (i.e., ‘9’ becomes ‘0’ and a (further) increment of 1 of the digit to the left).
  • A256096 (program): Expansion of (4+3x)/(1+3x).
  • A256101 (program): The broken eggs problem.
  • A256135 (program): a(n) = 5^A000120(n).
  • A256136 (program): a(n) = 6^A000120(n).
  • A256137 (program): a(2) = 1; a(3) = 4; for n >= 4, a(n) = 2 + Sum_ i=4..n d(i), where d(i) = i for even i, d(i) = i-3 for odd i.
  • A256162 (program): Positive integers a(n) such that number of digits in decimal expansion of a(n)^a(n) is divisible by a(n).
  • A256225 (program): Number of partitions of 5n into 5 parts.
  • A256233 (program): a(n) = L(2*n+1) - 2, where L is A000032.
  • A256235 (program): Sum of all the parts in the partitions of 5n into 5 parts.
  • A256243 (program): Smallest positive integer m such that n + 2m is a square.
  • A256244 (program): a(n) = sqrt(n + 2*A256243(n)).
  • A256249 (program): Partial sums of A006257 (Josephus problem).
  • A256250 (program): Total number of ON states after n generations of a cellular automaton on the square grid.
  • A256251 (program): First differences of A256250.
  • A256255 (program): Triangle read by rows: T(n,k) = 6*k + 1, n>=0, 0<=k<=(2^n-1).
  • A256256 (program): Total number of ON cells after n generations of cellular automaton on triangular grid, starting from a node, in which every 60-degree wedge looks like the Sierpiński’s triangle.
  • A256257 (program): 6 times numbers of Gould’s sequence A001316.
  • A256266 (program): Total number of ON states after n generations of cellular automaton based on triangles (see Comments lines for definition).
  • A256277 (program): C(2n,n) mod 2n+1.
  • A256302 (program): Least prime p such that p+3k(k+1) is prime for all k=0,…,n.
  • A256309 (program): Number of partitions of 2n into exactly 5 parts.
  • A256313 (program): Number of partitions of 3n into exactly 4 parts.
  • A256314 (program): Number of partitions of 3n into exactly 5 parts.
  • A256316 (program): Number of partitions of 4n into exactly 5 parts.
  • A256320 (program): Number of partitions of 4n into exactly 3 parts.
  • A256321 (program): Number of partitions of 5n into exactly 3 parts.
  • A256322 (program): Number of partitions of 7n into exactly 3 parts.
  • A256327 (program): Number of partitions of 5n into exactly 4 parts.
  • A256328 (program): Number of partitions of 6n into exactly 4 parts.
  • A256329 (program): Number of partitions of 7n into exactly 4 parts.
  • A256432 (program): Characteristic function of octahedral numbers.
  • A256436 (program): Characteristic function of pentatope numbers.
  • A256455 (program): Numbers that appear at least once in a Pythagorean triple (a, b, b+1).
  • A256494 (program): Expansion of -x^2(x^3+x-1) / ((x-1)(x+1)(2x-1)*(x^2+1)).
  • A256512 (program): n(1+(2n)^n).
  • A256524 (program): Number of partitions of 3n into at most 4 parts.
  • A256525 (program): Number of partitions of 3n into at most 5 parts.
  • A256532 (program): Product of n and the sum of remainders of n mod k, for k = 1, 2, 3, …, n.
  • A256533 (program): Product of n and the sum of all divisors of all positive integers <= n.
  • A256534 (program): Number of ON cells at n-th stage in simple 2-dimensional cellular automaton (see Comments lines for definition).
  • A256535 (program): The largest number of T-tetrominoes that fit within an n X n square.
  • A256539 (program): Number of partitions of 4n into at most 5 parts.
  • A256562 (program): Number of deficient numbers <= n.
  • A256595 (program): Triangle A074909(n) with 0’s as second column.
  • A256645 (program): 25-gonal pyramidal numbers: a(n) = n(n+1)(23*n-20)/6.
  • A256646 (program): 26-gonal pyramidal numbers: a(n) = n(n+1)(8*n-7)/2.
  • A256647 (program): 27-gonal pyramidal numbers: a(n) = n(n+1)(25*n-22)/6.
  • A256648 (program): 28-gonal pyramidal numbers: a(n) = n(n+1)(26*n-23)/6.
  • A256649 (program): 29-gonal pyramidal numbers: a(n) = n(n+1)(9*n-8)/2.
  • A256650 (program): 30-gonal pyramidal numbers: a(n) = n(n+1)(28*n-25)/6.
  • A256654 (program): Least Fibonacci number not less than n.
  • A256666 (program): a(n) = ( 2n(2n^2 + 11n + 26) - (-1)^n + 1 )/16.
  • A256676 (program): Digital roots of centered 11-gonal numbers (A069125).
  • A256680 (program): Minimal most likely sum for a roll of n 4-sided dice.
  • A256700 (program): Positive part of the minimal alternating triangular-number representation of n (defined at A255974).
  • A256701 (program): Positive part of the minimal alternating binary representation of n (defined at A245596).
  • A256702 (program): Nonpositive part of the minimal alternating binary representation of n (defined at A256696).
  • A256716 (program): a(n) = n(n+1)(22*n-19)/6.
  • A256718 (program): a(n) = n(n+1)(7*n-6)/2.
  • A256719 (program): Decimal expansion of the location of the near bifurcation cusp in the Zeeman catastrophe machine.
  • A256736 (program): Number of composites lying between successive pairs of primes, beginning with pair (3,5). Bisection of A046933.
  • A256737 (program): Number of composites lying between successive pairs of primes, beginning with pair (2,3). Bisection of A046933.
  • A256756 (program): a(n) = bitwise XOR of n and the reverse of n.
  • A256759 (program): Nonpositive part of the minimal alternating triangular-number representation of n (defined at A255974).
  • A256817 (program): Number of length n+2 0..1 arrays with at most two downsteps in every n consecutive neighbor pairs.
  • A256818 (program): Number of length n+3 0..1 arrays with at most two downsteps in every n consecutive neighbor pairs.
  • A256833 (program): a(n) = (4n+3)(4*n+2).
  • A256857 (program): a(n) = n(n^2 + 3n - 2)/2.
  • A256859 (program): a(n) = n(n + 1)(n + 2)*(n^2 - n + 4)/24.
  • A256871 (program): a(n) = 2^(n-1)*(2^n+11).
  • A256873 (program): a(n) = 2^(n-1)*(2^n+5).
  • A256882 (program): Numbers divisible by prime(d+1) for each digit d of their base-2 representation.
  • A256885 (program): a(n) = n*(n + 1)/2 - pi(n), where pi(n) = A000720(n) is the prime counting function.
  • A256888 (program): Terms of the continued fraction expansion of 1 + sqrt(64 / 37).
  • A256910 (program): Trace of the enhanced triangular-number representation of n.
  • A256911 (program): Number of terms in the enhanced triangular-number representation of n.
  • A256958 (program): The integers (shown from -50 on).
  • A256966 (program): Partial sums of A072649.
  • A256967 (program): a(n) = A256966(n) + 1.
  • A256970 (program): Smallest prime divisor of 4*n^2+1.
  • A256971 (program): Partial sums of A256970.
  • A256984 (program): Maximal number of joints that can be formed by n lines in space.
  • A256994 (program): a(n) = n + 1 when n <= 3, otherwise a(n) = 2^(n-2) + 3; also iterates of A005187 starting from a(1) = 2.
  • A257022 (program): Trace of n in the quarter-sum representation of n.
  • A257023 (program): Number of terms in the quarter-sum representation of n.
  • A257042 (program): a(n) = (3n+7)n^2.
  • A257051 (program): a(n) = cpg(n, 3) + cpg(n, 4) + … + cpg(n, n) where cpg(n, m) is the m-th n-th-order centered polygonal number.
  • A257052 (program): a(n) = cpg(3, n) + cpg(4, n) + … + cpg(n, n) where cpg(m, n) is the n-th m-th-order centered polygonal number.
  • A257055 (program): a(n) = n(n + 1)(n^2 - n + 3)/6.
  • A257063 (program): Number of length 1 1..(n+1) arrays with every leading partial sum divisible by 2 or 3.
  • A257075 (program): a(n) = (-1)^(n mod 3).
  • A257076 (program): Expansion of (1 - x^3) / (1 - x + x^2) in powers of x.
  • A257083 (program): Partial sums of A257088.
  • A257088 (program): a(2n) = 4n if n>0, a(2n + 1) = 2n + 1, a(0) = 1.
  • A257113 (program): a(1) = 2, a(2) = 3; thereafter a(n) is the sum of all the previous terms.
  • A257143 (program): a(2n) = 3n if n>0, a(2n + 1) = 2n + 1, a(0) = 1.
  • A257145 (program): a(n) = 5 * floor( (n+2) / 5) - n with a(0) = 1.
  • A257164 (program): Period 5 sequence: repeat [0, 2, 4, 1, 3].
  • A257170 (program): Expansion of (1 + x) * (1 + x^3) / (1 + x^4) in powers of x.
  • A257171 (program): Sum of numbers on n-th segment of Ulam’s spiral.
  • A257174 (program): a(n) = 4n/3 if n = 3k and n!=0, otherwise a(n) = n except a(0) = 1.
  • A257175 (program): The smallest m such that the m-th triangular number is greater than or equal to half the n-th triangular number.
  • A257179 (program): Expansion of (1 + x^5) / ((1 - x) * (1 + x^4)) in powers of x.
  • A257198 (program): Number of permutations of length n having exactly one descent such that the first element of the permutation is an odd number.
  • A257199 (program): a(n) = n(n+1)(n+2)(n^2+2n+17)/120.
  • A257200 (program): a(n) = n(n+1)(n+2)(n+3)(n^2+3*n+26)/720.
  • A257212 (program): Least d>0 such that floor(n/d) - floor(n/(d+1)) <= 1.
  • A257213 (program): Least d>0 such that floor(n/d) = floor(n/(d+1)).
  • A257272 (program): a(n) = 2^(n-1)*(2^n+7).
  • A257273 (program): a(n) = 2^(n-1)*(2^n+3).
  • A257285 (program): a(n) = 45^n - 34^n.
  • A257286 (program): a(n) = 56^n-45^n.
  • A257319 (program): Numbers n such that the n-th generation of Sawtooth 201 has minimum population in Conway’s Game of Life.
  • A257352 (program): G.f.: (1-2x+51x^2)/(1-x)^3.
  • A257418 (program): Number of pieces after a sheet of paper is folded n times and cut diagonally.
  • A257444 (program): Number of (n+2) X (5+2) 0..1 arrays with no 3 x 3 subblock diagonal sum 0 and no antidiagonal sum 3 and no row sum 1 and no column sum 1.
  • A257445 (program): Number of (n+2) X (6+2) 0..1 arrays with no 3 x 3 subblock diagonal sum 0 and no antidiagonal sum 3 and no row sum 1 and no column sum 1.
  • A257446 (program): Number of (n+2) X (7+2) 0..1 arrays with no 3 x 3 subblock diagonal sum 0 and no antidiagonal sum 3 and no row sum 1 and no column sum 1.
  • A257448 (program): a(n) = 13(2^n - 1) - 3n^2 - 9*n.
  • A257481 (program): Consider a hole-less cluster of n circles in the hexagonal lattice packing of circles; a(n) is the maximal number of circles that touch 6 circles.
  • A257487 (program): Expansion of ( -4+15x-8x^2 ) / ( (x-1)(x^2-4x+1) ).
  • A257507 (program): Row 2 of A257264: a(n) = A011371(A055938(n)).
  • A257510 (program): Number of nonleading zeros in factorial base representation of n (A007623).
  • A257531 (program): If 2^(n-1) mod n = 1, then 1 else 0.
  • A257542 (program): Square-sum pairs: Numbers n such that 0,1, …, 2n-1 can be partitioned into n pairs, where each pair adds up to a perfect square.
  • A257564 (program): Irregular triangle read by rows: T(n,k) = r(n+k)+r(n-k) with r(n) = (n-(n mod 2))/2 for n>=0 and -n<=k<=n.
  • A257567 (program): a(n) = the highest power of 3 that divides (prime(n)^2+2).
  • A257583 (program): a(0)=4; thereafter a(n)=8n(2n-1)a(n-1).
  • A257587 (program): If n = abcd… in decimal, a(n) = a^2-b^2+c^2-d^2+…
  • A257589 (program): a(n) = (2n+1)^2*Catalan(n).
  • A257594 (program): Consider the hexagonal lattice packing of circles; a(n) is the maximal number of circles that can be enclosed by a closed chain of n circles.
  • A257600 (program): Expansion of (4+15x-35x^2+20x^3-2x^5)/(1-x)^5.
  • A257601 (program): a(n) = n^4/12+5n^3/3+125n^2/12+125*n/6+2.
  • A257602 (program): Expansion of (1+x+21*x^2+x^3+x^4)/(1-x)^5.
  • A257633 (program): a(n) = binomial(4*n + 2,n).
  • A257637 (program): Maximal number of edges in an n-vertex triangle-free graph with maximal degree at most 4.
  • A257644 (program): First differences of A264100.
  • A257645 (program): a(n) = 15*n + 14.
  • A257686 (program): a(0) = 0, for n >= 1: a(n) = A099563(n) * A048764(n).
  • A257687 (program): Discard the most significant digit from factorial base representation of n, then convert back to decimal: a(n) = n - A257686(n).
  • A257721 (program): Hexagonal numbers (A000384) that are the sum of two consecutive hexagonal numbers.
  • A257775 (program): Decimal expansion of (e/2)^2.
  • A257811 (program): Circle of fifths cycle (clockwise).
  • A257834 (program): a(n) = 1 if n-th prime is == +1 or -1 mod 12; -1 if n-th prime is == 5 or 7 mod 12; and 0 if n-th prime is 2 or 3.
  • A257844 (program): a(n) = floor(n/4) * (n mod 4).
  • A257845 (program): a(n) = floor(n/5) * (n mod 5).
  • A257846 (program): a(n) = floor(n/6) * (n mod 6).
  • A257847 (program): a(n) = floor(n/7) * (n mod 7).
  • A257848 (program): a(n) = floor(n/8) * (n mod 8).
  • A257849 (program): a(n) = floor(n/9) * (n mod 9).
  • A257850 (program): a(n) = floor(n/10) * (n mod 10).
  • A257853 (program): a(n) = 2n^3 - floor(2^(1/3)n)^3.
  • A257857 (program): Sequentially filled binary triangle rotated 180 degrees and then superimposed and added to the original triangle.
  • A257872 (program): Decimal expansion of the Madelung type constant C(4 1) (negated).
  • A257888 (program): Number of nonintersecting (or self-avoiding) rook paths of length 2n+2 joining opposite corners of an n X n grid.
  • A257890 (program): Expansion of the g.f. (x^2-x+1)(x^2-3x+3)/(x-1)^6.
  • A257923 (program): Number of prime factors of the n-th Giuga number A007850(n).
  • A257925 (program): a(n) = (n^2 - n + 1)*(n^2 + n - 1).
  • A257932 (program): Expansion of 1/(1-x-x^2-x^3+x^5+x^7).
  • A257934 (program): Expansion of 1/(1-x-x^2-x^3-x^4+x^5+x^6+x^7).
  • A257936 (program): Decimal expansion of 11/18.
  • A257939 (program): x-values in the solutions to x^2 + x = 5*y^2 + y.
  • A257940 (program): y-values in the solutions to x^2 + x = 5*y^2 + y.
  • A257942 (program): a(n) = (n+1)*(n+2)/A014695(n+1), where A014695 is repeat (1, 2, 2, 1).
  • A257970 (program): a(1) = 1, a(2) = 2, a(3) = 5; thereafter a(n) = 2 * Sum_ k=1..n-1 a(k).
  • A257984 (program): Nonhomogeneous Beatty sequence: ceiling((n - 1/2)*Pi))
  • A257993 (program): Least gap in the partition having Heinz number n; index of the least prime not dividing n.
  • A257998 (program): Partial sums of A188967.
  • A258011 (program): Numbers remaining after the third stage of Lucky sieve.
  • A258016 (program): Unlucky numbers removed at the stage three of Lucky sieve.
  • A258054 (program): Circle of fifths cycle (counterclockwise).
  • A258055 (program): Concatenation of the decimal representations of the lengths (increased by 1) of the runs of zeros between successive ones in the binary representation of n.
  • A258059 (program): Let n = Sum_ i=0..k d_i*4^i be the base-4 expansion of n, with 0 <= d_i < 4. Then a(n) = minimal i such that d_i is not 1, or k+1 if there is no such i.
  • A258071 (program): Nonnegative integers that can be computed using exactly ten 10’s and the four basic arithmetic operations +, -, *, / .
  • A258073 (program): a(n) = 1 + 78557*2^n.
  • A258085 (program): Strictly increasing list of F and F - 1, where F = A000045, the Fibonacci numbers.
  • A258087 (program): Start with all terms set to 0. Then add n to the next n+2 terms for n=0,1,2,… .
  • A258109 (program): Number of balanced parenthesis expressions of length 2n and depth 3.
  • A258115 (program): a(n) = A208570(n)/n.
  • A258121 (program): Number of vertices of degree n in all Lucas cubes.
  • A258144 (program): Alternating row sums of A257241, Stifel’s version of the arithmetical triangle.
  • A258145 (program): Row lengths of the irregular array in A256598.
  • A258160 (program): a(n) = 8*Lucas(n).
  • A258197 (program): Arithmetic derivative of Pascal’s triangle.
  • A258198 (program): a(n) = largest k for which A001563(k) = k*k! <= n.
  • A258290 (program): Arithmetic derivative of central binomial coefficients, cf. A000984.
  • A258321 (program): a(n) = Fibonacci(n) + n*Lucas(n).
  • A258340 (program): a(n) = (7^n + 3^n - 2)/8.
  • A258376 (program): Number of edges connecting the subgraph on 1, …, n with the complement in the minimal graph on positive natural numbers where degree(n) equals n.
  • A258384 (program): a(n) = n^(n-1) * (n+1)^n.
  • A258385 (program): a(n) = n^(n+1) * (n-1)^n.
  • A258387 (program): a(n) = (n+1)^n + n^(n-1).
  • A258388 (program): a(n) = n^(n+1) + (n-1)^n.
  • A258402 (program): a(n) = (n^2 + 4*n + 6) * n^2.
  • A258434 (program): n^2 - phi(n).
  • A258439 (program): Powers of 3 alternating with powers of 2.
  • A258440 (program): Number of squares of all sizes in 3n(n+1)/2-ominoes in form of three-quarters of Aztec diamonds.
  • A258547 (program): Number of (n+1)X(1+1) 0..1 arrays with every 2X2 subblock ne-sw antidiagonal difference nondecreasing horizontally and nw+se diagonal sum nondecreasing vertically
  • A258582 (program): a(n) = n(2n + 1)(4n + 1)/3.
  • A258588 (program): Minimal most likely sum for a roll of n 10-sided dice.
  • A258589 (program): Minimal most likely sum for a roll of n 12-sided dice.
  • A258597 (program): a(n) = 13*3^n.
  • A258598 (program): a(n) = 17*3^n.
  • A258617 (program): a(n) = (4n+8)n^2.
  • A258618 (program): a(n) = (4n+9)n^2.
  • A258632 (program): Number of length 1 1..(n+1) arrays with every leading partial sum divisible by 2, 3, 5 or 7
  • A258644 (program): Fourth arithmetic derivative of n.
  • A258645 (program): Fifth arithmetic derivative of n.
  • A258646 (program): Sixth arithmetic derivative of n.
  • A258647 (program): Seventh arithmetic derivative of n.
  • A258648 (program): Eighth arithmetic derivative of n.
  • A258649 (program): Ninth arithmetic derivative of n.
  • A258650 (program): Tenth arithmetic derivative of n.
  • A258663 (program): Numbers n such that 9n-1 is prime.
  • A258684 (program): a(n) = A041105(4n+1).
  • A258703 (program): a(n) = floor(n/sqrt(2) - 1/2).
  • A258717 (program): If n even then 2n^2-4n else 2n^2-4n-3.
  • A258721 (program): a(n) = 24n^2 + 52n + 29.
  • A258774 (program): a(n) = 1 + sigma(n) + sigma(n)^2.
  • A258806 (program): a(n) = n^7 + 1.
  • A258807 (program): a(n) = n^5 - 1.
  • A258808 (program): a(n) = n^7 - 1.
  • A258809 (program): a(n) = n^8 - 1.
  • A258810 (program): a(n) = n^9 - 1.
  • A258812 (program): a(n) = n^11 - 1.
  • A258833 (program): Nonhomogeneous Beatty sequence: ceiling((n + 1/4)*sqrt(2)).
  • A258835 (program): Expansion of psi(x)^3 * psi(x^4) in powers of x where psi() is a Ramanujan theta function.
  • A258837 (program): a(n) = 1 - n^2.
  • A258841 (program): a(n) = 9n^2 - 237n + 1927.
  • A258869 (program): Expansion of 1 to the basis 1.880000478655… (A127583).
  • A258881 (program): a(n) = n + the sum of the squared digits of n.
  • A258935 (program): Independence number of Keller graphs.
  • A258948 (program): a(1)=1, a(2)=2; for n>2, a(n) = (1/2)a(n-1)a(n-2) + a(n-1) + a(n-2).
  • A258974 (program): a(n) = 1 + sigma(n)^2.
  • A258978 (program): a(n) = 1 + sigma(n) + sigma(n)^2 + sigma(n)^3 + sigma(n)^4.
  • A259022 (program): Period 9 sequence [ 1, -1, -1, 1, 0, -1, 1, 1, -1, …].
  • A259036 (program): Smallest divisor of n^2+1 >= sqrt(n^2+1).
  • A259042 (program): Period 8 sequence [0, 1, 1, 1, 2, 1, 1, 1, …].
  • A259044 (program): Period 8 sequence [ 0, 1, 0, 1, 1, 1, 0, 1, …].
  • A259054 (program): a(n) = 4n^2 - 4n + 19, n >= 1.
  • A259055 (program): a(n) = 9n^2 + 18n + 7.
  • A259058 (program): Numbers that are representable in at least two ways as sums of four distinct nonvanishing squares.
  • A259059 (program): One half of numbers representable in at least two different ways as sums of four distinct nonvanishing squares. See A259058 for these numbers and their representations.
  • A259060 (program): Numbers that are representable in at least two ways as sums of four distinct nonvanishing cubes.
  • A259076 (program): Powers of 80.
  • A259108 (program): a(n) = 2 * A000538(n).
  • A259109 (program): 2*A000540.
  • A259110 (program): 2*A000447(n).
  • A259131 (program): Numbers n such that 13*n^2 + 52 is a square.
  • A259157 (program): Positive triangular numbers (A000217) that are hexagonal numbers (A000384) divided by 2.
  • A259160 (program): Positive squares (A000290) that are octagonal numbers (A000567) divided by 2.
  • A259161 (program): Positive pentagonal numbers (A000326) that are triangular numbers (A000217) divided by 2.
  • A259167 (program): Positive octagonal numbers (A000567) that are squares (A000290) divided by 2.
  • A259175 (program): a(n) = 1 if n prime, otherwise prime(n).
  • A259181 (program): a(n) = n(n+1)(n+2)(n+3)(2n^2+6n+7)/360.
  • A259182 (program): a(n) = prime(n) if n prime otherwise 1.
  • A259184 (program): a(n) = 1 - sigma(n) + sigma(n)^2.
  • A259215 (program): Number of (n+1) X (1+1) 0..1 arrays with each 2 X 2 subblock having clockwise pattern 0000 0011 or 0101.
  • A259225 (program): Smallest oblong number greater than or equal to n.
  • A259243 (program): Number of (n+1) X (1+1) 0..1 arrays with each 2 X 2 subblock having clockwise pattern 0000 0011 or 0111.
  • A259251 (program): a(n) = 1 + sigma(n) + sigma(n)^2 + sigma(n)^3 + sigma(n)^4 + sigma(n)^5 + sigma(n)^6.
  • A259264 (program): Cyclotomic polynomial value Phi(5,n!).
  • A259280 (program): a(n) is the minimal sum of a positive integer sequence of length n with no duplicate substrings of length greater than 1.
  • A259285 (program): Expansion of psi(x^2) * f(x, x^7) in powers of x where psi(), f(,) are Ramanujan theta functions.
  • A259287 (program): Expansion of psi(x^2) * f(x^3, x^5) in powers of x where psi(), f(, ) are Ramanujan theta functions.
  • A259290 (program): Number of (n+1) X (1+1) 0..1 arrays with each 2 X 2 subblock having clockwise pattern 0001 0101 or 0111.
  • A259308 (program): a(n) = 1 + sigma(n)^4.
  • A259317 (program): a(n) = 2(2n+1)A000538(n) - 4A000330(n)^2.
  • A259319 (program): a(n) = 2*A002309(n).
  • A259320 (program): a(n) = 2nA259319(n) - A259110(n)^2.
  • A259322 (program): Sum of sixth powers of odd numbers.
  • A259323 (program): 2*A259322(n).
  • A259346 (program): If n = 2^k then a(n) = 3^k, otherwise a(n) = 0.
  • A259348 (program): a(n) = n^3 - 8.
  • A259361 (program): n occurs 2n+2 times.
  • A259362 (program): a(1) = 1, for n > 1: a(n) is the number of ways to write n as a nontrivial perfect power.
  • A259368 (program): Number of digits in n^n when written in binary.
  • A259369 (program): a(n) = 1 + sigma(n)^3 + sigma(n)^6.
  • A259410 (program): a(n) = 1 - sigma(n) + sigma(n)^2 - sigma(n)^3 + sigma(n)^4.
  • A259445 (program): Multiplicative with a(n) = n if n is odd and a(2^s)=2.
  • A259451 (program): a(n) = n^2*Fibonacci(n).
  • A259455 (program): n Sum_n Sum_n Sum_n.
  • A259486 (program): a(n) = 3n^2 - 3n + 1 + 6floor((n-1)(n-2)/6).
  • A259546 (program): a(n) = n^3*Fibonacci(n).
  • A259547 (program): a(n) = n^4*Fibonacci(n).
  • A259549 (program): Triangle T(n,k) with rows of length 2n-1 filled with consecutive integers, each appearing twice except for the last term, T(n,2n-1) = n(n+1)/2.
  • A259550 (program): a(n) = C(5n-1,2n)/3, n > 0, a(0) = 1.
  • A259552 (program): a(n) = (1/4)n^4 - (1/2)n^3 + (3/4)n^2 - (1/2)n + 41.
  • A259555 (program): a(n) = 2n^2 - 2n + 17.
  • A259557 (program): a(n) = binomial(4n-1, 2n).
  • A259566 (program): Numbers following gaps in the sequence of base-3 numbers that don’t contain 0.
  • A259568 (program): Numbers following gaps in the sequence of base-4 numbers that don’t contain 0.
  • A259595 (program): Numerators of the other-side convergents to sqrt(6).
  • A259599 (program): Infinite palindromic word (a(1),a(2),a(3),…) with initial word w(1) = (1,0,1) and midword sequence (a(n)); see Comments.
  • A259613 (program): a(n) = binomial(6n,2n)/3, n>0, a(0)=1.
  • A259614 (program): Numbers congruent to 17,29 mod 36.
  • A259623 (program): Strictly increasing list of F and F + 1, where F = A000045, the Fibonacci numbers.
  • A259624 (program): Strictly increasing list of F - 1, F, and F + 1, where F = A000045, the Fibonacci numbers.
  • A259625 (program): List of numbers L - 1 and L, where L = A000032, the Lucas numbers, sorted into increasing order and duplicates removed.
  • A259626 (program): List of numbers L and L + 1, where L = A000032, the Lucas numbers, sorted into increasing order and duplicates removed.
  • A259650 (program): Largest prime factor of the n-th pentagonal number (A000326).
  • A259651 (program): Number of distinct prime factors of the n-th pentagonal number (A000326).
  • A259652 (program): Number of prime factors, with multiplicity, of the n-th pentagonal number (A000326).
  • A259653 (program): a(0)=0, a(1)=1, a(n) = min 3 a(k) + (3^(n-k)-1)/2, k=0..(n-1) for n>=2.
  • A259665 (program): a(0)=0, a(1)=1, a(n) = min 4 a(k) + (4^(n-k)-1)/3, k=0..(n-1) for n>=2.
  • A259667 (program): Catalan numbers mod 6.
  • A259713 (program): a(n) = 32^n - 2(-1)^n.
  • A259748 (program): a(n) = (Sum_ 0<x<y<n x*y) mod n.
  • A259750 (program): Numbers that are congruent to 14,22 mod 24.
  • A259751 (program): Numbers that are congruent to 8,16 mod 24.
  • A259752 (program): a(n) = 24n + 6.
  • A259754 (program): Numbers that are congruent to 3,9,15,18,21 mod 24.
  • A259755 (program): Numbers that are congruent to 4,20 mod 24.
  • A259796 (program): Number of partitions of 3^n into n-th powers.
  • A259821 (program): a(n) = floor( (3^n+1)^2/3^n ).
  • A259925 (program): a(n) = (n^2 - n - 1)^n.
  • A259926 (program): a(n) = n^(2n) - n^(2n - 1).
  • A259968 (program): a(n) = a(n-1) + a(n-2) + a(n-4), with a(1)=1, a(2)=1, a(3)=3, a(4)=6.
  • A259969 (program): a(n) = n*A259968(n).
  • A259982 (program): Decimal expansion of 1/2^20.
  • A260006 (program): a(n) = f(1,n,n), where f is the Sudan function defined in A260002.
  • A260033 (program): Number of configurations of the general monomer-dimer model for a 2 X 2n square lattice.
  • A260076 (program): Cyclotomic polynomial value Phi(9,n!).
  • A260077 (program): Cyclotomic polynomial value Phi(10,n!).
  • A260112 (program): Minimal number of steps to get from 0 to n by (a) adding 1 or (b) multiplying by 4.
  • A260113 (program): Maximum number of queens on an n X n chessboard such that no queen attacks more than one other queen.
  • A260160 (program): a(n) = a(n-2) + a(n-6) - a(n-8) with n>8, the first eight terms are 0 except that for a(5) = a(7) = 1.
  • A260181 (program): Numbers whose last digit is prime.
  • A260188 (program): Greatest primorial less than or equal to n.
  • A260190 (program): Kronecker symbol(-6 / 2*n + 1).
  • A260192 (program): Kronecker symbol(-6 / 2*n + 7).
  • A260196 (program): 1, -3, followed by -1’s.
  • A260217 (program): Number of base-3 n-digit pandigital numbers.
  • A260220 (program): Number of symmetry-allowed, linearly-independent terms at n-th order in the expansion of T1 x t1 rovibrational perturbation matrix H(Jx,Jy,Jz).
  • A260233 (program): Smallest prime factor of the n-th hexagonal number (A000384).
  • A260234 (program): Largest prime factor of the n-th hexagonal number (A000384).
  • A260235 (program): Number of distinct prime factors of the n-th hexagonal number (A000384).
  • A260236 (program): Number of prime factors, with multiplicity, of the n-th hexagonal number (A000384).
  • A260260 (program): a(n) = n(16n^2 - 21*n + 7)/2.
  • A260300 (program): Bisection of A258409: a(n) = A258409(2n+1).
  • A260304 (program): a(n) = 5a(n-1) - 5a(n-2) for n>1, a(0)=2, a(1)=3.
  • A260307 (program): a(n) = a(n-1) + a(n-2) - a(n-3) + a(n-6) - a(n-7) - a(n-8) + a(n-9) with a(0) - a(8) as shown below.
  • A260316 (program): n/3 if 3 divides n, else n-1.
  • A260331 (program): Labelings of n diamond-shaped posets with 4 vertices per diamond where the labels follow the poset relations.
  • A260390 (program): Infinite palindromic word (a(1),a(2),a(3),…) with initial word w(1) = (1,0) and midword sequence (a(n)); see Comments.
  • A260393 (program): Infinite palindromic word (a(1),a(2),a(3),…) with initial word w(1) = (0,1) and midword sequence (a(n)); see Comments.
  • A260397 (program): Infinite palindromic word (a(1),a(2),a(3),…) with initial word w(1) = (1,1,0) and midword sequence (a(n)); see Comments.
  • A260440 (program): Unlucky numbers removed at the stage four of Lucky sieve.
  • A260444 (program): Infinite palindromic word (a(1),a(2),a(3),…) with initial word w(1) = (1,0,0) and midword sequence (a(n)); see A260390.
  • A260445 (program): Infinite palindromic word (a(1),a(2),a(3),…) with initial word w(1) = (0,0,1) and midword sequence (a(n)); see Comments.
  • A260446 (program): Infinite palindromic word (a(1),a(2),a(3),…) with initial word w(1) = (0,1,0) and midword sequence (a(n)); see Comments.
  • A260478 (program): Cyclotomic polynomial value Phi(8,n!).
  • A260479 (program): Positions of 0 in the infinite palindromic word at A260455.
  • A260484 (program): Complement of the Beatty sequence for e^(1/Pi) = A179706.
  • A260619 (program): Arithmetic derivative of hyperfactorial(n).
  • A260624 (program): a(n) = arithmetic derivative of the n-th composite number.
  • A260636 (program): a(n) = binomial(3n, n) mod n.
  • A260637 (program): Sums of seven consecutive squares: a(n) = n^2 + (n+1)^2 + (n+2)^2 + (n+3)^2 + (n+4)^2 + (n+5)^2 + (n+6)^2.
  • A260644 (program): Four steps forward, three steps back.
  • A260679 (program): a(n) = n+(17-n)^2.
  • A260686 (program): Period 6 zigzag sequence, repeat [0, 1, 2, 3, 2, 1].
  • A260699 (program): a(2n+6) = a(2n) + 12n + 20, a(2n+1) = (n+1)(2*n+1), with a(0)=0, a(2)=2, a(4)=9.
  • A260706 (program): Row sums of A260672.
  • A260708 (program): a(2n) = n(2n+1), a(2n+7) = a(2n+1) + 12*n + 28, with a(1)=1, a(3)=6, a(5)=16.
  • A260711 (program): Numbers of the form x^2 - y^2 with x >= y; x and y are odd, x + y is a power of 2.
  • A260714 (program): Row 4 of A260717.
  • A260751 (program): 25 primes in arithmetic progression: a(n) = 6171054912832631 + (n-1)*81737658082080 for n = 1, 2, …, 25.
  • A260775 (program): Certain directed lattice paths.
  • A260794 (program): Number of steps required by R. L. Graham’s generalized binary merging algorithm.
  • A260810 (program): a(n) = n^2(3n^2 - 1)/2.
  • A260812 (program): a(n) is the number of edges in a rooted 2-ary tree built from the binary representation of n: each vertex at level i (i=0,…,floor(log_2(n))) has two children if the i-th most significant bit is 1 and one child if the i-th bit is 0.
  • A260860 (program): Base-60 representation of a(n) is the concatenation of the base-60 representations of 1, 2, …, n, n-1, …, 1.
  • A260865 (program): Base-15 representation of a(n) is the concatenation of the base-15 representations of 1, 2, …, n, n-1, …, 1.
  • A260866 (program): Base-16 representation of a(n) is the concatenation of the base-16 representations of 1, 2, …, n, n-1, …, 1.
  • A260878 (program): Number of set partitions of 1, 2, …, 2*n with sizes in [n, n], [2n] .
  • A260918 (program): Number of squares of all sizes in polyominoes obtained by union of two pyramidal figures (A092498) with intersection equals A002623.
  • A260939 (program): Thirteen primes in arithmetic progression with difference 60060 and minimal initial term.
  • A260940 (program): a(n) is the smallest index j>n such that g(j)=0 for the sequence g defined (for indices > n) by g(n+1)=n and g(i) = g(i-1) - gcd(i,g(i-1)).
  • A260955 (program): Differences of the increasing arithmetic progression a^2+a, b^2+b, c^2+c, where b = 5a+2, c = 7a+3 and a >= 0.
  • A261009 (program): Write 2^n in base 3, add up the “digits”.
  • A261011 (program): Positive integers n such that ceiling(n^(1/3)) divides n.
  • A261012 (program): Sign(n) (with offset -1): a(n) = 1 if n>0, = -1 if n<0, = 0 if n = 0.
  • A261040 (program): Values of c such that the Diophantine equation 5a + 3b = c has no solutions in positive integers.
  • A261064 (program): a(n) = (3^n-1)*(n+1)/4.
  • A261085 (program): Number of steps needed to reach zero when starting from the n-th prime [i.e., setting k to A000040(n)] and repeatedly applying the map that replaces k with k - d(k), where d(k) is the number of divisors of k (A000005).
  • A261095 (program): First differences of A219640: a(n) = A219640(n+1) - A219640(n).
  • A261128 (program): Cyclotomic polynomial value Phi(7,n!).
  • A261140 (program): a(n) = 3486107472997423 + (n-1)*371891575525470.
  • A261143 (program): a(n) = H_n(1,2) where H_n is the n-th hyperoperator.
  • A261149 (program): a(n) = 515486946529943 + (n-1)*30526020494970.
  • A261150 (program): a(n) = 403185216600637 + (n-1)*2124513401010.
  • A261151 (program): a(n) = 11410337850553 + (n-1)*4609098694200.
  • A261152 (program): a(n) = 161004359399459161 + (n-1)*10644900609172830.
  • A261179 (program): Take the list of positive rationals R(n): n>=1 in the order defined by Calkin and Wilf (Recounting the Rationals, 1999); a(n) = numerator of R(prime(n)).
  • A261186 (program): binomial(3*n-2,n+1).
  • A261191 (program): 40-gonal numbers: a(n) = 38n(n-1)/2 + n.
  • A261193 (program): a(n) = n! - 2.
  • A261197 (program): Cubes of the successive terms of the decimal expansion of Pi.
  • A261225 (program): n minus the number of positive cubes needed to sum to n using the greedy algorithm: a(n) = n - A055401(n).
  • A261226 (program): a(n) = number of steps to reach 0 when starting from k = n and repeatedly applying the map that replaces k with k - A055401(k), where A055401(k) = the number of positive cubes needed to sum to k using the greedy algorithm.
  • A261231 (program): a(n) = number of steps to reach 0 when starting from k = n and repeatedly applying the map that replaces k with k - (sum of digits in base-3 representation of k).
  • A261241 (program): One half of numbers representable in at least two different ways as sums of four nonvanishing cubes. See A259060 for these numbers and their representations.
  • A261243 (program): Row lengths of the irregular triangles A258643 and A261242: maximal number of 0-islands (holes) of certain bisymmetric n X n matrices with 0 or 1 entries only.
  • A261271 (program): a(n) = a(n-1)-1+p, where p is the smallest prime number that is not a factor of a(n-1)-1.
  • A261276 (program): 100-gonal numbers: a(n) = 98n(n-1)/2 + n.
  • A261300 (program): Concatenate successive run lengths of 0’s in the binary expansion of n, each increased by 1.
  • A261327 (program): Numerators of 1 + n^2/4.
  • A261337 (program): Digit-sums in an incremental base that adjusts itself as the digits of n are generated from right to left.
  • A261343 (program): 50-gonal numbers: a(n) = 48n(n-1)/2 + n.
  • A261348 (program): a(1)=0; a(2)=0; for n>2: a(n) = A237591(n,2) = A237593(n,2).
  • A261366 (program): a(n) = number of even terms in row n of triangle A261363.
  • A261391 (program): a(n) = n^5 + 5n^3 + 5n.
  • A261397 (program): a(n) = 3^n*Fibonacci(n).
  • A261399 (program): a(1)=1; thereafter a(n) = (2/5)(96^(n-2)+1).
  • A261423 (program): Largest palindrome <= n.
  • A261424 (program): Difference between n and the largest palindrome <= n.
  • A261466 (program): Records in A261461.
  • A261468 (program): a(n) = prime(n+2) mod prime(n).
  • A261471 (program): Cyclotomic polynomial value Phi(6,n!).
  • A261491 (program): a(n) = ceiling(2 + sqrt(8*n-4)).
  • A261521 (program): a(n) = n^2 + 2*n + 29.
  • A261544 (program): a(n) = Sum_ k=0..n 1000^k.
  • A261547 (program): The 3 X 3 X … X 3 dots problem (3, n times): minimal number of straight lines (connected at their endpoints) required to pass through 3^n dots arranged in a 3 X 3 X … X 3 grid.
  • A261557 (program): a(0) = a(1) = 0; for n>1, a(n) = 2*n - a(n-1) - a(n-2).
  • A261671 (program): If n even, a(n) = 6n+3, otherwise a(n) = n.
  • A261676 (program): Numbers which when represented as a sum of palindromes using the greedy algorithm require more than 3 palindromes.
  • A261681 (program): a(n) = 2^n + binomial(n, floor(n/2)) - 1.
  • A261692 (program): Number of “ON” cells after n-th stage in a cellular automaton in a 90-degree wedge on the square grid. (See Comments lines for definition.)
  • A261693 (program): Irregular triangle read by rows in which row n lists the positive odd numbers in decreasing order starting with 2^n - 1. T(0, 1) = 0 and T(n, k) for n >= 1, 1 <= k <= 2^(n-1).
  • A261694 (program): a(n) = Fibonacci(n) mod 21.
  • A261695 (program): First differences of A256534.
  • A261723 (program): Interleave 2^n + 2 and 2^n + 1.
  • A261766 (program): a(n) is the number of partial derangements of an n-set with at least one orbit of size exactly n.
  • A261779 (program): a(n) = ceiling((n-1)! / n).
  • A261807 (program): a(n) = n XOR n^3.
  • A261872 (program): a(n) = phi(n) mod 5, where phi is the Euler totient function.
  • A261882 (program): Decimal expansion of 32/27.
  • A261893 (program): a(n) = (n+1)^3 - n^2.
  • A261898 (program): Values of G-hat_1(n) , a sum involving Stirling numbers of the second kind.
  • A261914 (program): Largest palindrome < n (or 0 if n=0).
  • A261953 (program): Start with a single equilateral triangle for n=0; for the odd n-th generation add a triangle at each expandable side of the triangles of the (n-1)-th generation (this is the “side to side” version); for the even n-th generation use the “vertex to vertex” version; a(n) is the number of triangles added in the n-th generation.
  • A261969 (program): Product of primes dividing n with maximum multiplicity.
  • A261971 (program): Number of unit cubes that have a side on the surface of a p X p X p cube composed of p^3 unit cubes, where p is the n-th prime.
  • A261972 (program): The first of three consecutive positive integers the sum of the squares of which is equal to the sum of the squares of four consecutive positive integers.
  • A262000 (program): a(n) = n^2(7n - 5)/2.
  • A262011 (program): a(n) = (1/n!) * Product_ k=1..n (k^3 + 1).
  • A262017 (program): The first of five consecutive positive integers the sum of the squares of which is equal to the sum of the squares of six consecutive positive integers.
  • A262021 (program): a(n) = prime(prime(n)) - n.
  • A262023 (program): Decimal expansion of 3*log(2)/2.
  • A262033 (program): Number of permutations of [n] beginning with at least floor(n/2) ascents.
  • A262034 (program): Number of permutations of [n] beginning with at least ceiling(n/2) ascents.
  • A262035 (program): Number of permutations of [2n+1] beginning with exactly n ascents.
  • A262037 (program): Replace the second half of digits of n with the first half in reverse order.
  • A262062 (program): The first of six consecutive positive integers the sum of the squares of which is equal to the sum of the squares of seven consecutive positive integers.
  • A262067 (program): a(n) = n^n - (n-2)^n.
  • A262070 (program): a(n) = ceiling( log_3( binomial(n,2) ) ).
  • A262074 (program): The first of seven consecutive positive integers the sum of the squares of which is equal to the sum of the squares of eight consecutive positive integers.
  • A262123 (program): a(1) + a(2) + … + a(n) is the representation as a sum of n squares of the smallest integer needing n squares (using the greedy algorithm).
  • A262139 (program): The first of eight consecutive positive integers the sum of the squares of which is equal to the sum of the squares of nine consecutive positive integers.
  • A262140 (program): The first of nine consecutive positive integers the sum of the squares of which is equal to the sum of the squares of eight consecutive positive integers.
  • A262141 (program): The first of nine consecutive positive integers the sum of the squares of which is equal to the sum of the squares of ten consecutive positive integers.
  • A262142 (program): The first of ten consecutive positive integers the sum of the squares of which is equal to the sum of the squares of nine consecutive positive integers.
  • A262183 (program): a(0) = 0, a(n) = 10a(n-1) + n(n+1)*(n+2)/6.
  • A262184 (program): a(n) = Fibonacci(n)^2 - Fibonacci(n) + 1.
  • A262221 (program): a(n) = 25n(n + 1)/2 + 1.
  • A262236 (program): Number of (n+3) X (1+3) 0..1 arrays with each row and column divisible by 11, read as a binary number with top and left being the most significant bits.
  • A262247 (program): Number of squares formed from a square composed of p^2 unit squares where p is n-th prime.
  • A262248 (program): Number of intersections of diagonals in the interior of a regular p-gon where p is the n-th prime.
  • A262267 (program): Number of (n+2) X (1+2) 0..1 arrays with each row and column divisible by 5, read as a binary number with top and left being the most significant bits.
  • A262268 (program): Number of (n+2) X (2+2) 0..1 arrays with each row and column divisible by 5, read as a binary number with top and left being the most significant bits.
  • A262302 (program): Rainbow index for n-th odd prime.
  • A262303 (program): Length of sequence of lower halves of n: repeatedly apply x->floor(x/2) starting at n; a(n) = number of steps until reach one of 2,3,4.
  • A262304 (program): Tail of sequence of lower halves of n: repeatedly apply x->floor(x/2) starting at n until reach one of 2,3,4; a(n) = whichever of 2,3,4 is reached.
  • A262333 (program): Number of (n+3) X (1+3) 0..1 arrays with each row and column divisible by 9, read as a binary number with top and left being the most significant bits.
  • A262334 (program): Number of (n+3)X(2+3) 0..1 arrays with each row and column divisible by 9, read as a binary number with top and left being the most significant bits.
  • A262335 (program): Number of (n+3)X(3+3) 0..1 arrays with each row and column divisible by 9, read as a binary number with top and left being the most significant bits.
  • A262342 (program): Area of Lewis Carroll’s paradoxical F(2n+1) X F(2n+3) rectangle.
  • A262343 (program): Numerator of 3*(1-2/n), for n >= 3.
  • A262354 (program): a(n) is the number of 2 X 2 matrices over Z_p with determinant in 1,-1 where p = prime(n).
  • A262355 (program): Minimal number of circles needed to intersect all the points of an n X n grid.
  • A262376 (program): a(n) = Sum_ k=0..n (k! - k).
  • A262389 (program): Numbers whose last digit is composite.
  • A262392 (program): a(n) = A007504(n) + A010693(n).
  • A262394 (program): a(n) = Sum_ k=1..n (kbinomial(n,k-1)binomial(2*n,n-k))/n.
  • A262397 (program): a(n) = floor(A261327(n)/9).
  • A262402 (program): a(n) = number of triangles that can be formed from the points of a 3 X n grid.
  • A262414 (program): Number of (n+1) X (2+1) 0..1 arrays with each row divisible by 3 and column not divisible by 3, read as a binary number with top and left being the most significant bits.
  • A262438 (program): Number of digits of hexadecimal representation of n.
  • A262439 (program): Number of primes not exceeding 1+n*(n+1)/2.
  • A262450 (program): Number of (n+3) X (1+3) 0..1 arrays with each row and column divisible by 15, read as a binary number with top and left being the most significant bits.
  • A262473 (program): Number of (3+1) X (n+1) 0..1 arrays with each row divisible by 3 and each column divisible by 5, read as a binary number with top and left being the most significant bits.
  • A262482 (program): Number of (n+3)X(1+3) 0..1 arrays with each row and column divisible by 13, read as a binary number with top and left being the most significant bits.
  • A262490 (program): The index of the first of two consecutive positive triangular numbers (A000217) the sum of which is equal to the sum of four consecutive positive triangular numbers.
  • A262518 (program): Even bisection of A155043.
  • A262519 (program): Odd bisection of A155043.
  • A262523 (program): a(n+3) = a(n) + 6*n + 13, a(0)=0, a(1)=2, a(2)=7.
  • A262543 (program): Number of rooted asymmetrical polyenoids of type U_n* having n edges.
  • A262564 (program): A politician’s answer to the question “What comes next after 2,3,5?”.
  • A262565 (program): A weaver’s answer to the question “What comes next after 2,3,5?”.
  • A262588 (program): Duplicate of A193140.
  • A262592 (program): a(n) = (3^(n+1) - 2n^2 + 4n + 5) / 8..
  • A262594 (program): Expansion of (1-2x)^2/((1-x)^4(1-4*x)).
  • A262613 (program): Sum of divisors of n-th generalized pentagonal number.
  • A262616 (program): Triangle read by rows: T(n,k) = 4^(n-k), n>=0, 0<=k<=n.
  • A262617 (program): First differences of A256266.
  • A262620 (program): Number of “ON” cells at n-th stage in simple 2-dimensional cellular automaton on the square grid (see Comments lines for definition).
  • A262621 (program): First differences of A262620.
  • A262672 (program): Expansion of (3-x-x^3) / ((x-1)^2*(1+x+x^2+x^3)).
  • A262683 (program): Characteristic function for A182859.
  • A262684 (program): Characteristic function for A080218.
  • A262685 (program): Least monotonic left inverse for A182859.
  • A262699 (program): List of currency denominations such that any value x > 0 is represented in exactly x ways as a sum of distinct denominations, where a repeated value represents a bill and a coin which count as distinct denominations.
  • A262710 (program): Powers of -4.
  • A262714 (program): a(n) = a(n-1)*a(n-2) + 1, with a(0) = a(1) = 2.
  • A262715 (program): a(n) = 29^(2*n+1).
  • A262716 (program): a(n) = 31^(2*n+1).
  • A262725 (program): The unique function f with f(1)=1 and f(jD!+k)=(-1)^j f(k) for all D, j=1..D, and k=1..D!.
  • A262734 (program): Period 16: repeat (1, 2, 3, 4, 5, 6, 7, 8, 9, 8, 7, 6, 5, 4, 3, 2).
  • A262735 (program): Expansion of x(1-x-x^2)/((1-x)(1-x-2*x^2-x^3)).
  • A262753 (program): Number of (n+2) X (2+2) 0..1 arrays with each row divisible by 5 and each column divisible by 7, read as a binary number with top and left being the most significant bits.
  • A262767 (program): Minimum perimeter of a rectangle with area n and integer sides.
  • A262773 (program): A Beatty sequence: a(n)=floor(q*n) where q=A231187.
  • A262782 (program): a(n) = sum_ k=1..n 3^prime(k).
  • A262786 (program): a(n) = 37^(2*n+1).
  • A262787 (program): a(n) = 41^(2*n+1).
  • A262789 (program): Number of (n+2) X (2+2) 0..1 arrays with each row divisible by 5 and column not divisible by 5, read as a binary number with top and left being the most significant bits.
  • A262804 (program): a(n) = 2*b(n), where b(n) is defined by the condition that Product_ d n (b(d) + 1) = 1, n > 1 and b(1) = 1.
  • A262808 (program): Triangle read by rows giving successive states of cellular automaton generated by “Rule 147” initiated with a single ON (black) cell.
  • A262843 (program): Inverse Moebius transform of n^(n-1).
  • A262855 (program): Triangle read by rows giving successive states of cellular automaton generated by “Rule 153” initiated with a single ON (black) cell.
  • A262864 (program): Decimal representation of the middle column of the “Rule 147” elementary cellular automaton starting with a single ON (black) cell.
  • A262867 (program): Total number of ON (black) cells after n iterations of the “Rule 153” elementary cellular automaton starting with a single ON (black) cell.
  • A262869 (program): Number of squarefree numbers appearing among the smaller parts of the partitions of n into two parts.
  • A262882 (program): Right diagonal of A262881.
  • A262925 (program): Sum of n consecutive fourth powers starting with n^4.
  • A262970 (program): Total cycle length of all iteration trajectories of all elements of random mappings from [n] to [n].
  • A262977 (program): a(n) = binomial(4*n-1,n).
  • A262997 (program): a(n+3) = a(n) + 24*n + 40, a(0)=0, a(1)=5, a(2)=19.
  • A263013 (program): a(0) = -a(1) = a(2) = 1, a(n) = 0 for n>2.
  • A263053 (program): Number of (n+1) X (1+1) 0..1 arrays with each row and column not divisible by 3, read as a binary number with top and left being the most significant bits.
  • A263084 (program): a(n) = A263086(n) - A263085(n).
  • A263085 (program): Partial sums of A099774 (A099774(n) = number of divisors of n-th odd number).
  • A263086 (program): Partial sums of A099777, where A099777(n) gives the number of divisors of n-th even number.
  • A263119 (program): Number of (n+3) X (1+3) 0..1 arrays with each row divisible by 15 and column not divisible by 15, read as a binary number with top and left being the most significant bits.
  • A263134 (program): a(n) = Sum_ k=0..n binomial(3*k+1,k).
  • A263135 (program): The maximum number of penny-to-penny connections when n pennies are placed on the vertices of a hexagonal tiling.
  • A263200 (program): Number of perfect matchings on a Möbius strip of width 3 and length 2n.
  • A263226 (program): a(n) = 15n^2 - 13n.
  • A263228 (program): a(n) = 2n(16*n - 13).
  • A263229 (program): a(n) = 4n(21*n - 26).
  • A263231 (program): a(n) = n(25n - 39)/2.
  • A263243 (program): Triangle read by rows giving successive states of cellular automaton generated by “Rule 155” initiated with a single ON (black) cell.
  • A263313 (program): Permutation of the nonnegative integers: [4k+3, 4k, 4k+1, 4k+2, …].
  • A263334 (program): Number of (n+2) X (1+2) 0..2 arrays with each row and column divisible by 13, read as a base-3 number with top and left being the most significant digits.
  • A263366 (program): Number of (n+1) X (1+1) 0..2 arrays with each row and column divisible by 7, read as a base-3 number with top and left being the most significant digits.
  • A263390 (program): a(3n) = n, otherwise a(n) = a(floor(2n/3)).
  • A263416 (program): a(n) = Product_ k=0..n (3*k+1)^(n-k).
  • A263418 (program): a(n) is the total number of pentagrams in a variant of pentagram fractal after n iterations.
  • A263426 (program): Permutation of the nonnegative integers: [4k+2, 4k+1, 4k, 4k+3, …].
  • A263449 (program): Permutation of the natural numbers: [4k+1, 4k+4, 4k+3, 4k+2, …].
  • A263459 (program): Number of (n+1) X (1+1) 0..4 arrays with each row and column divisible by 11, read as a base-5 number with top and left being the most significant digits.
  • A263483 (program): a(n) = prime(n)+(prime(n) modulo 6).
  • A263497 (program): Decimal expansion of the Gaussian Hypergeometric Function 2F1(2,2; 5/2; x) at x=1/4.
  • A263498 (program): Decimal expansion of the Gaussian Hypergeometric Function 2F1(1, 3; 5/2; x) at x=1/4.
  • A263511 (program): Total number of ON (black) cells after n iterations of the “Rule 155” elementary cellular automaton starting with a single ON (black) cell.
  • A263536 (program): Row sum of an equilateral triangle tiled with the 3,4,5 Pythagorean triple.
  • A263537 (program): Integers k such that A098531(k) is divisible by A000071(k+2).
  • A263613 (program): Palindromic numbers in base 4 that are cubes.
  • A263622 (program): a(n) = (3^(n+1)-2^(n+2)+2*n+1)/4.
  • A263689 (program): a(n) = (2n^6 - 6n^5 + 5*n^4 - n^2 + 12)/12.
  • A263727 (program): Largest square number less than or equal to the n-th Fibonacci number.
  • A263766 (program): a(n) = Product_ k=1..n (k^2 - 2).
  • A263770 (program): Smallest prime q such that ((prime(n)^2 + q*prime(n))/(prime(n) + 1) is an integer.
  • A263772 (program): Perimeters of integer-sided scalene triangles.
  • A263794 (program): Number of (n+1) X (3+1) 0..1 arrays with each row and column divisible by 3, read as a binary number with top and left being the most significant bits, and rows and columns lexicographically nonincreasing.
  • A263801 (program): Partial sums of odd double factorials (A001147) with alternating signs.
  • A263804 (program): Triangle read by rows giving successive states of cellular automaton generated by “Rule 157” initiated with a single ON (black) cell.
  • A263807 (program): Total number of ON (black) cells after n iterations of the “Rule 157” elementary cellular automaton starting with a single ON (black) cell.
  • A263824 (program): Permutation of the nonnegative integers: [6k+3, 6k+4, 6k+5, 6k, 6k+1, 6k+2, …].
  • A263845 (program): A258059(n)+1.
  • A263846 (program): Floor of cube root of n-th prime.
  • A263919 (program): Triangle read by rows giving successive states of cellular automaton generated by “Rule 163” initiated with a single ON (black) cell.
  • A263941 (program): Minimal most likely sum for a roll of n 8-sided dice.
  • A263942 (program): Positive integers n such that (n+4)^3 - n^3 is a square.
  • A263944 (program): Positive integers n such that (n+28)^3 - n^3 is a square.
  • A263981 (program): Least even k such that phi(k) >= n.
  • A263997 (program): Sequence of block lengths in a block spiral of width 1.
  • A264018 (program): Number of (2+1) X (n+1) arrays of permutations of 0..n*3+2 with each element having index change +-(.,.) 0,0 1,2 or 2,2.
  • A264041 (program): a(n) is the maximum number of diagonals that can be placed in an n X n grid made up of 1 X 1 unit squares when diagonals are placed in the unit squares in such a way that no two diagonals may cross or intersect at an endpoint.
  • A264060 (program): Number of (2+1)X(n+1) arrays of permutations of 0..n*3+2 with each element having index change +-(.,.) 0,0 1,2 or 2,-2.
  • A264080 (program): a(n) = 6F(n)F(n+1) + (-1)^n, where F = A000045.
  • A264092 (program): Number of (3+1)X(n+1) arrays of permutations of 0..n*4+3 with each element having index change +-(.,.) 0,0 0,1 or 2,-2.
  • A264100 (program): Sum of the lengths of the arithmetic progressions in 1,2,3,…,n , including trivial arithmetic progressions of lengths 1 and 2.
  • A264120 (program): Values of k such that A001163(k) is positive.
  • A264129 (program): Number of (n+1) X (4+1) arrays of permutations of 0..n*5+4 with each element having index change +-(.,.) 0,0 0,2 or 1,2.
  • A264147 (program): a(n) = nF(n+1) - (n+1)F(n), where F = A000045.
  • A264153 (program): a(n) = ((2*n)!)^2 / 2^n.
  • A264263 (program): The number of distinct nontrivial integral cevians of an isosceles triangle, with base of length 1 and legs of length n, that divide the base into two integral parts.
  • A264267 (program): Number of (n+1)X(3+1) arrays of permutations of 0..n*4+3 with each element having index change +-(.,.) 0,0 1,0 or 1,2.
  • A264359 (program): Number of (n+1)X(3+1) arrays of permutations of 0..n*4+3 with each element having directed index change 0,0 0,2 1,0 or -1,-2.
  • A264386 (program): Gergonne’s 27-card trick with three piles: finding a card after three dealings with pile information.
  • A264388 (program): Numerators of binomial(n-1, 2)/(6*n), for n >= 1. Numerators of Dedekind sum s(1, n).
  • A264389 (program): Denominator of binomial(n-1, 2)/(6*n), for n >= 1. Denominator of Dedekind sum s(1,n).
  • A264411 (program): a(n) = binomial(2*n^2, n).
  • A264440 (program): Row lengths of the irregular triangle A137510 (number of divisors d of n with 1 < d < n, or 0 if no such d exists).
  • A264443 (program): a(n) = n(n + 5)(n + 10)/6.
  • A264444 (program): a(n) = n(n + 7)(n + 14)/6.
  • A264445 (program): a(n) = n(n + 11)(n + 22)/6.
  • A264446 (program): a(n) = n(n + 5)(n + 10)*(n + 15)/24.
  • A264447 (program): a(n) = n(n + 7)(n + 14)*(n + 21)/24.
  • A264448 (program): a(n) = n(n + 11)(n + 22)*(n + 33)/24.
  • A264449 (program): a(n) = n(n + 7)(n + 14)(n + 21)(n + 28)/120.
  • A264450 (program): a(n) = n(n + 11)(n + 22)(n + 33)(n + 44)/120.
  • A264557 (program): Number of n X 1 arrays of permutations of 0..n*1-1 with rows nondecreasing modulo 2 and columns nondecreasing modulo 3.
  • A264596 (program): Let S_n be the list of the first n nonnegative numbers written in binary, with least significant bits on the left, and sorted into lexicographic order; a(n) = position of n in S_n, starting indexing at 0.
  • A264613 (program): Numbers n such that the Shevelev polynomial m, n has a root at m = -1.
  • A264618 (program): Working in binary, write n followed by 0 then n-reversed (including leading zeros); show result in base 10.
  • A264619 (program): a(0) = 1; for n>0, working in binary, write n followed by 1 then n-reversed (including leading zeros); show result in base 10.
  • A264663 (program): Catalan numbers written in base 2.
  • A264724 (program): a(n) = n^2 + phi(n).
  • A264740 (program): Sum of odd parts of divisors of n.
  • A264744 (program): Exponent of the prime power A264734(n).
  • A264749 (program): a(n) = floor(n/BL(n)) where BL(n) = A070939(n) is the binary length of n.
  • A264750 (program): Number of sequences of 5 throws of an n-sided die (with faces numbered 1, 2, …, n) in which the sum of the throws first reaches or exceeds n on the 5th throw.
  • A264754 (program): Expansion of (1 + 2x - 2x^3 + x^4)/((1 - x)^3*(1 + x)^2).
  • A264756 (program): An eventually quasilinear solution to Hofstadter’s Q recurrence.
  • A264763 (program): a(0) = a(1) = 1; for n>1, a(n) = a(n-1) + (a(n-2) mod 5).
  • A264782 (program): a(n) = Sum_ d n möbius(d)^(n/d).
  • A264788 (program): a(n) is the number of circles added at n-th iteration of the pattern starting with 2 circles. (See comment.)
  • A264800 (program): Nearly-Fibonacci sequence.
  • A264850 (program): a(n) = n(n + 1)(n + 2)(7n - 5)/12.
  • A264851 (program): a(n) = n(n + 1)(n + 2)(4n - 3)/6.
  • A264852 (program): a(n) = n(n + 1)(n + 2)(9n - 7)/12.
  • A264853 (program): a(n) = n(n + 1)(5n^2 + 5n - 4)/12.
  • A264854 (program): a(n) = n(n + 1)(11n^2 + 11n - 10)/24.
  • A264888 (program): a(n) = n(n + 1)(13n^2 + 13n - 14)/24.
  • A264889 (program): Partial sums of hyperfactorials (A002109).
  • A264891 (program): a(n) = n(5n - 3)(25n^2 - 15*n - 6)/8.
  • A264892 (program): a(n) = n(3n - 2)(9n^2 - 6*n - 2).
  • A264894 (program): a(n) = n(7n - 5)(49n^2 - 35*n - 10)/8.
  • A264895 (program): a(n) = n(4n - 3)(16n^2 - 12*n - 3).
  • A264938 (program): a(n) = n(2n-1) + floor(n/3).
  • A264980 (program): Base-3 reversal of 2^n: a(n) = A030102(A000079(n)).
  • A264981 (program): Highest power of 9 dividing n.
  • A265021 (program): Sum of fifth powers of the first n even numbers.
  • A265026 (program): First differences of A048701.
  • A265027 (program): First differences of A048701 divided by 6.
  • A265028 (program): First differences of A264618.
  • A265029 (program): First differences of A264619.
  • A265045 (program): Coordination sequence for a 6.6.6 point in the 3-transitive tiling 4.6.6, 6.6.6, 6.6.6.6 of the plane by squares and dominoes (hexagons).
  • A265046 (program): Coordination sequence for a 4.6.6 point in the 3-transitive tiling 4.6.6, 6.6.6, 6.6.6.6 of the plane by squares and dominoes (hexagons).
  • A265056 (program): Partial sums of A234275.
  • A265078 (program): Partial sums of A072154.
  • A265100 (program): a(n) = 9*A005836(n) + 5, n >= 1.
  • A265101 (program): a(n) = binomial(6n + 5, 3n + 1)/(6*n + 5).
  • A265102 (program): a(n) = binomial(8n + 6, 4n + 1)/(8*n + 6).
  • A265104 (program): a(n) = A265100(n+1) - 6, n >= 1.
  • A265127 (program): a(n) = prime(n) * 2^n.
  • A265129 (program): Triangle read by rows, formed as the sum of the two versions of the natural numbers filling an equilateral triangle.
  • A265160 (program): a(n) = 2^n + prime(n).
  • A265172 (program): Binary representation of the n-th iteration of the “Rule 90” elementary cellular automaton starting with a single ON cell.
  • A265185 (program): Non-vanishing traces of the powers of the adjacency matrix for the simple Lie algebra B_4: 2 * ((2 + sqrt(2))^n + (2 - sqrt(2))^n).
  • A265186 (program): Triangle read by rows giving successive states of cellular automaton generated by “Rule 175” initiated with a single ON (black) cell.
  • A265187 (program): Nonnegative m for which 2floor(m^2/11) = floor(2m^2/11).
  • A265188 (program): Nonnegative m for which 3floor(m^2/11) = floor(3m^2/11).
  • A265207 (program): Draw a square and follow these steps: Take a square and place at its edges isosceles right triangles with the edge as hypotenuse. Draw a square at every new edge of the triangles. Repeat for all the new squares of the same size. New figures are only placed on empty space. The structure is symmetric about the first square. The sequence gives the numbers of squares of equal size in successive rings around the center.
  • A265225 (program): Total number of ON (black) cells after n iterations of the “Rule 54” elementary cellular automaton starting with a single ON (black) cell.
  • A265227 (program): Nonnegative m for which kfloor(m^2/9) = floor(km^2/9), with 2 < k < 9.
  • A265228 (program): Interleave the even numbers with the numbers that are congruent to 1, 3, 7 mod 8.
  • A265278 (program): Expansion of (x^4+x^3-x^2+x)/(x^3+x^2-3*x+1).
  • A265283 (program): Number of ON (black) cells in the n-th iteration of the “Rule 94” elementary cellular automaton starting with a single ON (black) cell.
  • A265284 (program): Total number of ON (black) cells after n iterations of the “Rule 94” elementary cellular automaton starting with a single ON (black) cell.
  • A265326 (program): n-th prime minus its binary reversal.
  • A265333 (program): Characteristic function for A265334: a(n) = 1 if n >= k! but < 2*k! for some k, 0 otherwise.
  • A265334 (program): Numbers that are >= k! but < 2*k! for some k; numbers whose factorial base representation (A007623) begins with digit “1”.
  • A265359 (program): Spiralwise distance to the nearest inner neighbor in Ulam-style square-spirals using zero-based indexing: a(0) = 0, for n >= 1, a(n) = n - A265409(n).
  • A265381 (program): Decimal representation of the middle column of the “Rule 158” elementary cellular automaton starting with a single ON (black) cell.
  • A265382 (program): Total number of ON (black) cells after n iterations of the “Rule 158” elementary cellular automaton starting with a single ON (black) cell.
  • A265384 (program): Toothpick sequence starting at the vertex of y=3*abs(x).
  • A265409 (program): a(n) = index to the nearest inner neighbor in Ulam-style square-spirals using zero-based indexing.
  • A265411 (program): a(0) = 1, a(1) = 7, otherwise, if A240025(n-1) = 1 [when n is in A033638] a(n) = 3, otherwise a(n) = 1.
  • A265412 (program): Partial sums of A265411.
  • A265413 (program): Positions of records in A265410: a(0) = 1; for n >= 1, a(n) = 1 + A265412(n-1).
  • A265428 (program): Number of ON (black) cells in the n-th iteration of the “Rule 188” elementary cellular automaton starting with a single ON (black) cell.
  • A265429 (program): Total number of ON (black) cells after n iterations of the “Rule 188” elementary cellular automaton starting with a single ON (black) cell.
  • A265430 (program): Number of OFF (white) cells in the n-th iteration of the “Rule 188” elementary cellular automaton starting with a single ON (black) cell.
  • A265431 (program): Total number of OFF (white) cells after n iterations of the “Rule 188” elementary cellular automaton starting with a single ON (black) cell.
  • A265436 (program): a(n) is the least m (1 <= m <= n) such that the set of pairs (x, y) of distinct terms from [m, n] can be ordered in such a way that the corresponding sums (x+y) and products (x*y) are monotonic.
  • A265526 (program): Largest base-2 palindrome m <= n, written in base 2.
  • A265527 (program): Largest base-2 palindrome m <= 2n, written in base 10.
  • A265528 (program): Largest base-2 palindrome m <= 2n, written in base 2.
  • A265541 (program): Largest base-9 palindrome m <= n, written in base 10.
  • A265542 (program): Largest base-9 palindrome m <= n, written in base 9.
  • A265574 (program): LCM-transform of triangular numbers.
  • A265611 (program): a(n) = a(n-1) + floor((n-1)/2) - (-1)^n + 2 for n>=2, a(0)=1, a(1)=3.
  • A265645 (program): a(n) = n^2 * floor(n/2).
  • A265667 (program): Permutation of nonnegative integers: a(n) = n + floor(n/3)*(-1)^(n mod 3).
  • A265676 (program): a(n) is the total number of petals of the Flower of Life at the n-th iteration.
  • A265716 (program): a(n) = n IMPL (2*n), where IMPL is the bitwise logical implication.
  • A265722 (program): Number of ON (black) cells in the n-th iteration of the “Rule 1” elementary cellular automaton starting with a single ON (black) cell.
  • A265723 (program): Number of OFF (white) cells in the n-th iteration of the “Rule 1” elementary cellular automaton starting with a single ON (black) cell.
  • A265724 (program): Total number of OFF (white) cells after n iterations of the “Rule 1” elementary cellular automaton starting with a single ON (black) cell.
  • A265743 (program): a(n) = number of terms of A005187 needed to sum to n using the greedy algorithm.
  • A265888 (program): a(n) = n + floor(n/4)*(-1)^(n mod 4).
  • A265948 (program): Numbers whose name in German contains the letter Ö (O with Umlaut).
  • A265987 (program): Number of n X 3 integer arrays with each element equal to the number of horizontal and antidiagonal neighbors not equal to itself.
  • A266046 (program): Real part of Q^n, where Q is the quaternion 2 + j + k.
  • A266070 (program): Middle column of the “Rule 3” elementary cellular automaton starting with a single ON (black) cell.
  • A266072 (program): Number of ON (black) cells in the n-th iteration of the “Rule 3” elementary cellular automaton starting with a single ON (black) cell.
  • A266073 (program): Number of OFF (white) cells in the n-th iteration of the “Rule 3” elementary cellular automaton starting with a single ON (black) cell.
  • A266074 (program): Total number of OFF (white) cells after n iterations of the “Rule 3” elementary cellular automaton starting with a single ON (black) cell.
  • A266083 (program): a(n) = Sum_ k = 0..n - 1 (a(n - 1) + k) for n>0, a(0) = 1.
  • A266084 (program): Expansion of (5 - x - x^2 - x^3 - x^4 + 4*x^5)/( x^6 - x^5 - x + 1).
  • A266085 (program): Alternating sum of heptagonal numbers.
  • A266086 (program): Alternating sum of 9-gonal (or nonagonal) numbers.
  • A266087 (program): Alternating sum of 11-gonal (or hendecagonal) numbers.
  • A266088 (program): Alternating sum of 12-gonal (or dodecagonal) numbers.
  • A266155 (program): Triangle read by rows giving successive states of cellular automaton generated by “Rule 19” initiated with a single ON (black) cell.
  • A266178 (program): Triangle read by rows giving successive states of cellular automaton generated by “Rule 6” initiated with a single ON (black) cell.
  • A266179 (program): Binary representation of the n-th iteration of the “Rule 6” elementary cellular automaton starting with a single ON (black) cell.
  • A266180 (program): Decimal representation of the n-th iteration of the “Rule 6” elementary cellular automaton starting with a single ON (black) cell.
  • A266216 (program): Triangle read by rows giving successive states of cellular automaton generated by “Rule 7” initiated with a single ON (black) cell.
  • A266218 (program): Decimal representation of the n-th iteration of the “Rule 7” elementary cellular automaton starting with a single ON (black) cell.
  • A266220 (program): Number of ON (black) cells in the n-th iteration of the “Rule 7” elementary cellular automaton starting with a single ON (black) cell.
  • A266221 (program): Total number of ON (black) cells after n iterations of the “Rule 7” elementary cellular automaton starting with a single ON (black) cell.
  • A266222 (program): Number of OFF (white) cells in the n-th iteration of the “Rule 7” elementary cellular automaton starting with a single ON (black) cell.
  • A266223 (program): Total number of OFF (white) cells after n iterations of the “Rule 7” elementary cellular automaton starting with a single ON (black) cell.
  • A266224 (program): Least x such that prime(n)*x+x+1 is a prime, or -1 if no such x exists.
  • A266229 (program): a(n) = Sum_ j=0..12 (-n)^j.
  • A266246 (program): Middle column of the “Rule 9” elementary cellular automaton starting with a single ON (black) cell.
  • A266249 (program): Number of ON (black) cells in the n-th iteration of the “Rule 9” elementary cellular automaton starting with a single ON (black) cell.
  • A266250 (program): Total number of ON (black) cells after n iterations of the “Rule 9” elementary cellular automaton starting with a single ON (black) cell.
  • A266251 (program): Number of OFF (white) cells in the n-th iteration of the “Rule 9” elementary cellular automaton starting with a single ON (black) cell.
  • A266252 (program): Total number of OFF (white) cells after n iterations of the “Rule 9” elementary cellular automaton starting with a single ON (black) cell.
  • A266253 (program): Triangle read by rows giving successive states of cellular automaton generated by “Rule 11” initiated with a single ON (black) cell.
  • A266256 (program): Number of ON (black) cells in the n-th iteration of the “Rule 11” elementary cellular automaton starting with a single ON (black) cell.
  • A266257 (program): Total number of ON (black) cells after n iterations of the “Rule 11” elementary cellular automaton starting with a single ON (black) cell.
  • A266258 (program): Number of OFF (white) cells in the n-th iteration of the “Rule 11” elementary cellular automaton starting with a single ON (black) cell.
  • A266259 (program): Total number of OFF (white) cells after n iterations of the “Rule 11” elementary cellular automaton starting with a single ON (black) cell.
  • A266282 (program): Triangle read by rows giving successive states of cellular automaton generated by “Rule 13” initiated with a single ON (black) cell.
  • A266285 (program): Number of ON (black) cells in the n-th iteration of the “Rule 13” elementary cellular automaton starting with a single ON (black) cell.
  • A266286 (program): Number of OFF (white) cells in the n-th iteration of the “Rule 13” elementary cellular automaton starting with a single ON (black) cell.
  • A266287 (program): Total number of OFF (white) cells after n iterations of the “Rule 13” elementary cellular automaton starting with a single ON (black) cell.
  • A266297 (program): Numbers whose last digit is a square.
  • A266298 (program): Triangle read by rows giving successive states of cellular automaton generated by “Rule 14” initiated with a single ON (black) cell.
  • A266299 (program): Binary representation of the n-th iteration of the “Rule 14” elementary cellular automaton starting with a single ON (black) cell.
  • A266300 (program): Triangle read by rows giving successive states of cellular automaton generated by “Rule 15” initiated with a single ON (black) cell.
  • A266302 (program): Decimal representation of the n-th iteration of the “Rule 15” elementary cellular automaton starting with a single ON (black) cell.
  • A266303 (program): Number of ON (black) cells in the n-th iteration of the “Rule 15” elementary cellular automaton starting with a single ON (black) cell.
  • A266304 (program): Total number of OFF (white) cells after n iterations of the “Rule 15” elementary cellular automaton starting with a single ON (black) cell.
  • A266313 (program): Period 8 zigzag sequence; repeat [0, 1, 2, 3, 4, 3, 2, 1].
  • A266326 (program): Triangle read by rows giving successive states of cellular automaton generated by “Rule 20” initiated with a single ON (black) cell.
  • A266327 (program): Binary representation of the n-th iteration of the “Rule 20” elementary cellular automaton starting with a single ON (black) cell.
  • A266377 (program): Triangle read by rows giving successive states of cellular automaton generated by “Rule 21” initiated with a single ON (black) cell.
  • A266379 (program): Binary representation of the n-th iteration of the “Rule 21” elementary cellular automaton starting with a single ON (black) cell.
  • A266380 (program): Decimal representation of the n-th iteration of the “Rule 21” elementary cellular automaton starting with a single ON (black) cell.
  • A266387 (program): Number of orbits of Aut(Z^7) as function of the infinity norm n of the representative lattice point of the orbit, when the cardinality of the orbit is equal to 322560.
  • A266395 (program): Number of orbits of Aut(Z^7) as function of the infinity norm n of the representative lattice point of the orbit, when the cardinality of the orbit is equal to 161280.
  • A266396 (program): Number of orbits of Aut(Z^7) as function of the infinity norm n of the representative lattice point of the orbit, when the cardinality of the orbit is equal to 80640.
  • A266397 (program): Number of orbits of Aut(Z^7) as function of the infinity norm n of the representative lattice point of the orbit, when the cardinality of the orbit is equal to 26880.
  • A266398 (program): Number of orbits of Aut(Z^7) as function of the infinity norm n of the representative lattice point of the orbit, when the cardinality of the orbit is equal to 13440.
  • A266434 (program): Triangle read by rows giving successive states of cellular automaton generated by “Rule 23” initiated with a single ON (black) cell.
  • A266435 (program): Binary representation of the n-th iteration of the “Rule 23” elementary cellular automaton starting with a single ON (black) cell.
  • A266436 (program): Decimal representation of the n-th iteration of the “Rule 23” elementary cellular automaton starting with a single ON (black) cell.
  • A266437 (program): Number of ON (black) cells in the n-th iteration of the “Rule 23” elementary cellular automaton starting with a single ON (black) cell.
  • A266438 (program): Total number of ON (black) cells after n iterations of the “Rule 23” elementary cellular automaton starting with a single ON (black) cell.
  • A266439 (program): Number of OFF (white) cells in the n-th iteration of the “Rule 23” elementary cellular automaton starting with a single ON (black) cell.
  • A266440 (program): Total number of OFF (white) cells after n iterations of the “Rule 23” elementary cellular automaton starting with a single ON (black) cell.
  • A266444 (program): Middle column of the “Rule 25” elementary cellular automaton starting with a single ON (black) cell.
  • A266447 (program): Number of ON (black) cells in the n-th iteration of the “Rule 25” elementary cellular automaton starting with a single ON (black) cell.
  • A266448 (program): Total number of ON (black) cells after n iterations of the “Rule 25” elementary cellular automaton starting with a single ON (black) cell.
  • A266449 (program): Number of OFF (white) cells in the n-th iteration of the “Rule 25” elementary cellular automaton starting with a single ON (black) cell.
  • A266450 (program): Total number of OFF (white) cells after n iterations of the “Rule 25” elementary cellular automaton starting with a single ON (black) cell.
  • A266464 (program): Number of n X 2 binary arrays with rows and columns lexicographically nondecreasing and column sums nonincreasing.
  • A266491 (program): a(n) = n*A130658(n).
  • A266502 (program): Triangle read by rows giving successive states of cellular automaton generated by “Rule 28” initiated with a single ON (black) cell.
  • A266507 (program): a(n) = 6*a(n - 1) - a(n - 2) with a(0) = 2, a(1) = 8.
  • A266508 (program): Binary representation of the n-th iteration of the “Rule 28” elementary cellular automaton starting with a single ON (black) cell.
  • A266532 (program): Total number of Y-toothpicks after n-th stage in the “outward” version of the cellular automaton of A160120.
  • A266533 (program): First differences of A266532.
  • A266535 (program): Sums of two successive terms of A256249, with a(0) = 0.
  • A266538 (program): Twice the partial sums of A006257 (Josephus problem).
  • A266539 (program): Terms of A006257 (Josephus problem) repeated.
  • A266540 (program): Partial sums of A266539.
  • A266542 (program): Number of n X 3 binary arrays with rows and columns lexicographically nondecreasing and row and column sums nonincreasing.
  • A266550 (program): Independence number of the n-Mycielski graph.
  • A266561 (program): 12-dimensional square numbers.
  • A266591 (program): Middle column of the “Rule 37” elementary cellular automaton starting with a single ON (black) cell.
  • A266593 (program): Number of ON (black) cells in the n-th iteration of the “Rule 37” elementary cellular automaton starting with a single ON (black) cell.
  • A266594 (program): Total number of ON (black) cells after n iterations of the “Rule 37” elementary cellular automaton starting with a single ON (black) cell.
  • A266595 (program): Number of OFF (white) cells in the n-th iteration of the “Rule 37” elementary cellular automaton starting with a single ON (black) cell.
  • A266596 (program): Total number of OFF (white) cells after n iterations of the “Rule 37” elementary cellular automaton starting with a single ON (black) cell.
  • A266611 (program): Middle column of the “Rule 41” elementary cellular automaton starting with a single ON (black) cell.
  • A266613 (program): Decimal representation of the middle column of the “Rule 41” elementary cellular automaton starting with a single ON (black) cell.
  • A266620 (program): a(n) = least non-divisor of n!.
  • A266659 (program): Triangle read by rows giving successive states of cellular automaton generated by “Rule 47” initiated with a single ON (black) cell.
  • A266662 (program): Number of ON (black) cells in the n-th iteration of the “Rule 47” elementary cellular automaton starting with a single ON (black) cell.
  • A266663 (program): Total number of ON (black) cells after n iterations of the “Rule 47” elementary cellular automaton starting with a single ON (black) cell.
  • A266664 (program): Number of OFF (white) cells in the n-th iteration of the “Rule 47” elementary cellular automaton starting with a single ON (black) cell.
  • A266665 (program): Total number of OFF (white) cells after n iterations of the “Rule 47” elementary cellular automaton starting with a single ON (black) cell.
  • A266666 (program): Triangle read by rows giving successive states of cellular automaton generated by “Rule 51” initiated with a single ON (black) cell.
  • A266678 (program): Middle column of the “Rule 175” elementary cellular automaton starting with a single ON (black) cell.
  • A266698 (program): x-values of solutions to the Diophantine equation x^2 - 7*y^2 = 2.
  • A266719 (program): Middle column of the “Rule 59” elementary cellular automaton starting with a single ON (black) cell.
  • A266721 (program): Decimal representation of the middle column of the “Rule 59” elementary cellular automaton starting with a single ON (black) cell.
  • A266722 (program): Number of ON (black) cells in the n-th iteration of the “Rule 59” elementary cellular automaton starting with a single ON (black) cell.
  • A266723 (program): Total number of ON (black) cells after n iterations of the “Rule 59” elementary cellular automaton starting with a single ON (black) cell.
  • A266724 (program): Number of OFF (white) cells in the n-th iteration of the “Rule 59” elementary cellular automaton starting with a single ON (black) cell.
  • A266725 (program): Total number of OFF (white) cells after n iterations of the “Rule 59” elementary cellular automaton starting with a single ON (black) cell.
  • A266732 (program): a(n) = 10*binomial(n+4, 5).
  • A266733 (program): a(n) = 21*binomial(n+6,7).
  • A266753 (program): Decimal representation of the n-th iteration of the “Rule 163” elementary cellular automaton starting with a single ON (black) cell.
  • A266754 (program): Triangle read by rows giving successive states of cellular automaton generated by “Rule 165” initiated with a single ON (black) cell.
  • A266755 (program): Expansion of 1/((1-x^2)(1-x^3)(1-x^4)).
  • A266769 (program): Expansion of 1/((1-x)(1-x^2)^2(1-x^3)).
  • A266789 (program): Middle column of the “Rule 61” elementary cellular automaton starting with a single ON (black) cell.
  • A266797 (program): a(n) = (6^n + 4^n + 3*2^n)/8.
  • A266840 (program): Triangle read by rows giving successive states of cellular automaton generated by “Rule 69” initiated with a single ON (black) cell.
  • A266843 (program): Triangle read by rows giving successive states of cellular automaton generated by “Rule 70” initiated with a single ON (black) cell.
  • A266873 (program): Decimal representation of the n-th iteration of the “Rule 77” elementary cellular automaton starting with a single ON (black) cell.
  • A266883 (program): Numbers of the form m(4m+1)+1, where m = 0,-1,1,-2,2,-3,3,…
  • A266912 (program): Numbers n which are anagrams of n+18.
  • A266936 (program): Number of 3 X n binary arrays with rows lexicographically nondecreasing and columns lexicographically nondecreasing and row sums nondecreasing and column sums nonincreasing.
  • A266956 (program): Numbers m such that 9*m+7 is a square.
  • A266957 (program): Numbers m such that 9*m+10 is a square.
  • A266958 (program): Numbers m such that 9*m+13 is a square.
  • A266959 (program): Smallest n-digit number ending in n.
  • A266973 (program): a(n) = 4^n mod 17.
  • A266977 (program): Number of ON (black) cells in the n-th iteration of the “Rule 78” elementary cellular automaton starting with a single ON (black) cell.
  • A266978 (program): Triangle read by rows giving successive states of cellular automaton generated by “Rule 79” initiated with a single ON (black) cell.
  • A266981 (program): Number of ON (black) cells in the n-th iteration of the “Rule 79” elementary cellular automaton starting with a single ON (black) cell.
  • A266982 (program): Triangle read by rows giving successive states of cellular automaton generated by “Rule 81” initiated with a single ON (black) cell.
  • A266984 (program): Decimal representation of the n-th iteration of the “Rule 81” elementary cellular automaton starting with a single ON (black) cell.
  • A267006 (program): Triangle read by rows giving successive states of cellular automaton generated by “Rule 84” initiated with a single ON (black) cell.
  • A267017 (program): Digital roots of the stella octangula numbers.
  • A267027 (program): “Polyrhythmic sequence” P(3,4): numbers congruent to 1 mod 3 (A016777) or 1 mod 4 (A016813).
  • A267031 (program): a(n) = (32n^3 - 2n)/3.
  • A267034 (program): Triangle read by rows giving successive states of cellular automaton generated by “Rule 85” initiated with a single ON (black) cell.
  • A267036 (program): Decimal representation of the n-th iteration of the “Rule 85” elementary cellular automaton starting with a single ON (black) cell.
  • A267043 (program): Middle column of the “Rule 91” elementary cellular automaton starting with a single ON (black) cell.
  • A267045 (program): Decimal representation of the middle column of the “Rule 91” elementary cellular automaton starting with a single ON (black) cell.
  • A267047 (program): Total number of ON (black) cells after n iterations of the “Rule 91” elementary cellular automaton starting with a single ON (black) cell.
  • A267048 (program): Number of OFF (white) cells in the n-th iteration of the “Rule 91” elementary cellular automaton starting with a single ON (black) cell.
  • A267049 (program): Total number of OFF (white) cells after n iterations of the “Rule 91” elementary cellular automaton starting with a single ON (black) cell.
  • A267051 (program): Binary representation of the n-th iteration of the “Rule 92” elementary cellular automaton starting with a single ON (black) cell.
  • A267052 (program): Decimal representation of the n-th iteration of the “Rule 92” elementary cellular automaton starting with a single ON (black) cell.
  • A267053 (program): Triangle read by rows giving successive states of cellular automaton generated by “Rule 93” initiated with a single ON (black) cell.
  • A267068 (program): a(n) = (n+1) / A189733(n).
  • A267092 (program): a(n) is the number of P-positions for n-modular Nim with 2 piles.
  • A267097 (program): a(n) = number of 4k+1 primes among first n primes; least monotonic left inverse of A080147.
  • A267098 (program): a(n) = number of 4k+3 primes among first n primes; least monotonic left inverse of A080148.
  • A267133 (program): a(n) = (1/n)(2/n)(3/n)…((n-1)/n) where (k/n) is the Kronecker symbol, n >= 1.
  • A267141 (program): Number of weeks in n! seconds, for n >= 10.
  • A267142 (program): The characteristic function of the multiples of 9.
  • A267144 (program): Octagonal numbers with prime indices.
  • A267155 (program): Middle column of the “Rule 107” elementary cellular automaton starting with a single ON (black) cell.
  • A267182 (program): Row 2 of the square array in A267181.
  • A267185 (program): Column 2 of the square array in A267181.
  • A267208 (program): Middle column of the “Rule 109” elementary cellular automaton starting with a single ON (black) cell.
  • A267210 (program): Decimal representation of the middle column of the “Rule 109” elementary cellular automaton starting with a single ON (black) cell.
  • A267217 (program): 10-gonal (or decagonal) numbers with prime indices.
  • A267226 (program): Number of length-n 0..2 arrays with no following elements greater than or equal to the first repeated value.
  • A267233 (program): Number of length-4 0..n arrays with no following elements greater than or equal to the first repeated value.
  • A267238 (program): Sum of the triangular numbers whose indices are the digits of n.
  • A267256 (program): Middle column of the “Rule 111” elementary cellular automaton starting with a single ON (black) cell.
  • A267263 (program): Number of nonzero digits in representation of n in primorial base.
  • A267272 (program): Triangle read by rows giving successive states of cellular automaton generated by “Rule 117” initiated with a single ON (black) cell.
  • A267313 (program): Expansion of x(-1 + 2x + 3x^2 - 2x^3 + x^4)/((1 - x)^3*(1 + x + x^2)^2).
  • A267314 (program): Expansion of 2x(1 + 2x - x^2)/((1 - x)(1 + x^2)^2).
  • A267317 (program): a(n) = final digit of 2^n-1.
  • A267318 (program): Continued fraction expansion of e^(1/5).
  • A267319 (program): Continued fraction expansion of phi^8, where phi = (1 + sqrt(5))/2.
  • A267329 (program): Number of nX(n+1) arrays of permutations of n+1 copies of 0..n-1 with every element equal to or 1 greater than any southwest or northwest neighbors modulo n and the upper left element equal to 0.
  • A267352 (program): Number of ON (black) cells in the n-th iteration of the “Rule 123” elementary cellular automaton starting with a single ON (black) cell.
  • A267353 (program): Total number of ON (black) cells after n iterations of the “Rule 123” elementary cellular automaton starting with a single ON (black) cell.
  • A267354 (program): Number of OFF (white) cells in the n-th iteration of the “Rule 123” elementary cellular automaton starting with a single ON (black) cell.
  • A267368 (program): Total number of ON (black) cells after n iterations of the “Rule 126” elementary cellular automaton starting with a single ON (black) cell.
  • A267369 (program): Total number of OFF (white) cells after n iterations of the “Rule 126” elementary cellular automaton starting with a single ON (black) cell.
  • A267370 (program): Partial sums of A140091.
  • A267414 (program): Integers n such that n! = x^3 + y^3 + z^3 where x, y and z are nonnegative integers, is soluble.
  • A267442 (program): Middle column of the “Rule 129” elementary cellular automaton starting with a single ON (black) cell.
  • A267445 (program): Number of ON (black) cells in the n-th iteration of the “Rule 129” elementary cellular automaton starting with a single ON (black) cell.
  • A267446 (program): Total number of ON (black) cells after n iterations of the “Rule 129” elementary cellular automaton starting with a single ON (black) cell.
  • A267447 (program): Number of OFF (white) cells in the n-th iteration of the “Rule 129” elementary cellular automaton starting with a single ON (black) cell.
  • A267448 (program): Total number of OFF (white) cells after n iterations of the “Rule 129” elementary cellular automaton starting with a single ON (black) cell.
  • A267458 (program): Number of ON (black) cells in the n-th iteration of the “Rule 133” elementary cellular automaton starting with a single ON (black) cell.
  • A267459 (program): Total number of ON (black) cells after n iterations of the “Rule 133” elementary cellular automaton starting with a single ON (black) cell.
  • A267460 (program): Number of OFF (white) cells in the n-th iteration of the “Rule 133” elementary cellular automaton starting with a single ON (black) cell.
  • A267461 (program): Total number of OFF (white) cells after n iterations of the “Rule 133” elementary cellular automaton starting with a single ON (black) cell.
  • A267472 (program): Number of length-4 0..n arrays with no following elements larger than the first repeated value.
  • A267489 (program): a(n) = n^2 - 4*floor(n^2/6).
  • A267520 (program): Triangle read by rows giving successive states of cellular automaton generated by “Rule 139” initiated with a single ON (black) cell.
  • A267522 (program): a(n) = 4(n + 1)(n + 2)(4n + 3)/3.
  • A267528 (program): Number of ON (black) cells in the n-th iteration of the “Rule 141” elementary cellular automaton starting with a single ON (black) cell.
  • A267529 (program): Total number of ON (black) cells after n iterations of the “Rule 141” elementary cellular automaton starting with a single ON (black) cell.
  • A267530 (program): Number of OFF (white) cells in the n-th iteration of the “Rule 141” elementary cellular automaton starting with a single ON (black) cell.
  • A267531 (program): Total number of OFF (white) cells after n iterations of the “Rule 141” elementary cellular automaton starting with a single ON (black) cell.
  • A267533 (program): Triangle read by rows giving successive states of cellular automaton generated by “Rule 143” initiated with a single ON (black) cell.
  • A267536 (program): Decimal representation of the n-th iteration of the “Rule 143” elementary cellular automaton starting with a single ON (black) cell.
  • A267537 (program): Middle column of the “Rule 143” elementary cellular automaton starting with a single ON (black) cell.
  • A267539 (program): Decimal representation of the middle column of the “Rule 143” elementary cellular automaton starting with a single ON (black) cell.
  • A267541 (program): Expansion of (2 + 4x + x^2 + x^3 + 2x^4 + x^5)/(1 - x - x^5 + x^6).
  • A267551 (program): Lucas numbers written backwards.
  • A267573 (program): a(n) = prime(n) + (prime(n) mod 4).
  • A267576 (program): Triangle read by rows giving successive states of cellular automaton generated by “Rule 167” initiated with a single ON (black) cell.
  • A267579 (program): Middle column of the “Rule 167” elementary cellular automaton starting with a single ON (black) cell.
  • A267582 (program): Number of ON (black) cells in the n-th iteration of the “Rule 167” elementary cellular automaton starting with a single ON (black) cell.
  • A267583 (program): Total number of ON (black) cells after n iterations of the “Rule 167” elementary cellular automaton starting with a single ON (black) cell.
  • A267584 (program): a(0)=1; thereafter a(n) = 2^(1 + number of zeros in binary expansion of n).
  • A267587 (program): Middle column of the “Rule 169” elementary cellular automaton starting with a single ON (black) cell.
  • A267589 (program): Decimal representation of the middle column of the “Rule 169” elementary cellular automaton starting with a single ON (black) cell.
  • A267594 (program): Triangle read by rows giving successive states of cellular automaton generated by “Rule 173” initiated with a single ON (black) cell.
  • A267595 (program): Binary representation of the n-th iteration of the “Rule 173” elementary cellular automaton starting with a single ON (black) cell.
  • A267596 (program): Decimal representation of the n-th iteration of the “Rule 173” elementary cellular automaton starting with a single ON (black) cell.
  • A267597 (program): Number of sum-product knapsack partitions of n. Number of integer partitions y of n such that every sum of products of the parts of a multiset partition of any submultiset of y is distinct.
  • A267598 (program): Triangle read by rows giving successive states of cellular automaton generated by “Rule 177” initiated with a single ON (black) cell.
  • A267599 (program): Binary representation of the n-th iteration of the “Rule 177” elementary cellular automaton starting with a single ON (black) cell.
  • A267602 (program): Number of unlabeled, connected graphs on n vertices that are prime and have no induced subgraph isomorphic to a bull, a P5 or a P5-bar.
  • A267604 (program): Decimal representation of the middle column of the “Rule 175” elementary cellular automaton starting with a single ON (black) cell.
  • A267605 (program): Triangle read by rows giving successive states of cellular automaton generated by “Rule 181” initiated with a single ON (black) cell.
  • A267610 (program): Total number of OFF (white) cells after n iterations of the “Rule 182” elementary cellular automaton starting with a single ON (black) cell.
  • A267612 (program): Triangle read by rows giving successive states of cellular automaton generated by “Rule 185” initiated with a single ON (black) cell.
  • A267613 (program): Binary representation of the n-th iteration of the “Rule 185” elementary cellular automaton starting with a single ON (black) cell.
  • A267614 (program): Decimal representation of the n-th iteration of the “Rule 185” elementary cellular automaton starting with a single ON (black) cell.
  • A267615 (program): a(n) = 2^n + 11.
  • A267621 (program): Triangle read by rows giving successive states of cellular automaton generated by “Rule 187” initiated with a single ON (black) cell.
  • A267622 (program): Binary representation of the n-th iteration of the “Rule 187” elementary cellular automaton starting with a single ON (black) cell.
  • A267623 (program): Binary representation of the middle column of the “Rule 187” elementary cellular automaton starting with a single ON (black) cell.
  • A267635 (program): Triangle read by rows giving successive states of cellular automaton generated by “Rule 189” initiated with a single ON (black) cell.
  • A267638 (program): Number of nX2 0..1 arrays with every repeated value in every row and column unequal to the previous repeated value, and new values introduced in row-major sequential order.
  • A267647 (program): a(n) = g_n(4), where g is the weak Goodstein function defined in A266202.
  • A267649 (program): a(1) = a(2) = 2 then a(n) = 4 for n>2.
  • A267654 (program): Irregular triangle of palindromic subsequences. Every row has 2n+1 terms. From the second row, there are only two alternated numbers: 2n+4 and 2*n+2.
  • A267661 (program): Number of nX2 0..1 arrays with every repeated value in every row unequal to the previous repeated value, and in every column equal to the previous repeated value, and new values introduced in row-major sequential order.
  • A267668 (program): Number of 3Xn 0..1 arrays with every repeated value in every row unequal to the previous repeated value, and in every column equal to the previous repeated value, and new values introduced in row-major sequential order.
  • A267673 (program): Triangle read by rows giving successive states of cellular automaton generated by “Rule 195” initiated with a single ON (black) cell.
  • A267682 (program): a(n) = 2a(n-1) - 2a(n-3) + a(n-4) for n > 3, with initial terms 1, 1, 4, 8.
  • A267683 (program): Triangle read by rows giving successive states of cellular automaton generated by “Rule 203” initiated with a single ON (black) cell.
  • A267685 (program): Decimal representation of the n-th iteration of the “Rule 203” elementary cellular automaton starting with a single ON (black) cell.
  • A267687 (program): Triangle read by rows giving successive states of cellular automaton generated by “Rule 199” initiated with a single ON (black) cell.
  • A267691 (program): a(n) = (n + 1)(6n^4 - 21n^3 + 31n^2 - 31*n + 30)/30.
  • A267700 (program): “Tree” sequence in a 90 degree sector of the cellular automaton of A160720.
  • A267704 (program): Triangle read by rows giving successive states of cellular automaton generated by “Rule 205” initiated with a single ON (black) cell.
  • A267707 (program): a(n) = A000217(A000217(n)+1).
  • A267708 (program): Triangle read by rows giving successive states of cellular automaton generated by “Rule 206” initiated with a single ON (black) cell.
  • A267711 (program): Numbers k such that k mod 3 = k mod 5.
  • A267729 (program): Number of n X 2 0..1 arrays with every repeated value in every row and column greater than or equal to the previous repeated value.
  • A267730 (program): Number of nX3 0..1 arrays with every repeated value in every row and column greater than or equal to the previous repeated value.
  • A267747 (program): Numbers k such that k mod 2 = k mod 3 = k mod 5.
  • A267755 (program): Expansion of (1 + 2x + x^2 + x^3 + 4x^4 + 2*x^5)/(1 - x - x^5 + x^6).
  • A267773 (program): Triangle read by rows giving successive states of cellular automaton generated by “Rule 207” initiated with a single ON (black) cell.
  • A267774 (program): Decimal representation of the n-th iteration of the “Rule 207” elementary cellular automaton starting with a single ON (black) cell.
  • A267775 (program): Binary representation of the n-th iteration of the “Rule 207” elementary cellular automaton starting with a single ON (black) cell.
  • A267776 (program): Triangle read by rows giving successive states of cellular automaton generated by “Rule 209” initiated with a single ON (black) cell.
  • A267777 (program): Binary representation of the n-th iteration of the “Rule 209” elementary cellular automaton starting with a single ON (black) cell.
  • A267778 (program): Triangle read by rows giving successive states of cellular automaton generated by “Rule 211” initiated with a single ON (black) cell.
  • A267780 (program): Decimal representation of the n-th iteration of the “Rule 211” elementary cellular automaton starting with a single ON (black) cell.
  • A267783 (program): Number of n X 3 0..1 arrays with every repeated value in every row greater than or equal to, and in every column greater than, the previous repeated value.
  • A267796 (program): a(n) = (n+1)*4^(2n+1).
  • A267797 (program): Lucas numbers of the form (x^3 + y^3) / 2 where x and y are distinct positive integers.
  • A267799 (program): a(n) = (1 + 2^n + 3^n)/2.
  • A267800 (program): Triangle read by rows giving successive states of cellular automaton generated by “Rule 213” initiated with a single ON (black) cell.
  • A267802 (program): Decimal representation of the n-th iteration of the “Rule 213” elementary cellular automaton starting with a single ON (black) cell.
  • A267806 (program): a(0) = a(1) = 1; for n>1, a(n) = (a(n-1) mod 2) + a(n-2).
  • A267807 (program): a(0) = a(1) = 1; for n>1, a(n) = (a(n-1) mod 3) + a(n-2).
  • A267808 (program): a(0) = a(1) = 1; for n>1, a(n) = (a(n-1) mod 4) + a(n-2).
  • A267809 (program): a(1)=a(2)=1; if n>2 then a(n) = a(n-2) + (a(n-1) mod 10).
  • A267810 (program): Triangle read by rows giving successive states of cellular automaton generated by “Rule 217” initiated with a single ON (black) cell.
  • A267811 (program): Binary representation of the n-th iteration of the “Rule 217” elementary cellular automaton starting with a single ON (black) cell.
  • A267812 (program): Decimal representation of the n-th iteration of the “Rule 217” elementary cellular automaton starting with a single ON (black) cell.
  • A267813 (program): Triangle read by rows giving successive states of cellular automaton generated by “Rule 219” initiated with a single ON (black) cell.
  • A267814 (program): Triangle read by rows giving successive states of cellular automaton generated by “Rule 221” initiated with a single ON (black) cell.
  • A267815 (program): Binary representation of the n-th iteration of the “Rule 221” elementary cellular automaton starting with a single ON (black) cell.
  • A267816 (program): Decimal representation of the n-th iteration of the “Rule 221” elementary cellular automaton starting with a single ON (black) cell.
  • A267845 (program): Triangle read by rows giving successive states of cellular automaton generated by “Rule 227” initiated with a single ON (black) cell.
  • A267847 (program): Decimal representation of the n-th iteration of the “Rule 227” elementary cellular automaton starting with a single ON (black) cell.
  • A267848 (program): Triangle read by rows giving successive states of cellular automaton generated by “Rule 229” initiated with a single ON (black) cell.
  • A267850 (program): Binary representation of the n-th iteration of the “Rule 229” elementary cellular automaton starting with a single ON (black) cell.
  • A267851 (program): Decimal representation of the n-th iteration of the “Rule 229” elementary cellular automaton starting with a single ON (black) cell.
  • A267860 (program): An infinite ternary 3-Fibonacci sequence (replace each 00 factor of the Fibonacci word with 020).
  • A267866 (program): Triangle read by rows giving successive states of cellular automaton generated by “Rule 231” initiated with a single ON (black) cell.
  • A267867 (program): Binary representation of the n-th iteration of the “Rule 231” elementary cellular automaton starting with a single ON (black) cell.
  • A267868 (program): Triangle read by rows giving successive states of cellular automaton generated by “Rule 233” initiated with a single ON (black) cell.
  • A267869 (program): Triangle read by rows giving successive states of cellular automaton generated by “Rule 235” initiated with a single ON (black) cell.
  • A267870 (program): Triangle read by rows giving successive states of cellular automaton generated by “Rule 237” initiated with a single ON (black) cell.
  • A267871 (program): Triangle read by rows giving successive states of cellular automaton generated by “Rule 239” initiated with a single ON (black) cell.
  • A267872 (program): Number of ON (black) cells in the n-th iteration of the “Rule 237” elementary cellular automaton starting with a single ON (black) cell.
  • A267873 (program): Number of ON (black) cells in the n-th iteration of the “Rule 235” elementary cellular automaton starting with a single ON (black) cell.
  • A267874 (program): Total number of ON (black) cells after n iterations of the “Rule 235” elementary cellular automaton starting with a single ON (black) cell.
  • A267878 (program): Middle column of the “Rule 233” elementary cellular automaton starting with a single ON (black) cell.
  • A267880 (program): Decimal representation of the middle column of the “Rule 233” elementary cellular automaton starting with a single ON (black) cell.
  • A267881 (program): Number of ON (black) cells in the n-th iteration of the “Rule 233” elementary cellular automaton starting with a single ON (black) cell.
  • A267882 (program): Total number of ON (black) cells after n iterations of the “Rule 233” elementary cellular automaton starting with a single ON (black) cell.
  • A267883 (program): Number of OFF (white) cells in the n-th iteration of the “Rule 233” elementary cellular automaton starting with a single ON (black) cell.
  • A267884 (program): Total number of OFF (white) cells after n iterations of the “Rule 233” elementary cellular automaton starting with a single ON (black) cell.
  • A267886 (program): Decimal representation of the n-th iteration of the “Rule 235” elementary cellular automaton starting with a single ON (black) cell.
  • A267888 (program): Decimal representation of the n-th iteration of the “Rule 237” elementary cellular automaton starting with a single ON (black) cell.
  • A267890 (program): Decimal representation of the n-th iteration of the “Rule 239” elementary cellular automaton starting with a single ON (black) cell.
  • A267896 (program): a(n) = (Prime(n+1)^2 - Prime(n)^2) / 8.
  • A267897 (program): a(n) = prime(n)! - prime(n).
  • A267898 (program): a(n) = prime(n)! + prime(n).
  • A267905 (program): Number of n X 1 0..2 arrays with every repeated value in every row unequal to the previous repeated value, and in every column equal to the previous repeated value, and new values introduced in row-major sequential order.
  • A267906 (program): Number of n X 2 0..2 arrays with every repeated value in every row unequal to the previous repeated value, and in every column equal to the previous repeated value, and new values introduced in row-major sequential order.
  • A267919 (program): Triangle read by rows giving successive states of cellular automaton generated by “Rule 243” initiated with a single ON (black) cell.
  • A267920 (program): Binary representation of the n-th iteration of the “Rule 243” elementary cellular automaton starting with a single ON (black) cell.
  • A267921 (program): Decimal representation of the n-th iteration of the “Rule 243” elementary cellular automaton starting with a single ON (black) cell.
  • A267922 (program): Triangle read by rows giving successive states of cellular automaton generated by “Rule 245” initiated with a single ON (black) cell.
  • A267924 (program): Decimal representation of the n-th iteration of the “Rule 245” elementary cellular automaton starting with a single ON (black) cell.
  • A267925 (program): Binary representation of the n-th iteration of the “Rule 246” elementary cellular automaton starting with a single ON (black) cell.
  • A267926 (program): Decimal representation of the n-th iteration of the “Rule 246” elementary cellular automaton starting with a single ON (black) cell.
  • A267927 (program): Triangle read by rows giving successive states of cellular automaton generated by “Rule 249” initiated with a single ON (black) cell.
  • A267935 (program): Decimal representation of the n-th iteration of the “Rule 249” elementary cellular automaton starting with a single ON (black) cell.
  • A267936 (program): Triangle read by rows giving successive states of cellular automaton generated by “Rule 251” initiated with a single ON (black) cell.
  • A267937 (program): Binary representation of the n-th iteration of the “Rule 251” elementary cellular automaton starting with a single ON (black) cell.
  • A267938 (program): Decimal representation of the n-th iteration of the “Rule 251” elementary cellular automaton starting with a single ON (black) cell.
  • A267940 (program): Binary representation of the n-th iteration of the “Rule 253” elementary cellular automaton starting with a single ON (black) cell.
  • A267941 (program): Decimal representation of the n-th iteration of the “Rule 253” elementary cellular automaton starting with a single ON (black) cell.
  • A267942 (program): Interleave (n-1)^2 + 2 and (n+1)^2 + 2.
  • A267958 (program): 4 times A042965.
  • A267981 (program): a(n) = Catalan(n)^2*(4n + 2).
  • A267982 (program): a(n) = 4nCatalan(n)^2.
  • A267984 (program): Numbers congruent to 17, 23 mod 30.
  • A267985 (program): Numbers congruent to 7, 13 mod 30.
  • A267987 (program): a(n) = Catalan(n)^2*(4n + 4).
  • A268044 (program): The odd numbers congruent to 3, 4 mod 5.
  • A268085 (program): a(n) = Catalan(n)^2*n.
  • A268099 (program): a(n) = 2^(n mod 2)510^floor(n/2) - 1.
  • A268100 (program): a(n) = 2^((n-1) mod 2)510^floor((n-1)/2).
  • A268147 (program): A double binomial sum involving absolute values.
  • A268148 (program): A double binomial sum involving absolute values.
  • A268149 (program): A double binomial sum involving absolute values.
  • A268151 (program): A double binomial sum involving absolute values.
  • A268185 (program): a(n) = prime(n) + last digit of prime(n).
  • A268201 (program): a(n) = 4n^3 - 6n^2 + 3*n - 1.
  • A268218 (program): a(n) = (n!/3!)*Sum(1/k!,k=1..n-3).
  • A268219 (program): a(n) = (n!/4!)*Sum(1/k!,k=1..n-4).
  • A268220 (program): a(n) = (n!/5!)*Sum(1/k!,k=1..n-5).
  • A268226 (program): Complement of A056991.
  • A268227 (program): a(n) = sum of digits of (2n)^2.
  • A268228 (program): a(n) = sum of digits of (2n + 1)^2.
  • A268233 (program): Excess of number of 1’s over number of 0’s in terms 0 through n of A047999.
  • A268234 (program): Partial sums of A047999.
  • A268235 (program): a(n) = Sum_ k=1..n floor(n/k)*2^(k-1).
  • A268262 (program): Number of length-(3+1) 0..n arrays with new repeated values introduced in sequential order starting with zero.
  • A268263 (program): Number of length-(4+1) 0..n arrays with new repeated values introduced in sequential order starting with zero.
  • A268264 (program): Number of length-(5+1) 0..n arrays with new repeated values introduced in sequential order starting with zero.
  • A268272 (program): Negabinary evil numbers (see comment).
  • A268273 (program): Negabinary odious numbers (see comment).
  • A268289 (program): a(0)=0; thereafter a(n) = a(n-1) - A037861(n).
  • A268291 (program): a(n) = Sum_ k = 0..n (k mod 13).
  • A268292 (program): a(n) is the total number of isolated 1’s at the boundary between n-th and (n-1)-th iterations in the pattern of A267489.
  • A268295 (program): Terms at square positions in Pascal’s triangle when in flattened form.
  • A268306 (program): The number of even permutations p of 1,2,…,n such that -1<=p(i)-i<=2 for i=1,2,…,n
  • A268315 (program): Decimal expansion of 256/27.
  • A268340 (program): Characteristic function of the prime powers p^k, k >= 2.
  • A268342 (program): Number of edges in the unitary addition Cayley graph Gn.
  • A268351 (program): a(n) = 3n(9*n - 1)/2.
  • A268354 (program): Highest power of 7 dividing n.
  • A268355 (program): Highest power of 8 dividing n.
  • A268357 (program): Highest power of 11 dividing n.
  • A268361 (program): Lexicographically least sequence of a certain form that avoids additive squares.
  • A268363 (program): Number of n X 2 arrays containing 2 copies of 0..n-1 with row sums equal.
  • A268382 (program): Partial sums of A268411; the least monotonic left inverse of A268415.
  • A268383 (program): Least monotonic left inverse of A268412.
  • A268384 (program): Characteristic function of A001317.
  • A268398 (program): Partial sums of A085731.
  • A268411 (program): Parity of number of runs of 1’s in binary representation of n.
  • A268413 (program): a(n) = Sum_ k = 0..n (-1)^k*14^k.
  • A268414 (program): a(n) = 5a(n - 1) - 2n for n>0, a(0) = 1.
  • A268458 (program): Number of length-4 0..n arrays with no adjacent pair x,x+1 followed at any distance by x+1,x.
  • A268459 (program): Number of length-5 0..n arrays with no adjacent pair x,x+1 followed at any distance by x+1,x.
  • A268460 (program): Number of length-6 0..n arrays with no adjacent pair x,x+1 followed at any distance by x+1,x.
  • A268462 (program): Expansion of (2 x^4(5 - 12x + 8x^2))/(1 - 2x)^4.
  • A268484 (program): a(n) = (n + 1)(4n^2 + 14*n + 9)/3.
  • A268488 (program): Least number k of the form k = n*(k % 10) + [k / 10], where k % 10 = last digit of k, [k / 10] = k without its last digit.
  • A268514 (program): a(0)=0; thereafter a(2n+1)=3a(n)+1, a(2n)=2a(n)+a(n-1)+1.
  • A268524 (program): a(n) = ra(ceiling(n/2))+sa(floor(n/2)) with a(1)=1 and (r,s)=(3,1).
  • A268527 (program): a(n) = ra(ceiling(n/2))+sa(floor(n/2)) with a(1)=1 and (r,s)=(4,1).
  • A268539 (program): Numbers k such that 48*k+25 is a perfect square.
  • A268553 (program): Diagonal of the rational function 1/((1 - u v - u w - v w) * (1 - x y - x z - y z)).
  • A268579 (program): Expansion of (1 + 6x + x^2 + 12x^3 - 2x^4)/((1 - x)^4(1 + x)^3).
  • A268581 (program): a(n) = 2n^2 + 8n + 5.
  • A268586 (program): Expansion of (x^3(3x - 2))/(2*x - 1)^3.
  • A268598 (program): Expansion of x^5(4 - 5x)/(1 - 2*x)^4.
  • A268605 (program): a(1) = 0; a(n+1) is the smallest integer in which the difference between its digits sum and the a(n) digits sum is equal to the n-th prime.
  • A268613 (program): Lucas numbers mod 20.
  • A268615 (program): Lucas numbers mod 40.
  • A268622 (program): Number of n X 2 0..2 arrays with some element plus some horizontally or vertically adjacent neighbor totalling two no more than once.
  • A268631 (program): Number of ordered pairs (a,b) of positive integers less than n with the property that n divides ab.
  • A268633 (program): Number of n X 2 0..2 arrays with some element plus some horizontally or vertically adjacent neighbor totalling two exactly once.
  • A268643 (program): Number of 1’s in decimal representation of n.
  • A268644 (program): a(n) = 4n^3 - 3n^2 - 2*n - 1.
  • A268669 (program): a(n) = polynomial quotient (computed over GF(2), result is its binary encoding) that is left after all instances of polynomial (X+1) have been factored out of the polynomial that is encoded by the binary expansion of n. (See comments for details).
  • A268676 (program): a(n) = A101080(n,A268823(3+n)), where A101080(x,y) gives the Hamming distance between binary expansions of x and y.
  • A268682 (program): Decimal expansion of 1 - 1/sqrt(2).
  • A268683 (program): Decimal expansion of (sqrt(2) - 1)/2.
  • A268684 (program): a(n) = n(n + 1)(4*n - 1)/3.
  • A268685 (program): a(n) = 3(n + 1)(n + 2)(3n + 1)(3n + 4)/4.
  • A268716 (program): a(n) = 2*A006068(n); main diagonal of A268714.
  • A268717 (program): Permutation of natural numbers: a(0) = 0, a(n) = A003188(1+A006068(n-1)), where A003188 is binary Gray code and A006068 is its inverse.
  • A268718 (program): Permutation of natural numbers: a(0) = 0, a(n) = 1 + A003188(A006068(n)-1), where A003188 is binary Gray code and A006068 is its inverse.
  • A268722 (program): a(n) = A003188(3*A006068(n)), where A003188 is binary Gray code and A006068 is its inverse.
  • A268723 (program): Main diagonal of A268725: a(n) = A003188(A006068(n)^2), where A003188 is binary Gray code and A006068 is its inverse.
  • A268726 (program): Index of the toggled bit between n and A268717(n+1): a(n) = A000523(A003987(n, A268717(1+n))).
  • A268727 (program): One-based index of the toggled bit between n and A268717(n+1): a(n) = A070939(A003987(n,A268717(1+n))).
  • A268741 (program): a(n) = 2*a(n - 2) - a(n - 1) for n>1, a(0) = 4, a(1) = 5.
  • A268744 (program): Number of n X 2 binary arrays with some element plus some horizontally or vertically adjacent neighbor totalling two no more than once.
  • A268753 (program): Primes congruent to 1 mod 13.
  • A268775 (program): Number of n X 2 binary arrays with some element plus some horizontally, vertically, diagonally or antidiagonally adjacent neighbor totalling two no more than once.
  • A268810 (program): a(n) = 2floor(3n*(n+1)/4).
  • A268813 (program): Decimal expansion of sum(k>=0, 1/C(k)), where C(k) is a Catalan Number (A000108).
  • A268817 (program): Permutation of nonnegative integers: a(n) = A268717(A268717(n)).
  • A268818 (program): Permutation of nonnegative integers: a(n) = A268718(A268718(n)).
  • A268821 (program): Permutation of nonnegative integers: a(0) = 0, a(n) = A268717(1 + A268717(n-1)).
  • A268823 (program): Permutation of nonnegative integers: a(0) = 0, a(n) = A268717(1 + A268821(n-1)).
  • A268825 (program): Permutation of nonnegative integers: a(0) = 0, a(n) = A268717(1+A268823(n-1)).
  • A268827 (program): Permutation of nonnegative integers: a(0) = 0, a(n) = A268717(1+A268825(n-1)).
  • A268831 (program): Permutation of nonnegative integers: a(0) = 0, a(n) = A268717(1+A268827(n-1)).
  • A268836 (program): Antidiagonal sums of array A268714: a(n) = Sum_ k=0..n A006068(n)+A006068(n-k).
  • A268839 (program): a(n) = Sum_ j=1..10^n-1 2^f(j) where f(j) is the number of zero digits in the decimal representation of j.
  • A268866 (program): Records in A268865.
  • A268896 (program): Start at a(0)=1. a(n) = a(n-1)+2 if n == 1,2 (mod 3) and a(n)=a(n-1)+a(n-3) if n == 0 (mod 3).
  • A268898 (program): Number of n X 2 0..2 arrays with some element plus some horizontally or antidiagonally adjacent neighbor totalling two exactly once.
  • A268899 (program): Number of n X 3 0..2 arrays with some element plus some horizontally or antidiagonally adjacent neighbor totalling two exactly once.
  • A268900 (program): Number of n X 4 0..2 arrays with some element plus some horizontally or antidiagonally adjacent neighbor totalling two exactly once.
  • A268905 (program): Number of 2 X n 0..2 arrays with some element plus some horizontally or antidiagonally adjacent neighbor totalling two exactly once.
  • A268933 (program): Permutation of nonnegative integers: a(0) = 0, for n >= 1, a(n) = A268717(1 + A268831(n-1)).
  • A268945 (program): Number of length-4 0..n arrays with no repeated value unequal to the previous repeated value plus one mod n+1.
  • A268946 (program): Number of length-5 0..n arrays with no repeated value unequal to the previous repeated value plus one mod n+1.
  • A268947 (program): Number of length-6 0..n arrays with no repeated value unequal to the previous repeated value plus one mod n+1.
  • A268965 (program): Number of n X 2 0..2 arrays with some element plus some horizontally or antidiagonally adjacent neighbor totalling two not more than once.
  • A268966 (program): Number of n X 3 0..2 arrays with some element plus some horizontally or antidiagonally adjacent neighbor totalling two not more than once.
  • A268989 (program): Number of n X 2 binary arrays with some element plus some horizontally or antidiagonally adjacent neighbor totalling two not more than once.
  • A269019 (program): a(n) = 2^n + 2*(-1)^n - 1.
  • A269020 (program): a(n) = ceiling(n^(1+1/n)).
  • A269024 (program): a(n) = A269020(n) - n.
  • A269025 (program): a(n) = Sum_ k = 0..n 60^k.
  • A269027 (program): Parity of the number of 1’s in A039724(n).
  • A269036 (program): Number of 2 X n 0..2 arrays with some element plus some horizontally, diagonally or antidiagonally adjacent neighbor totalling two exactly once.
  • A269044 (program): a(n) = 13*n + 7.
  • A269059 (program): Construct a hollow square of 1’s of side n and fill its interior with 0’s to create a stack of n binary numbers. Express the sum of the stack in decimal.
  • A269098 (program): Expansion of (1 + 2x + 3x^2 + x^3 + x^5)/(1 - x^3)^2.
  • A269100 (program): a(n) = 13*n + 11.
  • A269110 (program): Numbers of unit circles packed in a triangle of smallest area admitting an equilateral triangle solution.
  • A269111 (program): a(n) = length of the repeating part of row n of A288097.
  • A269112 (program): a(n) = (3(n-1)n + (-1)^((n-1)*n/2) + 5)/2.
  • A269130 (program): a(n) = n + (n base 2 regarded as a decimal number).
  • A269132 (program): a(n) = n + floor(n(2n+1)/5).
  • A269160 (program): Formula for Wolfram’s Rule 30 cellular automaton: a(n) = n XOR (2n OR 4n).
  • A269161 (program): Formula for Wolfram’s Rule 86 cellular automaton: a(n) = 4n XOR (2n OR n).
  • A269169 (program): The least monotonic left inverse for A269164.
  • A269170 (program): a(n) = n OR floor(n/2), where OR is bitwise-OR (A003986).
  • A269173 (program): Formula for Wolfram’s Rule 126 cellular automaton: a(n) = (n XOR 2n) OR (n XOR 4n).
  • A269174 (program): Formula for Wolfram’s Rule 124 cellular automaton: a(n) = (n OR 2n) AND ((n XOR 2n) OR (n XOR 4n)).
  • A269221 (program): Factorial of the sum of decimal digits of n.
  • A269222 (program): Period 4: repeat [1,9,8,9].
  • A269223 (program): Factorial of the sum of digits of n in base 3.
  • A269224 (program): Factorial of the sum of digits of n in base 4.
  • A269226 (program): Period 6: repeat [3, 9, 6, 6, 9, 3].
  • A269232 (program): a(n) = (n + 1)(6n^2 + 15*n + 4)/2.
  • A269237 (program): a(n) = (n + 1)^2(5n^2 + 10*n + 2)/2.
  • A269241 (program): Number of times the digit 1 appears in the decimal expansion of n^3.
  • A269242 (program): Number of times the digit 2 appears in the decimal expansion of n^3.
  • A269243 (program): Number of times the digit 3 appears in the decimal expansion of n^3.
  • A269244 (program): Number of times the digit 4 appears in the decimal expansion of n^3.
  • A269245 (program): Number of times the digit 5 appears in the decimal expansion of n^3.
  • A269246 (program): Number of times the digit 6 appears in the decimal expansion of n^3.
  • A269247 (program): Number of times the digit 7 appears in the decimal expansion of n^3.
  • A269248 (program): Number of times the digit 8 appears in the decimal expansion of n^3.
  • A269249 (program): Number of times the digit 9 appears in the decimal expansion of n^3.
  • A269266 (program): a(n) = 2^n mod 31.
  • A269270 (program): Number of n X 2 0..3 arrays with some element plus some horizontally or antidiagonally adjacent neighbor totalling three exactly once.
  • A269304 (program): a(n) = n + n/gpf(n) + 1, where gpf(n) is the greatest prime factor of n or 1 if n = 1.
  • A269306 (program): a(n+1) is the smallest integer such that the difference between its digital sum and the digital sum of a(n) is n.
  • A269327 (program): a(n) = 7^prime(n).
  • A269342 (program): a(n) = (n + 1)(2n + 1)(4n + 9)/3.
  • A269352 (program): Kolakoski-(1,10) sequence: a(n) is length of n-th run.
  • A269362 (program): Least monotonic left inverse of A269389.
  • A269403 (program): Expansion of x(2 - x + 2x^2 + x^3)/((1 - x)^3*(1 + x + x^2 + x^3)).
  • A269410 (program): Number of length-4 0..n arrays with no repeated value greater than or equal to the previous repeated value.
  • A269412 (program): Number of length-6 0..n arrays with no repeated value greater than or equal to the previous repeated value.
  • A269416 (program): Expansion of 3(2 - x)/((1 - x)(1 + x)^2).
  • A269429 (program): Alternating sum of octagonal pyramidal numbers.
  • A269430 (program): Decimal expansion of (1 + Pi)/2.
  • A269436 (program): Number of length-4 0..n arrays with no repeated value greater than the previous repeated value.
  • A269442 (program): a(n) = n(n^8 + 1)(n^4 + 1)(n^2 + 1)(n + 1) + 1.
  • A269445 (program): a(n) = Sum_ k=0..n floor(k/13).
  • A269446 (program): a(n) = n(n^6 + n^3 + 1)(n^6 - n^3 + 1)(n^2 + n + 1)(n^2 - n + 1)*(n + 1) + 1.
  • A269457 (program): a(n) = 5(n + 1)(n + 4)/2.
  • A269468 (program): Number of length-4 0..n arrays with no repeated value equal to the previous repeated value.
  • A269469 (program): Number of length-5 0..n arrays with no repeated value equal to the previous repeated value.
  • A269470 (program): Number of length-6 0..n arrays with no repeated value equal to the previous repeated value.
  • A269486 (program): a(n) = Sum_ j=0..10 (-n)^j.
  • A269495 (program): Number of length-4 0..n arrays with no repeated value differing from the previous repeated value by one.
  • A269496 (program): Number of length-5 0..n arrays with no repeated value differing from the previous repeated value by one.
  • A269497 (program): Number of length-6 0..n arrays with no repeated value differing from the previous repeated value by one.
  • A269500 (program): a(n) = Fibonacci(10*n).
  • A269527 (program): a(n) = n^20 + n^15 + n^10 + n^5 + 1.
  • A269538 (program): Number of length-4 0..n arrays with no repeated value differing from the previous repeated value by other than one.
  • A269539 (program): Number of length-5 0..n arrays with no repeated value differing from the previous repeated value by other than one.
  • A269540 (program): Number of length-6 0..n arrays with no repeated value differing from the previous repeated value by other than one.
  • A269552 (program): Expansion of (-3x^2 + 94x - 3)/(x^3 - 99x^2 + 99x - 1).
  • A269584 (program): Number of length-4 0..n arrays with no repeated value differing from the previous repeated value by more than one.
  • A269585 (program): Number of length-5 0..n arrays with no repeated value differing from the previous repeated value by more than one.
  • A269607 (program): Number of length-4 0..n arrays with no repeated value differing from the previous repeated value by one or less.
  • A269608 (program): Number of length-5 0..n arrays with no repeated value differing from the previous repeated value by one or less.
  • A269609 (program): Number of length-6 0..n arrays with no repeated value differing from the previous repeated value by one or less.
  • A269620 (program): Number of length-4 0..n arrays with no repeated value differing from the previous repeated value by other than plus two, zero or minus 1.
  • A269621 (program): Number of length-5 0..n arrays with no repeated value differing from the previous repeated value by other than plus two, zero or minus 1.
  • A269641 (program): Number of length-4 0..n arrays with no repeated value differing from the previous repeated value by other than plus two or minus 1.
  • A269642 (program): Number of length-5 0..n arrays with no repeated value differing from the previous repeated value by other than plus two or minus 1.
  • A269643 (program): Number of length-6 0..n arrays with no repeated value differing from the previous repeated value by other than plus two or minus 1.
  • A269657 (program): Number of length-4 0..n arrays with no adjacent pair x,x+1 repeated.
  • A269658 (program): Number of length-5 0..n arrays with no adjacent pair x,x+1 repeated.
  • A269679 (program): Number of length-4 0..n arrays with no repeated value differing from the previous repeated value by other than plus or minus one modulo n+1.
  • A269680 (program): Number of length-5 0..n arrays with no repeated value differing from the previous repeated value by other than plus or minus one modulo n+1.
  • A269681 (program): Number of length-6 0..n arrays with no repeated value differing from the previous repeated value by other than plus or minus one modulo n+1.
  • A269684 (program): Number of length-n 0..2 arrays with no repeated value differing from the previous repeated value by plus or minus one modulo 2+1.
  • A269691 (program): Number of length-5 0..n arrays with no repeated value differing from the previous repeated value by plus or minus one modulo n+1.
  • A269696 (program): Number of active (ON,black) cells at stage 2^n-1 of the two-dimensional cellular automaton defined by “Rule 6”, based on the 5-celled von Neumann neighborhood.
  • A269701 (program): Cyclic Fibonacci sequence, restricted to maximum=6
  • A269705 (program): Numbers k such that prime(k) == 1 (mod 9).
  • A269707 (program): Decimal expansion of x = 3*Sum_ n in E 1/10^n where E is the set of numbers whose base-4 representation consists of only 0’s and 1’s.
  • A269712 (program): Number of active (ON,black) cells at stage 2^n-1 of the two-dimensional cellular automaton defined by “Rule 20”, based on the 5-celled von Neumann neighborhood.
  • A269723 (program): Start with A_0 = 0, then extend by setting B_k = complement of A_k and A_ k+1 = A_k A_k B_k B_k; sequence is limit of A_k as k -> infinity.
  • A269745 (program): Maximal number of 1’s in an n X n 0,1 Toeplitz matrix with property that no four 1’s form a square with sides parallel to the edges of the matrix.
  • A269746 (program): Maximal number of 1’s in an equilateral triangle of 0’s and 1’s with n points on each side, the entries being constant on vertical lines, with property that no three 1’s form a triangle with sides parallel to the edges of the triangle.
  • A269760 (program): Number of n X 1 0..5 arrays with some element plus some horizontally or vertically adjacent neighbor totalling five exactly once.
  • A269777 (program): Number of length-5 0..n arrays with every repeated value unequal to the previous repeated value plus one mod n+1.
  • A269792 (program): a(n) = 5*n^4.
  • A269819 (program): Numbers that are congruent to 5, 11, 13, 19 mod 24.
  • A269822 (program): Number of n X 1 0..4 arrays with some element plus some horizontally, diagonally, antidiagonally or vertically adjacent neighbor totalling four exactly once.
  • A269845 (program): Irregular triangle read by rows: T(n,k) = (k/2+1/2)^2 if odd-k otherwise T(n,k) = (n-k/2)^2 where n >= 1, k = 0..2*n-1.
  • A269849 (program): a(n) = number of integers k <= n for which prime(k+1)-prime(k) is not a multiple of three.
  • A269850 (program): a(n) = number of integers k <= n for which prime(k+1)-prime(k) is a multiple of three.
  • A269862 (program): Least monotonic left inverse of A269861.
  • A269876 (program): Number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by “Rule 43”, based on the 5-celled von Neumann neighborhood.
  • A269878 (program): Partial sums of the number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by “Rule 43”, based on the 5-celled von Neumann neighborhood.
  • A269879 (program): First differences of number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by “Rule 43”, based on the 5-celled von Neumann neighborhood.
  • A269895 (program): Number of n X 1 0..6 arrays with some element plus some horizontally or vertically adjacent neighbor totalling six exactly once.
  • A269906 (program): Number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by “Rule 1”, based on the 5-celled von Neumann neighborhood.
  • A269907 (program): Number of active (ON,black) cells at stage 2^n-1 of the two-dimensional cellular automaton defined by “Rule 1”, based on the 5-celled von Neumann neighborhood.
  • A269908 (program): Partial sums of the number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by “Rule 1”, based on the 5-celled von Neumann neighborhood.
  • A269909 (program): First differences of number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by “Rule 1”, based on the 5-celled von Neumann neighborhood.
  • A269910 (program): Number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by “Rule 3”, based on the 5-celled von Neumann neighborhood.
  • A269911 (program): Number of active (ON,black) cells at stage 2^n-1 of the two-dimensional cellular automaton defined by “Rule 3”, based on the 5-celled von Neumann neighborhood.
  • A269912 (program): Partial sums of the number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by “Rule 3”, based on the 5-celled von Neumann neighborhood.
  • A269913 (program): First differences of number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by “Rule 3”, based on the 5-celled von Neumann neighborhood.
  • A269956 (program): Triangle read by rows, T(n,k) = binomial(3*n,n+k) for n>=0 and 0<=k<=n.
  • A270003 (program): Least prime p such that n = p + q - r for some primes q and r with q > p.
  • A270006 (program): Number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by “Rule 5”, based on the 5-celled von Neumann neighborhood.
  • A270007 (program): Number of active (ON,black) cells at stage 2^n-1 of the two-dimensional cellular automaton defined by “Rule 5”, based on the 5-celled von Neumann neighborhood.
  • A270008 (program): Partial sums of the number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by “Rule 5”, based on the 5-celled von Neumann neighborhood.
  • A270010 (program): Number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by “Rule 7”, based on the 5-celled von Neumann neighborhood.
  • A270012 (program): Partial sums of the number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by “Rule 7”, based on the 5-celled von Neumann neighborhood.
  • A270026 (program): a(n) is the smallest b for which the base-b representation of n contains at least one 0 (or 0 if no such base exists).
  • A270027 (program): a(n) is the smallest b >= 3 for which the base-b representation of n contains at least one 0 (or 0 if no such base exists).
  • A270028 (program): a(n) is the smallest b >= 3 for which the base-b representation of n contains at least one 1 (or 0 if no such base exists).
  • A270029 (program): a(n) is the smallest b for which the base-b representation of n contains at least one 3 (or 0 if no such base exists).
  • A270030 (program): a(n) is the smallest b for which the base-b representation of n contains at least one 4 (or 0 if no such base exists).
  • A270031 (program): a(n) is the smallest b for which the base-b representation of n contains at least one 5 (or 0 if no such base exists).
  • A270032 (program): a(n) is the smallest b for which the base-b representation of n contains at least one 6 (or 0 if no such base exists).
  • A270033 (program): a(n) is the smallest b for which the base-b representation of n contains at least one 7 (or 0 if no such base exists).
  • A270034 (program): a(n) is the smallest b for which the base-b representation of n contains at least one 8 (or 0 if no such base exists).
  • A270035 (program): a(n) is the smallest b for which the base-b representation of n contains at least one 9 (or 0 if no such base exists).
  • A270059 (program): Number of distinct digits needed to write n in all bases >= 2.
  • A270106 (program): Partial sums of the number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by “Rule 84”, based on the 5-celled von Neumann neighborhood.
  • A270109 (program): a(n) = n^3 + (n+1)*(n+2).
  • A270111 (program): Number of n X 1 0..7 arrays with some element plus some horizontally or vertically adjacent neighbor totalling seven exactly once.
  • A270126 (program): Number of active (ON,black) cells at stage 2^n-1 of the two-dimensional cellular automaton defined by “Rule 86”, based on the 5-celled von Neumann neighborhood.
  • A270200 (program): a(0) = 0; for n >= 1, a(n) = A054429(A005187(1+A054429(n-1))).
  • A270204 (program): a(n) = n^12 - n^10 + n^8 - n^6 + n^4 - n^2 + 1.
  • A270205 (program): Number of 2 X 2 planar subsets in an n X n X n cube.
  • A270222 (program): Number of active (ON,black) cells at stage 2^n-1 of the two-dimensional cellular automaton defined by “Rule 131”, based on the 5-celled von Neumann neighborhood.
  • A270226 (program): a(n) is the number of terms in the n-th block of consecutive integers of A136119.
  • A270257 (program): Number of 2X2X2 triangular 0..n arrays with some element plus some adjacent element totalling n exactly once.
  • A270272 (program): a(n) = binomial(n+3,n)^3.
  • A270296 (program): Numbers which are representable as a sum of five but no fewer consecutive nonnegative integers.
  • A270297 (program): Numbers which are representable as a sum of seven but no fewer consecutive nonnegative integers.
  • A270369 (program): Expansion of (1-7x)/(1-9x).
  • A270383 (program): Number of ordered pairs (i,j) with i >= j, i , j <= n, and i * j <= n.
  • A270444 (program): Expansion of 2(1+2x) / (1-8x+4x^2).
  • A270445 (program): Expansion of 2x(1+4x) / (1-12x+16*x^2).
  • A270454 (program): Number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by “Rule 163”, based on the 5-celled von Neumann neighborhood.
  • A270455 (program): Partial sums of the number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by “Rule 163”, based on the 5-celled von Neumann neighborhood.
  • A270456 (program): First differences of number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by “Rule 163”, based on the 5-celled von Neumann neighborhood.
  • A270471 (program): Expansion of (1-3x)/(1-7x).
  • A270472 (program): Expansion of (1-2x)/(1-9x).
  • A270473 (program): Expansion of (1-5x)/(1-9x).
  • A270510 (program): Number of 2X2X2 triangular 0..n arrays with some element plus some adjacent element totalling n+1 exactly once.
  • A270545 (program): Number of equilateral triangle units forming perimeter of equilateral triangle.
  • A270567 (program): Expansion of (1+4x)/(1-5x).
  • A270568 (program): Expansion of (1+4x)/(1-8x).
  • A270576 (program): Expansion of (1+2x)/(1-6x).
  • A270607 (program): Number of 2X2X2 triangular 0..n arrays with some element plus some adjacent element totalling n+1 or n-1 exactly once.
  • A270653 (program): Integers n such that A003266(n) is divisible by n.
  • A270681 (program): Number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by “Rule 190”, based on the 5-celled von Neumann neighborhood.
  • A270683 (program): Partial sums of the number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by “Rule 190”, based on the 5-celled von Neumann neighborhood.
  • A270684 (program): First differences of number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by “Rule 190”, based on the 5-celled von Neumann neighborhood.
  • A270700 (program): Triangular Star of David numbers (the figurate number of triangles framing a hexagram: a(0) = 12; thereafter a(n) = 36*n+6).
  • A270704 (program): Even 14-gonal (or tetradecagonal) numbers.
  • A270710 (program): a(n) = 3n^2 + 2n - 1.
  • A270740 (program): Period 9: repeat 0,1,2,2,0,1,1,2,0.
  • A270742 (program): Binary expansion of C = (1/2)(3/4)(7/8)*(15/16)… .
  • A270743 (program): Runlength sequence of the zero-one sequence A270742.
  • A270775 (program): a(n) is the number of invertible 2 X 2 upper triangular matrices over Z_p where p = prime(n).
  • A270788 (program): Unique fixed point of the 3-symbol Fibonacci morphism phi-hat_2.
  • A270796 (program): The prime/nonprime compound sequence BBA.
  • A270797 (program): a(n) = J(n) if n odd, or 4*J(n) if n even, where J = Jacobsthal numbers A001045.
  • A270803 (program): Formal inverse of Thue-Morse sequence A010060.
  • A270804 (program): 0 followed by the positions of the 1’s in the inverse Thue-Morse sequence A270803.
  • A270809 (program): a(n) = n^3/3 - 7*n/3 + 4.
  • A270810 (program): Expansion of (x - x^2 + 2x^3 + 2x^4)/(1 - 3x + 2x^2).
  • A270814 (program): a(1)=0; thereafter a(2k)=k+a(k), a(2k+1)=6k+4+a(6k+4).
  • A270819 (program): a(n) is the number of arithmetic progressions of length 3 among the quadratic residues modulo prime(n).
  • A270826 (program): Maximum number of iterations needed in the Euclid algorithm for gcd(x,y) in [1..n].
  • A270841 (program): a(1) = 5; a(n) is the sum of a(m) - m for m < n.
  • A270851 (program): Number of 2X2X2 triangular 0..n arrays with some element plus some adjacent element totalling n+1, n or n-1 exactly once.
  • A270867 (program): a(n) = n^3 + 2n^2 + 4n + 1.
  • A270868 (program): a(n) = n^4 + 3n^3 + 8n^2 + 9*n + 2.
  • A270869 (program): a(n) = n^5 + 4n^4 + 13n^3 + 23n^2 + 25n + 3.
  • A270870 (program): a(n) = n^6 + 5n^5 + 19n^4 + 44n^3 + 72n^2 + 69*n + 5.
  • A270889 (program): Integers n such that the circular graph C_n has a square size deficiency.
  • A270935 (program): Number of active (ON,black) cells at stage 2^n-1 of the two-dimensional cellular automaton defined by “Rule 221”, based on the 5-celled von Neumann neighborhood.
  • A270968 (program): Reduced 5x+1 function R applied to the odd integers: a(n) = R(2n-1), where R(k) = (5k+1)/2^r, with r as large as possible.
  • A270993 (program): Values of A076336(n) such that A076336(n) = A076336(n+1) - 14.
  • A270994 (program): a(n) = 9454129 + 11184810*n.
  • A271017 (program): Number of active (ON,black) cells at stage 2^n-1 of the two-dimensional cellular automaton defined by “Rule 251”, based on the 5-celled von Neumann neighborhood.
  • A271027 (program): a(n) = 3661529 + 11184810*n.
  • A271035 (program): Number of 3 X 3 X 3 triangular 0..n arrays with some element less than a w, nw or ne neighbor exactly once.
  • A271040 (program): Number of different 3 against 3 matches given n players.
  • A271060 (program): Number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by “Rule 261”, based on the 5-celled von Neumann neighborhood.
  • A271061 (program): Number of active (ON,black) cells at stage 2^n-1 of the two-dimensional cellular automaton defined by “Rule 261”, based on the 5-celled von Neumann neighborhood.
  • A271062 (program): Partial sums of the number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by “Rule 261”, based on the 5-celled von Neumann neighborhood.
  • A271114 (program): Expansion of (1+x)*(2+x)/(1-x)^2.
  • A271187 (program): Triangle T(n,k) read by rows: T(n,k) is the squarefree part of C(n,k).
  • A271208 (program): a(n) = n^5 + n - 1.
  • A271209 (program): a(n) = n^5 + n + 1.
  • A271216 (program): a(n) = 2^n floor(n/2)!
  • A271220 (program): Concatenate sum of digits of previous term and product of digits of previous term, starting with 6.
  • A271320 (program): Number of prime factors, with multiplicity, of the n-th n-gonal number (A060354).
  • A271324 (program): a(n) = n + floor(n/4) + (n mod 4).
  • A271342 (program): Sum of all even divisors of all positive integers <= n.
  • A271346 (program): Numbers k such that the final digit of k^k is 6.
  • A271350 (program): a(n) = 3^n mod 83.
  • A271355 (program): Triangular array: T(n,k) = round[(r^n)*(s^k) , where r = golden ratio = (1+ sqrt(5))/2, s = (1 - sqrt(5))/2, 1 < = k <= n, n > = 0.
  • A271357 (program): a(n) = kFibonacci(2n+1) + (k+1)Fibonacci(2n), where k=3.
  • A271358 (program): a(n) = kFibonacci(2n+1) + (k+1)Fibonacci(2n), where k=4.
  • A271359 (program): a(n) = kFibonacci(2n+1) + (k+1)Fibonacci(2n), where k=5.
  • A271378 (program): a(n) = 5^n mod 31.
  • A271379 (program): a(n) = 5^n mod 101.
  • A271380 (program): a(n) = 5^n mod 163.
  • A271385 (program): a(n) = Product_ k=0..floor((n - 1)/2) (n - 2k)^(n - 2k).
  • A271388 (program): a(n) = 4*a(n-1) + a(n-2) - n for n > 1, with a(0) = 0, a(1) = 1.
  • A271389 (program): a(n) = 2*a(n-1) + a(n-2) + n^2 for n > 1, with a(0) = 0, a(1) = 1.
  • A271390 (program): a(n) = (2n + 1)^(2floor((n-1)/2) + 1).
  • A271391 (program): Expansion of (1 + x + 2x^2 + 6x^3 + x^4 + x^5)/(1 - x^2)^3.
  • A271427 (program): a(n) = 7^n - a(n-1) for n>0, a(0)=0.
  • A271439 (program): If n is a triangular number, a(n) = 0, otherwise a(n) = n - A002024(n) + 1
  • A271440 (program): a(n) = sigma(prime(n)^n) - phi(prime(n)^n).
  • A271473 (program): a(1)=0; thereafter a(2k)=k+a(k), a(2k+1)=k+a(6k+4).
  • A271475 (program): Total number of burnt pancakes flipped using the Max(n) greedy algorithm.
  • A271476 (program): Total number of burnt pancakes flipped using the Min-bar(n) greedy algorithm.
  • A271477 (program): Total number of burnt pancakes flipped using the Max-bar(n) greedy algorithm.
  • A271478 (program): If n is even, a(n)=n/2, otherwise 2*n+2.
  • A271479 (program): Number of steps for the trajectory of n under the map k -> A271478(k) to reach 1.
  • A271480 (program): Dimension of n-qubit subspace H^ MPS _ 2,n for bond dimension 2.
  • A271484 (program): Expansion of x^5/((1-x^2)(1-x^4))+x^10/((1-x^4)(1-x^6)).
  • A271490 (program): Size of maximal subset of points of n X n grid such that no two points are at the same distance.
  • A271508 (program): Numbers that are congruent to 1,4 mod 10.
  • A271511 (program): a(n) = (p+1)*(p+2)/2 where p is the n-th prime.
  • A271512 (program): a(n) = (p+1)(p+2)(p+3)/6 where p is the n-th prime.
  • A271519 (program): Let n = (2i + 1)2^j; then a(n) = i + j.
  • A271527 (program): a(n) = 1000^n + 1.
  • A271528 (program): a(n) = 2*(10^n - 1)^2/27.
  • A271535 (program): a(n) = ( n(n + 1)(2*n + 1)/6 )^2.
  • A271567 (program): Convolution of nonzero triangular numbers (A000217) and nonzero tetradecagonal numbers (A051866).
  • A271572 (program): a(n) = n^7 mod 32.
  • A271573 (program): Numerator of (0 followed by A005126(n)= 2, 4, 7, …)/2^n.
  • A271574 (program): Decimal expansion of Sum_ n>=0 1/(n!)^3.
  • A271578 (program): Magic sums of 4 X 4 magic squares composed of primes.
  • A271624 (program): a(n) = 2n^2 - 4n + 4.
  • A271625 (program): a(n) = 2n^2 + 4n - 3.
  • A271636 (program): a(n) = 4n(4*n^2 + 3).
  • A271649 (program): a(n) = 2*(n^2 - n + 2).
  • A271662 (program): Convolution of nonzero pentagonal numbers (A000326) with themselves.
  • A271663 (program): Convolution of nonzero squares (A000290) with nonzero pentagonal numbers (A000326).
  • A271675 (program): Numbers m such that 3*m + 4 is a square.
  • A271713 (program): Numbers n such that 3*n - 5 is a square.
  • A271723 (program): Numbers k such that 3*k - 8 is a square.
  • A271740 (program): a(n) = 3n^2 - 2n + 2.
  • A271743 (program): Number of set partitions of [n] such that 4 is the largest element of the last block.
  • A271751 (program): Period 10 zigzag sequence; repeat: [0, 1, 2, 3, 4, 5, 4, 3, 2, 1].
  • A271771 (program): Maximum total Hamming distance between pairs of consecutive elements in any permutation of all 2^n binary words of length n.
  • A271779 (program): a(n) = n^3 + 2n^2 + 5n + 11.
  • A271800 (program): Five steps forward, four steps back.
  • A271827 (program): Expansion of (x^5-2x^4+2x^3-x+1)/(x^4-2x^3+3x^2-3*x+1).
  • A271828 (program): a(n) = 4n^3 - 18n^2 + 27*n - 12.
  • A271830 (program): Expansion of (3 - 4x + 3x^2 + x^4)/((1 - x)^2*(1 + x^2 + x^4)).
  • A271832 (program): Period 12 zigzag sequence: repeat [0,1,2,3,4,5,6,5,4,3,2,1].
  • A271860 (program): a(n) = -Sum_ i=1..n (-1)^floor(n/i).
  • A271870 (program): Convolution of nonzero hexagonal numbers (A000384) with themselves.
  • A271906 (program): Size of the largest subset S of the points of an n X n square grid such that no three of the points of S form a right isosceles triangle.
  • A271907 (program): Size of the largest subset S of the points of an n X n square grid such that no three of the points of S form an isosceles triangle.
  • A271911 (program): Number of ways to choose three distinct points from a 2 X n grid so that they form an isosceles triangle.
  • A271936 (program): Commutative powers: numbers of the form a^b = b^a.
  • A271937 (program): a(n) = (7/4)n^2 + (5/2)n + (7 + (-1)^n)/8.
  • A271939 (program): Number of edges in the n-th order Sierpinski carpet graph.
  • A271994 (program): The chalcogen sequence (a(n) = A018227(n)-2).
  • A271995 (program): The Pnictogen sequence: a(n) = A018227(n)-3.
  • A271996 (program): The crystallogen sequence (a(n) = A018227(n)-4).
  • A271997 (program): The icosagen sequence : a(n) = A018227(n)-5, for n >= 2.
  • A271998 (program): Volatile sequence: a(n) = A018227(n)-6.
  • A272000 (program): Coinage sequence: a(n) = A018227(n)-7.
  • A272007 (program): Number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by “Rule 413”, based on the 5-celled von Neumann neighborhood.
  • A272009 (program): Partial sums of the number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by “Rule 413”, based on the 5-celled von Neumann neighborhood.
  • A272027 (program): a(n) = 3*sigma(n).
  • A272039 (program): a(n) = 10n^2 + 4n + 1.
  • A272058 (program): Start with all terms set to 0. Then add n to the next n+3 terms for n=0,1,2,… .
  • A272066 (program): a(n) = (10^n-1)^3.
  • A272067 (program): a(n) = (10^n-1)^4.
  • A272071 (program): Expansion of x(3 - 2x + x^2)/((1 - x)^2*(1 + x + x^2)).
  • A272073 (program): Exponents of x in the numerator of cluster variables of rank 2 cluster algebras.
  • A272100 (program): Integers n that are the sum of three nonzero squares while n*(n+1) is not.
  • A272104 (program): Sum of the even numbers among the larger parts of the partitions of n into two parts.
  • A272124 (program): a(n) = 12n^4 + 16n^3 + 10n^2 + 4n + 1.
  • A272125 (program): a(n) = n^3(2n^2+1)/3.
  • A272126 (program): a(n) = 120n^3 + 60n^2 + 2*n + 1.
  • A272129 (program): a(n) = 32n^2 - 56n + 25.
  • A272130 (program): a(n) = 16n^3 + 10n^2 + 4*n + 1.
  • A272134 (program): a(n) = n(15n^2 - 15*n + 4).
  • A272144 (program): Convolution of A000217 and A001045.
  • A272162 (program): a(n) = n^5-n+1.
  • A272171 (program): Triangle read by rows: T(n,k) in which row n lists the first n terms of A000005 in reverse order.
  • A272172 (program): Triangle read by rows: T(n,k) in which row n lists the first n terms of A000203 in reverse order.
  • A272179 (program): a(n) = Product_ k=0..n (n^2 - k).
  • A272180 (program): a(n) = Product_ k=0..n (n^2 + k).
  • A272188 (program): Triangle with 2*n+1 terms per row, read by rows: the first row is 1 (by decree), following rows contain 0 to 2n+1 but omitting 2n.
  • A272211 (program): Product of n-th prime and the sum of the divisors of n.
  • A272212 (program): Sum of the odd numbers among the larger parts of the partitions of n into two parts.
  • A272263 (program): a(n) = numerator of A000032(n) - 1/2^n.
  • A272297 (program): a(n) = n^4 + 64.
  • A272298 (program): a(n) = n^4 + 324.
  • A272299 (program): a(n) = n + 2floor(n/2) + 3floor(n/3).
  • A272303 (program): Magic sums of 4 X 4 semimagic squares composed of primes.
  • A272341 (program): Numbers n such that 6^n is not of the form (x^3 + y^3 + z^3) / 3 where x > y > z > 0.
  • A272342 (program): a(n) = 27*8^n.
  • A272352 (program): a(n) is the number of ways of putting n labeled balls into 2 indistinguishable boxes such that each box contains at least 3 balls.
  • A272356 (program): (Sum_ i=1..n prime(i)) mod 4.
  • A272361 (program): Numbers n such that (2^n + 1) / gcd(n, 2^n + 1) is not squarefree.
  • A272365 (program): a(n) = 9a(n-1) - 9a(n-2) + a(n-3).
  • A272370 (program): Number of geometrically inscriptible regular polygons with fewer than 2^n + 1 sides.
  • A272378 (program): a(n) = n(6n^2 - 8*n + 3).
  • A272398 (program): The union of hexagonal numbers (A000384) and centered 9-gonal numbers (A060544).
  • A272399 (program): The intersection of hexagonal numbers (A000384) and centered 9-gonal numbers (A060544).
  • A272417 (program): Number of active (ON,black) cells at stage 2^n-1 of the two-dimensional cellular automaton defined by “Rule 469”, based on the 5-celled von Neumann neighborhood.
  • A272459 (program): The total number of different isosceles trapezoids, excluding squares, that can be drawn on an n X n square grid where the corners of each individual trapezoid lie on a lattice point.
  • A272470 (program): 7 times the primes.
  • A272476 (program): a(n) = n if n is prime, a(n) = 2*n+3 otherwise.
  • A272525 (program): Convolution of nonzero repunits (A002275) with themselves.
  • A272532 (program): Single bit representation of the sum of two sinusoids with periods 2 and 2*sqrt(2).
  • A272549 (program): Expansion of x(1 + 5x - 3x^2 + 7x^3 + 3x^4 + 3 *x^5 - x^6 + x^7)/((1 - x)^3(1 + x + x^2 + x^3)^2).
  • A272574 (program): a(n) = f(9, f(8, n)), where f(k,m) = floor(m*k/(k-1)).
  • A272576 (program): a(n) = f(10, f(9, n)), where f(k,m) = floor(m*k/(k-1)).
  • A272590 (program): a(n) is the smallest number m such that the multiplicative group modulo m is the direct product of n cyclic groups.
  • A272647 (program): a(n) = A001517(n) mod 7.
  • A272651 (program): The no-3-in-line problem: maximal number of points from an n X n square grid so that no three lie on a line.
  • A272664 (program): (001)(001)(001)(10)*.
  • A272666 (program): a(n) = A011371(n) + 5*n.
  • A272669 (program): A 13-ordering of T = 0,1,2,3,5,8,10,11,12 + 13*Z.
  • A272705 (program): Number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by “Rule 515”, based on the 5-celled von Neumann neighborhood.
  • A272707 (program): Partial sums of the number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by “Rule 515”, based on the 5-celled von Neumann neighborhood.
  • A272708 (program): First differences of number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by “Rule 515”, based on the 5-celled von Neumann neighborhood.
  • A272718 (program): Partial sums of gcd-sum sequence A018804.
  • A272743 (program): Number of active (ON,black) cells at stage 2^n-1 of the two-dimensional cellular automaton defined by “Rule 526”, based on the 5-celled von Neumann neighborhood.
  • A272756 (program): a(n) is the least k such that k > A070939(n * k).
  • A272775 (program): Squares of the form P(n, 5) + n, where P(x,k) is the Pochhammer function and n = square (A000290).
  • A272850 (program): a(n) = (n^2 + (n+1)^2)(n^2 + (n+1)^2 + 2n*(n+1)).
  • A272870 (program): Real part of (n + i)^4.
  • A272871 (program): Imaginary part of (n + i)^4.
  • A272887 (program): Number of ways to write prime(n) as (4x + 2)y + 4*x + 1 where x and y are nonnegative integers.
  • A272900 (program): Fibonacci-products fractal sequence.
  • A272912 (program): Difference sequence of the sequence A116470 of all distinct Fibonacci numbers and Lucas numbers (A000032).
  • A272914 (program): Sixth powers ending in digit 6.
  • A272915 (program): a(n) = n + floor(5*n/6).
  • A272918 (program): Fibonacci numbers with the base 10 digits sorted into increasing order.
  • A272928 (program): Partial sums of A147562.
  • A272931 (program): a(n) = 2^(n+1)cos(narctan(sqrt(15))).
  • A272975 (program): Numbers that are congruent to 0,7 mod 12.
  • A272978 (program): Numbers not in the range of the sum of perfect divisors function.
  • A273003 (program): Arrange the base 10 digits of the n-th Fibonacci number in descending order.
  • A273005 (program): Sum of coefficients in the hereditary representation of n in base 10.
  • A273045 (program): Fibonacci numbers with digits in nondecreasing order.
  • A273053 (program): Numbers n such that 15*n^2 + 16 is a square.
  • A273092 (program): a(n) = 2^n - 1 written backwards.
  • A273109 (program): Numbers n such that in the difference triangle of the divisors of n (including the divisors of n) the diagonal from the bottom entry to n gives the divisors of n.
  • A273123 (program): Values of A007692(n) that are not of the form x^2 + y^2 + z^2 where x, y, z are nonzero integers.
  • A273129 (program): The Rote-Fibonacci infinite sequence.
  • A273149 (program): a(n) = A053839(n)+1.
  • A273182 (program): a(n) is the second number in a triple consisting of 3 numbers, which when squared are part of a right diagonal of a magic square of squares.
  • A273187 (program): a(n) is the third number in a triple consisting of 3 numbers, which when squared are part of a right diagonal of magic square of squares.
  • A273189 (program): a(n) is the third number in a triple consisting of 3 numbers, which when squared are part of a right diagonal of a magic square of squares.
  • A273220 (program): a(n) = 8n^2 - 12n + 1.
  • A273227 (program): Consider all ways of writing the n-th composite number as the product of two divisors d1d2 = d3d4 = …; a(n) is the minimum of the sums d1 + d2, d3 + d4, … .
  • A273308 (program): Maximum population of a 2 X n still life in Conway’s Game of Life.
  • A273309 (program): Number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by “Rule 641”, based on the 5-celled von Neumann neighborhood.
  • A273310 (program): Number of active (ON,black) cells at stage 2^n-1 of the two-dimensional cellular automaton defined by “Rule 641”, based on the 5-celled von Neumann neighborhood.
  • A273311 (program): Partial sums of the number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by “Rule 641”, based on the 5-celled von Neumann neighborhood.
  • A273312 (program): First differences of number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by “Rule 641”, based on the 5-celled von Neumann neighborhood.
  • A273313 (program): Number of active (ON,black) cells at stage 2^n-1 of the two-dimensional cellular automaton defined by “Rule 643”, based on the 5-celled von Neumann neighborhood.
  • A273314 (program): Partial sums of the number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by “Rule 643”, based on the 5-celled von Neumann neighborhood.
  • A273315 (program): First differences of number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by “Rule 643”, based on the 5-celled von Neumann neighborhood.
  • A273316 (program): Partial sums of the number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by “Rule 645”, based on the 5-celled von Neumann neighborhood.
  • A273321 (program): Wiener index of graph of b.c.c. unit cells in a line = Sum of distances in a b.c.c. row graph.
  • A273322 (program): Wiener index of graphs of f.c.c. unit cells in a line = Sum of distances in face-centered cubic grid unit cells connected in a row.
  • A273324 (program): Integers n such that n^2 + 3 is the sum of 4 but no fewer nonzero squares.
  • A273325 (program): Number of endofunctions on [2n] such that the minimal cardinality of the nonempty preimages equals n.
  • A273334 (program): Number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by “Rule 657”, based on the 5-celled von Neumann neighborhood.
  • A273335 (program): Number of active (ON,black) cells at stage 2^n-1 of the two-dimensional cellular automaton defined by “Rule 657”, based on the 5-celled von Neumann neighborhood.
  • A273336 (program): Partial sums of the number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by “Rule 657”, based on the 5-celled von Neumann neighborhood.
  • A273337 (program): First differences of number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by “Rule 657”, based on the 5-celled von Neumann neighborhood.
  • A273365 (program): Numbers k such that 10*k+4 is a perfect square.
  • A273366 (program): a(n) = 10n^2 + 10n + 2.
  • A273367 (program): Numbers k such that 10*k+6 is a perfect square.
  • A273368 (program): Numbers k such that 10*k+9 is a perfect square.
  • A273372 (program): Squares ending in digit 1.
  • A273373 (program): Squares ending in digit 6.
  • A273374 (program): Squares ending in digit 9.
  • A273375 (program): Squares ending in digit 4.
  • A273384 (program): Number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by “Rule 659”, based on the 5-celled von Neumann neighborhood.
  • A273385 (program): Number of active (ON,black) cells at stage 2^n-1 of the two-dimensional cellular automaton defined by “Rule 659”, based on the 5-celled von Neumann neighborhood.
  • A273386 (program): Partial sums of the number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by “Rule 659”, based on the 5-celled von Neumann neighborhood.
  • A273387 (program): First differences of number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by “Rule 659”, based on the 5-celled von Neumann neighborhood.
  • A273398 (program): a(n) = Catalan(Fibonacci(n)).
  • A273405 (program): Number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by “Rule 673”, based on the 5-celled von Neumann neighborhood.
  • A273406 (program): Partial sums of the number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by “Rule 673”, based on the 5-celled von Neumann neighborhood.
  • A273407 (program): First differences of number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by “Rule 673”, based on the 5-celled von Neumann neighborhood.
  • A273408 (program): Partial sums of the number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by “Rule 675”, based on the 5-celled von Neumann neighborhood.
  • A273409 (program): Partial sums of the number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by “Rule 678”, based on the 5-celled von Neumann neighborhood.
  • A273443 (program): Number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by “Rule 721”, based on the 5-celled von Neumann neighborhood.
  • A273447 (program): Partial sums of the number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by “Rule 721”, based on the 5-celled von Neumann neighborhood.
  • A273448 (program): First differences of number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by “Rule 721”, based on the 5-celled von Neumann neighborhood.
  • A273465 (program): Numbers generated by starting at 1 and adding twice and subtracting once following the sequence of positive integers.
  • A273480 (program): Partial sums of the number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by “Rule 737”, based on the 5-celled von Neumann neighborhood.
  • A273481 (program): First differences of number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by “Rule 737”, based on the 5-celled von Neumann neighborhood.
  • A273514 (program): a(n) is the number of arithmetic progressions m < n < p (three numbers in arithmetic progression) such that m and p contain no 2’s in their ternary representation.
  • A273526 (program): Number of 123-avoiding indecomposable permutations.
  • A273539 (program): Number of active (ON,black) cells at stage 2^n-1 of the two-dimensional cellular automaton defined by “Rule 779”, based on the 5-celled von Neumann neighborhood.
  • A273570 (program): Number of active (ON,black) cells at stage 2^n-1 of the two-dimensional cellular automaton defined by “Rule 798”, based on the 5-celled von Neumann neighborhood.
  • A273618 (program): Numbers n = 2*k+1 where k is odd with the property that 3^k mod n == 1 and k^k mod n == 1.
  • A273628 (program): a(n) = (7n)!/((5n)!*n!^2).
  • A273629 (program): a(n) = (9n)!/((7n)!*n!^2).
  • A273652 (program): Number of forests of labeled rooted trees of height at most 1, with n labels, two of which are used for root nodes and any root may contain >= 1 labels.
  • A273663 (program): Least monotonic left inverse for A273670: a(1) = 0; for n > 1, a(n) = A257680(A225901(n)) + a(n-1).
  • A273669 (program): Decimal representation ends with either 2 or 9.
  • A273675 (program): Number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by “Rule 833”, based on the 5-celled von Neumann neighborhood.
  • A273677 (program): Partial sums of the number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by “Rule 833”, based on the 5-celled von Neumann neighborhood.
  • A273678 (program): First differences of number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by “Rule 833”, based on the 5-celled von Neumann neighborhood.
  • A273711 (program): The Hadamard product of omega(n) and A007875(n).
  • A273724 (program): Place n equally-spaced points around a circle, labeled 0,1,2,…,n-1. For each i = 0..n-1 such that 3i != i mod n, draw an (undirected) chord from i to (3i mod n). Then a(n) is the total number of distinct chords.
  • A273743 (program): Number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by “Rule 901”, based on the 5-celled von Neumann neighborhood.
  • A273744 (program): Partial sums of the number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by “Rule 901”, based on the 5-celled von Neumann neighborhood.
  • A273745 (program): First differences of number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by “Rule 901”, based on the 5-celled von Neumann neighborhood.
  • A273751 (program): Triangle of the natural numbers written by decreasing antidiagonals.
  • A273766 (program): Number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by “Rule 913”, based on the 5-celled von Neumann neighborhood.
  • A273768 (program): Partial sums of the number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by “Rule 913”, based on the 5-celled von Neumann neighborhood.
  • A273769 (program): First differences of number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by “Rule 913”, based on the 5-celled von Neumann neighborhood.
  • A273780 (program): Number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by “Rule 929”, based on the 5-celled von Neumann neighborhood.
  • A273781 (program): Partial sums of the number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by “Rule 929”, based on the 5-celled von Neumann neighborhood.
  • A273782 (program): First differences of number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by “Rule 929”, based on the 5-celled von Neumann neighborhood.
  • A273789 (program): Number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by “Rule 931”, based on the 5-celled von Neumann neighborhood.
  • A273790 (program): Partial sums of the number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by “Rule 931”, based on the 5-celled von Neumann neighborhood.
  • A273791 (program): First differences of number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by “Rule 931”, based on the 5-celled von Neumann neighborhood.
  • A273801 (program): Numbers n for which n = (x - phi(x)) * (y - phi(y)), where n = x + y and x - phi(x) is the Euler cototient function of x.
  • A273831 (program): Number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by “Rule 961”, based on the 5-celled von Neumann neighborhood.
  • A273832 (program): Number of active (ON,black) cells at stage 2^n-1 of the two-dimensional cellular automaton defined by “Rule 961”, based on the 5-celled von Neumann neighborhood.
  • A273833 (program): Partial sums of the number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by “Rule 961”, based on the 5-celled von Neumann neighborhood.
  • A273834 (program): First differences of number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by “Rule 961”, based on the 5-celled von Neumann neighborhood.
  • A273847 (program): Number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by “Rule 969”, based on the 5-celled von Neumann neighborhood.
  • A273849 (program): Partial sums of the number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by “Rule 969”, based on the 5-celled von Neumann neighborhood.
  • A273850 (program): First differences of number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by “Rule 969”, based on the 5-celled von Neumann neighborhood.
  • A273893 (program): Denominator of n/3^n.
  • A273926 (program): Given G(x) such that G( G(x)^2 - G(x)^3 ) = x^2, then G(x) = Sum_ n>=1 A273925(n)*x^n / 2^a(n).
  • A273960 (program): a(n) = (-1)^n*prime(n).
  • A273982 (program): Number of little cubes visible around an n X n X n cube with a face on a table.
  • A274004 (program): First differences of A002960.
  • A274008 (program): Number of length-n ternary sequences where the sum of each block differs by at most 1 from every other block of the same length.
  • A274009 (program): 1’s distance from a number in its binary expansion.
  • A274010 (program): Boris Stechkin function: a(n) is the number of m with 2 <= m <= n and floor(n(m-1)/m) divisible by m-1.
  • A274039 (program): Expansion of (x^4 + x^10) / (1 - 2*x + x^2).
  • A274047 (program): Diameter of Generalized Petersen Graph G(n, 2).
  • A274070 (program): Integer part of the sum of the inverses of the first n primes.
  • A274072 (program): a(n) = 5^n-(-1)^n.
  • A274073 (program): a(n) = 6^n-(-1)^n.
  • A274074 (program): a(n) = 6^n+(-1)^n.
  • A274077 (program): a(n) = n^3 + 4.
  • A274089 (program): Numbers repeated except that powers of 2 only appear once.
  • A274093 (program): a(0)=0; thereafter (-1)^n*n appears n times.
  • A274094 (program): a(0)=0; thereafter (-1)^(n+1)*n appears n times.
  • A274099 (program): Number of partitions of n*(n-1)/2 into at most four parts.
  • A274104 (program): a(n) = Sum_ k=0..n (3k+2)Catalan(k).
  • A274110 (program): Number of equivalence classes of ballot paths of length n for the string uu.
  • A274119 (program): a(n) = (Product_ i=0..4 (in+2) - Product_ i=0..4 (-in-1))/(4*n+3).
  • A274139 (program): a(n) = 2^A000265(n) = 2^numerator(n/2^n), a sequence related to Oresme numbers.
  • A274140 (program): Sum of primes dividing n-th triangular number, counted with multiplicity.
  • A274179 (program): Expansion of f(x^1, x^6) in powers of x where f() is Ramanujan’s general theta function.
  • A274221 (program): List of quadruples: 3n(3n-1), 3n(3n+1), (3n+1)^2, (3n+2)^2.
  • A274230 (program): Number of holes in a sheet of paper when you fold it n times and cut off the four corners.
  • A274232 (program): Number of partitions of 2^n into at most three parts.
  • A274233 (program): Number of partitions of n*(n-1)/2 into at most three parts.
  • A274248 (program): Row sums of A273751.
  • A274250 (program): Number of partitions of n^2 into at most three parts.
  • A274251 (program): Number of partitions of n^3 into at most three parts.
  • A274252 (program): Number of partitions of n^5 into at most three parts.
  • A274265 (program): a(n) = (3*n - 1)^(n-1).
  • A274267 (program): a(n) = (4*n - 1)^(n-1).
  • A274269 (program): a(n) = (5*n - 1)^(n-1).
  • A274278 (program): a(n) = ((n+1)^(n-1) - (n-1)^(n-1))/2 for n>=1.
  • A274304 (program): A bisection of A002866.
  • A274323 (program): Number of partitions of n^4 into at most two parts.
  • A274324 (program): Number of partitions of n^3 into at most two parts.
  • A274325 (program): Number of partitions of n^5 into at most two parts.
  • A274332 (program): Team size n for which there exists a balanced tournament for 2n+1 players so that in 2n+1 matches each player plays exactly n-1 times with and n times against each other player.
  • A274337 (program): Numbers n such that 2^n is not the sum of 5 positive cubes.
  • A274339 (program): The 3-cycle of the iterated sum of deficient divisors function.
  • A274340 (program): A 4-cycle of the iterated sum of deficient divisors function.
  • A274380 (program): A 4-cycle of the iterated sum of deficient divisors function.
  • A274382 (program): a(n) = gcd(n, n*(n+1)/2 - sigma(n)).
  • A274406 (program): Numbers m such that 9 divides m*(m + 1).
  • A274427 (program): Positions in A274426 of products of distinct Fibonacci numbers > 1.
  • A274430 (program): Positions in A274429 of products of distinct Fibonacci numbers > 1.
  • A274431 (program): Positions in A274426 of products of distinct Lucas numbers > 1 (excluding 2).
  • A274497 (program): Sum of the degrees of asymmetry of all binary words of length n.
  • A274499 (program): Sum of the degrees of asymmetry of all ternary words of length n.
  • A274502 (program): a(n) = 90binomial(n-1,7) + 9binomial(n-1,6).
  • A274520 (program): a(n) = ((1 + sqrt(7))^n - (1 - sqrt(7))^n)/sqrt(7).
  • A274526 (program): a(n) = ((1 + sqrt(11))^n - (1 - sqrt(11))^n)/sqrt(11).
  • A274535 (program): a(n) = 5*sigma(n).
  • A274536 (program): a(n) = 6 * sigma(n).
  • A274575 (program): For m=1,2,3,… write all the 2^m binary vectors of length m in increasing order, and replace each vector with (number of 1’s) - (number of 0’s). Start with an initial 0 for the empty vector.
  • A274576 (program): a(2n) = floor(n/2), a(2n+1) = a(n), a(0)=0.
  • A274580 (program): Digital difference of n: the most significant decimal digit of n minus the sum of the other digits.
  • A274583 (program): Expansion of (1 + x + x^2 - x^3 - x^4 + x^6)/((1 - x)^3*(1 + x + x^2)^2).
  • A274593 (program): a(0) = 0; thereafter, a(2n+1) = a(n)+2n+1, otherwise a(n) = n.
  • A274601 (program): a(n) = 2*3^(s-1) - n, where s is the number of trits of n in balanced ternary form.
  • A274603 (program): Numbers n such that 2n+1 and 3n+1 are both triangular numbers.
  • A274616 (program): Maximal number of non-attacking queens on a right triangular board with n cells on each side.
  • A274638 (program): Main diagonal of A274637.
  • A274681 (program): Numbers k such that 4*k + 1 is a triangular number.
  • A274682 (program): Numbers n such that 8*n-1 is a triangular number.
  • A274698 (program): a(n)=prime(n)-(2*last digit of prime(n)).
  • A274701 (program): First differences of A259280.
  • A274716 (program): a(2n+1) = a(2floor(n/2)+1) + n, a(2*n) = a(n), for n>=1 with a(1)=0.
  • A274743 (program): Repunits with odd indices multiplied by 99, i.e., 99*(1, 111, 11111, 1111111, …).
  • A274755 (program): Repunits with even indices multiplied by 99, i.e., 99*(11, 1111, 111111, 11111111, …).
  • A274757 (program): Numbers k such that 6*k+1 is a triangular number (A000217).
  • A274766 (program): Multiplication of pair of contiguous repunits, i.e., (01, 111, 11111, 1111111, 1111*11111, …).
  • A274772 (program): Zero together with the partial sums of A056640.
  • A274773 (program): a(n) = floor(sqrt(2n-1) + 1/2) - abs(2(n-1) - (floor(sqrt(2*n-1) + 1/2))^2) + 1.
  • A274830 (program): Numbers n such that 7*n+1 is a triangular number (A000217).
  • A274868 (program): Number of set partitions of [n] into exactly four blocks such that all odd elements are in blocks with an odd index and all even elements are in blocks with an even index.
  • A274922 (program): a(n) = (-1)^n * n if n>0, a(0) = 1.
  • A274933 (program): Maximal number of non-attacking queens on a quarter chessboard containing n^2 squares.
  • A274973 (program): Centered cubohemioctahedral numbers: a(n) = 2n^3+9n^2+n+1.
  • A274974 (program): Centered octahemioctahedral numbers: a(n) = (4n^3+24n^2+8*n+3)/3.
  • A274978 (program): Integers of the form m*(m + 6)/7.
  • A274979 (program): Integers of the form m*(m + 7)/8.
  • A274981 (program): Decimal expansion of gamma(2) = 7/5.
  • A275015 (program): Number of neighbors of each new term in an isosceles triangle read by rows.
  • A275019 (program): 2-adic valuation of tetrahedral numbers C(n+2,3) = n(n+1)(n+2)/6 = A000292.
  • A275112 (program): Zero together with the partial sums of A064412.
  • A275113 (program): a(n) is the minimal number of squares needed to enclose n squares with a wall so that there is a gap of at least one cell between the wall and the enclosed cells.
  • A275138 (program): Number of n X 4 0..2 arrays with no element equal to any value at offset (-2,-2) (-1,-2) or (0,-1) and new values introduced in order 0..2.
  • A275151 (program): a(1) = 8; a(n) = 3a(n-1) + 2sqrt(2a(n-1)(a(n-1)-7)) - 7 for n > 1.
  • A275155 (program): a(1) = 18; a(n) = 3a(n - 1) + 2sqrt(2a(n - 1)(a(n - 1) - 14)) - 14 for n > 1.
  • A275161 (program): Number of sides of a polygon formed by tiling n squares in a spiral.
  • A275163 (program): a(n) = 13*2^(n+1) - 19.
  • A275202 (program): Subword complexity (number of distinct blocks of length n) of the period doubling sequence A096268.
  • A275229 (program): Number of 3 X n 0..2 arrays with no element equal to any value at offset (-2,-1) (-2,1) or (-1,0) and new values introduced in order 0..2.
  • A275314 (program): Euler’s gradus (“suavitatis gradus”, or degrees of softness) function.
  • A275324 (program): Expansion of (x(1-4x^2)^(-3/2) + (1-4*x^2)^(-1/2) + x + 1)/2.
  • A275346 (program): In Go, minimum total number of liberties player 1 (black) can have on a standard 19 X 19 board after n moves when no player passes a move, with no repeating game positions allowed.
  • A275363 (program): a(1)=3, a(2)=6, a(3)=3; thereafter a(n) = a(n-a(n-1)) + a(n-1-a(n-2)).
  • A275365 (program): a(1)=2, a(2)=2; thereafter a(n) = a(n-a(n-1)) + a(n-a(n-2)).
  • A275367 (program): Number of odd divisors of n^2.
  • A275379 (program): Number of prime factors (with multiplicity) of generalized Fermat number 6^(2^n) + 1.
  • A275380 (program): Number of odd prime factors (with multiplicity) of generalized Fermat number 7^(2^n) + 1.
  • A275434 (program): Sum of the degrees of asymmetry of all compositions of n.
  • A275437 (program): Triangle read by rows: T(n,k) is the number of 01-avoiding binary words of length n having degree of asymmetry equal to k (n >= 0; 0 <= k <= floor(n/2)).
  • A275464 (program): a(n) = n - A038802(n).
  • A275486 (program): Decimal expansion of Pi_3, the analog of Pi for generalized trigonometric functions of order p=3.
  • A275495 (program): a(n) = Sum_ k=2..n floor(n/k) - 2floor(n/(2k)).
  • A275496 (program): a(n) = n^2(2n^2 + (-1)^n).
  • A275505 (program): Number of 5 X n 0..2 arrays with no element equal to any value at offset (-2,-1) (-2,0) or (-1,-1) and new values introduced in order 0..2.
  • A275535 (program): a(n) = the smallest positive multiple of n that is the sum of more than 1 consecutive positive integers.
  • A275536 (program): Differences of the exponents of the adjacent distinct powers of 2 in the binary representation of n (with -1 subtracted from the least exponent present) are concatenated as decimal digits in reverse order.
  • A275543 (program): A081585 and A069129 interleaved.
  • A275574 (program): ((-1)^n - 1 + 2*(n^floor((n + 1)/2)))/4
  • A275580 (program): Add square root of sum of terms.
  • A275581 (program): Numbers n such that A010846(n) >= n/2.
  • A275591 (program): a(n) = n^2 + 9*n + 1.
  • A275615 (program): Decimal expansion of 22/111.
  • A275635 (program): a(n) = (3^n-1)(3^n-3)(3^n+3)/4!.
  • A275636 (program): a(n) = (3^n-1)*(3^n+3)/3!.
  • A275645 (program): Numbers n such that the n X n queens graph is colorable with n colors.
  • A275673 (program): List of numbers that are in a spoke of a hexagonal spiral.
  • A275704 (program): Digital root of n + (n+1)^2.
  • A275709 (program): a(n) = 2n^3 + 3n^2.
  • A275766 (program): a(n) = (5^(2*(n + 1)) - 1)/4.
  • A275779 (program): a(n) = (2^(n^2) - 1)/(1 - 1/2^n).
  • A275788 (program): a(0) = 0, a(n+1) = 2*a(n) + (-1)^floor(n/3).
  • A275793 (program): The x members of the positive proper solutions (x = x1(n), y = y1(n)) of the first class for the Pell equation x^2 - 2*y^2 = +7^2.
  • A275794 (program): One half of the y members of the positive proper solutions (x = x1(n), y = y1(n)) of the first class for the Pell equation x^2 - 2*y^2 = +7^2.
  • A275795 (program): The x members of the positive proper solutions (x = x2(n), y = y2(n)) of the second class for the Pell equation x^2 - 2*y^2 = +7^2.
  • A275796 (program): One half of the y members of the positive proper solutions (x = x2(n), y = y2(n)) of the second class for the Pell equation x^2 - 2*y^2 = +7^2.
  • A275799 (program): Number of inequivalent (modulo C_4 rotations) square n X n grids with squares coming in two colors and three squares have one of the colors.
  • A275812 (program): Sum of exponents larger than one in the prime factorization of n: A001222(n) - A056169(n).
  • A275854 (program): Number of labeled directed graphs on n nodes (allowing self loops) such that the out-degree of each node is at most 2.
  • A275855 (program): Platinum mean sequence: fixed point of the morphism 0 -> 0001, 1 -> 001.
  • A275868 (program): Numbers n tracing out a spiral path in a pentagonal Z module thereby creating a ten-fold twin pattern with relations to quasicrystals.
  • A275874 (program): a(n) = (n-4)(n+1)(n+3)/6.
  • A275876 (program): a(n) = 4n(n^2 - 3*n - 1)/3.
  • A275906 (program): Expansion of (1+x+x^2) / (1-4x-4x^2-x^3).
  • A275910 (program): Numbers not congruent to 0, 1 or 8 mod 9.
  • A275929 (program): a(n) = 2*(n-1)! + n + 1.
  • A275937 (program): The number of distinct patterns of the smallest number of unit squares required to enclose n units of area, where corner contact is allowed.
  • A275970 (program): a(n) = 3*2^n + n - 1.
  • A275973 (program): A binary sequence due to Harold Jeffreys.
  • A275974 (program): Partial sums of the Jeffreys binary sequence A275973.
  • A275989 (program): a(n) = prime(prime(n)+1) - prime(n).
  • A275990 (program): a(n) = prime(prime(n)-1) - prime(n).
  • A276000 (program): Least k such that n! divides phi(k!) (k > 0).
  • A276026 (program): a(n) = Sum_ k=0..7 (n + k)^2.
  • A276032 (program): Number of refinements of the partition n^1 with all numbers taken modulo 2.
  • A276041 (program): Exponential convolution of odd numbers (A005408) with themselves.
  • A276084 (program): a(n) = Number of trailing zeros in primorial base representation of n (A049345); largest k such that A002110(k) divides n.
  • A276086 (program): Prime product form of primorial base expansion of n: digits in primorial base representation of n become the exponents of successive prime factors whose product a(n) is.
  • A276087 (program): a(n) = A276086(A276086(n)).
  • A276133 (program): Exponent of highest power of 2 dividing product of composite numbers between n-th prime and (n+1)-st prime.
  • A276134 (program): a(5n) = a(n), a(5n+1) = a(5n+2) = a(5n+3) = a(5n+4) = a(n) + 1, a(0) = 0.
  • A276135 (program): Ben Ames Williams’s Monkey and Coconuts Problem.
  • A276150 (program): Sum of digits when n is written in primorial base (A049345); minimal number of primorials (A002110) that add to n.
  • A276151 (program): n minus the greatest primorial number (A002110) which divides n: a(n) = n - A053589(n).
  • A276152 (program): a(n) = smallest prime not dividing n times greatest primorial number which divides n = A053669(n) * A053589(n).
  • A276153 (program): The most significant digit when n is written in primorial base (A049345).
  • A276163 (program): a(n) is the maximum first-player score difference of a “Coins in a Row” game over all permutations of coins 1..n with both players using a minimax strategy.
  • A276190 (program): Sum of the squares of the digits of the base-4 representation of n.
  • A276191 (program): Sum of the squares of the digits of the base-5 representation of n.
  • A276229 (program): a(n+3) = -a(n+2) - 2*a(n+1) + a(n) with a(0)=0, a(1)=0, a(2)=1.
  • A276233 (program): a(n) = (n+256)/gcd(n,256).
  • A276234 (program): a(n) = n/gcd(n, 256).
  • A276254 (program): With respect to the dictionary ordering of words over the alphabet a,b , i.e., e,a,b,aa,ab,ba,bb,aaa,…, the sequence is the characteristic function of the language of words that have no consecutive b’s.
  • A276265 (program): Expansion of (1 + 2x)/(1 - 6x + 6*x^2).
  • A276273 (program): Replacing every “mixed pair” of integers with the smallest integer of the said pair rebuilds the sequence itself (see “Comments” for the definition of a “mixed pair”).
  • A276278 (program): Complement of A026474.
  • A276283 (program): Expansion of (1 + x + 3x^2 + x^3)/((1 - x)^2(1 + x^2)).
  • A276289 (program): Expansion of x(1 + x)/(1 - 2x)^3.
  • A276293 (program): Number of n X 2 0..2 arrays with no element equal to any value at offset (-2,-1) (-1,1) or (0,-1) and new values introduced in order 0..2.
  • A276300 (program): Number of 3 X n 0..2 arrays with no element equal to any value at offset (-2,-1) (-1,1) or (0,-1) and new values introduced in order 0..2.
  • A276333 (program): The most significant digit in greedy A001563-base (A276326): a(n) = floor(n/A258199(n)), a(0) = 0.
  • A276349 (program): Numbers consisting of a nonempty string of 1’s followed by a nonempty string of 0’s.
  • A276351 (program): a(n) = 2*(3 + 2 n + 3 n^2 + 3 n^3 + 3 n^4 + n^5 + n^6).
  • A276352 (program): a(n) = 100^n - 10^n.
  • A276376 (program): Exponent of highest power of 3 dividing product of composite numbers between n-th prime and (n+1)-st prime.
  • A276382 (program): a(1) = 1, and a(n) = a(n-1) + floor(3*n/2) + 1 for n >= 2.
  • A276383 (program): Complement of A158919: complementary Beatty sequence to the Beatty sequence defined by the tribonacci constant tau = A058265.
  • A276384 (program): Defined by the properties that it starts with 0, and when you successively apply DIFF, RUNS, BISECT, RUNS you get (4,1,3,1) repeated infinitely often.
  • A276385 (program): Defined by the properties that it starts with 2, and when you successively apply DIFF, RUNS, BISECT, RUNS you get (4,1,3,1) repeated infinitely often.
  • A276390 (program): Bisection of A115716.
  • A276391 (program): G.f. satisfies A(x) - 4*A(x^2) = x/(1+x).
  • A276394 (program): Characteristic word associated with the fraction 36/25.
  • A276395 (program): Characteristic function of floor(36*n/25).
  • A276482 (program): a(n) = 5^nGamma(n+1/5)Gamma(n+1)/Gamma(1/5).
  • A276509 (program): Numbers n in base 10 such that the digits of 2 + n are the digits of 2n written in reverse order.
  • A276555 (program): Number of steps to reach 1 when starting from n and iterating the map x -> x - A061395(x).
  • A276561 (program): For n-th odd prime prime(n) in binary form, a(n) is the decimal value of the bits in between the most significant and least significant bits which are both 1. Since there are no middle bits for odd_prime(1) = 3 = (11)_2, a(1) = 0.
  • A276598 (program): Values of m such that m^2 + 3 is a triangular number (A000217).
  • A276602 (program): Values of k such that k^2 + 10 is a triangular number (A000217).
  • A276634 (program): Sum of cubes of proper divisors of n.
  • A276647 (program): Number of squares after the n-th generation in a symmetric (with 45 degree angles) non-overlapping Pythagoras tree.
  • A276659 (program): Accumulation of the upper left triangle used in binomial transform of nonnegative integers.
  • A276666 (program): a(n) = (n-1)*Catalan(n).
  • A276670 (program): Numerator of (n-1)n(n+1)/4.
  • A276677 (program): Number of squares added at the n-th generation of a symmetric (with 45-degree angles), non-overlapping Pythagoras tree.
  • A276678 (program): Number of divisors of the n-th pentagonal number.
  • A276679 (program): Number of divisors of the n-th hexagonal number.
  • A276680 (program): Number of divisors of the n-th heptagonal number.
  • A276681 (program): Number of divisors of the n-th octagonal number.
  • A276682 (program): Number of divisors of the n-th 9-gonal number.
  • A276683 (program): Number of divisors of the n-th 10-gonal number.
  • A276704 (program): Records in A249859.
  • A276706 (program): Indices of records in A249860.
  • A276764 (program): 1^2 + 3^2, 2^2 + 4^2, 5^2 + 7^2, 6^2 + 8^2, …
  • A276781 (program): a(n) = 1+n-(nearest power of prime <= n); for n > 1, a(n) = minimal b such that the numbers binomial(n,k) for b <= k <= n-b have a common divisor greater than 1.
  • A276795 (program): Folding numbers with an odd number of bits (see A277238 for definition).
  • A276806 (program): Height of the shortest binary factorization tree of n.
  • A276819 (program): a(n) = a(n-1) + 9*n - 5 with a(0) = 1.
  • A276833 (program): Sum of mu(d)*phi(d) over divisors d of n.
  • A276849 (program): a(0) = 5, a(1) = 2; for n>1, a(n) = 2*a(n-1) + a(n-2).
  • A276854 (program): Beatty sequence for 1 + sqrt(5).
  • A276855 (program): Beatty sequence for (3 + golden ratio).
  • A276856 (program): First differences of the Beatty sequence A022840 for sqrt(6).
  • A276857 (program): First differences of the Beatty sequence A022841 for sqrt(7).
  • A276858 (program): First differences of the Beatty sequence A022842 for sqrt(8).
  • A276859 (program): First differences of the Beatty sequence A022843 for e.
  • A276860 (program): First differences of the Beatty sequence A276853 for 2*e.
  • A276862 (program): First differences of the Beatty sequence A003151 for 1 + sqrt(2).
  • A276864 (program): First differences of the Beatty sequence A001952 for 2 + sqrt(2).
  • A276865 (program): First differences of the Beatty sequence A003512 for 2 + sqrt(3).
  • A276867 (program): First differences of the Beatty sequence A003231 for 2 + tau, where tau = golden ratio = (1 + sqrt(5))/2.
  • A276868 (program): First differences of the Beatty sequence A276855 for 3 + tau, where tau = golden ratio = (1 + sqrt(5))/2.
  • A276869 (program): First differences of the Beatty sequence A182769 for 2 + sqrt(1/2).
  • A276871 (program): Sums-complement of the Beatty sequence for sqrt(5).
  • A276872 (program): Sums-complement of the Beatty sequence for sqrt(6).
  • A276873 (program): Sums-complement of the Beatty sequence for sqrt(7).
  • A276874 (program): Sums-complement of the Beatty sequence for sqrt(8).
  • A276875 (program): Sums-complement of the Beatty sequence for e.
  • A276876 (program): Sums-complement of the Beatty sequence for 2e.
  • A276877 (program): Sums-complement of the Beatty sequence for Pi.
  • A276878 (program): Sums-complement of the Beatty sequence for 2*Pi.
  • A276879 (program): Sums-complement of the Beatty sequence for 1 + sqrt(2).
  • A276880 (program): Sums-complement of the Beatty sequence for 1 + sqrt(3).
  • A276881 (program): Sums-complement of the Beatty sequence for 1 + sqrt(5).
  • A276882 (program): Sums-complement of the Beatty sequence for 2 + sqrt(2).
  • A276883 (program): Sums-complement of the Beatty sequence for 2 + sqrt(3).
  • A276884 (program): Sums-complement of the Beatty sequence for 2 + sqrt(5).
  • A276885 (program): Sums-complement of the Beatty sequence for 1 + phi.
  • A276886 (program): Sums-complement of the Beatty sequence for 2 + phi.
  • A276887 (program): Sums-complement of the Beatty sequence for 3 + tau.
  • A276888 (program): Sums-complement of the Beatty sequence for 2 + sqrt(1/2).
  • A276889 (program): Sums-complement of the Beatty sequence for sqrt(2) + sqrt(3).
  • A276914 (program): Subsequence of triangular numbers obtained by adding a square and two smaller triangles, a(n) = n^2 + 2*A000217(A052928(n)).
  • A276915 (program): Indices of triangular numbers in A276914 which are also pentagonal.
  • A276916 (program): Subsequence of centered square numbers obtained by adding four triangles from A276914 and a central element, a(n) = 4*A276914(n) + 1.
  • A276918 (program): a(2n) = A060867(n+1), a(2n+1) = A092440(n+1).
  • A276950 (program): Characteristic function for A273670: 1 if there is at least one maximal digit present in the factorial representation of n (A007623), otherwise 0.
  • A276952 (program): Partial sums of A276950.
  • A276960 (program): a(n) = A000262(n)^2.
  • A276978 (program): a(n) = (ceiling(n/2))^n.
  • A276979 (program): a(n) = (floor(n/2)+1)^n.
  • A276984 (program): Sum of squares of numbers less than n that do not divide n.
  • A277050 (program): a(n) = floor(2*n/sqrt(Pi)).
  • A277070 (program): Row length of A276380(n).
  • A277082 (program): Generalized 15-gonal (or pentadecagonal) numbers: n(13n - 11)/2, n = 0,+1,-1,+2,-2,+3,-3, …
  • A277091 (program): a(n) = ((1 + sqrt(15))^n - (1 - sqrt(15))^n)/sqrt(15).
  • A277094 (program): Numbers k such that sin(k) > 0 and sin(k+2) < 0.
  • A277097 (program): a(n) = 5 - (prime(n) mod 10).
  • A277104 (program): a(n) = 9*3^n - 15.
  • A277105 (program): a(n) = (27*3^n - 63)/2.
  • A277106 (program): a(n) = 8*3^n - 12.
  • A277107 (program): a(n) = 16*3^n - 48.
  • A277108 (program): a(n) = 4n*(n+5).
  • A277131 (program): Magic numbers of anti-Mackay icosahedra.
  • A277169 (program): Product of squares of proper divisors of n.
  • A277178 (program): a(n) = Sum_ k=0..n kbinomial(2k,k)/2.
  • A277209 (program): Partial sums of repdigit numbers (A010785).
  • A277228 (program): Convolution of the even-indexed triangular numbers (A014105) and the squares (A000290).
  • A277229 (program): Convolution of the odd-indexed triangular numbers (A000384(n+1)) and the squares (A000290).
  • A277236 (program): Number of strings of length n composed of symbols from the circular list [1,2,3,4] such that adjacent symbols in the string must be adjacent in the list. No runs of length 2 or more are allowed for symbols 1 and 3.
  • A277237 (program): Number of strings of length n composed of symbols from the circular list [1,2,3,4,5,6] such that adjacent symbols in the string must be adjacent in the list. No runs of length 2 or more are allowed for symbols 1, 3 and 5.
  • A277267 (program): Minimum number of single-direction edges in leveled binary trees with n nodes.
  • A277314 (program): Number of nonzero coefficients in Stern polynomial B(n,t).
  • A277329 (program): a(0)=0, for n >= 1, a(2n) = a(n)+1, a(4n-1) = a(n)+1, a(4n+1) = a(n)+1.
  • A277342 (program): Base-100 digital root of n (equivalent to repeatedly adding pairs of decimal digits starting from the least significant pair).
  • A277347 (program): a(n) = Product_ k=1..n (2k(k-1)+1).
  • A277351 (program): Value of (n+1,n) concatenated in binary representation.
  • A277354 (program): a(n) = Product_ k=1..n (4*k^2+1).
  • A277357 (program): a(1) = 1; for n > 1, a(n) = (2^n-1)*a(n-1) + 1.
  • A277369 (program): a(0) = 5, a(1) = 8; for n>1, a(n) = 2*a(n-1) + a(n-2).
  • A277385 (program): Records in A277384.
  • A277411 (program): Column 1 of triangle A277410.
  • A277425 (program): a(n) = sqrt(16t^2 - 32t + k^2 + 8k - 8k*t + 16), where t = ceiling(sqrt(n)) and k = t^2 - n.
  • A277426 (program): a(n) = 2^(6n+5).
  • A277433 (program): Martin Gardner’s minimal no-3-in-a-line problem, all slopes version.
  • A277450 (program): a(1) = 1, a(n) = floor(n*Sum_ k=1..n-1 a(k)/2^k - Sum_ k=1..n-1 a(k)) for n > 1.
  • A277451 (program): Number of edges in geodesic dome generated from icosahedron by recursively dividing each triangle in 4.
  • A277452 (program): a(n) = Sum_ k=0..n binomial(n,k) * n^k * k!.
  • A277453 (program): a(n) = Sum_ k=0..n binomial(n,k) * 2^k * n^k * k!.
  • A277542 (program): a(n) = denominator((n^2 + 3*n + 2)/n^3).
  • A277543 (program): a(n) = n/5^m mod 5, where 5^m is the greatest power of 5 that divides n.
  • A277544 (program): a(n) = n/6^m mod 6, where 6^m is the greatest power of 6 that divides n.
  • A277545 (program): a(n) = n/7^m mod 7, where 7^m is the greatest power of 7 that divides n.
  • A277546 (program): a(n) = n/8^m mod 8, where 8^m is the greatest power of 8 that divides n.
  • A277547 (program): a(n) = n/9^m mod 9, where 9^m is the greatest power of 9 that divides n.
  • A277560 (program): Binary representation of the x-axis, from the left edge to the origin, or from the origin to the right edge, of the n-th stage of growth of the two-dimensional cellular automaton defined by “Rule 7”, based on the 5-celled von Neumann neighborhood.
  • A277561 (program): a(n) = Sum_ k=0..n ( binomial(n+2k,2k)*binomial(n,k) mod 2).
  • A277584 (program): a(n) = binomial(3n-1, n-1)^2.
  • A277592 (program): Numbers k such that k/10^m == 5 mod 10, where 10^m is the greatest power of 10 that divides n.
  • A277618 (program): Lexicographically earliest nonnegative sequence such that a(n+1)-a(n) is a prime number, and no number occurs twice; a(0) = 0.
  • A277636 (program): Number of 3 X 3 matrices having all elements in 0,…,n with determinant = permanent.
  • A277644 (program): Beatty sequence for sqrt(6)/2.
  • A277645 (program): Beatty sequence for 3+sqrt(6).
  • A277690 (program): Smallest possible number of sides of a regular polygon with unit sides and circumradius n.
  • A277692 (program): Mendelsohn-Rodney sequence: number of court balanced tournament designs that are available for a given set of teams n.
  • A277708 (program): a(n) = Least prime divisor of n with an odd exponent, or 1 if n is a perfect square.
  • A277722 (program): a(n) = floor(n*tau^2) where tau is the tribonacci constant (A058265).
  • A277723 (program): a(n) = floor(n*tau^3) where tau is the tribonacci constant (A058265).
  • A277757 (program): a(n) = 2^(6n+1).
  • A277792 (program): Squares that are also pentagonal pyramidal numbers.
  • A277799 (program): Decimal representation of the x-axis, from the left edge to the origin, of the n-th stage of growth of the two-dimensional cellular automaton defined by “Rule 1”, based on the 5-celled von Neumann neighborhood.
  • A277800 (program): Decimal representation of the x-axis, from the origin to the right edge, of the n-th stage of growth of the two-dimensional cellular automaton defined by “Rule 1”, based on the 5-celled von Neumann neighborhood.
  • A277801 (program): a(n) = 2^(n - 1) - prime(n).
  • A277808 (program): a(n) = number of iterations of map k -> A003188(A006068(k)/2) that are required (when starting from k = n) until k is an odious number.
  • A277812 (program): a(n) = the first odious number encountered when starting from k = n and iterating the map k -> A003188(A006068(k)/2).
  • A277813 (program): a(n) = A115384(A277812(n)) = index of the row where n is located in array A277880.
  • A277822 (program): a(n) = index of the column where n is located in array A277880.
  • A277823 (program): a(n) = A048724(A065621(n)).
  • A277864 (program): Binary representation of the x-axis, from the left edge to the origin, of the n-th stage of growth of the two-dimensional cellular automaton defined by “Rule 3”, based on the 5-celled von Neumann neighborhood.
  • A277866 (program): Decimal representation of the x-axis, from the left edge to the origin, of the n-th stage of growth of the two-dimensional cellular automaton defined by “Rule 3”, based on the 5-celled von Neumann neighborhood.
  • A277867 (program): Decimal representation of the x-axis, from the origin to the right edge, of the n-th stage of growth of the two-dimensional cellular automaton defined by “Rule 3”, based on the 5-celled von Neumann neighborhood.
  • A277885 (program): a(n) = index of the least non-unitary prime divisor of n or 0 if no such prime-divisor exists.
  • A277924 (program): a(n) = Sum_ i=0..n+1 binomial(2*n,n-i+1).
  • A277928 (program): Decimal representation of the x-axis, from the left edge to the origin, of the n-th stage of growth of the two-dimensional cellular automaton defined by “Rule 5”, based on the 5-celled von Neumann neighborhood.
  • A277929 (program): Decimal representation of the x-axis, from the origin to the right edge, of the n-th stage of growth of the two-dimensional cellular automaton defined by “Rule 5”, based on the 5-celled von Neumann neighborhood.
  • A277935 (program): Number of ways 2*n-1 people can vote on three candidates so that the Condorcet paradox arises.
  • A277936 (program): Decimal representation of the x-axis, from the left edge to the origin, or from the origin to the right edge, of the n-th stage of growth of the two-dimensional cellular automaton defined by “Rule 7”, based on the 5-celled von Neumann neighborhood.
  • A277953 (program): Binary representation of the x-axis, from the origin to the right edge, of the n-th stage of growth of the two-dimensional cellular automaton defined by “Rule 14”, based on the 5-celled von Neumann neighborhood.
  • A277954 (program): Decimal representation of the x-axis, from the left edge to the origin, of the n-th stage of growth of the two-dimensional cellular automaton defined by “Rule 14”, based on the 5-celled von Neumann neighborhood.
  • A277955 (program): Decimal representation of the x-axis, from the origin to the right edge, of the n-th stage of growth of the two-dimensional cellular automaton defined by “Rule 14”, based on the 5-celled von Neumann neighborhood.
  • A277975 (program): a(n) = nx^n + (n-1)x^(n-1) + . . . + x + 1 for x=5.
  • A277976 (program): a(n) = n(3n + 23).
  • A277977 (program): a(n) = n(1-3n+2n^2+2*n^3)/2.
  • A277978 (program): a(n) = 3n(n+3).
  • A277979 (program): a(n) = 4n^2 + 18n.
  • A277980 (program): a(n) = 12n^2 + 18n.
  • A277981 (program): a(n) = 4n^2 + 18n - 20.
  • A277982 (program): a(n) = 12n^2 + 10n - 30.
  • A277983 (program): a(n) = 54n^2 - 78n + 36.
  • A277984 (program): a(n) = 6n(9*n-5).
  • A277985 (program): a(n) = 3(9n - 1)(3n - 2).
  • A277986 (program): a(n) = 74*n - 14.
  • A277987 (program): a(n) = 100*n - 28.
  • A277988 (program): a(n) = 352*2^n + 34.
  • A277989 (program): a(n) = 424*2^n + 37.
  • A277990 (program): a(n) = 54n^2 + 6n.
  • A277991 (program): a(n) = 81n^2 - 9n.
  • A277992 (program): b(n, 2) where b(n, m) is defined by expansion of ((Product_ k>=1 (1 - x^(prime(n)*k))/(1 - x^k)^prime(n)) - 1)/prime(n) in powers of x.
  • A278049 (program): a(n) = 3*(Sum_ k=1..n phi(k)) - 1, where phi = A000010.
  • A278078 (program): a(n) is the number of composite numbers prime(n) dominates.
  • A278105 (program): a(n) = floor(3/n).
  • A278122 (program): a(n) = 204*2^n - 248.
  • A278123 (program): a(n) = 247*2^n - 300.
  • A278124 (program): a(n) = 172*2^n - 176.
  • A278125 (program): a(n) = 225*2^n - 235.
  • A278126 (program): a(n) = 78*n + 66.
  • A278127 (program): a(n) = 99*n + 71.
  • A278128 (program): a(n) = 288*2^n - 156.
  • A278129 (program): a(n) = 348*2^n - 188.
  • A278130 (program): a(n) = 492*2^n - 222.
  • A278131 (program): a(n) = 591*2^n - 273.
  • A278142 (program): Denominators of partial sums of a Ramanujan series converging to 2^(3/2)/(sqrt(Pi)*Gamma(3/4)^2) given in A278146.
  • A278145 (program): Denominator of partial sums of the m=1 member of an m-family of series considered by Hardy with value 4/Pi (see A088538).
  • A278169 (program): Characteristic function for A000960.
  • A278182 (program): Number of dots in Maya numeral representation of n.
  • A278290 (program): Number of neighbors of each new term in a square array read by antidiagonals.
  • A278299 (program): a(n) is the tile count of the smallest polyomino with an n-coloring such that every color is adjacent to every other distinct color at least once.
  • A278310 (program): Numbers m such that T(m) + 3*T(m+1) is a square, where T = A000217.
  • A278312 (program): a(n) = denominator of n/(2^(2*n+1)).
  • A278313 (program): Number of letters “I” in Roman numeral representation of n.
  • A278375 (program): Edge-distinguishing chromatic number of ladder graph with 2n vertices.
  • A278403 (program): a(n) = Sum_ d n d^2 * (d+1)/2.
  • A278417 (program): a(n) = n*((2+sqrt(3))^n + (2-sqrt(3))^n)/2.
  • A278438 (program): Numbers m such that T(m) + 2*T(m+1) is a square, where T = A000217.
  • A278475 (program): a(n) = floor(phi^7*a(n-1)) for n>0, a(0) = 1, where phi is the golden ratio (A001622).
  • A278476 (program): a(n) = floor((1 + sqrt(2))^3*a(n-1)) for n>0, a(0) = 1.
  • A278481 (program): Number of neighbors of the n-th term in a full isosceles triangle read by rows.
  • A278484 (program): Main diagonal of A278482.
  • A278536 (program): First differences of A273324.
  • A278545 (program): Number of neighbors of the n-th term in a full square array read by antidiagonals.
  • A278597 (program): One half of A278481.
  • A278603 (program): A prime mountain: peaks and valleys beyond the origin correspond to prime abscissa (see Comments for precise definition).
  • A278617 (program): Number of distinct odd primes less than or equal to 2n-3 that appear as a part in the partitions of 2n into two parts.
  • A278620 (program): Expansion of x/(1 - 99x + 99x^2 - x^3).
  • A278718 (program): Numerators of A189733: periodic sequence repeating [0, 1, 1, 1, 0, -1].
  • A278741 (program): Odd numbers n such that tau(n-1) is a prime.
  • A278756 (program): Decimal representation of the x-axis, from the origin to the right edge, of the n-th stage of growth of the two-dimensional cellular automaton defined by “Rule 65”, based on the 5-celled von Neumann neighborhood.
  • A278814 (program): a(n) = ceiling(sqrt(3n+1)).
  • A278816 (program): Numbers that can be produced from their own digits by applying one or more of the eight operations +, -, *, /, sqrt(), ^, !, concat11() , with no operation used more than once, where “concat11()” means the operation of concatenating two single digits.
  • A278818 (program): a(n) is the least k > n such that k + n is square.
  • A278831 (program): Minimal number of possible moves at the n-th ply of a chess game, excluding positions where no move is possible.
  • A278832 (program): Maximal material difference at the end of the n-th ply of a chess game.
  • A278933 (program): Number of 2 X 2 matrices with entries in 0,1,…,n and permanent = trace with no entry repeated.
  • A279019 (program): Least possible number of diagonals of simple convex polyhedron with n faces.
  • A279028 (program): Binary representation of the x-axis, from the left edge to the origin, of the n-th stage of growth of the two-dimensional cellular automaton defined by “Rule 129”, based on the 5-celled von Neumann neighborhood.
  • A279030 (program): Decimal representation of the x-axis, from the left edge to the origin, of the n-th stage of growth of the two-dimensional cellular automaton defined by “Rule 129”, based on the 5-celled von Neumann neighborhood.
  • A279043 (program): Numbers k such that 3k+1 and 4k+1 are both triangular numbers (A000217).
  • A279053 (program): Binary representation of the x-axis, from the left edge to the origin, of the n-th stage of growth of the two-dimensional cellular automaton defined by “Rule 131”, based on the 5-celled von Neumann neighborhood.
  • A279054 (program): Largest integer m for which binomial(m,n-1) > binomial(m-1,n).
  • A279075 (program): Maximum starting value of X such that repeated replacement of X with X-ceiling(X/5) requires n steps to reach 0.
  • A279076 (program): Maximum starting value of X such that repeated replacement of X with X-ceiling(X/6) requires n steps to reach 0.
  • A279077 (program): Maximum starting value of X such that repeated replacement of X with X-ceiling(X/7) requires n steps to reach 0.
  • A279078 (program): Maximum starting value of X such that repeated replacement of X with X-ceiling(X/8) requires n steps to reach 0.
  • A279079 (program): Maximum starting value of X such that repeated replacement of X with X-ceiling(X/9) requires n steps to reach 0.
  • A279080 (program): Maximum starting value of X such that repeated replacement of X with X-ceiling(X/10) requires n steps to reach 0.
  • A279081 (program): Number of divisors of the n-th tetrahedral number.
  • A279100 (program): a(n) = Sum_ k=0..n ceiling(phi^k), where phi is the golden ratio (A001622).
  • A279101 (program): a(n) = Sum_ k=0..n ceiling((1 + sqrt(2))^k).
  • A279118 (program): Binary representation of the x-axis, from the left edge to the origin, (and also from the origin to the right edge) of the n-th stage of growth of the two-dimensional cellular automaton defined by “Rule 209”, based on the 5-celled von Neumann neighborhood.
  • A279124 (program): Number of Hangul letters (initials, medials and finals of syllables) in Sino-Korean name of n. If there are several different spellings, use the shorter one.
  • A279169 (program): a(n) = floor( 4*n^2/5 ).
  • A279211 (program): Fill an array by antidiagonals upwards; in the n-th cell, enter the number of earlier cells that can be seen from that cell.
  • A279230 (program): Expansion of 1/((1-x)^2(1-2x+2*x^2)).
  • A279231 (program): Expansion of 1/((1-x)^2(1-3x+3*x^2)).
  • A279241 (program): Let f(n) = 4n^2 + 2n + 41. The values f(n) are primes for all n in the range -20 to 19 (but not for n=-21 or 20). The sequence lists this maximal run of primes in the order in which they appear.
  • A279260 (program): Numbers which are cyclops palindromic in their binary reflected Gray code representation.
  • A279289 (program): Numbers n such that phi(n) > tau(n).
  • A279313 (program): Period 14 zigzag sequence: repeat [0,1,2,3,4,5,6,7,6,5,4,3,2,1].
  • A279316 (program): Period 7: repeat [0, 1, 2, 3, 3, 2, 1].
  • A279319 (program): Period 16 zigzag sequence: repeat [0,1,2,3,4,5,6,7,8,7,6,5,4,3,2,1].
  • A279321 (program): Period 7: repeat [1, 3, 5, 7, 5, 3, 1].
  • A279340 (program): First differences of A055938.
  • A279363 (program): Sum of 4th powers of proper divisors of n.
  • A279364 (program): Sum of 5th powers of proper divisors of n.
  • A279415 (program): Triangle read by rows: T(n,k), n>=k>=1, is the number of right isosceles triangles with integral coordinates that have a bounding box of size n X k.
  • A279437 (program): Number of ways to place 3 points on an n X n square grid so that no more than 2 points are on a vertical or horizontal straight line.
  • A279482 (program): Sum of the first n Lucas numbers whose indices are prime.
  • A279511 (program): Sierpinski square-based pyramid numbers: a(n) = 5*a(n-1) - (2^(n+1)+7).
  • A279512 (program): Sierpinski octahedron numbers a(n) = 26^n + 32^n + 1.
  • A279521 (program): Maximum number of single-direction edges in leveled binary trees with n nodes.
  • A279539 (program): Sum of ceilings of natural logs of first n integers.
  • A279561 (program): Number of length n inversion sequences avoiding the patterns 101, 102, 201, and 210.
  • A279620 (program): Limit of the sequence of words defined by w(1) = 1, w(2) = 1221, and w(n) = w(n-1) 2 w(n-2) 2 w(n-1) for n >= 2. Also the fixed point of the map 1 -> 122, 2 -> 12.
  • A279635 (program): Denominator of (0 followed by A005126(n)= 2, 4, 7, …)/2^n, a sequence corresponding to A271573.
  • A279704 (program): Number of n X 3 0..1 arrays with no element equal to a strict majority of its horizontal and antidiagonal neighbors and with new values introduced in order 0 sequentially upwards.
  • A279735 (program): Number of n X 2 0..1 arrays with no element equal to a strict majority of its horizontal and antidiagonal neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.
  • A279758 (program): Expansion of Product_ k>=1 1/(1 - x^(k(5k^2-5*k+2)/2)).
  • A279766 (program): Number of odd digits in the decimal expansions of integers 1 to n.
  • A279816 (program): Digital roots of tetrahedral numbers (A000292).
  • A279847 (program): a(n) = Sum_ k=1..n k^2*(floor(n/k) - 1).
  • A279872 (program): Decimal representation of the x-axis, from the left edge to the origin, (and also from the origin to the right edge) of the n-th stage of growth of the two-dimensional cellular automaton defined by “Rule 209”, based on the 5-celled von Neumann neighborhood.
  • A279882 (program): a(n) = 2^(prime(n) + 1) - 1.
  • A279891 (program): Triangle read by rows, T(n,k) = 2*n, with n>=k>=0.
  • A279895 (program): a(n) = n(5n + 11)/2.
  • A279905 (program): Number of 2 X 2 matrices with entries in 0,1,…,n and odd trace with no elements repeated.
  • A279910 (program): a(n) = Sum_ k=1..n prime(k+1)*floor(n/prime(k+1)).
  • A280014 (program): Numbers n == +- 2 (mod 10) but not n == 2 (mod 6).
  • A280022 (program): Expansion of phi_ 5, 4 (x) where phi_ r, s (x) = Sum_ n, m>0 m^r * n^s * x^ m*n .
  • A280025 (program): Expansion of phi_ 7, 4 (x) where phi_ r, s (x) = Sum_ n, m>0 m^r * n^s * x^ m*n .
  • A280026 (program): Fill an infinite square array by following a spiral around the origin; in the n-th cell, enter the number of earlier cells that can be seen from that cell.
  • A280050 (program): a(n) = Sum_ k=2..n k/lpf(k), where lpf(k) is the least prime dividing k (A020639).
  • A280055 (program): Nachos sequence based on 1 plus primes (A008578).
  • A280056 (program): Number of 2 X 2 matrices with entries in 0,1,…,n and even trace with no entries repeated.
  • A280058 (program): Number of 2 X 2 matrices with entries in 0,1,…,n with determinant = permanent with no entries repeated.
  • A280059 (program): Number of 2 X 2 matrices having all elements in -n,..,0,..,n with determinant = permanent.
  • A280062 (program): a(n) = A049502(A000142(n)).
  • A280070 (program): Indices of 10-gonal numbers (A001107) that are also centered 10-gonal numbers (A062786).
  • A280071 (program): Indices of 11-gonal numbers (A051682) that are also centered 11-gonal numbers (A060544).
  • A280076 (program): Numbers n such that Sum_ d n tau(d) = Product_ d n tau(d).
  • A280084 (program): 1 together with the Pythagorean primes.
  • A280089 (program): a(n) = 4 * n^3 - 3 * n + 1.
  • A280097 (program): Sum of the divisors of 24*n - 1.
  • A280098 (program): The sum of the divisors of 24*n - 1, divided by 24.
  • A280111 (program): Indices of triangular numbers (A000217) that are also centered 10-gonal numbers (A062786).
  • A280112 (program): Indices of centered 10-gonal numbers (A062786) that are also triangular numbers (A000217).
  • A280113 (program): Triangular numbers (A000217) that are also centered 10-gonal numbers (A062786).
  • A280154 (program): a(n) = 5*Lucas(n).
  • A280166 (program): a(2n) = 4n if n>0, a(2n + 1) = -(2n + 1), a(0) = 1.
  • A280167 (program): a(2n) = 3n if n>0, a(2n + 1) = -(2n + 1), a(0) = 1.
  • A280173 (program): a(0) = 1, a(n+1) = 2*a(n) + periodic sequence of length 2: repeat [5, -4].
  • A280181 (program): Indices of centered 9-gonal numbers (A060544) that are also squares (A000290).
  • A280185 (program): a(n) = n - A004090(n), where A004090 is the sum of digits of the Fibonacci numbers A000045.
  • A280186 (program): Number of 3-element subsets of S = 1..n whose sum is odd.
  • A280193 (program): a(2n) = 2, a(2n + 1) = -1, a(0) = 1.
  • A280211 (program): a(n) = n*(2^(n^2)).
  • A280237 (program): Period length 8 sequence [0, 1, 0, 1, -1, 1, 0, 1, …].
  • A280261 (program): Period length 12 sequence [0, 1, -1, 0, -1, -1, 0, -1, 1, 0, 1, 1, …].
  • A280279 (program): Number of n X 1 0..2 arrays with no element equal to more than one of its horizontal and vertical neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.
  • A280292 (program): a(n) = sopfr(n) - sopf(n).
  • A280293 (program): a(0) = 3, a(n+1) = 2*a(n) + periodic sequence of length 2: repeat [-5, 4].
  • A280304 (program): a(n) = 3n(n^2 + 3*n + 4).
  • A280321 (program): Number of 2 X 2 matrices with all elements in 0,..,n having determinant = n*permanent.
  • A280344 (program): Number of 2 X 2 matrices with all elements in 0,…,n with determinant = permanent^n.
  • A280345 (program): a(0) = 3, a(n+1) = 2*a(n) + periodic sequence of length 2: repeat [1, -2].
  • A280363 (program): a(n) = floor(log_p(n)) where p = A020639(n), i.e., the least prime factor of n.
  • A280364 (program): Number of 2 X 2 matrices with all elements in 0,…,n with permanent = determinant^n.
  • A280392 (program): Number of nX2 0..2 arrays with no element unequal to a strict majority of its horizontal and antidiagonal neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.
  • A280399 (program): Number of 1 X n 0..2 arrays with no element unequal to a strict majority of its horizontal and antidiagonal neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.
  • A280410 (program): Binary representation of the x-axis, from the left edge to the origin, of the n-th stage of growth of the two-dimensional cellular automaton defined by “Rule 261”, based on the 5-celled von Neumann neighborhood.
  • A280412 (program): Decimal representation of the x-axis, from the left edge to the origin, of the n-th stage of growth of the two-dimensional cellular automaton defined by “Rule 261”, based on the 5-celled von Neumann neighborhood.
  • A280428 (program): a(n) = 1729*n^3.
  • A280429 (program): Longest word T from a string S using no breakpoint-reuse.
  • A280510 (program): Index sequence of the Thue-Morse sequence (A010060) as a block-fractal sequence.
  • A280511 (program): Index sequence of the block-fractal sequence A001468.
  • A280512 (program): Index sequence of the Thue-Morse sequence (A010060, using offset 1) as a reverse block-fractal sequence.
  • A280513 (program): Index sequence of the reverse block-fractal sequence A001468.
  • A280514 (program): Index sequence of the reverse block-fractal sequence A003849.
  • A280523 (program): a(n) = Fibonacci(2n + 1) - n.
  • A280556 (program): a(n) = Sum_ k=1..n k^2 * (k+1)!.
  • A280560 (program): a(n) = (-1)^n * 2 if n!=0, with a(0) = 1.
  • A280577 (program): a(n) = eulerphi(n) + floor(n/2).
  • A280637 (program): Sum of the digits of n^2+1.
  • A280658 (program): Numbers ending with their digital root in decimal representation.
  • A280682 (program): Integers m such that floor(sqrt(m)) is even.
  • A280700 (program): Binary weight of terms of A005187: a(n) = A000120(A005187(n)).
  • A280710 (program): Characteristic function of squarefree semiprimes.
  • A280713 (program): Partial sums of A055067 where A055067(n) is the product of non-divisors of n.
  • A280724 (program): Expansion of 1/(1 - x) + (1/(1 - x)^2)*Sum_ k>=0 x^(3^k).
  • A280737 (program): a(n) = A007302(n)-1.
  • A280761 (program): Solutions y_n to the negative Pell equation y^2 = 72*x^2 - 8.
  • A280797 (program): a(n) = (n^n - 1)(n^n + 1)/(n + 1).
  • A280799 (program): a(n) = A049502(phi(n)).
  • A280814 (program): The maximum number of squares among the partial sums of any permutation of the integers [1..n].
  • A280818 (program): a(0)=1; for n > 0, if 4n+1 is prime, then a(n)=4n+1, otherwise a(n)=(4n+1)/LPF(4n+1).
  • A280843 (program): a(n) = A049502(sigma(n)).
  • A280845 (program): a(n) = 16^n * n * (n!)^4.
  • A280913 (program): Number of dots in International Morse numeral representation of n.
  • A280931 (program): a(n) = 2F(n-1) + 9F(n-4) + 9*F(n-7) where n >= 7 and F = A000045.
  • A280945 (program): List of primitive triples (x, y, z) of positive integers for which xy - z, yz - x, and zx - y are powers of 2.
  • A280995 (program): a(n) is the number produced when n is converted to binary reflected Gray code, the binary digits are reversed and the code is converted back to decimal.
  • A281005 (program): Numbers n having at least one odd divisor greater than sqrt(2*n).
  • A281006 (program): a(n) = A000203(n) - A052928(n-1).
  • A281023 (program): Partial sums of A067392.
  • A281026 (program): a(n) = floor(3n(n+1)/4).
  • A281098 (program): a(n) is the GCD of the sequence d(n) = A261327(k+n) - A261327(k) for all k.
  • A281122 (program): Triangle T read by rows: n-th row (n>=0) gives the non-vanishing coefficients of the polynomial q(n,x) = ((x+1)^(2^n) - (x-1)^(2^n))/2.
  • A281151 (program): a(n) = floor(4n(n+1)/5).
  • A281166 (program): a(n) = 3a(n-1) - 3a(n-2) + 2*a(n-3) for n>2, a(0)=a(1)=1, a(2)=3.
  • A281199 (program): Number of n X 2 0..1 arrays with no element equal to more than one of its horizontal and antidiagonal neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.
  • A281200 (program): Number of n X 3 0..1 arrays with no element equal to more than one of its horizontal and antidiagonal neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.
  • A281228 (program): Expansion of (Sum_ k>=0 x^(3^k))^2 [even terms only].
  • A281234 (program): Solutions y to the negative Pell equation y^2 = 72*x^2 - 288 with x,y >= 0.
  • A281237 (program): Solutions x to the negative Pell equation y^2 = 72*x^2 - 73728 with x,y >= 0.
  • A281238 (program): Solutions y to the negative Pell equation y^2 = 72*x^2 - 73728 with x,y >= 0.
  • A281258 (program): Digital root of n(n+1)(n+2)/2.
  • A281264 (program): Base-2 logarithm of denominator of Sum_ k=0..n^2-1 ((-1)^ksqrt(Pi)/(Gamma(1/2-k)Gamma(1+k)))-n).
  • A281298 (program): a(n) is the n-th decimal digit from the right in n^n.
  • A281320 (program): Number of n X 2 0..2 arrays with no element equal to more than one of its horizontal and antidiagonal neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.
  • A281333 (program): a(n) = 1 + floor(n/2) + floor(n^2/3).
  • A281362 (program): a(0) = 1, a(1) = 2; for n>1, a(n) = a(n-1) + a(n-2) + floor(n/2).
  • A281367 (program): “Nachos” sequence based on triangular numbers.
  • A281372 (program): Coefficients in q-expansion of (E_2*E_4 - E_6)/720, where E_2, E_4, E_6 are the Eisenstein series shown in A006352, A004009, A013973, respectively.
  • A281375 (program): a(n) = floor(2^(n+1)/n).
  • A281376 (program): Total number of counts where floor(N/k) < floor((N+k)/n) for k = 1, 2, …, n-1 and N >= n.
  • A281381 (program): a(n) = n(n + 1)(4*n + 5)/2.
  • A281384 (program): Least integer with more than 1 digit in base n, such that the set of its base-n digits equals the set of its binary digits.
  • A281387 (program): Pairs (x, y) of relatively prime positive integers such that (x^2 - 5)/y and (y^2 - 5)/x are both positive integers.
  • A281392 (program): Number of occurrences of “01” as a subsequence in the binary expansion of n.
  • A281445 (program): Nonnegative k for which (2*k^2 + 1)/11 is an integer.
  • A281481 (program): a(n) = 2^(n - 1) * (2^n + 1) + 1.
  • A281482 (program): a(n) = 2^(n + 1) * (2^n + 1) - 1.
  • A281500 (program): Reduced denominators of f(n) = (n+1)/(2^(2+n)-2) with A026741(n+1) as numerators.
  • A281546 (program): a(n) = 27*n + 2.
  • A281553 (program): Write n in binary reflected Gray code, rotate one binary place to the right and convert the code back to decimal.
  • A281580 (program): a(n) = binomial(9*n, n-9).
  • A281582 (program): Number of rolls of a die with n sides that maximizes the average ratio of highest number of occurrences of a face value to lowest number.
  • A281593 (program): a(n) = b(n) - Sum_ j=0..n-1 b(n) with b(n) = binomial(2*n, n).
  • A281594 (program): The radical of the Catalan number which is the largest squarefree number dividing binomial(2*n,n)/(n+1).
  • A281626 (program): a(n) = (sum of trivial divisors of n) - (sum of nontrivial divisors of n).
  • A281660 (program): The least common multiple of 1+n and 1+n^2.
  • A281661 (program): The least common multiple of 1 + n^2 and 1 + n^3.
  • A281664 (program): Numbers k such that A000005(k) = A000005(A000217(k)).
  • A281680 (program): a(0)=1; for n > 0, if 2n+1 is prime, then a(n)=1, otherwise a(n) = (2n+1)/(largest proper divisor of 2n+1).
  • A281699 (program): Sierpinski stellated octahedron numbers: a(n) = 2(-32^(n+1) + 2^(2n+3) + 5).
  • A281726 (program): Triangular array T(n,k) is the number of elements in an n X k matrix that will be assigned the same value whether the integers from 1 to n*k are assigned to elements in row-major order or column-major order.
  • A281727 (program): a(n) = (-1)^n * 2 if n = 3*k and n!=0, otherwise a(n) = (-1)^n.
  • A281746 (program): Nonnegative numbers k such that k == 0 (mod 3) or k == 0 (mod 5).
  • A281773 (program): Number of distinct topologies on an n-set that have exactly 4 open sets.
  • A281787 (program): a(n) = sum of all numbers between 1 and 10^n that are divisible by 3 or 5.
  • A281813 (program): a(0) = 3, a(n) = 8*n + 4 for n > 0.
  • A281814 (program): Expansion of f(x, x^8) in powers of x where f(, ) is Ramanujan’s general theta function.
  • A281899 (program): a(n) = n + 6*floor(n/3).
  • A281912 (program): Number of sequences of balls colored with at most n colors such that exactly one ball is of a color seen earlier in the sequence.
  • A281959 (program): a(n) = sigma_25(n), the sum of the 25th powers of the divisors of n.
  • A281997 (program): a(n) = (n-1)^n * n^n.
  • A282004 (program): Decimal representation of the x-axis, from the left edge to the origin, of the n-th stage of growth of the two-dimensional cellular automaton defined by “Rule 413”, based on the 5-celled von Neumann neighborhood.
  • A282005 (program): Decimal representation of the x-axis, from the origin to the right edge, of the n-th stage of growth of the two-dimensional cellular automaton defined by “Rule 413”, based on the 5-celled von Neumann neighborhood.
  • A282022 (program): Start with 1; multiply alternately by 3 and 4.
  • A282023 (program): Start with 1; multiply alternately by 4 and 3.
  • A282029 (program): a(n) = n - pi(n/2).
  • A282039 (program): Let p = n-th prime == 7 mod 8; a(n) = sum of quadratic residues mod p that are < p/2.
  • A282050 (program): Coefficients in q-expansion of (E_4^2 - E_2*E_6)/1008, where E_2, E_4, E_6 are the Eisenstein series shown in A006352, A004009, A013973, respectively.
  • A282057 (program): Odd numbers n such that for all k >= 1 the numbers n4^k - 1 and n4^k + 1 do not form a twin prime pair.
  • A282060 (program): Coefficients in q-expansion of E_4(E_2E_4 - E_6)/720, where E_2, E_4, E_6 are the Eisenstein series shown in A006352, A004009, A013973, respectively.
  • A282079 (program): Number of n-element subsets of [n+2] having an even sum.
  • A282088 (program): Binary representation of the x-axis, from the left edge to the origin, of the n-th stage of growth of the two-dimensional cellular automaton defined by “Rule 553”, based on the 5-celled von Neumann neighborhood.
  • A282097 (program): Coefficients in q-expansion of (3E_2E_4 - 2*E_6 - E_2^3)/1728, where E_2, E_4, E_6 are the Eisenstein series shown in A006352, A004009, A013973, respectively.
  • A282099 (program): Coefficients in q-expansion of (E_2^2E_4 - 2E_2*E_6 + E_4^2)/1728, where E_2, E_4, E_6 are the Eisenstein series shown in A006352, A004009, A013973, respectively.
  • A282122 (program): Binary representation of the x-axis, from the origin to the right edge, of the n-th stage of growth of the two-dimensional cellular automaton defined by “Rule 430”, based on the 5-celled von Neumann neighborhood.
  • A282123 (program): Decimal representation of the x-axis, from the left edge to the origin, of the n-th stage of growth of the two-dimensional cellular automaton defined by “Rule 430”, based on the 5-celled von Neumann neighborhood.
  • A282124 (program): Decimal representation of the x-axis, from the origin to the right edge, of the n-th stage of growth of the two-dimensional cellular automaton defined by “Rule 430”, based on the 5-celled von Neumann neighborhood.
  • A282142 (program): Binary representation of the x-axis, from the origin to the right edge, of the n-th stage of growth of the two-dimensional cellular automaton defined by “Rule 553”, based on the 5-celled von Neumann neighborhood.
  • A282153 (program): Expansion of x(1 - 2x + 3x^2)/((1 - x)(1 - 2x)(1 - x + x^2)).
  • A282154 (program): Coefficients in expansion of Eisenstein series -q(d/dq)(q(d/dq)E_2).
  • A282162 (program): Difference sequence of the upper Wythoff sequence, A001950, with 2 prepended.
  • A282166 (program): a(n) is the minimal sum of a positive integer sequence of length n with no duplicate substrings of length greater than 1, and every number different from its neighbors.
  • A282167 (program): a(n) is the minimal sum of a positive integer sequence of length n with no duplicate substrings (forward or backward) of length greater than 1, and no self-adjacent terms.
  • A282168 (program): a(n) is the minimal sum of a positive integer sequence of length n with no duplicate substrings (forward or backward) of length greater than 1.
  • A282211 (program): Coefficients in q-expansion of (6E_2^2E_4 - 8E_2E_6 + 3*E_4^2 - E_2^4)/6912, where E_2, E_4, E_6 are the Eisenstein series shown in A006352, A004009, A013973, respectively.
  • A282213 (program): Coefficients in q-expansion of (E_2^3E_4 - 3E_2^2E_6 + 3E_2E_4^2 - E_4E_6)/3456, where E_2, E_4, E_6 are the Eisenstein series shown in A006352, A004009, A013973, respectively.
  • A282232 (program): a(n) = ((3*n + 1)^6 - 1)/9.
  • A282254 (program): Coefficients in q-expansion of (3E_4^3 + 2E_6^2 - 5E_2E_4*E_6)/1584, where E_2, E_4, E_6 are the Eisenstein series shown in A006352, A004009, A013973, respectively.
  • A282284 (program): Least common multiple of 3n+1 and 3n-1.
  • A282285 (program): Least common multiple of 5n+1 and 5n-1.
  • A282286 (program): Least common multiple of 7n+1 and 7n-1.
  • A282329 (program): Start with 2, then successively subtract the primes 3, 5, 7, …
  • A282411 (program): Binary representation of the x-axis, from the left edge to the origin, of the n-th stage of growth of the two-dimensional cellular automaton defined by “Rule 467”, based on the 5-celled von Neumann neighborhood.
  • A282413 (program): Decimal representation of the x-axis, from the left edge to the origin, of the n-th stage of growth of the two-dimensional cellular automaton defined by “Rule 467”, based on the 5-celled von Neumann neighborhood.
  • A282414 (program): Decimal representation of the x-axis, from the origin to the right edge, of the n-th stage of growth of the two-dimensional cellular automaton defined by “Rule 467”, based on the 5-celled von Neumann neighborhood.
  • A282417 (program): Decimal representation of the x-axis, from the left edge to the origin, of the n-th stage of growth of the two-dimensional cellular automaton defined by “Rule 469”, based on the 5-celled von Neumann neighborhood.
  • A282453 (program): Decimal representation of the x-axis, from the left edge to the origin, of the n-th stage of growth of the two-dimensional cellular automaton defined by “Rule 475”, based on the 5-celled von Neumann neighborhood.
  • A282454 (program): Decimal representation of the x-axis, from the origin to the right edge, of the n-th stage of growth of the two-dimensional cellular automaton defined by “Rule 475”, based on the 5-celled von Neumann neighborhood.
  • A282462 (program): Integers but with the primes cubed.
  • A282464 (program): a(n) = Sum_ i=0..n i*Fibonacci(i)^2.
  • A282465 (program): a(n) = 11*Fibonacci(n+3) + Fibonacci(n-8) with n>=0.
  • A282466 (program): a(n) = n*a(n-1) + n!, with n>0, a(0)=5.
  • A282513 (program): a(n) = floor((3*n + 2)^2/24 + 1/3).
  • A282532 (program): Position where the discrete difference of the Poissonian probability distribution function with mean n takes its lowest value. In case of a tie, pick the smallest value.
  • A282548 (program): Expansion of phi_ 12, 1 (x) where phi_ r, s (x) = Sum_ n, m>0 m^r * n^s * x^ m*n .
  • A282563 (program): One third of the number of edges in the metrically regular triangulation of the n-th approximation of the Koch snowflake fractal.
  • A282577 (program): Decimal representation of the x-axis, from the left edge to the origin, of the n-th stage of growth of the two-dimensional cellular automaton defined by “Rule 553”, based on the 5-celled von Neumann neighborhood.
  • A282579 (program): Decimal representation of the x-axis, from the origin to the right edge, of the n-th stage of growth of the two-dimensional cellular automaton defined by “Rule 553”, based on the 5-celled von Neumann neighborhood.
  • A282597 (program): Expansion of phi_ 14, 1 (x) where phi_ r, s (x) = Sum_ n, m>0 m^r * n^s * x^ m*n .
  • A282600 (program): a(n) = Sum_(k=1..phi(n)) floor(d_k/2) where d_k are the totatives of n.
  • A282612 (program): Number of inequivalent 3 X 3 matrices with entries in 1,2,3,..,n up to row permutations.
  • A282613 (program): Number of inequivalent 3 X 3 matrices with entries in 1,2,3,..,n up to rotations.
  • A282622 (program): Number of digits of the representation of n in the alternating sexagesimal-decimal number system.
  • A282626 (program): Exponential expansion of the real root y = y(x) of y^3 - 3xy - 1.
  • A282630 (program): Number of steps to reach 1 when starting from n and iterating the map x -> x - A055396(x).
  • A282671 (program): Twice composite numbers.
  • A282692 (program): a(n) = maximal number of nonzero real roots of any of the 3^(n+1) polynomials c_0 + c_1x + c_2x^2 + … + c_n*x^n where the coefficients c_i are -1, 0, or 1.
  • A282701 (program): a(n) = maximal number of real roots of any of the polynomials c_0 + c_1x + c_2x^2 + … + c_n*x^n where the coefficients c_i are -1, 0, or 1, c_0 != 0, and c_n != 0.
  • A282702 (program): a(n) = 3*a(n-1) + a(n-2), with a(0)=4, a(1)=11.
  • A282703 (program): a(n) = 3*a(n-1) + a(n-2), with a(0)=7, a(1)=26.
  • A282704 (program): (Twice product of first n primes) - 1.
  • A282737 (program): Expansion of (x^6 - x^4 + x^3 - x - 1)/((x - 1)^3*(x + 1)^2).
  • A282738 (program): First differences of A282737.
  • A282751 (program): Expansion of phi_ 7, 2 (x) where phi_ r, s (x) = Sum_ n, m>0 m^r * n^s * x^ m*n .
  • A282753 (program): Expansion of phi_ 9, 2 (x) where phi_ r, s (x) = Sum_ n, m>0 m^r * n^s * x^ m*n .
  • A282777 (program): Expansion of phi_ 16, 1 (x) where phi_ r, s (x) = Sum_ n, m>0 m^r * n^s * x^ m*n .
  • A282779 (program): Period of cubes mod n.
  • A282798 (program): Decimal representation of the x-axis, from the left edge to the origin, of the n-th stage of growth of the two-dimensional cellular automaton defined by “Rule 505”, based on the 5-celled von Neumann neighborhood.
  • A282799 (program): Decimal representation of the x-axis, from the origin to the right edge, of the n-th stage of growth of the two-dimensional cellular automaton defined by “Rule 505”, based on the 5-celled von Neumann neighborhood.
  • A282802 (program): Decimal representation of the x-axis, from the left edge to the origin, of the n-th stage of growth of the two-dimensional cellular automaton defined by “Rule 507”, based on the 5-celled von Neumann neighborhood.
  • A282816 (program): Number of inequivalent ways to color the faces of a cube using at most n colors so that no two opposite sides have the same color.
  • A282817 (program): Number of inequivalent ways to color the faces of a cube using at most n colors so that no color appears more than twice.
  • A282819 (program): Number of inequivalent ways to color the edges of a tetrahedron using at most n colors so that no two opposite edges have the same color.
  • A282820 (program): Number of inequivalent ways to color the edges of a tetrahedron using at most n colors so that no color appears more than twice.
  • A282822 (program): a(n) = (n - 4)*n! for n>=0.
  • A282848 (program): a(n) = 2*n + 1 + n mod 4.
  • A282850 (program): 38-gonal numbers: a(n) = n(18n-17).
  • A282851 (program): 35-gonal numbers: a(n) = n(33n-31)/2.
  • A282852 (program): 37-gonal numbers: a(n) = n(35n-33)/2.
  • A282853 (program): 36-gonal numbers: a(n) = n(17n-16).
  • A282854 (program): 34-gonal numbers: a(n) = n(32n-30)/2.
  • A282939 (program): Maximum number of straight lines required to draw the boundary of any polyomino with n squares.
  • A283001 (program): a(n) = (A004186(n) - n)/9.
  • A283026 (program): Number of inequivalent 4 X 4 matrices with entries in 1,2,3,..,n up to row permutations.
  • A283027 (program): Number of inequivalent 4 X 4 matrices with entries in 1,2,3,…,n up to rotations.
  • A283028 (program): Number of inequivalent 4 X 4 matrices with entries in 1,2,3,…,n up to vertical and horizontal reflections.
  • A283029 (program): Number of inequivalent 5 X 5 matrices with entries in 1,2,3,..,n when a matrix and its transpose are considered equivalent.
  • A283030 (program): Number of inequivalent 5 X 5 matrices with entries in 1,2,3,…,n up to row permutations.
  • A283049 (program): Numbers of configurations of A’Campo forests with co-dimension 1 and degree n>0.
  • A283070 (program): Sierpinski tetrahedron or tetrix numbers: a(n) = 2*4^n + 2.
  • A283078 (program): a(n) = sigma(7*n).
  • A283107 (program): Numbers n such that tau(4*(n - 1)) is prime.
  • A283118 (program): a(n) = sigma(5*n).
  • A283122 (program): a(n) = sigma(8*n).
  • A283123 (program): a(n) = sigma(9*n).
  • A283149 (program): Largest k such that (p-1)! == -1 (mod p^k), where p = prime(n).
  • A283208 (program): Minimal exponent integer sequence associated with Vietoris sequence.
  • A283233 (program): 2*A000201.
  • A283234 (program): 2*A001950.
  • A283237 (program): a(n) = sigma_2(3*n).
  • A283310 (program): Nim value of complete graph K_n
  • A283316 (program): Image of 0 under repeated applications of the morphism 0 -> 0,0,0,1, 1 -> 1,1,1,0.
  • A283318 (program): Image of 0 under repeated applications of the morphism 0 -> 0,1,0,0, 1 -> 1,1,0,1.
  • A283323 (program): a(n) = 4*a(n-2)+1 with initial terms 1,3,7.
  • A283351 (program): Binary representation of the x-axis, from the left edge to the origin, of the n-th stage of growth of the two-dimensional cellular automaton defined by “Rule 619”, based on the 5-celled von Neumann neighborhood.
  • A283352 (program): Binary representation of the x-axis, from the origin to the right edge, of the n-th stage of growth of the two-dimensional cellular automaton defined by “Rule 619”, based on the 5-celled von Neumann neighborhood.
  • A283353 (program): Decimal representation of the x-axis, from the origin to the right edge, of the n-th stage of growth of the two-dimensional cellular automaton defined by “Rule 619”, based on the 5-celled von Neumann neighborhood.
  • A283393 (program): a(n) = gcd(n^2-1, n^2+9).
  • A283394 (program): a(n) = 3n(3*n + 7)/2 + 4.
  • A283419 (program): a(n) is the multiplicative inverse of 3 modulo the n-th prime (n > 3).
  • A283437 (program): Periodic 1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1 .
  • A283442 (program): a(n) = lcm(n,5) / gcd(n,5).
  • A283443 (program): a(n) = lcm(n,6) / gcd(n,6).
  • A283444 (program): a(n) = lcm(n,7) / gcd(n,7).
  • A283483 (program): Sums of distinct nonzero terms of A003462: a(n) = Sum_ k>=0 A030308(n,k)*A003462(1+k).
  • A283498 (program): a(n) = Sum_ d n d^(d+1).
  • A283506 (program): Decimal representation of the x-axis, from the left edge to the origin, of the n-th stage of growth of the two-dimensional cellular automaton defined by “Rule 641”, based on the 5-celled von Neumann neighborhood.
  • A283507 (program): Decimal representation of the x-axis, from the origin to the right edge, of the n-th stage of growth of the two-dimensional cellular automaton defined by “Rule 641”, based on the 5-celled von Neumann neighborhood.
  • A283508 (program): Binary representation of the x-axis, from the origin to the right edge, of the n-th stage of growth of the two-dimensional cellular automaton defined by “Rule 643”, based on the 5-celled von Neumann neighborhood.
  • A283523 (program): Decimal representation of the x-axis, from the left edge to the origin, of the n-th stage of growth of the two-dimensional cellular automaton defined by “Rule 913”, based on the 5-celled von Neumann neighborhood.
  • A283526 (program): Pierce expansion of the number Sum_ k >= 1 1/(2^(2^k - 1)).
  • A283551 (program): a(n) = -1 + 5*n/6 + n^3/6.
  • A283556 (program): Digital root of the sum of the first n primes.
  • A283591 (program): Decimal representation of the x-axis, from the left edge to the origin, of the n-th stage of growth of the two-dimensional cellular automaton defined by “Rule 657”, based on the 5-celled von Neumann neighborhood.
  • A283592 (program): Decimal representation of the x-axis, from the origin to the right edge, of the n-th stage of growth of the two-dimensional cellular automaton defined by “Rule 657”, based on the 5-celled von Neumann neighborhood.
  • A283623 (program): a(n) = prime(n) + (1 + prime(1 + n))/2.
  • A283641 (program): Binary representation of the x-axis, from the left edge to the origin, of the n-th stage of growth of the two-dimensional cellular automaton defined by “Rule 678”, based on the 5-celled von Neumann neighborhood.
  • A283642 (program): Decimal representation of the x-axis, from the origin to the right edge, of the n-th stage of growth of the two-dimensional cellular automaton defined by “Rule 678”, based on the 5-celled von Neumann neighborhood.
  • A283650 (program): Decimal representation of the x-axis, from the left edge to the origin, of the n-th stage of growth of the two-dimensional cellular automaton defined by “Rule 705”, based on the 5-celled von Neumann neighborhood.
  • A283683 (program): Unique sequence with a(1)=0, a(2)=1, representing an array T(i,j) read by antidiagonals in which every row is this sequence itself.
  • A283707 (program): Binary representation of the x-axis, from the left edge to the origin, of the n-th stage of growth of the two-dimensional cellular automaton defined by “Rule 721”, based on the 5-celled von Neumann neighborhood.
  • A283709 (program): Decimal representation of the x-axis, from the left edge to the origin, of the n-th stage of growth of the two-dimensional cellular automaton defined by “Rule 721”, based on the 5-celled von Neumann neighborhood.
  • A283733 (program): a(n) = a(n-1) + 1 + floor(n*golden ratio), with a(0) = 1.
  • A283750 (program): a(n) = n^2 XOR (n + 1)^2.
  • A283794 (program): Positions of 1 in A288375; complement of A288625.
  • A283810 (program): Numbers of variables for which the Shapiro inequality holds.
  • A283833 (program): For t >= 0, if 2^t + t - 3 <= n <= 2^t + t - 1 then a(n) = 2^t - 1, while if 2^t + t - 1 < n < 2^(t+1) + t - 3 then a(n) = 2^(t+1) + t - 2 - n.
  • A283834 (program): Number of length-n binary vectors beginning with 0, ending with 1, and avoiding 4 consecutive 0’s and 4 consecutive 1’s.
  • A283845 (program): Square array read by antidiagonals: T(1,1) = T(1,2) = T(2,1) = T(2,2) = 1; thereafter T(m,n) = min T(m,n-2) + T(m,n-1), T(m-2,n) + T(m-1,n), T(m-2,n-2) + T(m-1,n-1) .
  • A283874 (program): The Pierce expansion of the number Sum_ k>=1 1/3^((2^k) - 1).
  • A283878 (program): An eventually quasilinear solution to Hofstadter’s Q recurrence.
  • A283968 (program): a(n) = a(n-1) + 1 + floor(n*(3 + sqrt(5))/2), a(0) = 1.
  • A283969 (program): a(n) = n + 1 + Sum_( k=0..n floor((n-k)/r, where r = (3+sqrt(5))/2).
  • A283971 (program): a(n) = n except a(4n + 2) = 2n + 1.
  • A283980 (program): a(n) = A003961(n)*A006519(n).
  • A284013 (program): a(n) = n - A002487(n).
  • A284016 (program): a(-1)=-1; a(n) = 2*A000108(n) for n >= 0.
  • A284097 (program): Sum_ d n, d=1 mod 5 d.
  • A284098 (program): Sum_ d n, d=1 mod 6 d.
  • A284103 (program): a(n) = Sum_ d n, d=4 mod 5 d.
  • A284104 (program): a(n) = Sum_ d n, d=5 mod 6 d.
  • A284122 (program): Number of binary words w of length n for which s, the longest proper suffix of w that appears at least twice in w, is of length 1 (i.e., either s = 0 or s = 1).
  • A284237 (program): Decimal representation of the x-axis, from the left edge to the origin, of the n-th stage of growth of the two-dimensional cellular automaton defined by “Rule 833”, based on the 5-celled von Neumann neighborhood.
  • A284248 (program): Every binary string w of length n has a subword of length a(n) that appears at least twice in w.
  • A284280 (program): Sum_ d n, d = 2 mod 5 d.
  • A284281 (program): Sum_ d n, d = 3 mod 5 d.
  • A284307 (program): Permutation of the natural numbers partitioned into quadruples [4k-3, 4k, 4k-2, 4k-1], k > 0.
  • A284351 (program): Binary representation of the x-axis, from the left edge to the origin, of the n-th stage of growth of the two-dimensional cellular automaton defined by “Rule 899”, based on the 5-celled von Neumann neighborhood.
  • A284353 (program): Decimal representation of the x-axis, from the left edge to the origin, of the n-th stage of growth of the two-dimensional cellular automaton defined by “Rule 899”, based on the 5-celled von Neumann neighborhood.
  • A284354 (program): Decimal representation of the x-axis, from the origin to the right edge, of the n-th stage of growth of the two-dimensional cellular automaton defined by “Rule 899”, based on the 5-celled von Neumann neighborhood.
  • A284359 (program): Double triangle (2n+2 terms by row). Every row is 2n + 1 followed by 2n + 1 times 2n + 2.
  • A284395 (program): Positions of 1 in A284394.
  • A284396 (program): Positions of 2 in A284394.
  • A284403 (program): Binary representation of the x-axis, from the left edge to the origin, of the n-th stage of growth of the two-dimensional cellular automaton defined by “Rule 913”, based on the 5-celled von Neumann neighborhood.
  • A284405 (program): Decimal representation of the x-axis, from the origin to the right edge, of the n-th stage of growth of the two-dimensional cellular automaton defined by “Rule 913”, based on the 5-celled von Neumann neighborhood.
  • A284413 (program): Exponent of 3 in 2^n + 1.
  • A284429 (program): A quasilinear solution to Hofstadter’s Q recurrence.
  • A284443 (program): Sum_ d n, d = 2 mod 7 d.
  • A284444 (program): Sum_ d n, d = 3 mod 7 d.
  • A284445 (program): Sum_ d n, d = 4 mod 7 d.
  • A284446 (program): Sum_ d n, d = 5 mod 7 d.
  • A284494 (program): a(n) = A284016(n)^2.
  • A284517 (program): Periodic with period [1, 4, 3, 4, 1, 6] of length 6.
  • A284574 (program): a(n) = A048724(n) mod 3.
  • A284575 (program): a(n) = A048725(n) mod 3.
  • A284620 (program): 00->2 -transform of the infinite Fibonacci word A003849.
  • A284621 (program): Positions of 0 in A284620.
  • A284624 (program): Positions of 1 in A284749.
  • A284625 (program): Positions of 2 in A284749.
  • A284633 (program): Numbers n with digits 3 and 6 only.
  • A284647 (program): Number of nonisomorphic unfoldings in an n-gonal Archimedean antiprism.
  • A284721 (program): Smallest odd prime that is relatively prime to 2n+1.
  • A284722 (program): (2n+1-A284721(n))/2.
  • A284723 (program): Smallest odd prime that is relatively prime to n.
  • A284775 (program): Fixed point of the morphism 0 -> 01, 1 -> 0011.
  • A284776 (program): Positions of 0 in A284775; complement of A284777.
  • A284777 (program): Positions of 1 in A284775; complement of A284776.
  • A284794 (program): Positions of -1 in A284793.
  • A284796 (program): Positions of 1’s in A284793.
  • A284811 (program): Fixed points of the transform A267193.
  • A284816 (program): Sum of entries in the first cycles of all permutations of [n].
  • A284817 (program): a(n) = 2n - 1 - A284776(n).
  • A284818 (program): Positions of 0 in A284817.
  • A284819 (program): Positions of 1 in A284817.
  • A284850 (program): a(n) = 4^n - 3^n - n.
  • A284920 (program): Numbers with digits 2 and 4 only.
  • A284948 (program): 1-limiting word of the morphism 0 -> 10, 1 -> 00
  • A284965 (program): a(n) is the number of self-conjugate partitions of n which represent Chomp positions with Sprague-Grundy value 1.
  • A284968 (program): Least hairpin family matchings with n edges that are both L&P and C&C whose leftmost edge is part of a hairpin.
  • A284972 (program): Numbers with digits 4 and 8 only.
  • A285008 (program): Numerator of (3/4)^n * binomial(2*n,n).
  • A285009 (program): Subset sums (see Comments).
  • A285019 (program): Numerator of (-1/3)^nsqrt(Pi)/(Gamma(1/2 - n)Gamma(1 + n)).
  • A285043 (program): Expansion of cosh(3arctanh(2sqrt(x))).
  • A285052 (program): Number of idempotent equivalence classes for multiplication in Zn.
  • A285054 (program): Numbers whose sum of digits are congruent (mod 10) to the string 1,2, …, 9.
  • A285073 (program): 0-limiting word of the morphism 0->10, 1-> 010.
  • A285074 (program): Positions of 0 in A285073; complement of A285075.
  • A285075 (program): Positions of 1 in A285073; complement of A285074.
  • A285076 (program): 1-limiting word of the morphism 0->10, 1-> 010.
  • A285077 (program): Positions of 0 in A285076; complement of A285078.
  • A285078 (program): Positions of 1 in A285076; complement of A285077.
  • A285097 (program): a(n) = difference between the positions of two least significant 1-bits in base-2 representation of n, or 0 if there are less than two 1-bits in n (when n is either zero or a power of 2).
  • A285098 (program): Row sums of irregular triangle A070168.
  • A285109 (program): a(n) = n multiplied by its smallest prime factor; a(1) = 1.
  • A285120 (program): Min( d(k+1-i) - d(i) , for i = 1..k, where d(1),..,d(k) are the divisors of n(n+1)/2.
  • A285122 (program): Min( d(k+1-i) - d(i) , for i = 1..k, where d(1),..,d(k) are the divisors of n^2+1.
  • A285124 (program): Min( d(k+1-i) - d(i) , for i = 1..k, where d(1),..,d(k) are the divisors of prime(n) + 1.
  • A285173 (program): Numbers n such that A002496(n+1) < A002496(n)^(1+1/n).
  • A285184 (program): a(n) = 2*a(n-1) + a(n-3) with initial terms 1,3,5.
  • A285188 (program): a(n) = Sum_ k=1..n (k^2*floor(k/2)).
  • A285192 (program): Array read by antidiagonals: T(n,k) = nk(3+n*k)/2 (n >= 0, k >= 0).
  • A285193 (program): Expansion of 1/(1+x+2*x^2) mod 3.
  • A285196 (program): If A_k denotes the first 2*3^k terms, then A_0 = 01, A_ k+1 = A_k A_k B_k, where B_k is obtained from A_k by interchanging 0’s and 1’s.
  • A285198 (program): Binomial coefficients C(9,n).
  • A285201 (program): Stage at which Ken Knowlton’s elevator (version 1) reaches floor n for the first time.
  • A285203 (program): Local high points in A285200.
  • A285204 (program): Row lengths of triangle A285202.
  • A285305 (program): Fixed point of the morphism 0 -> 10, 1 -> 1001.
  • A285306 (program): Positions of 0 in A285305; complement of A285307.
  • A285307 (program): Positions of 1 in A285305; complement of A285306.
  • A285326 (program): a(0) = 0, for n > 0, a(n) = n + A006519(n).
  • A285329 (program): a(n) = A013928(A007947(n)).
  • A285351 (program): a(n) = 2n + 1 - A285346(n).
  • A285361 (program): The number of tight 3 X n pavings.
  • A285383 (program): Limiting 0-word of the morphism 0 -> 11, 1 -> 01.
  • A285384 (program): Limiting 1-word of the morphism 0 -> 11, 1 -> 01.
  • A285399 (program): Start with a single cell at coordinates (0, 0, 0), then iteratively subdivide the grid into 3 X 3 X 3 cells and remove the cells whose sum of modulo 2 coordinates is 0 or 2; a(n) is the number of cells after n iterations.
  • A285400 (program): Start with a single cell at coordinates (0, 0, 0), then iteratively subdivide the grid into 3 X 3 X 3 cells and remove the cells whose sum of modulo 2 coordinates is 0 or 3; a(n) is the number of cells after n iterations.
  • A285406 (program): Base-2 logarithm of denominator of Sum_ k=0..n^2-1 ((-1)^ksqrt(Pi)/(Gamma(1/2-k)Gamma(1+k)))/n).
  • A285440 (program): Consider the sums of the numbers < n that share the same greatest common divisor with n. Sequence lists numbers that have only one of those sums equal to n.
  • A285473 (program): Binary representation of the diagonal from the corner to the origin of the n-th stage of growth of the two-dimensional cellular automaton defined by “Rule 3”, based on the 5-celled von Neumann neighborhood.
  • A285474 (program): Binary representation of the diagonal from the origin to the corner of the n-th stage of growth of the two-dimensional cellular automaton defined by “Rule 3”, based on the 5-celled von Neumann neighborhood.
  • A285475 (program): Decimal representation of the diagonal from the origin to the corner of the n-th stage of growth of the two-dimensional cellular automaton defined by “Rule 3”, based on the 5-celled von Neumann neighborhood.
  • A285476 (program): Binary representation of the diagonal from the origin to the corner of the n-th stage of growth of the two-dimensional cellular automaton defined by “Rule 6”, based on the 5-celled von Neumann neighborhood.
  • A285524 (program): a(n) is the value d<n/2 maximizing the expression d!(d + 1)!(2^(n-2d-1)stirling2(n-d, d+1), for n>=4.
  • A285525 (program): The indices that mark the beginning of four consecutive equal terms in A285524.
  • A285526 (program): Terms of A285524 that mark the beginning of four consecutive equal values.
  • A285540 (program): Binary representation of the diagonal from the corner to the origin of the n-th stage of growth of the two-dimensional cellular automaton defined by “Rule 35”, based on the 5-celled von Neumann neighborhood.
  • A285542 (program): Decimal representation of the diagonal from the corner to the origin of the n-th stage of growth of the two-dimensional cellular automaton defined by “Rule 35”, based on the 5-celled von Neumann neighborhood.
  • A285612 (program): Binary representation of the diagonal from the corner to the origin of the n-th stage of growth of the two-dimensional cellular automaton defined by “Rule 62”, based on the 5-celled von Neumann neighborhood.
  • A285679 (program): Positions of 2 in A285677.
  • A285682 (program): Positions of 1 in A285680.
  • A285683 (program): Positions of 2 in A285680.
  • A285685 (program): Characteristic sequence of the Beatty sequence, A022839, of sqrt(5).
  • A285700 (program): a(n) = Number of iterations x -> 2x-1 needed to get a nonprime number, when starting with x = n.
  • A285703 (program): a(n) = A000203(A064216(n)).
  • A285704 (program): a(n) = A285703(n) - n = A000203(A064216(n)) - n.
  • A285705 (program): a(n) = 2n - A285703(n) = 2n - A000203(A064216(n)).
  • A285715 (program): a(n) = A000120(A245611(n)).
  • A285716 (program): a(n) = A080791(A245611(n)).
  • A285726 (program): a(1) = a(2) = 0; for n > 2, a(n) = A252736(n) - (1-A000035(n)).
  • A285738 (program): Greatest prime less than 2*n^2 for n > 1, a(1) = 1.
  • A285766 (program): Maximum spillway height for a zero or one bend minimal area lake in a number square.
  • A285779 (program): Parity index: number of integers z with 1 <= z <= n for which A010060(z) = A010060(n), negated if A010060(n) = 1.
  • A285869 (program): a(n) is the number of zeros of the Chebyshev S(n, x) polynomial in the open interval (-sqrt(2), +sqrt(2)).
  • A285870 (program): a(n) = floor(n/2) - floor((n+1)/6), n >= 0.
  • A285872 (program): a(n) is the number of zeros of the Chebyshev S(n, x) polynomial (A049310) in the open interval (-sqrt(3), +sqrt(3)).
  • A285879 (program): Number of odd squarefree numbers <= n.
  • A285881 (program): Number of even squarefree numbers <= n.
  • A285896 (program): Sum of divisors d of n such that n/d is not congruent to 0 mod 5.
  • A285899 (program): Total number of parts in all partitions of all positive integers <= n into consecutive parts.
  • A285900 (program): Sum of all parts of all partitions of all positive integers <= n into consecutive parts.
  • A285902 (program): Total number of partitions of all positive integers <= n into an even number of consecutive parts.
  • A285949 (program): 0->01, 1->0 -transform of the Thue-Morse word A010060.
  • A285950 (program): Positions of 0’s in A285949; complement of A285951.
  • A285951 (program): Positions of 1’s in A285949; complement of A285950.
  • A285952 (program): 0->1, 1->10 -transform of the Thue-Morse word A010060.
  • A285953 (program): Positions of 0 in A285952; complement of A285954.
  • A285954 (program): Positions of 1 in A285952; complement of A285953.
  • A285958 (program): Positions of 0 in A285957; complement of A285959.
  • A285962 (program): Positions of 1 in A285960; complement of A285961.
  • A285967 (program): Positions of 0 in A285966; complement of A285968.
  • A285974 (program): Positions of 1 in A285972; complement of A285973.
  • A285977 (program): Positions of 1 in A285975; complement of A285976.
  • A285982 (program): a(n) = n! (mod n + 3).
  • A285985 (program): Numbers a(n) = (T(b(n)))^2, where T(b(n)) is the triangular number of b(n)= A000217(b(n)) and b(n)=A006451(n). Also a(n) = parameters K of the Bachet Mordell equation y^2=x^3+K, where x= T(b(n)) = A006454(n) and y= T(b(n))* sqrt(T(b(n))+1) = A285955(n)
  • A285998 (program): a(n) = Sum_ k=0..floor(n/2) (n-k)*(k+1).
  • A285999 (program): Total number of odd divisors of all positive integers <= n, minus the total number of middle divisors of all positive integers <= n.
  • A286002 (program): a(n) = 2n - d(n), where d(n) is the number of divisors of n (A000005).
  • A286016 (program): Signed continued fraction expansion with all signs negative of tanh(1).
  • A286032 (program): a(n) = a(n-1) - n*a(n-2); a(0) = a(1) = 1.
  • A286033 (program): a(n) = binomial(2*n-2, n-1) + (-1)^n.
  • A286045 (program): Positions of 0 in A286044; complement of A003157.
  • A286062 (program): a(n) = 2*a(n-1) + a(n-2) - a(n-3), where a(0) = 2, a(1) = 3, a(2) = 6.
  • A286063 (program): Fixed point of the mapping 00->001, 1->100, starting with 00.
  • A286100 (program): Square array A(n,k): If n = k, then A(n,k) = n, otherwise 0, read by antidiagonals as A(1,1), A(1,2), A(2,1), A(1,3), A(2,2), A(3,1), etc.
  • A286183 (program): Number of connected induced (non-null) subgraphs of the antiprism graph with 2n nodes.
  • A286186 (program): Number of connected induced (non-null) subgraphs of the friendship graph with 2n+1 nodes.
  • A286191 (program): a(n) = (2^n-1)^2 + 2*n.
  • A286264 (program): a(n) = 2*(ceiling((n^2)/2)+1) - 1.
  • A286282 (program): Stage at which Ken Knowlton’s elevator (version 2) reaches floor n for the first time.
  • A286283 (program): a(n) = floor(7*n^2/48).
  • A286286 (program): a(0) = 0; thereafter, a(n) = (2n-1)a(n-1) + 1.
  • A286298 (program): a(0) = 0, a(1) = 1; thereafter, a(2n) = a(n) + 1 + (n mod 2), a(2n+1) = a(n) + 2 - (n mod 2).
  • A286357 (program): One more than the exponent of the highest power of 2 dividing sigma(n): a(n) = A001511(A000203(n)).
  • A286380 (program): a(n) = the minimum number of iterations of the reduced Collatz function R required to yield 1. The function R (A139391) is defined as R(k) = (3k+1)/2^r, with r as large as possible.
  • A286387 (program): a(n) = A002487(n^2).
  • A286429 (program): Highest elevation of an island above sea level in a number square.
  • A286430 (program): Least volume of water to surround the largest possible island in a number square.
  • A286437 (program): Number of ways to tile an n X n X n triangular area with two 2 X 2 X 2 triangular tiles and an appropriate number (= n^2-8) of 1 X 1 X 1 tiles.
  • A286444 (program): Number of non-equivalent ways to tile an n X n X n triangular area with two 2 X 2 X 2 triangular tiles and an appropriate number (= n^2-8) of 1 X 1 X 1 tiles.
  • A286507 (program): Binary representation of the diagonal from the corner to the origin of the n-th stage of growth of the two-dimensional cellular automaton defined by “Rule 190”, based on the 5-celled von Neumann neighborhood.
  • A286508 (program): Binary representation of the diagonal from the origin to the corner of the n-th stage of growth of the two-dimensional cellular automaton defined by “Rule 190”, based on the 5-celled von Neumann neighborhood.
  • A286519 (program): Binary representation of the diagonal from the origin to the corner (or of the corner to the origin) of the n-th stage of growth of the two-dimensional cellular automaton defined by “Rule 659”, based on the 5-celled von Neumann neighborhood.
  • A286521 (program): Decimal representation of the diagonal from the origin to the corner (or of the corner to the origin) of the n-th stage of growth of the two-dimensional cellular automaton defined by “Rule 659”, based on the 5-celled von Neumann neighborhood.
  • A286529 (program): a(n) = d(n+d(n)), where d(n) is the number of divisors of n (A000005).
  • A286546 (program): a(n) = A006068(n) - n.
  • A286548 (program): a(n) = A003188(n) - n.
  • A286577 (program): If n = 3k-1 then a(n) = a(k), otherwise a(n) = n.
  • A286582 (program): a(n) = A001222(A048673(n)).
  • A286583 (program): a(n) = A007814(A048673(n)).
  • A286584 (program): a(n) = A048673(n) mod 4.
  • A286585 (program): a(n) = A053735(A048673(n)).
  • A286630 (program): a(0) = 1; for n >= 1, a(n) = A000040(n) * A002110(n).
  • A286655 (program): Characteristic sequence of the Beatty sequence, A022842, of sqrt(8).
  • A286665 (program): 0->01 -transform of the Pell word, A171588.
  • A286666 (program): Positions of 0 in A286665; complement of A286667.
  • A286667 (program): Positions of 1 in A286665; complement of A286666.
  • A286679 (program): Numbers of the form (2*prime(n)^2 + 1)/3.
  • A286685 (program): 0->01, 1->10 -transform of the Pell word, A171588.
  • A286686 (program): Positions of 0 in A286685; complement of A286687.
  • A286687 (program): Positions of 1 in A286685; complement of A286686.
  • A286688 (program): 0->00, 1->10 -transform of the Pell word, A171588.
  • A286689 (program): Positions of 0 in A286688; complement of A286690.
  • A286690 (program): Positions of 1 in A286688; complement of A286689.
  • A286692 (program): Positions of 0 in A286691; complement of A286693.
  • A286716 (program): a(n) = floor(n/2) - floor((n+1)/5), n >= 0.
  • A286717 (program): a(n) is the number of zeros of the Chebyshev S(n, x) polynomial (A049310) in the open interval (-phi, +phi), with the golden section phi = (1 + sqrt(5))/2.
  • A286725 (program): Third column of triangle A286724: Lah2,1, n >= 0.
  • A286726 (program): 0->10, 1->01 -transform of the Pell word, A171588.
  • A286727 (program): Positions of 0 in A286063; complement of A286728.
  • A286728 (program): Positions of 1 in A286063; complement of A286727.
  • A286748 (program): Characteristic sequence of the Beatty sequence, A194028, of sqrt(12).
  • A286750 (program): Positions of 0 in A286749; complement of A286751.
  • A286751 (program): Positions of 1 in A286749; complement of A286750.
  • A286752 (program): 010010->null -transform of the infinite Fibonacci word A003849.
  • A286753 (program): Positions of 0 in A286752; complement of A286753.
  • A286754 (program): Positions of 1 in A286752; complement of A286753.
  • A286770 (program): Binary representation of the diagonal from the corner to the origin of the n-th stage of growth of the two-dimensional cellular automaton defined by “Rule 221”, based on the 5-celled von Neumann neighborhood.
  • A286772 (program): Decimal representation of the diagonal from the corner to the origin of the n-th stage of growth of the two-dimensional cellular automaton defined by “Rule 221”, based on the 5-celled von Neumann neighborhood.
  • A286773 (program): Decimal representation of the diagonal from the origin to the corner of the n-th stage of growth of the two-dimensional cellular automaton defined by “Rule 221”, based on the 5-celled von Neumann neighborhood.
  • A286778 (program): Sum of the common path length over all 2-tuples of nodes in a complete binary tree of height n.
  • A286806 (program): Positions of 1 in A286804; complement of A286805.
  • A286807 (program): Fixed point of the mapping 00->001, 1->101, starting with 00.
  • A286808 (program): Positions of 0 in A286807; complement of A286809.
  • A286809 (program): Positions of 1 in A286807; complement of A286808.
  • A286810 (program): Number of non-attacking bishop positions on a cylindrical 2 X 2n chessboard.
  • A286812 (program): a(n) = 105 - 2^n.
  • A286814 (program): Number of matchings in the n-helm graph.
  • A286863 (program): Binary representation of the diagonal from the corner to the origin of the n-th stage of growth of the two-dimensional cellular automaton defined by “Rule 814”, based on the 5-celled von Neumann neighborhood.
  • A286865 (program): Decimal representation of the diagonal from the corner to the origin of the n-th stage of growth of the two-dimensional cellular automaton defined by “Rule 814”, based on the 5-celled von Neumann neighborhood.
  • A286874 (program): Maximal number of binary vectors of length n such that the union (or bitwise OR) of any 2 distinct vectors does not contain any other vector.
  • A286888 (program): Floor of the average gap between consecutive primes among the first n primes, for n > 1.
  • A286904 (program): Positions of 0 in A286903; complement of A286905.
  • A286905 (program): Positions of 1 in A286903; complement of A286904.
  • A286907 (program): 0->00,1->01 -transform of the Sturmian word A080764.
  • A286909 (program): Positions of 1 in A286907; complement of A286908.
  • A286923 (program): Positions of 0 in A286922; complement of A286924.
  • A286924 (program): Positions of 1 in A286922; complement of A286923.
  • A286925 (program): 0->01,1->00 -transform of the Sturmian word A080764.
  • A286926 (program): Positions of 0 in A286925; complement of A286927.
  • A286927 (program): Positions of 1 in A286925; complement of A286926.
  • A286930 (program): Integers whose double is a square and whose triple is a cube.
  • A286986 (program): Number of connected dominating sets in the n-antiprism graph.
  • A286988 (program): Positions of 0 in A286987; complement of A286989.
  • A287015 (program): Lucas numbers written in base 2.
  • A287057 (program): a(n) = 2*n^2 + n - (n+1) mod 2.
  • A287190 (program): Binary representation of the diagonal from the corner to the origin of the n-th stage of growth of the two-dimensional cellular automaton defined by “Rule 253”, based on the 5-celled von Neumann neighborhood.
  • A287191 (program): Binary representation of the diagonal from the origin to the corner of the n-th stage of growth of the two-dimensional cellular automaton defined by “Rule 253”, based on the 5-celled von Neumann neighborhood.
  • A287192 (program): Decimal representation of the diagonal from the corner to the origin of the n-th stage of growth of the two-dimensional cellular automaton defined by “Rule 253”, based on the 5-celled von Neumann neighborhood.
  • A287193 (program): Decimal representation of the diagonal from the origin to the corner of the n-th stage of growth of the two-dimensional cellular automaton defined by “Rule 253”, based on the 5-celled von Neumann neighborhood.
  • A287194 (program): Binary representation of the diagonal from the corner to the origin of the n-th stage of growth of the two-dimensional cellular automaton defined by “Rule 259”, based on the 5-celled von Neumann neighborhood.
  • A287195 (program): Independence and clique covering number of the n-triangular honeycomb acute knight graph.
  • A287197 (program): Decimal representation of the diagonal from the corner to the origin of the n-th stage of growth of the two-dimensional cellular automaton defined by “Rule 259”, based on the 5-celled von Neumann neighborhood.
  • A287272 (program): a(n) is the number of zeros of the Laguerre L(n, x) polynomial in the open interval (-1, +1).
  • A287275 (program): Number of set partitions of [n] such that for each block all absolute differences between consecutive elements are <= three.
  • A287326 (program): Triangle read by rows: T(n, k) = 6k(n-k) + 1; n >= 0, 0 <= k <= n.
  • A287327 (program): Number of independent vertex sets (and vertex covers) in the 2n-crossed prism graph.
  • A287335 (program): Nonnegative numbers k such that 3*k + 2 is a cube.
  • A287349 (program): Number of matchings in the n-gear graph.
  • A287381 (program): a(n) = a(n-1) + 2*a(n-2) - a(n-3), where a(0) = 2, a(1) = 4, a(2) = 7.
  • A287392 (program): Domination number for lion’s graph on an n X n board.
  • A287393 (program): Domination number for knight’s graph on a 2 X n board.
  • A287394 (program): Domination number for camel’s graph on a 2 X n board.
  • A287425 (program): Number of maximal matchings in the n-gear graph.
  • A287426 (program): Number of connected induced subgraphs in the n-sun graph.
  • A287431 (program): Number of connected dominating sets in the n-gear graph.
  • A287435 (program): Positions of 0 in A053838.
  • A287436 (program): Positions of 1 in A053838.
  • A287437 (program): Positions of 2 in A053838.
  • A287451 (program): Start with 0 and repeatedly substitute 0->012, 1->201, 2->120.
  • A287468 (program): Binary representation of the diagonal from the corner to the origin of the n-th stage of growth of the two-dimensional cellular automaton defined by “Rule 276”, based on the 5-celled von Neumann neighborhood.
  • A287470 (program): Decimal representation of the diagonal from the origin to the corner of the n-th stage of growth of the two-dimensional cellular automaton defined by “Rule 276”, based on the 5-celled von Neumann neighborhood.
  • A287479 (program): Expansion of (x + x^2)/(1 + 3*x^2).
  • A287523 (program): Fixed point starting with 1 of the morphism 0->01, 1->101.
  • A287533 (program): Fibonacci numbers modulo 20.
  • A287549 (program): Total number of unordered factorizations of all positive integers <= n into distinct factors greater than 1.
  • A287552 (program): Positions of 0 in A053839.
  • A287553 (program): Positions of 1 in A053839.
  • A287554 (program): Positions of 2 in A053839.
  • A287555 (program): Positions of 3 in A053839.
  • A287594 (program): Number of independent vertex sets in the n-helm graph.
  • A287657 (program): 0->01, 1->10 -transform of the infinite Fibonacci word A003849.
  • A287658 (program): Positions of 0 in A287657; complement of A287659.
  • A287659 (program): Positions of 1 in A287657; complement of A287658.
  • A287664 (program): Positions of 0’s in A287663; complement of A287665.
  • A287665 (program): Positions of 1’s in A287663; complement of A287664.
  • A287675 (program): Positions of 0 in A287674; complement of A287676.
  • A287676 (program): Positions of 1 in A287674; complement of A287675.
  • A287702 (program): a(n) = (3!)^3 * [z^3] hypergeom([], [1,1], z)^n.
  • A287724 (program): Positions of 1 in A287722; complement of A287723.
  • A287726 (program): Positions of 0 in A287725; complement of A287727.
  • A287733 (program): First differences of A069497.
  • A287742 (program): Binary representation of the diagonal from the corner to the origin of the n-th stage of growth of the two-dimensional cellular automaton defined by “Rule 342”, based on the 5-celled von Neumann neighborhood.
  • A287744 (program): Decimal representation of the diagonal from the corner to the origin of the n-th stage of growth of the two-dimensional cellular automaton defined by “Rule 342”, based on the 5-celled von Neumann neighborhood.
  • A287746 (program): First differences of A154293.
  • A287765 (program): Period 4: repeat [1, 3, 5, 3].
  • A287774 (program): Positions of 0 in A287773; complement of A287777.
  • A287775 (program): Positions of 0 in A287772; complement of A050140 (conjectured and proved).
  • A287802 (program): Positions of 0 in A287801; complement of A287803.
  • A287803 (program): Positions of 1 in A287801; complement of A287802.
  • A287807 (program): Number of senary sequences of length n such that no two consecutive terms have distance 2.
  • A287841 (program): Number of iterations of number of distinct prime factors (A001221) needed to reach 1 starting at n (n is counted).
  • A287864 (program): Consider a symmetric pyramid-shaped chessboard with rows of squares of lengths n, n-2, n-4, …, ending with either 2 or 1 squares; a(n) is the maximal number of mutually non-attacking queens that can be placed on this board.
  • A287866 (program): n - A274933(n).
  • A287867 (program): Floor(n/2) - A287864(n).
  • A287893 (program): a(n) = floor(n*(n+2)/9).
  • A287922 (program): a(n) = prime(1)^2 + prime(n)^2.
  • A287925 (program): a(n) = prime(1)^4 + prime(n)^4
  • A288023 (program): Number of steps to reach 1 in the Collatz 3x+1 problem starting with the n-th triangular number, or -1 if 1 is never reached.
  • A288035 (program): Number of (undirected) paths in the complete bipartite graph K_n,n.
  • A288038 (program): Number of independent vertex sets in the n-Andrasfai graph.
  • A288040 (program): Integers whose number of distinct decimal digits is prime.
  • A288132 (program): Fixed point of the mapping 00->0010, 1->11, starting with 00.
  • A288133 (program): Positions of 0 in A288132; complement of A288134.
  • A288134 (program): Positions of 1 in A288132; complement of A288133.
  • A288156 (program): Two even followed by three odd integers: the pattern is (0+2k,0+2k,1+2k,1+2k,1+2k) for k>=0.
  • A288170 (program): a(n) = 3a(n-1) - a(n-2) - 4a(n-3) + 2*a(n-4) for n >= 4, where a(0) = 2, a(1) = 4, a(2) = 8, a(3) = 16, a(4) = 34, a(5) = 70 .
  • A288196 (program): Decimal representation of the diagonal from the corner to the origin of the n-th stage of growth of the two-dimensional cellular automaton defined by “Rule 430”, based on the 5-celled von Neumann neighborhood.
  • A288203 (program): Fixed point of the mapping 00->0010, 1->010, starting with 00.
  • A288204 (program): Positions of 0 in A288203; complement of A288205.
  • A288205 (program): Positions of 1 in A288203; complement of A288204.
  • A288206 (program): a(n) = 3a(n-1) - a(n-2) - 3a(n-3) + 2*a(n-4), where a(0) = 2, a(1) = 4, a(2) = 8, a(3) = 18.
  • A288213 (program): Fixed point of the mapping 00->0010, 1->011, starting with 00.
  • A288219 (program): a(n) = a(n-1) + a(n-2) for n >= 3, where a(0) = 2, a(1) = 4, a(2) = 7.
  • A288309 (program): a(n) = 2a(n-1) + 2a(n-2) - 3*a(n-3), where a(0) = 2, a(1) = 4, a(2) = 8.
  • A288327 (program): Decuple factorial, 10-factorial, n!10, n!!!!!!!!!!.
  • A288349 (program): Partial sums of A059268.
  • A288381 (program): Fixed point of the mapping 00->0001, 1->11, starting with 00.
  • A288382 (program): Positions of 0 in A288381; complement of A288383.
  • A288383 (program): Positions of 1 in A288381; complement of A288382.
  • A288429 (program): a(n) = 2*a(n-1) - a(n-2) + a(n-3) - a(n-4), where a(0) = 2, a(1) = 4, a(2) = 5, a(3) = 6.
  • A288443 (program): a(n) = (2n + 1)2^(2n + 1); numbers k such that v(k)2^v(k) = k, where v(n) = A007814(n) is 2-adic valuation of n.
  • A288465 (program): a(n) = 2*a(n-1) - a(n-4), where a(0) = 2, a(1) = 4, a(2) = 6, a(3) = 10.
  • A288469 (program): a(n) = n if n is a nonprime, otherwise take the prime index of n and repeat until you get a nonprime which is then a(n).
  • A288477 (program): a(n) = (2^49 - 2)*n/3 + 247371098957.
  • A288486 (program): Square rings obtained by adding four identical cuboids from A169938, a(n) = 4n(n+1)(n(n+1)+1).
  • A288487 (program): Cuboids that fit in square rings from A288486 obtaining a fifth power.
  • A288492 (program): Indices of terms of A288349 that are powers of 2.
  • A288516 (program): Number of (undirected) paths in the ladder graph P_2 X P_n.
  • A288534 (program): a(n) = n(2n^2 + 3), n >= 1; a(0)=1.
  • A288599 (program): a(n) = 2*a(n-1) - a(n-4) for n >= 4, where a(0) = 2, a(1) = 4, a(2) = 6, a(3) = 10, a(4) = 16.
  • A288601 (program): Positions of 0 in A288600; complement of A288602.
  • A288602 (program): Positions of 1 in A288600; complement of A288601.
  • A288603 (program): a(n) = 2*a(n-1) - a(n-3) for n >= 3, where a(0) = 2, a(1) = 4, a(2) = 6, a(3) = 8.
  • A288604 (program): a(n) = (n^9 - n)/10.
  • A288625 (program): Positions of 0 in A288375; complement of A283794.
  • A288636 (program): Height of power-tower factorization of n. Row lengths of A278028.
  • A288663 (program): Decimal representation of the diagonal from the corner to the origin of the n-th stage of growth of the two-dimensional cellular automaton defined by “Rule 493”, based on the 5-celled von Neumann neighborhood.
  • A288687 (program): Number of n-digit biquanimous strings using digits 0,1,2,3 .
  • A288697 (program): Binary representation of the diagonal from the corner to the origin of the n-th stage of growth of the two-dimensional cellular automaton defined by “Rule 494”, based on the 5-celled von Neumann neighborhood.
  • A288699 (program): Decimal representation of the diagonal from the corner to the origin of the n-th stage of growth of the two-dimensional cellular automaton defined by “Rule 494”, based on the 5-celled von Neumann neighborhood.
  • A288700 (program): Decimal representation of the diagonal from the origin to the corner of the n-th stage of growth of the two-dimensional cellular automaton defined by “Rule 494”, based on the 5-celled von Neumann neighborhood.
  • A288707 (program): 0-limiting word of the mapping 00->1000, 10->00, starting with 00.
  • A288709 (program): Positions of 1’s in A288707; complement of A288708.
  • A288711 (program): 1-limiting word of the mapping 00->1000, 10->00, starting with 00.
  • A288713 (program): Positions of 1 in A288711; complement of A288712.
  • A288732 (program): a(n) = a(n-1) + 2a(n-4) - 2a(n-5) for n >= 5, where a(0) = 2, a(1) = 4, a(2) = 6, a(3) = 8, a(4) = 10.
  • A288773 (program): a(n) is the largest of all positive integers whose partitions into consecutive parts can be totally represented in the first n rows of the table described in A286000.
  • A288774 (program): a(n) is the largest positive integers whose partitions into consecutive parts can be totally represented in the first n rows of the table described in A286000.
  • A288780 (program): Zero together with the row sums of A288778.
  • A288795 (program): a(n) = 4^n + 3^(n + 1) - 2.
  • A288825 (program): Binary representation of the diagonal from the corner to the origin of the n-th stage of growth of the two-dimensional cellular automaton defined by “Rule 515”, based on the 5-celled von Neumann neighborhood.
  • A288826 (program): Binary representation of the diagonal from the origin to the corner of the n-th stage of growth of the two-dimensional cellular automaton defined by “Rule 515”, based on the 5-celled von Neumann neighborhood.
  • A288827 (program): Decimal representation of the diagonal from the corner to the origin of the n-th stage of growth of the two-dimensional cellular automaton defined by “Rule 515”, based on the 5-celled von Neumann neighborhood.
  • A288828 (program): Decimal representation of the diagonal from the origin to the corner of the n-th stage of growth of the two-dimensional cellular automaton defined by “Rule 515”, based on the 5-celled von Neumann neighborhood.
  • A288834 (program): a(n) = (n+1) * 3^(n-1).
  • A288835 (program): a(n) = (1/2!)3^n(n+3)*(n).
  • A288836 (program): a(n) = (1/3!)3^(n+1)(n+5)(n+1)(n).
  • A288876 (program): a(n) = binomial(n+4, n)^2. Square of the fifth diagonal sequence of A007318 (Pascal). Fifth diagonal sequence of A008459.
  • A288913 (program): a(n) = Lucas(4*n + 3).
  • A288918 (program): Number of 4-cycles in the n X n king graph.
  • A288919 (program): Number of 5-cycles in the n X n king graph.
  • A288930 (program): Positions of 0 in A288929; complement of A288931.
  • A288932 (program): Fixed point of the mapping 00->1000, 10->10101, starting with 00.
  • A288933 (program): Positions of 0 in A288932; complement of A288934.
  • A288934 (program): Positions of 1 in A288932; complement of A288933.
  • A288937 (program): Positions of 0 in A288936; complement of A288938.
  • A288938 (program): Positions of 1 in A288936; complement of A288937.
  • A288958 (program): Number of cliques in the n X n rook graph.
  • A288959 (program): a(n) = n^2*(n^2 - 1)^2/2.
  • A288961 (program): Number of 3-cycles in the n X n rook graph.
  • A288962 (program): Number of 4-cycles in the n X n rook graph.
  • A288963 (program): Number of 5-cycles in the n X n rook graph.
  • A288966 (program): a(n) = the number of iterations the “HyperbolaTiles” algorithm takes to factorize n.
  • A288994 (program): a(n) = n(n+3) when n is congruent to 0 or 3 (mod 4), and n(n+3)/2 otherwise.
  • A288997 (program): Fixed point of the mapping 00->0010, 01->001, 10->001, starting with 00.
  • A288998 (program): Positions of 0 in A288997; complement of A288999.
  • A288999 (program): Positions of 1 in A288997; complement of A288998.
  • A289001 (program): Fixed point of the mapping 00->0010, 01->001, 10->010, starting with 00.
  • A289034 (program): Fixed point of the morphism 0->010, 1->10 starting with 1.
  • A289036 (program): Positions of 0 in A289035; complement of A289037.
  • A289037 (program): Positions of 1 in A289035; complement of A289036.
  • A289060 (program): a(n) = 3a(n-1) - 3a(n-2) + *a(n-3) for n >= 8, where a(0) = 2, a(1) = 4, a(2) = 7, a(3) = 11, a(4) = 17, a(5) = 25, a(6) = 36, a(7) = 51.
  • A289098 (program): Decimal representation of the diagonal from the corner to the origin of the n-th stage of growth of the two-dimensional cellular automaton defined by “Rule 545”, based on the 5-celled von Neumann neighborhood.
  • A289111 (program): a(n) = (2^49 - 2)*n/3 + 444813635231.
  • A289120 (program): a(n) is the number of odd integers divisible by 7 in ]2(n-1)^2, 2n^2[.
  • A289121 (program): a(n) = (8 - 2n + 11n^2 - 6*n^3 + n^4)/4.
  • A289122 (program): a(n) is number of odd integers divisible by 11 in the interval ]2(n-1)^2, 2n^2[.
  • A289133 (program): a(n) is the number of odd integers divisible by 9 in ]2(n-1)^2, 2n^2[.
  • A289134 (program): a(n) = 21n^2 - 33n + 13.
  • A289139 (program): a(n) is the number of odd integers divisible by 7 in ]4(n-1)^2, 4n^2[.
  • A289144 (program): The difference between the second divisor of n and the penultimate divisor of n.
  • A289156 (program): Largest area of triangles with integer sides and area = n times perimeter.
  • A289161 (program): Number of 3-cycles in the n X n black bishop graph.
  • A289179 (program): Edge count of the n X n white bishop graph.
  • A289189 (program): Upper bound for certain restricted sumsets.
  • A289195 (program): a(n) is the number of odd integers divisible by 5 in ]4(n-1)^2, 4n^2[.
  • A289199 (program): a(n) is the number of odd integers divisible by 13 in the open interval (12(n-1)^2, 12n^2).
  • A289203 (program): Number of maximum independent vertex sets in the n X n knight graph.
  • A289207 (program): a(n) = max(0, n-2).
  • A289223 (program): Number of ways to select 2 disjoint point triples from an n X n X n triangular point grid, each point triple forming an 2 X 2 X 2 triangle.
  • A289254 (program): a(n) = 4^n - 3*n - 1.
  • A289255 (program): a(n) = 4^n - 2*n - 1.
  • A289296 (program): a(n) = (n - 1)(2floor(n/2) + 1).
  • A289356 (program): Least number k such that n^2 + n + k is prime.
  • A289357 (program): Least number k such that n^2 + n - k is prime.
  • A289382 (program): a(n) = 2^n mod triangular(n).
  • A289399 (program): Total path length of the complete ternary tree of height n.
  • A289404 (program): Binary representation of the diagonal from the corner to the origin of the n-th stage of growth of the two-dimensional cellular automaton defined by “Rule 566”, based on the 5-celled von Neumann neighborhood.
  • A289437 (program): The arithmetic function v_2(n,4).
  • A289443 (program): a(0)=2, a(1)=6; thereafter a(n) = 3*n^2.
  • A289451 (program): Related to number of mesh patterns of length 2 that avoid the pattern 231.
  • A289521 (program): Number of vertices in a planar Apollonian graph at iteration n.
  • A289615 (program): A246604 (Catalan(n)-n) with initial terms 1,0,0,2 changed to 1,1,1,3.
  • A289617 (program): a(n) = A005187(A001222(n)).
  • A289642 (program): Number of 2-digit numbers whose digits add up to n.
  • A289643 (program): n(2n+1)*binomial(n+2,n)/3.
  • A289652 (program): Catalan numbers - 2 (A120304) with first three terms changed to 1,1,1.
  • A289653 (program): Catalan numbers - 2 (A120304) with first four terms changed to 1,1,1,4.
  • A289682 (program): Catalan numbers read modulo 16.
  • A289692 (program): The number of partitions of [n] with exactly 2 blocks without peaks.
  • A289715 (program): The order of the semigroup of orientation-preserving full transformations on n elements.
  • A289719 (program): a(n) = (n/2)binomial(2n, n) + 1.
  • A289721 (program): Let a(0)=1. Then a(n) = sums of consecutive strings of positive integers of length 3*n, starting with the integer 2.
  • A289744 (program): Coefficients in expansion of q*E’_8 where E_8 is the Eisenstein Series (A008410).
  • A289745 (program): Coefficients in expansion of -q*E’_10 where E_10 is the Eisenstein Series (A013974).
  • A289746 (program): Coefficients in expansion of -q*E’_14 where E_14 is the Eisenstein Series (A058550).
  • A289748 (program): Thue-Morse constant converted to base -2.
  • A289761 (program): Maximum length of a perfect Wichmann ruler with n segments.
  • A289764 (program): Decimal representation of the diagonal from the corner to the origin of the n-th stage of growth of the two-dimensional cellular automaton defined by “Rule 597”, based on the 5-celled von Neumann neighborhood.
  • A289812 (program): n for which a Factor Pair Latin Square of order n exists.
  • A289814 (program): A binary encoding of the twos in ternary representation of n (see Comments for precise definition).
  • A289849 (program): Cardinality of the maximal set of ordered factor pairs such that a Quasi-Factor Pair Latin Square of order n exists.
  • A289870 (program): a(n) = n(n + 1) for n odd, otherwise a(n) = (n - 1)(n + 1).
  • A289873 (program): Related to perfect Wichmann rulers: a(n) = ( n^2 - (mod(n, 6) - 3)^2 ) / 3.
  • A289877 (program): Number of maximal cliques in the n-triangular honeycomb queen graph.
  • A289896 (program): Number of (undirected) cycles in the n-triangular honeycomb rook graph.
  • A289945 (program): a(n) = Sum_ k=1..n k!^4.
  • A289948 (program): a(n) = Sum_ k=0..n k!^3.
  • A289949 (program): a(n) = Sum_ k=0..n k!^4.
  • A289999 (program): Sierpinski cuboctahedral numbers: a(n) = 164^n - 122^n + 9.
  • A290026 (program): Number of 3-cycles in the n-halved cube graph.
  • A290031 (program): Number of 6-cycles in the n-hypercube graph.
  • A290055 (program): Expansion of x(1 + 4x + x^2)/((1 - x)^5*(1 + x)^4).
  • A290056 (program): Number of cliques in the n-triangular graph.
  • A290059 (program): a(n) = binomial(2*prime(n)-1, prime(n)-1) where prime(n) is the n-th prime.
  • A290061 (program): a(n) = (1/24)(n + 3)(3n^3 + 5n^2 - 6*n + 16).
  • A290073 (program): Decimal representation of the diagonal from the corner to the origin of the n-th stage of growth of the two-dimensional cellular automaton defined by “Rule 641”, based on the 5-celled von Neumann neighborhood.
  • A290074 (program): Decimal representation of the diagonal from the origin to the corner of the n-th stage of growth of the two-dimensional cellular automaton defined by “Rule 641”, based on the 5-celled von Neumann neighborhood.
  • A290080 (program): a(1) = 0; for n > 1, a(n) = sigma(bigomega(n)).
  • A290111 (program): Binary representation of the diagonal from the corner to the origin of the n-th stage of growth of the two-dimensional cellular automaton defined by “Rule 643”, based on the 5-celled von Neumann neighborhood.
  • A290112 (program): Binary representation of the diagonal from the origin to the corner of the n-th stage of growth of the two-dimensional cellular automaton defined by “Rule 643”, based on the 5-celled von Neumann neighborhood.
  • A290113 (program): Decimal representation of the diagonal from the corner to the origin of the n-th stage of growth of the two-dimensional cellular automaton defined by “Rule 643”, based on the 5-celled von Neumann neighborhood.
  • A290114 (program): Decimal representation of the diagonal from the origin to the corner of the n-th stage of growth of the two-dimensional cellular automaton defined by “Rule 643”, based on the 5-celled von Neumann neighborhood.
  • A290124 (program): a(n) = a(n-1) + 12*a(n-2) with a(1) = 1 and a(2) = 2.
  • A290140 (program): The number of maximal subsemigroups of the Jones monoid on the set [1..n].
  • A290148 (program): a(n) is the integer resulting from the concatenation of the unit digit of n-1 to the digits of n without its own unit digit.
  • A290168 (program): If n is even then a(n) = n^2(n+2)/8, otherwise a(n) = (n-1)n*(n+1)/8.
  • A290191 (program): Binary representation of the diagonal from the corner to the origin of the n-th stage of growth of the two-dimensional cellular automaton defined by “Rule 673”, based on the 5-celled von Neumann neighborhood.
  • A290196 (program): Binary representation of the diagonal from the corner to the origin of the n-th stage of growth of the two-dimensional cellular automaton defined by “Rule 721”, based on the 5-celled von Neumann neighborhood.
  • A290197 (program): Binary representation of the diagonal from the origin to the corner of the n-th stage of growth of the two-dimensional cellular automaton defined by “Rule 721”, based on the 5-celled von Neumann neighborhood.
  • A290198 (program): Decimal representation of the diagonal from the corner to the origin of the n-th stage of growth of the two-dimensional cellular automaton defined by “Rule 721”, based on the 5-celled von Neumann neighborhood.
  • A290199 (program): Decimal representation of the diagonal from the origin to the corner of the n-th stage of growth of the two-dimensional cellular automaton defined by “Rule 721”, based on the 5-celled von Neumann neighborhood.
  • A290233 (program): Binary representation of the diagonal from the origin to the corner of the n-th stage of growth of the two-dimensional cellular automaton defined by “Rule 773”, based on the 5-celled von Neumann neighborhood.
  • A290235 (program): Decimal representation of the diagonal from the origin to the corner of the n-th stage of growth of the two-dimensional cellular automaton defined by “Rule 773”, based on the 5-celled von Neumann neighborhood.
  • A290251 (program): a(n) is the number of parts in the integer partition having viabin number n.
  • A290254 (program): The viabin numbers of the self-conjugate integer partitions.
  • A290255 (program): Number of 0’s following directly the first 1 in the binary representation of n.
  • A290256 (program): a(n) is the number of parts equal to 1 in the integer partition having viabin number n.
  • A290257 (program): a(n) is the size of the Durfee square of the integer partition having viabin number n.
  • A290268 (program): Number of terms in the fully expanded n-th derivative of x^(x^2).
  • A290312 (program): Third diagonal sequence of the Sheffer triangle A094816 (special Charlier).
  • A290325 (program): Number of minimal dominating sets (and maximal irredundant sets) in the complete tripartite graph K_ n,n,n .
  • A290391 (program): Number of 5-cycles in the n-triangular honeycomb obtuse knight graph.
  • A290452 (program): Triangle formed by reading the triangle of Eulerian numbers (A173018) mod 2.
  • A290479 (program): Product of nonprime squarefree divisors of n.
  • A290506 (program): Decimal expansion of 1 - 1/e^(1/2).
  • A290561 (program): a(n) = n + cos(n*Pi/2).
  • A290562 (program): a(n) = n - cos(n*Pi/2).
  • A290599 (program): Number of numbers from 1 to A002808(n) - 1 that are non-coprime to A002808(n).
  • A290604 (program): a(0) = 2, a(1) = 2; for n > 1, a(n) = a(n-1) + 2*a(n-2) + 3.
  • A290631 (program): a(n) = (n^2 + 1) * (2*n - 1).
  • A290651 (program): a(n) = 5 - 2^(n - 1) + 3^(n - 1) + n - 2.
  • A290660 (program): Binary representation of the diagonal from the corner to the origin of the n-th stage of growth of the two-dimensional cellular automaton defined by “Rule 899”, based on the 5-celled von Neumann neighborhood.
  • A290662 (program): Decimal representation of the diagonal from the origin to the corner of the n-th stage of growth of the two-dimensional cellular automaton defined by “Rule 899”, based on the 5-celled von Neumann neighborhood.
  • A290681 (program): Binary representation of the diagonal from the origin to the corner of the n-th stage of growth of the two-dimensional cellular automaton defined by “Rule 929”, based on the 5-celled von Neumann neighborhood.
  • A290682 (program): Decimal representation of the diagonal from the corner to the origin of the n-th stage of growth of the two-dimensional cellular automaton defined by “Rule 929”, based on the 5-celled von Neumann neighborhood.
  • A290683 (program): Decimal representation of the diagonal from the origin to the corner of the n-th stage of growth of the two-dimensional cellular automaton defined by “Rule 929”, based on the 5-celled von Neumann neighborhood.
  • A290699 (program): a(n) = 2^n - n + n^2.
  • A290707 (program): a(n) = 2^(n+1) + n^2 - 1.
  • A290709 (program): Number of irredundant sets in the complete tripartite graph K_ n,n,n .
  • A290718 (program): a(n) = 2^(n + 1) + 4^(n - 1) - 2.
  • A290721 (program): a(n) = 4^n - n - 1.
  • A290743 (program): Maximum number of distinct Lyndon factors that can appear in words of length n over an alphabet of size 2.
  • A290744 (program): Maximum number of distinct Lyndon factors that can appear in words of length n over an alphabet of size 5.
  • A290745 (program): Maximum number of distinct Lyndon factors that can appear in words of length n over an alphabet of size 10.
  • A290764 (program): Number of (non-null) connected induced subgraphs in the 2 X n king graph.
  • A290768 (program): a(n) = 3/2*(n^2 - n + 2).
  • A290781 (program): a(n) = 20*n + 15.
  • A290829 (program): Decimal representation of the diagonal from the origin to the corner of the n-th stage of growth of the two-dimensional cellular automaton defined by “Rule 961”, based on the 5-celled von Neumann neighborhood.
  • A290856 (program): Binary representation of the diagonal from the corner to the origin of the n-th stage of growth of the two-dimensional cellular automaton defined by “Rule 1006”, based on the 5-celled von Neumann neighborhood.
  • A290858 (program): Decimal representation of the diagonal from the corner to the origin of the n-th stage of growth of the two-dimensional cellular automaton defined by “Rule 1006”, based on the 5-celled von Neumann neighborhood.
  • A290859 (program): Decimal representation of the diagonal from the origin to the corner of the n-th stage of growth of the two-dimensional cellular automaton defined by “Rule 1006”, based on the 5-celled von Neumann neighborhood.
  • A290890 (program): p-INVERT of the positive integers, where p(S) = 1 - S^2.
  • A290902 (program): p-INVERT of the positive integers, where p(S) = 1 - 3*S.
  • A290903 (program): p-INVERT of the positive integers, where p(S) = 1 - 5*S.
  • A290908 (program): p-INVERT of the positive integers, where p(S) = 1 - 4*S^2.
  • A290917 (program): p-INVERT of the positive integers, where p(S) = (1 - S)^2.
  • A290922 (program): p-INVERT of the positive integers, where p(S) = 1 - S - 2*S^2.
  • A290953 (program): The number of permutations in S_n for which the number of reduced words is maximized with respect to the numbers of braid and commutation classes: R(w) = B(w) * C(w) .
  • A290959 (program): Matrix rank of the number of dots in the pairwise intersections of Ferrers diagrams.
  • A290988 (program): The arithmetic function v+-(n,3).
  • A291000 (program): p-INVERT of (1,1,1,1,1,…), where p(S) = 1 - S - S^2 - S^3.
  • A291004 (program): p-INVERT of (1,1,1,1,1,…), where p(S) = (1 - 3*S)^2.
  • A291008 (program): p-INVERT of (1,1,1,1,1,…), where p(S) = 1 - 7*S^2.
  • A291009 (program): p-INVERT of (1,1,1,1,1,…), where p(S) = (1 - S)(1 - 3 S).
  • A291010 (program): p-INVERT of (1,1,1,1,1,…), where p(S) = (1 - 2 S)(1 - 3 S).
  • A291011 (program): p-INVERT of (1,1,1,1,1,…), where p(S) = (1 - S)^2 (1 - 2 S).
  • A291012 (program): p-INVERT of (1,1,1,1,1,…), where p(S) = (1 - S^2)(1 - 2 S).
  • A291015 (program): p-INVERT of (1,1,1,1,1,…), where p(S) = (1 - S^3)^2.
  • A291016 (program): p-INVERT of (1,1,1,1,1,…), where p(S) = 1 - 4 S + S^2.
  • A291017 (program): p-INVERT of (1,1,1,1,1,…), where p(S) = 1 - 5 S + S^2.
  • A291018 (program): p-INVERT of (1,1,1,1,1,…), where p(S) = 1 - 6 S + S^2.
  • A291023 (program): p-INVERT of (1,1,1,1,1,…), where p(S) = 1 - 3 S^2 + 2 S^3.
  • A291024 (program): p-INVERT of (1,1,1,1,1,…), where p(S) = (1 - 2 S^2)^2.
  • A291033 (program): p-INVERT of the positive integers, where p(S) = 1 - 6*S.
  • A291034 (program): p-INVERT of the positive integers, where p(S) = 1 - 7*S.
  • A291040 (program): The arithmetic function u(n,3,2).
  • A291064 (program): a(n) = 2^n(n + 1) - 3(n - 1).
  • A291066 (program): Number of edges in the n-Menger sponge graph.
  • A291092 (program): 1 followed by infinitely many 9’s.
  • A291097 (program): a(n) = 2^n*(n/8 + 1) - n.
  • A291108 (program): Expansion of Sum_ k>=2 k^2x^(2k)/(1 - x^k).
  • A291142 (program): a(n) = (1/4)*A291024(n).
  • A291154 (program): Red numbers on the roulette wheel.
  • A291171 (program): Black numbers on the roulette wheel.
  • A291181 (program): p-INVERT of the positive integers, where p(S) = 1 - 8*S.
  • A291264 (program): p-INVERT of (0,1,0,1,0,1,…), where p(S) = (1 - 2 S)^2.
  • A291267 (program): The arithmetic function v_2(n,3).
  • A291268 (program): The arithmetic function v_3(n,2).
  • A291271 (program): The arithmetic function v_4(n,2).
  • A291289 (program): The Padovan sequence A000931 doubled.
  • A291299 (program): Partial domination number of Fibonacci cube Gamma_n.
  • A291304 (program): The arithmetic function v_5(n,2).
  • A291305 (program): The arithmetic function v_5(n,1).
  • A291306 (program): The arithmetic function v_6(n,1).
  • A291307 (program): The arithmetic function v_6(n,2).
  • A291317 (program): A variation of the Josephus problem: a(n) is the surviving integer under the following elimination process. Arrange 1,2,3,…,n in a circle, increasing clockwise. Starting with i=1, at k-th stage, move k places clockwise and delete the current number.
  • A291330 (program): The arithmetic function v_4(n,1).
  • A291338 (program): Number of n X n X n triangular binary arrays symmetric under rotations of 120 degrees.
  • A291357 (program): The arithmetic function u(n,2,3).
  • A291358 (program): The arithmetic function u(n,2,4).
  • A291359 (program): The arithmetic function u(n,2,5).
  • A291361 (program): The arithmetic function u(n,2,6).
  • A291362 (program): The arithmetic function u(n,2,7).
  • A291363 (program): The arithmetic function u(n,2,8).
  • A291364 (program): The arithmetic function u(n,3,3).
  • A291366 (program): The arithmetic function u(n,3,4).
  • A291367 (program): The arithmetic function u(n,3,5).
  • A291368 (program): The arithmetic function u(n,3,6).
  • A291385 (program): a(n) = (1/4)*A073388(n+1).
  • A291423 (program): The arithmetic function u(n,4,2).
  • A291454 (program): Number of half tones between successive pitches in a major scale.
  • A291484 (program): Expansion of e.g.f. arctanh(x)*exp(x).
  • A291497 (program): The arithmetic function uhat(n,1,3).
  • A291498 (program): The arithmetic function uhat(n,1,4).
  • A291499 (program): The arithmetic function uhat(n,1,5).
  • A291500 (program): The arithmetic function uhat(n,1,6).
  • A291501 (program): The arithmetic function uhat(n,1,7).
  • A291509 (program): The arithmetic function uhat(n,2,4).
  • A291510 (program): The arithmetic function uhat(n,2,5), negated.
  • A291512 (program): The arithmetic function uhat(n,2,7).
  • A291514 (program): The arithmetic function uhat(n,3,5).
  • A291516 (program): The arithmetic function uhat(n,3,7), negated.
  • A291517 (program): The arithmetic function uhat(n,3,8).
  • A291520 (program): The arithmetic function uhat(n,4,2).
  • A291521 (program): The arithmetic function uhat(n,4,6).
  • A291522 (program): The arithmetic function uhat(n,4,7).
  • A291526 (program): a(n) = 2^n*(n - 3) + 4.
  • A291557 (program): a(n) = 23*2^n - 1.
  • A291567 (program): The arithmetic function uhat(n,5,2).
  • A291568 (program): The arithmetic function uhat(n,5,5).
  • A291574 (program): The arithmetic function uhat(n,6,6).
  • A291578 (program): The arithmetic function uhat(n,7,7).
  • A291582 (program): Maximum number of 6 sphinx tile shapes in a sphinx tiled hexagon of order n.
  • A291584 (program): The arithmetic function uhat(n,8,8).
  • A291632 (program): Column 1 of A122832.
  • A291658 (program): a(n) is the sum of all integers from 5^n to 5^(n+1)-1.
  • A291662 (program): Number of ordered rooted trees with 2n non-root nodes such that the maximal outdegree equals n.
  • A291665 (program): a(n) = binomial(n, 2^floor(log_2(n))).
  • A291681 (program): First differences of A067046.
  • A291699 (program): a(n) = n^n(2n)!/(n!*(n + 1)!).
  • A291773 (program): Domination number of the n-Apollonian network.
  • A291778 (program): a(n) = 2^floor(2*n/3).
  • A291779 (program): a(n) = 2^n - 2^floor(2n/3).
  • A291783 (program): Partial sums of A064415(k)^2.
  • A291832 (program): Numbers k such that k^6 is sum of two positive 7th powers.
  • A291900 (program): Sum of the divisors of 24*n - 1, divided by 24, minus n.
  • A291910 (program): Number of 4-cycles in the n X n rook complement graph.
  • A291916 (program): Number of (not necessarily maximum) cliques in the n-Fibonacci cube graph.
  • A291919 (program): Number of (undirected) paths in the n-wheel graph.
  • A291938 (program): a(n) = 2^(n - 1) (n - mod(n, 2)).
  • A291943 (program): a(0)=0; for n>0, a(n) = (2n)-th digit after the decimal point in the decimal expansion of 1/(2n+1).
  • A291945 (program): Powers of 1111.
  • A291962 (program): Decimal repunits written in base 2.
  • A292000 (program): Number of (undirected) paths in the n-gear graph.
  • A292001 (program): Number of (undirected) paths in the n-helm graph.
  • A292018 (program): Wiener index for the n-Andrasfai graph.
  • A292022 (program): a(n) = 4n(n^2+2).
  • A292044 (program): Wiener index of the n-halved cube graph.
  • A292045 (program): Wiener index of the n X n X n grid graph.
  • A292046 (program): The list of distinct values of A072464.
  • A292051 (program): Wiener index of the n X n black bishop graph.
  • A292053 (program): Wiener index of the n X n king graph.
  • A292057 (program): Wiener index of the n X n queen graph.
  • A292058 (program): Wiener index of the n X n rook complement graph.
  • A292059 (program): Wiener index of the n X n white bishop graph.
  • A292060 (program): Minimum number of points of the square lattice falling strictly inside an equilateral triangle of side n.
  • A292061 (program): a(n) = (n-3)(n-2)^2(n-1)^2*n/24.
  • A292077 (program): a(n) = 0 if n=1; a(n) = 1-a(n-2) if n is odd; a(n) = 1-a(n/2) if n is even.
  • A292117 (program): Coefficients of a power series f(q) with coefficients +1 or -1 such that Product_ m >= 1 f(q^(2m-1)) = Sum_ m = -oo..oo q^(m(3m-1)/2).
  • A292246 (program): Base-2 expansion of a(n) encodes the steps where numbers of the form 3k+2 are encountered when map x -> A253889(x) is iterated down to 1, starting from x=n.
  • A292251 (program): The 3-adic valuation of A048673(n).
  • A292269 (program): If n is 1 or a prime, then a(n) = 1, otherwise a(n) = the third smallest divisor of n.
  • A292272 (program): a(n) = n - A048735(n) = n - (n AND floor(n/2)).
  • A292273 (program): For odd n: a(n) = 0, and for even n: a(n) = -mu(n), where mu is Moebius function (A008683).
  • A292277 (program): a(n) = 2^nF(n)F(n+1), where F = A000045.
  • A292278 (program): a(n) = (Fibonacci(3*n-1) + 1)/2 for n >= 1.
  • A292282 (program): a(n) = 2(n-1)^3n^2*(n+1).
  • A292286 (program): a(n) = k if the product of the divisors of n is n^k for some integer k, or -1 if no such k exists. For the ambiguous case, define a(1) = 0.
  • A292290 (program): Number of vertices of type A at level n of the hyperbolic Pascal pyramid.
  • A292291 (program): Number of vertices of type B at level n of the hyperbolic Pascal pyramid.
  • A292295 (program): Sum of values of vertices of type A at level n of the hyperbolic Pascal pyramid.
  • A292296 (program): Sum of values of vertices of type B at level n of the hyperbolic Pascal pyramid.
  • A292301 (program): p-INVERT of A010892, where p(S) = 1 + S - S^2.
  • A292302 (program): Expansion of (1 - x)Sum_ k>=1 kphi(k)*x^k/(1 - x^k), where phi() is the Euler totient function (A000010).
  • A292343 (program): The PI index of the Aztec diamond AZ(n) (see the Imran et al. reference).
  • A292344 (program): The first Zagreb index of the Aztec diamond AZ(n) (see the Ramanes et al. reference, Theorem 2.1).
  • A292345 (program): The second Zagreb index of the Aztec diamond AZ(n) (see the Ramanes et al. reference, Theorem 2.2).
  • A292346 (program): The forgotten topological index of the Aztec diamond AZ(n) (see the Ramanes et al. reference, Theorem 2.1).
  • A292350 (program): Number of Lyndon words (aperiodic necklaces) with 6 beads of n colors.
  • A292360 (program): a(n) = n(Lucas(n)Lucas(n+1) - 2).
  • A292400 (program): p-INVERT of (1,2,2,2,2,2,2,…) (A040000), where p(S) = (1 - S)^2.
  • A292410 (program): Difference between (2n+1)^2 and highest power of 2 less than or equal to (2n+1)^2.
  • A292412 (program): Numbers of the form Fibonacci(2k-1) or Lucas(2k-1); i.e., union of sequences A001519 and A002878.
  • A292423 (program): a(n) = 82*a(n-1) + a(n-2), where a(0) = 0, a(1) = 1.
  • A292443 (program): a(n) = (5/32)A000045(6n)^2.
  • A292444 (program): Number of non-isomorphic finite multisets that cannot be expressed as the multiset-union of a set of sets.
  • A292465 (program): a(n) = nF(n)F(n+1), where F = A000045.
  • A292510 (program): a(n) = smallest k >= 1 such that 1, p(n,2), p(n,3), …, p(n,k) can be partitioned into two sets with equal sums, where p(n,m) is m-th n-gonal number.
  • A292531 (program): a(n) = 0 if n is a power of 2. Otherwise, product of 2 numbers nearest n that have more 2’s in their prime factorization than n.
  • A292537 (program): Number of cliques in the n-Sierpinski tetrahedron graph.
  • A292540 (program): Number of 3-cycles in the n-Sierpinski tetrahedron graph.
  • A292542 (program): Number of 4-cycles in the n-Sierpinski tetrahedron graph.
  • A292543 (program): Number of 5-cycles in the n-Sierpinski tetrahedron graph.
  • A292545 (program): Number of 6-cycles in the n-Sierpinski tetrahedron graph.
  • A292552 (program): Nontotients of the form 10^k - 2.
  • A292564 (program): Take 1, skip 3 * 1 - 1, take 2, skip 3 * 2 - 1, take 3, skip 3 * 3 - 1, …
  • A292565 (program): Take 0, skip 3 * 1 + 1, take 1, skip 3 * 2 + 1, take 2, skip 3 * 3 + 1, …
  • A292576 (program): Permutation of the natural numbers partitioned into quadruples [4k-1, 4k-3, 4k-2, 4k], k > 0.
  • A292586 (program): a(n) = A002110(A001221(n)) = product of first omega(n) primes.
  • A292598 (program): a(n) is the number of odd primes in the sequence [n, floor(n/2), floor(n/4), …, 1].
  • A292600 (program): a(n) = A006068(floor(n/2)); A006068 with every term duplicated, where A006068 is the inverse of binary gray code.
  • A292601 (program): a(n) = n - A292600(n).
  • A292608 (program): a(n) = 2*n + 1 + valuation(n, 2) with valuation(n, 2) = A007814(n).
  • A292611 (program): Skip 3 triangle numbers, take 1 triangle number, skip 4 triangle numbers, take 2 triangle numbers, skip 5 triangle numbers, take 3 triangle numbers, …
  • A292638 (program): Rank of (3-r)n when all the numbers (3-r)j and (3+r)*k, where r = sqrt(5), j>=1, k>=1, are jointly ranked.
  • A292639 (program): Rank of (3+r)n when all the numbers (3-r)j and (3+r)*k, where r = sqrt(5), j>=1, k>=1, are jointly ranked.
  • A292769 (program): Partial sums of A051612.
  • A292779 (program): Interpret the values of the Moebius function mu(k) for k = n to 1 as a balanced ternary number.
  • A292784 (program): a(n) = n! * [x^n] 1/sqrt(1 - 2nx).
  • A292918 (program): Let A_n be a square n X n matrix with entries A_n(i,j)=1 if i+j is prime, and A_n(i,j)=0 otherwise. Then a(n) counts the 1’s in A_n.
  • A292936 (program): a(n) = the least k >= 0 such that floor(n/(2^k)) is a nonprime; a(n) is degree of the “safeness” of prime, 0 if n is not a prime, 1 for unsafe primes (A059456), and k >= 2 for primes that are (k-1)-safe but not k-safe.
  • A292987 (program): Beatty sequence of the real root of x^5 - x^4 - x^2 - 1; complement of A292988.
  • A292988 (program): Beatty sequence of the real root of 2x^5 - 9x^4 + 13x^3 - 11x^2 + 5*x - 1; complement of A292987.
  • A292995 (program): Sum of digits of 3^n (A004166) divided by 9.
  • A293004 (program): Expansion of 2*x^2 / (x^3 + x^2 - 3x + 1).
  • A293005 (program): Number of associative, quasitrivial, and order-preserving binary operations on the n-element set 1,…,n .
  • A293006 (program): Expansion of 2x^2(x+1) / (2x^3-3x+1).
  • A293007 (program): Expansion of 2x^2 / (1-2x-2*x^2).
  • A293014 (program): a(n) = a(n-1) + a(n-2) - a(n-3) + a(n-4) for n > 4, where a(n)=0 for n < 4 and a(4) = 1.
  • A293046 (program): Number of even permutations on 1,2,…,n with exactly 2 weak excedances.
  • A293047 (program): Number of odd permutations on 1,2,…,n with exactly 2 weak excedances.
  • A293064 (program): Number of vertices of type B at level n of the hyperbolic Pascal pyramid PP_(4,5).
  • A293065 (program): Number of vertices of type D at level n of the hyperbolic Pascal pyramid PP_(4,5).
  • A293066 (program): Number of vertices at level n of the hyperbolic Pascal pyramid PP_(4,5).
  • A293067 (program): Sum of values of vertices of type A at level n of the hyperbolic Pascal pyramid PP_(4,5).
  • A293077 (program): Number of letters (0’s and 1’s) in the n-th iterate of the final-letter-removed mapping defined at A289035.
  • A293078 (program): a(n) = (1/2)*A293077(n).
  • A293137 (program): a(0) = 0, and a(n) = floor(2*sqrt(n)) - 1 for n >= 1.
  • A293162 (program): Take every third term of the 0,1 -version of the Thue-Morse sequence: a(n) = A010060(3n).
  • A293163 (program): a(n) = A010060(3n+1).
  • A293164 (program): a(n) = A010060(3n+2).
  • A293167 (program): a(n) = sum k = 1 to n d(d(d(k))), where d(k) is the number of divisors of k (A000005).
  • A293168 (program): Partial sums of A054868.
  • A293169 (program): a(n) = Sum_ k=0..n binomial(k, 6*(n-k)).
  • A293239 (program): Number of terms in the fully expanded n-th derivative of x^x.
  • A293270 (program): a(n) = n^nbinomial(2n-1, n).
  • A293292 (program): Numbers with last digit less than 5 (in base 10).
  • A293296 (program): a(n) = 2*n^2 - floor(n/4).
  • A293322 (program): Greatest integer k such that k/2^n < 1/tau, where tau = (1+sqrt(5))/2 = golden ratio.
  • A293323 (program): Least integer k such that k/2^n > 1/tau, where tau = (1+sqrt(5))/2 = golden ratio.
  • A293337 (program): Least integer k such that k/2^n > e.
  • A293342 (program): Least integer k such that k/2^n > Pi.
  • A293400 (program): Greatest integer k such that k/n^2 < (1 + sqrt(5))/2 (the golden ratio).
  • A293401 (program): Least integer k such that k/n^2 > (1 + sqrt(5))/2 (the golden ratio).
  • A293402 (program): The integer k that minimizes k/n^2 - tau , where tau = (1+sqrt(5))/2 (golden ratio).
  • A293403 (program): Greatest integer k such that k/n^2 < (3 + sqrt(5))/2.
  • A293404 (program): Least integer k such that k/n^2 > (3 + sqrt(5))/2 (the golden ratio).
  • A293405 (program): The integer k that minimizes k/n^2 - tau^2 , where tau = (1+sqrt(5))/2 (golden ratio).
  • A293407 (program): Least integer k such that k/n^2 > (-1 + sqrt(5))/2 (the golden ratio).
  • A293408 (program): The integer k that minimizes k/n^2 - 1/tau , where tau = (1+sqrt(5))/2 (golden ratio).
  • A293410 (program): Least integer k such that k/n^2 > sqrt(3).
  • A293411 (program): a(n) = a(n-1) + a(n-3) + a(n-4), where a(0) = 1, a(1) = 2, a(2) = 3, a(3) = 4.
  • A293458 (program): Numerator of probability that a permutation of elements of some subset of set 1,2,…,n is a permutation of elements of some set of the form 1..k, k <= n.
  • A293475 (program): a(n) = (3n + 4)Pochhammer(n, 4) / 4!.
  • A293476 (program): a(n) = ((n + 1)/2)(n + 2)Pochhammer(n, 5) / 4!.
  • A293481 (program): Numbers with last digit greater than or equal to 5 (in base 10).
  • A293497 (program): Triangular array read by rows: row n >= 1 is the list of integers from 0 to 2n-1.
  • A293502 (program): Greatest integer k such that k/n^2 < sqrt(2).
  • A293503 (program): Least integer k such that k/n^2 > sqrt(2).
  • A293504 (program): The integer k that minimizes k/n^2 - sqrt(2) .
  • A293505 (program): a(n) is the integer k that minimizes k/Fibonacci(n) - 1/2 .
  • A293543 (program): a(n) is the least integer k such that k/Fibonacci(n) > 1/3.
  • A293544 (program): a(n) is the integer k that minimizes k/Fibonacci(n) - 1/3 .
  • A293545 (program): a(n) is the greatest integer k such that k/Fibonacci(n) < 2/3.
  • A293546 (program): a(n) is the least integer k such that k/Fibonacci(n) > 2/3.
  • A293547 (program): a(n) is the integer k that minimizes k/Fibonacci(n) - 2/3 .
  • A293552 (program): a(n) is the least integer k such that k/Fibonacci(n) > 1/4.
  • A293553 (program): a(n) is the integer k that minimizes k/Fibonacci(n) - 1/4 .
  • A293604 (program): E.g.f.: exp(x * (1 - x)).
  • A293608 (program): a(n) = (3n + 7)Pochhammer(n, 5) / 4!.
  • A293615 (program): a(n) = Pochhammer(n, 5) / 2.
  • A293626 (program): Numbers of the form (2^(2p) + 1)/5, where p is a prime > 5.
  • A293631 (program): Greatest integer k such that k/Fibonacci(n) <= 3/4.
  • A293632 (program): Least integer k such that k/Fibonacci(n) >= 3/4.
  • A293633 (program): a(n) is the integer k that minimizes k/Fibonacci(n) - 3/4 .
  • A293637 (program): a(n) is the least integer k such that k/Fibonacci(n) > 1/5.
  • A293638 (program): a(n) is the integer k that minimizes k/Fibonacci(n) - 1/5 .
  • A293639 (program): a(n) is the greatest integer k such that k/Fibonacci(n) < 2/5.
  • A293640 (program): a(n) is the least integer k such that k/Fibonacci(n) > 2/5.
  • A293641 (program): a(n) is the integer k that minimizes k/Fibonacci(n) - 2/5 .
  • A293642 (program): a(n) is the greatest integer k such that k/Fibonacci(n) < 3/5.
  • A293643 (program): a(n) is the least integer k such that k/Fibonacci(n) > 3/5.
  • A293644 (program): a(n) is the integer k that minimizes k/Fibonacci(n) - 3/5 .
  • A293653 (program): Young urn sequence (number of possible evolutions in n steps of the “Young” Pólya urn).
  • A293656 (program): a(n) = binomial(n+1,2)*n!/n!!.
  • A293668 (program): First differences of A292046.
  • A293671 (program): a(n) is the greatest integer k such that k/Fibonacci(n) < 4/5.
  • A293672 (program): a(n) is the least integer k such that k/Fibonacci(n) > 4/5.
  • A293673 (program): a(n) is the integer k that minimizes k/Fibonacci(n) - 4/5 .
  • A293688 (program): Partial sums of A002251.
  • A293710 (program): Expansion of x^2/(1 - 4x - 4x^2 - x^3).
  • A293754 (program): Numbers k such that c(k,0) < c(k,1), where c(k,d) = number of d’s in the first k digits of the base-2 expansion of tau (the golden ratio, (1+sqrt(5))/2).
  • A293810 (program): The truncated kernel function of n: the product of distinct primes dividing n, but excluding the largest prime divisor of n.
  • A293821 (program): Number of integer-sided quadrilaterals having perimeter n, modulo rotations but not reflections.
  • A293838 (program): “Look once to the left” sequence starting with 1,2 (see comment).
  • A293896 (program): Number of proper divisors of the form 3k+2.
  • A293956 (program): Maximum over all sets of n points in the plane of the number of second-smallest distances between the points.
  • A293958 (program): Smallest odd prime divisor of (2n+1)^2 + 1.
  • A293962 (program): Number of linear chord diagrams having n chords and maximal chord length n, a(0)=1.
  • A293990 (program): a(n) = (3*n + ((n-2) mod 4))/2.
  • A294013 (program): Sum of the differences of the larger and smaller parts in the partitions of 2n into two parts with the smaller part prime.
  • A294015 (program): Sum of the even divisors of 2n, minus the (n-1)st odd number.
  • A294016 (program): a(n) = sum of all divisors of all positive integers <= n, minus the sum of remainders of n mod k, for k = 1, 2, 3, …, n.
  • A294017 (program): Partial sums of A294016.
  • A294023 (program): Sum of the differences of the larger and smaller parts in the partitions of n into two parts with the smaller part prime.
  • A294039 (program): a(n) = eGamma(2n,1).
  • A294060 (program): Sum of the differences of the larger and smaller parts in the partitions of n into two parts with the smaller part squarefree.
  • A294062 (program): Sum of the differences of the larger and smaller parts in the partitions of 2n into two parts with the smaller part squarefree.
  • A294070 (program): a(n) = (1/4)(n^2 - 2n)^2 + (9/4)(n^2 - 2n) + 6.
  • A294091 (program): Numbers k such that (k - 1)/2 is prime that are not congruent to -1 mod 8.
  • A294116 (program): Fibonacci sequence beginning 2, 21.
  • A294129 (program): Numbers n for which exactly one length minimal language exists having exactly n nonempty words over a countably infinite alphabet such that within each prefix of a word every letter of the alphabet is at least as frequent as the subsequent alphabet letter.
  • A294140 (program): Number of total dominating sets in the n-crown graph.
  • A294152 (program): Chromatic invariant of the n-antiprism graph.
  • A294157 (program): Fibonacci sequence beginning 2, 8.
  • A294172 (program): Maximum value of the cyclic convolution of first n positive integers with themselves.
  • A294178 (program): a(2n) = 2n + 1, a(2n+1) = 6n + 3.
  • A294234 (program): Number of partitions of n into two parts such that the smaller part is nonsquarefree.
  • A294246 (program): Sum of the smaller parts of the partitions of 2n into two parts with smaller part nonsquarefree.
  • A294259 (program): a(n) = n(n^3 + 2n^2 - 5*n + 10)/8.
  • A294262 (program): a(n) = 3a(n-1) + 5a(n-2) + a(n-3), with a(0) = a(1) = 1 and a(2) = 7, a linear recurrence which is a trisection of A005252.
  • A294269 (program): a(n) is the smallest number not already in the sequence which shares a factor with an even number of preceding terms; a(1) = 1.
  • A294286 (program): Sum of the squares of the parts in the partitions of n into two distinct parts.
  • A294287 (program): Sum of the cubes of the parts in the partitions of n into two distinct parts.
  • A294288 (program): Sum of the fourth powers of the parts in the partitions of n into two distinct parts.
  • A294300 (program): Sum of the fifth powers of the parts in the partitions of n into two distinct parts.
  • A294301 (program): Sum of the sixth powers of the parts in the partitions of n into two distinct parts.
  • A294302 (program): Sum of the seventh powers of the parts in the partitions of n into two distinct parts.
  • A294303 (program): Sum of the eighth powers of the parts in the partitions of n into two distinct parts.
  • A294304 (program): Sum of the ninth powers of the parts of the partitions of n into two distinct parts.
  • A294305 (program): Sum of the tenth powers of the parts in the partitions of n into two distinct parts.
  • A294315 (program): a(n) = 3*n^3 + n^2.
  • A294317 (program): Triangle read by rows: T(n, k) = 2*n-k, k <= n.
  • A294327 (program): a(n) = ((9n + 8)10^n - 8)/9.
  • A294328 (program): a(n) = ((9n + 8)10^n - 8)/81.
  • A294329 (program): a(n) = 8((9n + 8)*10^n - 8)/81.
  • A294344 (program): a(n) = ((-9n + 82)10^n - 1)/81.
  • A294352 (program): Product of first n terms of the binomial transform of the factorial.
  • A294389 (program): a(n) = 2^(n-3) mod n, for n >= 3.
  • A294390 (program): a(n) = 2^(n-4) mod n, for n >= 4.
  • A294398 (program): Solution of the complementary equation a(n) = a(n-1) + b(n-2) + 2, where a(0) = 1, a(1) = 3, b(0) = 2, b(1) = 4.
  • A294406 (program): Positive odd numbers k such that both (sigma(m) - 2m) and (2m - sigma(m)) are never equal to k, where sigma(.) is the sum of divisors function A000203 (conjectured).
  • A294433 (program): Expansion of (1+11x+24x^2+11*x^3+x^4)/(1-x)^5.
  • A294456 (program): a(1)=0, a(2)=1; thereafter a(n) = a(floor(n/2)) + a(ceiling(n/2)) + 2.
  • A294473 (program): Sum of the areas of the squares on the sides of the distinct rectangles that can be made with positive integer sides such that L + W = n, W < L.
  • A294486 (program): a(n) = binomial(2n,n) * (2n+1)^2.
  • A294566 (program): a(n) is the smallest positive integer of length (distance from origin) n in the Cayley graph of the integers generated by all powers of 5.
  • A294614 (program): Sum of the divisors of 12*n - 1, divided by 12, minus n.
  • A294619 (program): a(0) = 0, a(1) = 1, a(2) = 2 and a(n) = 1 for n > 2.
  • A294627 (program): Expansion of x(1 + x)/((1-2x)*(1+x+x^2)).
  • A294628 (program): a(n) = 8*(sigma(n) - n + (1/2)).
  • A294629 (program): Partial sums of A294628.
  • A294630 (program): Partial sums of A294629.
  • A294640 (program): G.f. A(x) = Sum_ n>=0 x^n/a(n) satisfies: A(x) = A(x^2) + Integral A(x^2) dx.
  • A294645 (program): a(n) = Sum_ d n d^(n+1).
  • A294646 (program): a(n) = (1/2)^(2n) mod (2n+1).
  • A294732 (program): Maximal diameter of the connected cubic graphs on 2*n vertices.
  • A294774 (program): a(n) = 2n^2 + 2n + 5.
  • A294790 (program): Subtract n from partial sums of partial sums of Catalan numbers.
  • A294810 (program): a(n) = Sum_ d n d^(n+2).
  • A294885 (program): a(n) = A004125(n) mod n = [Sum_ i=1..n (n mod i)] mod n.
  • A294899 (program): a(n) = A000203(n) XOR A005187(n), where XOR is bitwise-XOR, A003987.
  • A294912 (program): Numbers n such that 2^(n-1), (2n-1)(2^((n-1)/2)), (4ceiling((3/4)n)-2), and (2^((n+1)/2) + floor((1/4)n)2^(((n+1)/2)+1)) are all congruent to 1 (mod n).
  • A294919 (program): Numbers n such that 2^(n-1), (2n-1)(2^((n-1)/2)), (4ceiling((1/4)n)-2), and (2^((n+1)/2) + floor((3/4)n)2^(((n+1)/2)+1)) are all congruent to 1 (mod n).
  • A294924 (program): Numbers n such that the whole sequence of the first n terms of A293699 is a palindrome.
  • A294934 (program): Characteristic function for deficient numbers (A005100): a(n) = 1 if A001065(n) < n, 0 otherwise.
  • A294935 (program): Characteristic function for nonabundant numbers (A263837): a(n) = 1 if A001065(n) <= n, 0 otherwise.
  • A294936 (program): Characteristic function for nondeficient numbers (A023196): a(n) = 1 if A001065(n) >= n, 0 otherwise.
  • A294937 (program): Characteristic function for abundant numbers (A005101): a(n) = 1 if A001065(n) > n, 0 otherwise.
  • A294969 (program): Decimal expansion of sqrt(14)/2 = sqrt(7/2) = A010471/2.
  • A294993 (program): Numbers n > 1 such that all of 2^(n-1), 3^(n-1), 5^(n-1), (2n-1)(2^((n-1)/2)), 4ceiling((3/4)n)-2, and (2^((n+1)/2) + floor(n/4)*2^((n+3)/2)) are congruent to 1 (mod n).
  • A295012 (program): a(n) = sigma(12n - 1)/12, where sigma = sum of divisors (A000203).
  • A295077 (program): a(n) = 2n(n-1) + 2^n - 1.
  • A295089 (program): a(n) = 3*n^2 + n + 3.
  • A295130 (program): a(n) = 3n(64*n^2 + 1).
  • A295150 (program): Numbers that have exactly two representations as a sum of five nonnegative squares.
  • A295220 (program): a(n) = Sum_ i=1..floor(n/2) floor((n+i)/i) - floor((n-i-1)/i).
  • A295282 (program): a(n) > n is chosen to minimize the difference between ratios a(n):n and n:(a(n) - n), so that they are matching approximations to the golden ratio.
  • A295284 (program): Number of partitions of n into two distinct parts such that the larger part is nonsquarefree.
  • A295286 (program): Sum of the products of the smaller and larger parts of the partitions of n into two parts with the smaller part odd.
  • A295287 (program): Sum of the products of the smaller and larger parts of the partitions of n into two parts with the smaller part even.
  • A295288 (program): Binomial transform of the centered triangular numbers A005448.
  • A295294 (program): Sum of the divisors of the powerful part of n: a(n) = A000203(A057521(n)).
  • A295295 (program): Sum of squarefree divisors of the powerful part of n: a(n) = A048250(A057521(n)).
  • A295297 (program): a(n) = (A000120(n) + A000203(n)) mod 2.
  • A295301 (program): a(n) = n - phi(sigma(n)), where phi = A000010 and sigma = A000203.
  • A295302 (program): a(n) = sigma(phi(n)) - n, where phi = A000010 and sigma = A000203.
  • A295308 (program): Characteristic function for A066694: a(n) = 1 if n < phi(sigma(n)), 0 otherwise.
  • A295309 (program): Characteristic function for A295307: a(n) = 1 if n > phi(sigma(n)), 0 otherwise.
  • A295310 (program): a(n) = gcd(n, A062401(n)), where A062401(n) = phi(sigma(n)).
  • A295311 (program): a(n) = n / A295310(n) = n / gcd(n, phi(sigma(n))).
  • A295314 (program): a(n) = sigma(n) / gcd(sigma(n), phi(sigma(n))).
  • A295316 (program): a(n) = 1 if there are no even exponents in the prime factorization of n, 0 otherwise.
  • A295317 (program): Sum of the products of the smaller and larger parts of the partitions of n into two distinct parts with the smaller part odd.
  • A295318 (program): Sum of the products of the smaller and larger parts of the partitions of n into two distinct parts with the smaller part even.
  • A295319 (program): a(n) is the sum of all n-digit palindromes.
  • A295340 (program): Numbers congruent to 11 or 13 mod 15.
  • A295388 (program): a(n) is the least k > n such that n divides k, and n+1 divides k+1, and n+2 divides k+2.
  • A295405 (program): a(n) = 1 if n^2+1 is prime, 0 otherwise.
  • A295473 (program): a(0) = 0; for n>0, a(n) = 9*n!.
  • A295513 (program): a(n) = n*bil(n) - 2^bil(n) where bil(0) = 0 and bil(n) = floor(log_2(n)) + 1 for n>0.
  • A295514 (program): a(n) = 2^bil(n) - bil(n) where bil(0) = 0 and bil(n) = floor(log_2(n)) + 1 for n > 0.
  • A295515 (program): The Euclid tree, read across levels.
  • A295518 (program): a(n) = e^2 * Sum_ k=0..n-1 Gamma(k + 1, 2).
  • A295519 (program): a(n) = e^3 * Sum_ k=0..n-1 Gamma(k + 1, 3).
  • A295556 (program): a(n) = 0 for n <= 1; thereafter a(n) = a(floor(n/2)) + a(ceiling(n/2)) + floor(n/2) if n not congruent to 0 mod 4, a(n) = a(n/2-1) + a(n/2+1) + n/2 if n == 0 (mod 4).
  • A295622 (program): Number of nonequivalent dissections of an n-gon into 3 polygons by nonintersecting diagonals rooted at a cell up to rotation.
  • A295632 (program): Write 1/Product_ n > 1 (1 - 1/n^s) in the form Product_ n > 1 (1 + a(n)/n^s).
  • A295643 (program): Squares repeated 4 times; a(n) = (floor(n/4))^2.
  • A295657 (program): Multiplicative with a(p^e) = p^floor((e-1)/2).
  • A295660 (program): Binary weight of Euler phi: a(n) = A000120(A000010(n)).
  • A295664 (program): Exponent of the highest power of 2 dividing number of divisors of n: a(n) = A007814(A000005(n)); 2-adic valuation of tau(n).
  • A295680 (program): a(n) = a(n-1) + a(n-3) + a(n-4), where a(0) = 0, a(1) = 0, a(2) = 0, a(3) = 2.
  • A295689 (program): a(n) = a(n-1) + a(n-3) + a(n-4), where a(0) = 2, a(1) = 0, a(2) = 2, a(3) = 1
  • A295771 (program): a(n) is the minimum size of a planar additive basis for the square [0,n]^2.
  • A295773 (program): a(n) = Sum_ k=0..n binomial(k^2, k).
  • A295774 (program): a(n) is the minimum size of a restricted planar additive basis for the square [0,2n]^2.
  • A295796 (program): The only integers that cannot be partitioned into a sum of seven positive squares.
  • A295821 (program): Number of coprime pairs (a,b) with -n <= a <= n, -2 <= b <= 2.
  • A295822 (program): Number of coprime pairs (a,b) with -n <= a <= n, -3 <= b <= 3.
  • A295838 (program): Largest value corresponding to a string of n printable ASCII characters.
  • A295866 (program): Number of decimal digits in the number of partitions of n.
  • A295869 (program): Numbers not divisible by 2, 3 or 5 (A007775) with digital root 8.
  • A295889 (program): a(n) = 1 if binary weights of n and 3n have the same parity, 0 otherwise.
  • A295890 (program): a(n) = 1 if binary weights of n and 3n have different parity, 0 otherwise; a(n) = A010060(n) XOR A010060(3n).
  • A295896 (program): a(n) = 1 if there are no odd runs of 1’s in the binary expansion of n followed by a 0 to their right, 0 otherwise.
  • A295904 (program): Number of (not necessarily maximum) cliques in the n-sun graph.
  • A295905 (program): Number of (not necessarily maximum) cliques in the n X n knight graph.
  • A295906 (program): Number of (not necessarily maximum) cliques in the n X n king graph.
  • A295911 (program): Number of (not necessarily maximal) cliques in the n-Hanoi graph.
  • A295921 (program): Number of (not necessarily maximum) cliques in the n-folded cube graph.
  • A295926 (program): Number of (not necessarily maximum) cliques in the n-cube-connected cycle graph.
  • A295933 (program): Number of (not necessarily maximum) cliques in the n-Sierpinski sieve graph.
  • A296020 (program): Number of primes of the form 4k+3 <= 4n+3.
  • A296021 (program): Number of primes of the form 4k+1 <= 4n+1.
  • A296028 (program): Characteristic function of primes in the nonmultiples of 3.
  • A296058 (program): Numbers k such that floor((3*k - 1)/2) is prime.
  • A296062 (program): Base-2 logarithm of the number of different shapes of balanced binary trees with n nodes (A110316).
  • A296063 (program): a(n) is the smallest number (in absolute value) not yet in the sequence such that the arithmetic mean of the first n terms a(1), a(2), …, a(n) is an integer. Preference is given to positive values of a(n); a(1)=1; 0 not allowed.
  • A296065 (program): Partial sums of A296064.
  • A296066 (program): a(n) = A296065(n)/n.
  • A296069 (program): a(1)=0; thereafter a(n) is the smallest number (in absolute value) not yet in the sequence such that the arithmetic mean of the first n terms a(1), a(2), …, a(n) is a nonzero integer. Preference is given to positive values of a(n).
  • A296070 (program): Partial sums of A296069.
  • A296079 (program): a(n) = 1 if 1+phi(n) is prime, 0 otherwise, where phi = A000010, Euler totient function.
  • A296135 (program): 0->01 -transform of the Fibonacci word A003849.
  • A296141 (program): Sum of the smaller parts of the partitions of n into two distinct parts with the larger part even.
  • A296159 (program): Sum of the smaller parts in the partitions of n into two distinct parts with the larger part odd.
  • A296160 (program): Sum of the larger parts of the partitions of n into two parts such that the smaller part is even.
  • A296161 (program): Sum of the larger parts of the partitions of n into two parts such that the smaller part is odd.
  • A296168 (program): Decimal expansion of BesselJ(1,2)/BesselJ(0,2).
  • A296180 (program): Triangle read by rows: T(n, k) = 3(n - k)k + 1, n >= 0, 0 <= k <= n.
  • A296182 (program): Decimal expansion of (2 + phi)/2, with the golden section phi from A001622.
  • A296184 (program): Decimal expansion of 2 + phi, with the golden section phi from A001622.
  • A296185 (program): Numbers that are not the sum of 3 squares and an 8th power.
  • A296196 (program): Harary index of the n X n queen graph.
  • A296197 (program): Harary index of the n X n bishop graph.
  • A296198 (program): Harary index of the n X n black bishop graph.
  • A296200 (program): Harary index of the n X n white bishop graph.
  • A296210 (program): Characteristic function for A104210: a(n) = 1 if n is divisible by at least 2 consecutive primes, 0 otherwise.
  • A296211 (program): a(n) = 1 if sigma(n)-1 is a prime, 0 otherwise.
  • A296212 (program): a(n) = 1 if sigma(n) + 1 is prime, 0 otherwise.
  • A296306 (program): a(n) = A001157(n)/A050999(n).
  • A296349 (program): Position where binary expansion of n starts in the binary Champernowne sequence A030190.
  • A296357 (program): a(n) = ceiling of n/Pi.
  • A296363 (program): a(1)=0; for n>1, a(n) = 4n^3 - 3n^2 - 3*n + 4.
  • A296367 (program): Number of triangles on a 4 X n grid.
  • A296368 (program): Coordination sequence for the Cairo or dual-3.3.4.3.4 tiling with respect to a trivalent point.
  • A296420 (program): Period of last digit of multiples of n.
  • A296442 (program): Initial digit of n-th Mersenne number.
  • A296515 (program): Number of edges in a maximal planar graph with n vertices.
  • A296579 (program): Numbers that are not the sum of 3 squares and a nonnegative 9th power.
  • A296590 (program): a(n) = Product_ k=0..n binomial(2*n - k, k).
  • A296601 (program): L.g.f.: -log(Product_ k>=1 (1 - kx^k)^k) = Sum_ n>=1 a(n)x^n/n.
  • A296613 (program): Smallest k such that either k >= n and k is a power of 2, or k >= 5n/3 and the prime divisors of k are precisely 2 and 5.
  • A296779 (program): Detour index of the n X n grid graph.
  • A296819 (program): Maximum detour index of any bipartite graph on n nodes.
  • A296903 (program): Numbers n whose base-20 digits d(m), d(m-1), …, d(0) have #(pits) = #(peaks); see Comments.
  • A296906 (program): Numbers n whose base-60 digits d(m), d(m-1), …, d(0) have #(pits) = #(peaks); see Comments.
  • A296909 (program): Partial sums of A296368.
  • A296910 (program): a(0)=1, a(1)=4; thereafter a(n) = 4n-2(-1)^n.
  • A296911 (program): Partial sums of A296910.
  • A296943 (program): Number of bisymmetric and quasitrivial operations on an arbitrary n-element set.
  • A296944 (program): Expansion of (2xexp(x)-3)/(1-x).
  • A296953 (program): Number of bisymmetric, quasitrivial, and order-preserving binary operations on the n-element set 1,…,n .
  • A296954 (program): Expansion of x(1 - x + 4x^2) / ((1 - x)(1 - 2x)).
  • A296955 (program): Sum of the smaller parts of the partitions of n into two distinct parts such that the smaller part divides the larger.
  • A296964 (program): Expansion of (x*exp(x)-1)/(1-x).
  • A296965 (program): Expansion of x(1 - x + 2x^2) / ((1 - x)(1 - 2x)).
  • A296966 (program): Sum of all the parts in the partitions of n into two distinct parts such that the smaller part divides the larger.
  • A297024 (program): Sum of the smaller parts of the partitions of n into two parts such that the smaller part does not divide the larger.
  • A297086 (program): a(n) = 1 if gcd(n, phi(n)) == 1 otherwise 0.
  • A297109 (program): If n is prime(k)^e, e >= 1, then a(n) = k, otherwise 0.
  • A297155 (program): a(1) = a(2) = 0, after which, a(n) = 1+a(n/2) if n is of the form 4k+2, otherwise a(n) = a(A252463(n)).
  • A297180 (program): a(n) is the smallest positive integer of length (distance from origin) n in the Cayley graph of the integers generated by all powers of 7.
  • A297181 (program): a(n) is the smallest positive integer of length (distance from origin) n in the Cayley graph of the integers generated by all powers of 11.
  • A297182 (program): a(n) is the smallest positive integer of length (distance from origin) n in the Cayley graph of the integers generated by all powers of 13.
  • A297217 (program): Most common value of the number of divisors function among all composites up to composite(n) inclusive, or 0 if there is a tie.
  • A297250 (program): Numbers whose base-3 digits having equal up-variation and down-variation; see Comments.
  • A297251 (program): Numbers whose base-3 digits have greater up-variation than down-variation; see Comments.
  • A297351 (program): Smallest number k such that, for any set S of k distinct nonzero residues mod p = prime(n), any residue mod p can be represented as a sum of zero or more distinct elements of S.
  • A297382 (program): Denominator of -A023900(n)/2.
  • A297402 (program): a(n) = gcd_ k=1..n (prime(k+1)^n-1)/2.
  • A297405 (program): Binary “cubes”; numbers whose binary representation consists of three consecutive identical blocks.
  • A297439 (program): Number of maximum independent vertex sets and minimum vertex covers in the n-web graph.
  • A297444 (program): a(n) = a(n-1) + 9a(n-2) - 9a(n-3), where a(0) = 1, a(1) = 3, a(2) = 6, a(3) = 33.
  • A297445 (program): a(n) = a(n-1) + 9a(n-2) - 9a(n-3), where a(0) = 1, a(1) = 5, a(2) = 11.
  • A297464 (program): Solution (a(n)) of the system of 4 complementary equations in Comments.
  • A297469 (program): Solution (bb(n)) of the system of 3 complementary equations in Comments.
  • A297619 (program): a(n) = 2a(n-1) + 2a(n-2) - 4*a(n-3), a(1) = 0, a(2) = 0, a(3) = 8.
  • A297662 (program): Number of chordless cycles in the complete tripartite graph K_n,n,n.
  • A297663 (program): a(n) = 5*n + 2^n.
  • A297670 (program): Number of chordless cycles in the n-triangular graph.
  • A297675 (program): a(n) = 3*(n^2+n-4)/2.
  • A297792 (program): a(n) = Sum_ d n min(d, n/d)^2.
  • A297793 (program): a(n) = Sum_ d n min(d, n/d)^3.
  • A297794 (program): a(n) = Sum_ d n min(d, n/d)^4.
  • A297795 (program): a(n) = Sum_ d n min(d, n/d)^5.
  • A297928 (program): a(n) = 24^n + 32^n - 1.
  • A297970 (program): Numbers that are not the sum of 3 squares and a nonnegative 7th power.
  • A297996 (program): a(1)=2, a(2)=3, a(3)=5 and a(n) = (a(1) + a(2) + a(3) + … + a(n-1))/a(n-1).
  • A298011 (program): If n = Sum_ i=1..h 2^b_i with 0 <= b_1 < … < b_h, then a(n) = Sum_ i=1..h i * 2^b_i.
  • A298016 (program): Coordination sequence of snub-632 tiling with respect to a hexavalent node.
  • A298019 (program): Partial sums of A298016.
  • A298022 (program): Coordination sequence for Dual(3^3.4^2) tiling with respect to a trivalent node.
  • A298023 (program): Partial sums of A298022.
  • A298024 (program): G.f.: (x^4+3x^3+6x^2+3x+1)/((1-x)(1-x^3)).
  • A298025 (program): Partial sums of A298024.
  • A298026 (program): Coordination sequence of Dual(3.6.3.6) tiling with respect to a hexavalent node.
  • A298027 (program): Partial sums of A298026.
  • A298028 (program): Coordination sequence of Dual(3.6.3.6) tiling with respect to a trivalent node.
  • A298029 (program): Coordination sequence of Dual(3.4.6.4) tiling with respect to a trivalent node.
  • A298030 (program): Partial sums of A298029.
  • A298031 (program): Coordination sequence of Dual(3.4.6.4) tiling with respect to a tetravalent node.
  • A298032 (program): Partial sums of A298031.
  • A298033 (program): Coordination sequence of the Dual(3.4.6.4) tiling with respect to a hexavalent node.
  • A298034 (program): Partial sums of A298033.
  • A298035 (program): Coordination sequence of Dual(3.12.12) tiling with respect to a trivalent node.
  • A298036 (program): Coordination sequence of Dual(4.6.12) tiling with respect to a 12-valent node.
  • A298037 (program): Partial sums of A298036.
  • A298038 (program): Coordination sequence of Dual(4.6.12) tiling with respect to a hexavalent node.
  • A298040 (program): Coordination sequence of Dual(4.6.12) tiling with respect to a tetravalent node.
  • A298043 (program): If n = Sum_ i=1..h 2^b_i with b_1 > … > b_h >= 0, then a(n) = Sum_ i=1..h i * 2^b_i.
  • A298078 (program): a(n) = 7n^2 - 7n - 43.
  • A298101 (program): Expansion of x(1 + x)/((1 - x)(1 - 322*x + x^2)).
  • A298125 (program): The hex numbers (A003215) together with 3.
  • A298198 (program): Number of Eulerian cycles in the graph Cartesian product of C_n and a double edge.
  • A298252 (program): Even integers n such that n-3 is prime.
  • A298267 (program): a(n) is the maximum number of heptiamonds in a hexagon of order n.
  • A298271 (program): Expansion of x/((1 - x)(1 - 322x + x^2)).
  • A298360 (program): Numbers congruent to 3, 7, 13, 27 mod 30.
  • A298364 (program): Permutation of the natural numbers partitioned into quadruples [4k-2, 4k-1, 4k-3, 4k] for k > 0.
  • A298375 (program): Partial sums of A230584.
  • A298397 (program): Pentagonal numbers divisible by 4.
  • A298468 (program): Solution (aa(n)) of the system of 3 complementary equations in Comments.
  • A298474 (program): a(n) is the least k such that A090701(k) = n.
  • A298564 (program): a(n) = (3^(n+2)+11)/2 - 52^(n+1) + 2n.
  • A298677 (program): a(n) = 110*a(n-1) - a(n-2) for n >= 2, a(0)=1, a(1)=111.
  • A298705 (program): Numbers from the 15-theorem for universal Hermitian lattices.
  • A298720 (program): EBCDIC codes for lower case letters.
  • A298728 (program): EBCDIC codes for upper case letters.
  • A298735 (program): Number of odd squares dividing n.
  • A298784 (program): Expansion of (1 + x^2)(1 + 3x + x^2) / ((1 - x)*(1 - x^3)).
  • A298785 (program): Partial sums of A298784.
  • A298786 (program): Expansion of (x^4 + 2x^3 + 4x^2 + 2x + 1) / ((1 - x)(1 - x^3)).
  • A298787 (program): Partial sums of A298786.
  • A298788 (program): Coordination sequence for bey tiling (or net) with respect to a trivalent node.
  • A298789 (program): Coordination sequence for bey tiling (or net) with respect to a tetravalent node.
  • A298790 (program): Partial sums of A298788.
  • A298791 (program): Partial sums of A298789.
  • A298861 (program): Rank of n-th prime when all the primes and twice-primes are jointly ranked.
  • A298862 (program): Rank of n-th twice-prime when all the primes and twice-primes are jointly ranked.
  • A298863 (program): Ranks of primes p when all primes p and products 3*p are jointly ranked.
  • A298864 (program): Ranks of products 3p when all primes p and products 3p are jointly ranked.
  • A298866 (program): Positions of primes p when all p and 4*p are arranged in increasing order.
  • A298867 (program): Positions of numbers 4p when all primes p and products 4p are arranged in increasing order.
  • A298881 (program): a(0) = 0; for n>0, a(n) = 6*n!.
  • A298950 (program): Numbers k such that 5*k - 4 is a square.
  • A298952 (program): First put a(n)=0 for all n, then start with a(0) = 1 and add at step n >= 0 the term 1 at position 2*n + a(n).
  • A299017 (program): Intersection of A264041 and A000217.
  • A299090 (program): Number of “digits” in the binary representation of the multiset of prime factors of n.
  • A299120 (program): a(n) = (n-1)(n-2)(n+3)*(n+2)/12.
  • A299143 (program): a(n) is the least k > n such that gcd(k,n) > 1 and gcd(k+1,n+1) > 1.
  • A299174 (program): The even positive integers.
  • A299198 (program): a(n) = n^4/6 - 2n^3/3 - n^2/6 + 5n/3 + 1.
  • A299231 (program): Ranks of 2,3 -power towers that start with 2; see Comments.
  • A299232 (program): Ranks of 2,3 -power towers that start with 3; see Comments.
  • A299250 (program): Numbers congruent to 9, 11, 21, 29 mod 30.
  • A299254 (program): Coordination sequence for 3D uniform tiling formed by stacking parallel layers of the 3^4.6 2D tiling (cf. A250120).
  • A299255 (program): Coordination sequence for 3D uniform tiling formed by stacking parallel layers of the 3.3.4.3.4 2D tiling (cf. A219529).
  • A299256 (program): Coordination sequence for 3D uniform tiling formed by stacking parallel layers of the 3.6.3.6 2D tiling (cf. A008579).
  • A299258 (program): Coordination sequence for 3D uniform tiling formed by stacking parallel layers of the 4.6.12 2D tiling (cf. A072154).
  • A299259 (program): Coordination sequence for 3D uniform tiling formed by stacking parallel layers of the 4.8.8 2D tiling (cf. A008576).
  • A299260 (program): Partial sums of A299254.
  • A299261 (program): Partial sums of A299255.
  • A299262 (program): Partial sums of A299256.
  • A299264 (program): Partial sums of A299258.
  • A299265 (program): Partial sums of A299259.
  • A299276 (program): Partial sums of A008137.
  • A299283 (program): Coordination sequence for “svh” 3D uniform tiling.
  • A299284 (program): Partial sums of A299283.
  • A299285 (program): Coordination sequence for “tea” 3D uniform tiling.
  • A299286 (program): Partial sums of A299285.
  • A299287 (program): Coordination sequence for “tcd” 3D uniform tiling.
  • A299288 (program): Partial sums of A299287.
  • A299289 (program): Coordination sequence for “tsi” 3D uniform tiling.
  • A299290 (program): Partial sums of A299289.
  • A299335 (program): Expansion of 1 / ((1 - x)^7*(1 + x)^2).
  • A299336 (program): Expansion of 1 / ((1 - x)^7*(1 + x)^4).
  • A299337 (program): Expansion of 1 / ((1 - x)^7*(1 + x)^5).
  • A299338 (program): Expansion of 1 / ((1 - x)^7*(1 + x)^6).
  • A299412 (program): Pentagonal pyramidal numbers divisible by 3.
  • A299429 (program): a(n) = binomial((n+1)(2n+1), n) / ((n+1)(2n+1)).
  • A299641 (program): Solution (d(n)) of the system of 5 complementary equations in Comments.
  • A299645 (program): Numbers of the form m(8m + 5), where m is an integer.
  • A299646 (program): a(n) = Sum_ k = n..2*n+1 k^2.
  • A299647 (program): Positive solutions to x^2 == -2 (mod 11).
  • A299692 (program): a(n) is the total area that is visible in the perspective view of the stepped pyramid with n levels described in A245092.
  • A299763 (program): a(n) = 1 + A182986(n).
  • A299766 (program): Greatest odd noncomposite divisor of n.
  • A299795 (program): Numbers of the form p*2^(p-1) where p is prime.
  • A299822 (program): Product of Euler’s totient and the squarefree kernel, a(n) = phi(n)*rad(n).
  • A299913 (program): a(n) = a(n-1) + 2a(n-2) if n even, or 3a(n-1) + 4*a(n-2) if n odd, starting with 0, 1.
  • A299960 (program): a(n) = ( 4^(2*n+1) + 1 )/5.
  • A299965 (program): Number of triangles in a Star of David of size n.