List of integer sequences with links to LODA programs.

  • A249999 (program): Expansion of 1/((1-x)^2*(1-2*x)*(1-3*x)).
  • 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.
  • A250025 (program): Lesser of twin prime pairs of the form (40n - 21, 40n - 19).
  • A250060 (program): Number of length 1+6 0..n arrays with no seven consecutive terms having the maximum of any two terms equal to the minimum of the remaining five terms.
  • A250068 (program): Maximum width of any region in the symmetric representation of sigma(n).
  • 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.
  • A250092 (program): a(n) = binomial( prime(n+4), prime(n) ).
  • A250094 (program): Positive integers k such that the numerator of the harmonic mean of the divisors of k is equal to k.
  • A250098 (program): Number of triangles in minimal triangulation of the orientable closed surface of genus n (S_n).
  • A250102 (program): a(n) = 2*5^n - (1+2i)^(2n) - (1-2i)^(2n) where i = sqrt(-1).
  • A250103 (program): Expansion of (1+x)/(1+x-2*x^2-3*x^3).
  • A250104 (program): Triangle read by rows: T(n,k) = number of partitions of n with k circular successions (n>=0, 0 <= k <= n).
  • A250105 (program): Column 1 of triangle in A250104 (or A124323).
  • A250106 (program): Column 2 of triangle in A250104 (or A124323).
  • A250107 (program): Column 3 of triangle in A250104 (or A124323).
  • A250108 (program): n*(n-1)/2 mod 2 + n*(n-1)/2 - n*( (n-1) mod 2 ).
  • A250111 (program): Number of orbits of size 2 in vertices of Fibonacci cube Gamma_n under the action of its automorphism group.
  • 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.
  • A250128 (program): Number of triforces generated at iteration n in a Koch-Sierpiński Ninja Star.
  • 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.
  • A250142 (program): Number of length 3+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.
  • A250204 (program): Sierpiński problem in base 6: Least k > 0 such that n*6^k+1 is prime, or 0 if no such k exists.
  • A250207 (program): The number of quartic terms in the multiplicative group modulo n.
  • A250208 (program): Ratio of the primitive part of 2^n-1 to the product of primitive prime factors of 2^n-1.
  • A250212 (program): Second partial sums of seventh powers (A001015).
  • A250222 (program): a(n) = phi(2n+1) - phi(2n), where phi is A000010.
  • 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.
  • A250256 (program): Least positive integer whose decimal digits divide the plane into n regions (A249572 variant).
  • A250257 (program): Least nonnegative integer whose decimal digits divide the plane into n regions.
  • A250258 (program): Least nonnegative integer whose decimal digits divide the plane into n regions (A250257 variant).
  • A250271 (program): Number of length n+1 0..2 arrays with the sum of the squares of adjacent differences multiplied by some arrangement of +-1 equal to zero.
  • A250309 (program): a(n) = a(n-1)*(1 + a(n-1)/a(n-3)), with a(0) = a(1) = a(2) = 1.
  • A250310 (program): Numbers whose squares are of the form x^2 + y^2 + 3 where x >= y >= 0 (repetitions omitted).
  • A250313 (program): Number of length n+2 0..1 arrays with the sum of second differences squared multiplied by some arrangement of +-1 equal to zero.
  • A250327 (program): Numerator of the harmonic mean of the first n pentagonal numbers.
  • A250328 (program): Denominator of the harmonic mean of the first n pentagonal numbers.
  • 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.
  • A250344 (program): Numerator of the harmonic mean of the first n hexagonal numbers.
  • A250345 (program): Numerator of the harmonic mean of the first n heptagonal numbers.
  • 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.
  • A250400 (program): Numerator of the harmonic mean of the first n octagonal numbers.
  • A250420 (program): Number of length 3+1 0..n arrays with the sum of the minimum of each adjacent pair multiplied by some arrangement of +-1 equal to zero.
  • A250425 (program): Number of (n+1) X (n+1) 0..1 arrays with nondecreasing sum of every two consecutive values in every row and column.
  • A250426 (program): Number of (n+1)X(2+1) 0..1 arrays with nondecreasing sum of every two consecutive values in every row and column.
  • 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
  • A250428 (program): Number of (n+1)X(4+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
  • A250430 (program): Number of (n+1)X(6+1) 0..1 arrays with nondecreasing sum of every two consecutive values in every row and column
  • A250431 (program): Number of (n+1)X(7+1) 0..1 arrays with nondecreasing sum of every two consecutive values in every row and column
  • A250437 (program): Number of (n+1)X(2+1) 0..2 arrays with nondecreasing sum of every two consecutive values in every row and column
  • A250438 (program): Number of (n+1)X(3+1) 0..2 arrays with nondecreasing sum of every two consecutive values in every row and column
  • A250439 (program): Number of (n+1)X(4+1) 0..2 arrays with nondecreasing sum of every two consecutive values in every row and column
  • A250440 (program): Number of (n+1)X(5+1) 0..2 arrays with nondecreasing sum of every two consecutive values in every row and column
  • A250441 (program): Number of (n+1)X(6+1) 0..2 arrays with nondecreasing sum of every two consecutive values in every row and column
  • A250442 (program): Number of (n+1)X(7+1) 0..2 arrays with nondecreasing sum of every two consecutive values in every row and column
  • A250445 (program): a(n) = gcd(n!, Fibonacci(n)) as n runs through A250444.
  • 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.
  • A250473 (program): Length of the maximal prefix of noncomposite numbers on row n of A249821.
  • A250474 (program): Number of times prime(n) occurs as the least prime factor among numbers 1 .. prime(n)^3: a(n) = A078898(A030078(n)).
  • 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.
  • A250486 (program): A(n,k) is the n^k-th Fibonacci number; square array A(n,k), n>=0, k>=0, read by antidiagonals.
  • A250497 (program): Number of (n+2)X(1+2) 0..1 arrays with nondecreasing medians of every three consecutive values in every row and column
  • A250548 (program): Numerator of the harmonic mean of the first n 9-gonal numbers.
  • A250549 (program): Denominator of the harmonic mean of the first n 9-gonal numbers.
  • A250550 (program): Numerator of the harmonic mean of the first n 10-gonal numbers.
  • A250551 (program): Denominator of the harmonic mean of the first n positive 10-gonal numbers.
  • 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.
  • A250577 (program): Number of (n+1) X (2+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.
  • A250604 (program): Number of (n+1)X(n+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
  • 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.
  • A250613 (program): Number of (n+1)X(1+1) 0..2 arrays with nondecreasing maximum of every two consecutive values in every row and column
  • A250652 (program): Number of (n+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
  • 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
  • A250731 (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 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.
  • A250742 (program): T(n,k)=Number of (n+1)X(k+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
  • A250744 (program): Denominator of the harmonic mean of the first n positive Fibonacci numbers.
  • 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.
  • A250752 (program): Number of (n+1) X (5+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.
  • A250773 (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 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.
  • A250784 (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.
  • A250791 (program): Number of (n+1) X (2+1) 0..1 arrays with nondecreasing min(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.
  • A250798 (program): Number of (1+1) X (n+1) 0..1 arrays with nondecreasing min(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.
  • A250799 (program): Number of (2+1) X (n+1) 0..1 arrays with nondecreasing min(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.
  • A250808 (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 min(x(i,j),x(i-1,j)) in the j direction.
  • A250809 (program): Number of (n+1) X (5+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.
  • A250810 (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 min(x(i,j),x(i-1,j)) in the j direction.
  • A250811 (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 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.
  • A250871 (program): Number of (n+1) X (2+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.
  • A250872 (program): Number of (n+1) X (3+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.
  • A250873 (program): Number of (n+1) X (4+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.
  • A250885 (program): G.f. A(x) satisfies: x = A(x) * (1 - A(x)) * (1 - 3*A(x)).
  • A250886 (program): G.f. A(x) satisfies: x = A(x) * (1 + A(x)) * (1 - 2*A(x)).
  • A250887 (program): G.f. A(x) satisfies: x = A(x) * (1 + A(x)) * (1 - 3*A(x)).
  • A250888 (program): G.f. A(x) satisfies: x = A(x) * (1 + A(x)) * (1 - 4*A(x)).
  • A250889 (program): G.f. A(x) satisfies: x = A(x) * (1 + 2*A(x)) * (1 - 3*A(x)).
  • A250890 (program): G.f. A(x) satisfies: x = A(x) * (1 + 2*A(x)) * (1 - 5*A(x)).
  • A250899 (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 absolute value of x(i,j)-x(i-1,j) in the j direction.
  • A250914 (program): E.g.f.: (18 - 17*cosh(x)) / (25 - 24*cosh(x)).
  • A250915 (program): E.g.f.: (32 - 31*cosh(x)) / (41 - 40*cosh(x)).
  • A250916 (program): E.g.f.: exp(C(x)^2 - 1) where C(x) = 1 + x*C(x)^2 is the g.f. of the Catalan numbers, A000108.
  • A250917 (program): E.g.f.: exp( x*C(x)^3 ) where C(x) = (1 - sqrt(1-4*x))/(2*x) is the g.f. of the Catalan numbers, A000108.
  • A251091 (program): a(n) = n^2 / gcd(n+2, 4).
  • A251092 (program): a(n) is the number of primes in the n-th group of consecutive primes among the odd numbers.
  • A251122 (program): Number of (n+1) X (2+1) 0..1 arrays with no 2 X 2 subblock having the sum of its diagonal elements greater than the maximum of its antidiagonal elements.
  • A251143 (program): Number of (n+1) X (2+1) 0..2 arrays with every 2 X 2 subblock summing to 4 and no 2 X 2 subblock having exactly two nonzero entries.
  • A251144 (program): Number of (n+1) X (3+1) 0..2 arrays with every 2 X 2 subblock summing to 4 and no 2 X 2 subblock having exactly two nonzero entries.
  • A251145 (program): Number of (n+1) X (4+1) 0..2 arrays with every 2 X 2 subblock summing to 4 and no 2 X 2 subblock having exactly two nonzero entries.
  • A251146 (program): Number of (n+1) X (5+1) 0..2 arrays with every 2 X 2 subblock summing to 4 and no 2 X 2 subblock having exactly two nonzero entries.
  • A251147 (program): Number of (n+1) X (6+1) 0..2 arrays with every 2 X 2 subblock summing to 4 and no 2 X 2 subblock having exactly two nonzero entries.
  • A251148 (program): Number of (n+1) X (7+1) 0..2 arrays with every 2 X 2 subblock summing to 4 and no 2 X 2 subblock having exactly two nonzero entries.
  • A251182 (program): a(n) = Sum_{k=0..n} binomial(n, k) * (2^k - 1)^k.
  • A251183 (program): a(n) = Sum_{k=0..n} binomial(n,k) * (-1)^(n-k) * (2^k + 1)^k.
  • A251184 (program): a(n) = Sum_{k=0..n} binomial(n,k) * (2^k + 3)^k.
  • A251187 (program): Number of (n+2)X(1+2) 0..1 arrays with nondecreasing sum of every three consecutive values in every row and column
  • A251194 (program): Number of (n+1) X (1+1) 0..1 arrays with no 2 X 2 subblock having the minimum of its diagonal elements less than the absolute difference of its antidiagonal elements.
  • A251203 (program): Number of (n+1) X (1+1) 0..2 arrays with every 2 X 2 subblock summing to a nonzero multiple of 2.
  • A251212 (program): Number of (n+1) X (1+1) 0..1 arrays with no 2 X 2 subblock having zero or two 1’s.
  • A251221 (program): Number of (n+1) X (1+1) 0..1 arrays with no 2 X 2 subblock having the minimum of its diagonal elements greater than the absolute difference of its antidiagonal elements.
  • A251251 (program): Number of (n+1) X (1+1) 0..1 arrays with every 2 X 2 subblock having a single 1 or two 1s on the same edge.
  • 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.
  • A251276 (program): Number of (n+1) X (1+1) 0..3 arrays with no 2 X 2 subblock having its maximum diagonal element less than its minimum antidiagonal element.
  • A251285 (program): Number of (n+1) X (1+1) 0..1 arrays with every 2 X 2 subblock having a single 1 or two 1s on the same edge or main diagonally.
  • A251310 (program): Number of (n+1) X (1+1) 0..1 arrays with no 2 X 2 subblock having the maximum of its diagonal elements greater than the absolute difference of its antidiagonal elements.
  • A251319 (program): Number of (n+1) X (1+1) 0..1 arrays with every 2 X 2 subblock having one or two 1s.
  • A251328 (program): Number of (n+1) X (1+1) 0..2 arrays with every 2 X 2 subblock summing to 2 4 or 6.
  • A251336 (program): Number of (n+1) X (1+1) 0..3 arrays with every 2 X 2 subblock summing to a nonzero multiple of 3.
  • A251344 (program): Number of (n+1) X (1+1) 0..2 arrays with every 2 X 2 subblock summing to 3 4 or 5.
  • A251364 (program): Difference between average of two consecutive odd primes and the sum of all prime factors of the average.
  • A251366 (program): Number of (n+1) X (1+1) 0..2 arrays with every 2 X 2 subblock summing to 1 2 3 4 5 6 or 7.
  • A251383 (program): Number of (n+1) X (1+1) 0..2 arrays with every 2 X 2 subblock summing to 2 3 4 5 or 6.
  • 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.
  • A251484 (program): Number of (n+1) X (1+1) 0..3 arrays with no 2 X 2 subblock having the sum of its diagonal elements less than the minimum of its antidiagonal elements.
  • A251517 (program): Number of (n+1) X (1+1) 0..3 arrays with every 2 X 2 subblock summing to 2 3 4 5 6 7 8 9 or 10.
  • A251561 (program): A permutation of the natural numbers: interchange p and 2p for every prime p.
  • A251568 (program): E.g.f.: exp(x*C(x)^2) where C(x) = 1 + x*C(x)^2 is the g.f. of the Catalan numbers, A000108.
  • A251569 (program): E.g.f.: exp(x*G(x)) where G(x) = 1 + x*G(x)^3 is the g.f. of A001764.
  • A251573 (program): E.g.f.: exp(3*x*G(x)^2) / G(x)^2 where G(x) = 1 + x*G(x)^3 is the g.f. of A001764.
  • A251574 (program): E.g.f.: exp(4*x*G(x)^3) / G(x)^3 where G(x) = 1 + x*G(x)^4 is the g.f. of A002293.
  • A251575 (program): E.g.f.: exp(5*x*G(x)^4) / G(x)^4 where G(x) = 1 + x*G(x)^5 is the g.f. of A002294.
  • A251576 (program): E.g.f.: exp(6*x*G(x)^5) / G(x)^5 where G(x) = 1 + x*G(x)^6 is the g.f. of A002295.
  • A251577 (program): E.g.f.: exp(7*x*G(x)^6) / G(x)^6 where G(x) = 1 + x*G(x)^7 is the g.f. of A002296.
  • A251578 (program): E.g.f.: exp(8*x*G(x)^7) / G(x)^7 where G(x) = 1 + x*G(x)^8 is the g.f. of A007556.
  • A251579 (program): E.g.f.: exp(9*x*G(x)^8) / G(x)^8 where G(x) = 1 + x*G(x)^9 is the g.f. of A062994.
  • A251580 (program): E.g.f.: exp(10*x*G(x)^9) / G(x)^9 where G(x) = 1 + x*G(x)^10 is the g.f. of A059968.
  • A251583 (program): a(n) = 3^(n-1) * (n+1)^(n-3) * (n+3).
  • A251584 (program): a(n) = 4^(n-2) * (n+1)^(n-4) * (3*n^2 + 13*n + 16).
  • A251585 (program): a(n) = 5^(n-3) * (n+1)^(n-5) * (16*n^3 + 87*n^2 + 172*n + 125).
  • A251586 (program): a(n) = 6^(n-4) * (n+1)^(n-6) * (125*n^4 + 810*n^3 + 2095*n^2 + 2586*n + 1296).
  • A251587 (program): a(n) = 7^(n-5) * (n+1)^(n-7) * (1296*n^5 + 9720*n^4 + 30555*n^3 + 50665*n^2 + 44621*n + 16807).
  • A251588 (program): a(n) = 8^(n-6) * (n+1)^(n-8) * (16807*n^6 + 143031*n^5 + 525875*n^4 + 1074745*n^3 + 1294846*n^2 + 876856*n + 262144).
  • A251589 (program): a(n) = 9^(n-7) * (n+1)^(n-9) * (262144*n^7 + 2494464*n^6 + 10470208*n^5 + 25229505*n^4 + 37857568*n^3 + 35537670*n^2 + 19414368*n + 4782969).
  • A251590 (program): a(n) = 10^(n-8) * (n+1)^(n-10) * (4782969*n^8 + 50309748*n^7 + 237013938*n^6 + 655232760*n^5 + 1166624361*n^4 + 1374998212*n^3 + 1051760172*n^2 + 479277840*n + 100000000).
  • 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.
  • A251626 (program): Denominator of fraction equal to the continued fraction [2,7,1,8,2,…] (first n digits of e).
  • 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.
  • A251634 (program): Numerators of inverse Riordan triangle of Riordan triangle A029635. Riordan (1/(1-x), x/(1+2*x)). Triangle read by rows for 0 <= m <= n.
  • A251635 (program): Riordan array (1-2*x,x), inverse of Riordan array (1/(1-2*x), x) = A130321.
  • A251636 (program): Inverse of the Riordan array A251634: Riordan ((1-3*x)/(1-2*x), x/(1-2*x)).
  • A251653 (program): 5-step Fibonacci sequence starting with 0,0,1,0,0.
  • A251654 (program): 4-step Fibonacci sequence starting with 0, 1, 1, 0.
  • A251655 (program): 4-step Fibonacci sequence starting with 0, 1, 1, 1.
  • A251656 (program): 4-step Fibonacci sequence starting with 1,0,1,0.
  • A251657 (program): a(n) = (2^n + 3)^n.
  • A251663 (program): E.g.f.: exp( 3*x*G(x)^2 ) / G(x), where G(x) = 1 + x*G(x)^3 is the g.f. A001764.
  • A251664 (program): E.g.f.: exp(4*x*G(x)^3) / G(x) where G(x) = 1 + x*G(x)^4 is the g.f. of A002293.
  • A251665 (program): E.g.f.: exp(5*x*G(x)^4) / G(x) where G(x) = 1 + x*G(x)^5 is the g.f. of A002294.
  • A251666 (program): E.g.f.: exp(6*x*G(x)^5) / G(x) where G(x) = 1 + x*G(x)^6 is the g.f. of A002295.
  • A251667 (program): E.g.f.: exp(7*x*G(x)^6) / G(x) where G(x) = 1 + x*G(x)^7 is the g.f. of A002296.
  • A251668 (program): E.g.f.: exp(8*x*G(x)^7) / G(x) where G(x) = 1 + x*G(x)^8 is the g.f. of A007556.
  • A251669 (program): E.g.f.: exp(9*x*G(x)^8) / G(x) where G(x) = 1 + x*G(x)^9 is the g.f. of A062994.
  • A251670 (program): E.g.f.: exp(10*x*G(x)^9) / G(x) where G(x) = 1 + x*G(x)^10 is the g.f. of A059968.
  • A251671 (program): a(n) = Sum_{k=0..n} C(n,k) * (2^k + 3^k)^k.
  • A251672 (program): 8-step Fibonacci sequence starting with 0,0,0,0,0,0,1,0.
  • A251684 (program): G.f.: exp( Sum_{n>=1} A047863(n)*x^n/n ), where A047863(n) = Sum_{k=0..n} binomial(n, k) * (2^k)^(n-k).
  • A251693 (program): a(n) = (n+1) * (2*n+1)^(n-2) * 3^n.
  • A251701 (program): a(n) = 3^n + n^2.
  • A251703 (program): 4-step Fibonacci sequence starting with 1,1,0,0.
  • A251704 (program): 4-step Fibonacci sequence starting with 1, 1, 0, 1.
  • A251705 (program): 4-step Fibonacci sequence starting with 1, 1, 1, 0.
  • A251706 (program): 6-step Fibonacci sequence starting with (0,0,0,0,1,0).
  • A251707 (program): 6-step Fibonacci sequence starting with (0,0,0,1,0,0).
  • A251708 (program): 6-step Fibonacci sequence starting with (0,0,1,0,0,0).
  • A251709 (program): 6-step Fibonacci sequence starting with (0,1,0,0,0,0).
  • A251710 (program): 7-step Fibonacci sequence starting with (0,0,0,0,0,1,0).
  • A251711 (program): 7-step Fibonacci sequence starting with (0,0,0,0,1,0,0).
  • A251712 (program): 7-step Fibonacci sequence starting with (0,0,0,1,0,0,0).
  • A251713 (program): 7-step Fibonacci sequence starting with (0,0,1,0,0,0,0).
  • A251714 (program): 7-step Fibonacci sequence starting with (0,1,0,0,0,0,0).
  • A251719 (program): a(n) = the least k such that A250474(k) > n.
  • A251720 (program): a(n) = (p_n)^2 * p_{n+1}, where p_n is the n-th prime, A000040(n).
  • A251723 (program): First differences of A054272, A250473 and A250474: a(n) = A054272(n+1) - A054272(n).
  • A251726 (program): Numbers n > 1 for which gpf(n) < lpf(n)^2, where lpf and gpf (least and greatest prime factor of n) are given by A020639(n) and A006530(n).
  • A251727 (program): Numbers n > 1 for which gpf(n) > spf(n)^2, where spf and gpf (smallest and greatest prime factor of n) are given by A020639(n) and A006530(n).
  • A251728 (program): Semiprimes p*q for which p <= q < p^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.
  • A251732 (program): a(n) = 3^n*A123335(n). Rational parts of the integers in Q(sqrt(2)) giving the length of a Lévy C-curve variant at iteration step n.
  • A251733 (program): a(n) = 3^n*A077985(n-1), A077985(-1) = 0. Irrational parts of the integers in Q(sqrt(2)) giving the length of a Lévy C-curve variant at iteration step n.
  • A251740 (program): 8-step Fibonacci sequence starting with 0,0,0,0,0,1,0,0.
  • A251741 (program): 8-step Fibonacci sequence starting with 0,0,0,0,1,0,0,0.
  • A251742 (program): 8-step Fibonacci sequence starting with 0,0,0,1,0,0,0,0.
  • A251743 (program): Pairs of nodes in a complete binary tree that are at an absolute height difference of less than 2 from each other.
  • A251744 (program): 8-step Fibonacci sequence starting with 0,0,1,0,0,0,0,0.
  • A251745 (program): 8-step Fibonacci sequence starting with 0,1,0,0,0,0,0,0.
  • A251746 (program): 9-step Fibonacci sequence starting with 0,0,0,0,0,0,0,1,0.
  • A251747 (program): 9-step Fibonacci sequence starting with 0,0,0,0,0,0,1,0,0.
  • A251748 (program): 9-step Fibonacci sequence starting with 0,0,0,0,0,1,0,0,0.
  • A251749 (program): 9-step Fibonacci sequence starting with 0,0,0,0,1,0,0,0,0.
  • A251750 (program): 9-step Fibonacci sequence starting with 0,0,0,1,0,0,0,0,0.
  • A251751 (program): 9-step Fibonacci sequence starting with 0,0,1,0,0,0,0,0,0.
  • A251752 (program): 9-step Fibonacci sequence starting with 0,1,0,0,0,0,0,0,0.
  • 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_1*d_2 + d_2*d_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).
  • A251793 (program): Numbers n such that the sum of the triangular numbers T(n) and T(n+1) is equal to the sum of the octagonal numbers N(m) and N(m+1) for some m.
  • A251861 (program): Number of non-palindromic words (length n>0) over the alphabet of 26 letters.
  • A251863 (program): Numbers n such that the sum of the octagonal numbers N(n), N(n+1) and N(n+2) is equal to the sum of the pentagonal numbers P(m), P(m+1), P(m+2) for some m.
  • A251864 (program): Numbers n such that the sum of the pentagonal numbers P(n), P(n+1) and P(n+2) is equal to the sum of the octagonal numbers N(m), N(m+1) and N(m+2) for some m.
  • 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.
  • A251895 (program): Numbers n such that the sum of the octagonal numbers N(n) and N(n+1) is equal to another octagonal number.
  • A251896 (program): Numbers n such that the octagonal number N(n) is equal to the sum of the octagonal numbers N(m) and N(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.
  • A251927 (program): Numbers n such that the sum of the triangular numbers T(n) and T(n+1) is equal to a heptagonal number H(m) for some m.
  • A251928 (program): Number of length n+2 0..1 arrays with the sum of the maximum minus the median of adjacent triples multiplied by some arrangement of +-1 equal to zero.
  • 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.
  • A251969 (program): Number of (n+1)X(2+1) 0..3 arrays with nondecreasing sum of every two consecutive values in every row and column
  • A251971 (program): Number of (n+1)X(5+1) 0..3 arrays with nondecreasing sum of every two consecutive values in every row and column
  • A251973 (program): Number of (n+1)X(7+1) 0..3 arrays with nondecreasing sum of every two consecutive values in every row and column
  • A251984 (program): Smallest number such that a carry occurs when adding it to n in decimal representation.
  • 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.
  • A252076 (program): Numbers n such that the sum of the heptagonal numbers H(n) and H(n+1) is equal to the hexagonal number X(m) for some m.
  • A252077 (program): Numbers n such that the hexagonal number X(n) is equal to the sum of the heptagonal number H(m) and H(m+1) for some m.
  • A252089 (program): Primes p such that p + 26 is prime.
  • A252090 (program): Primes p such that p + 28 is also prime.
  • A252091 (program): Primes p such that p + 34 is prime.
  • A252096 (program): Largest prime divisor of n^2+1 - smallest prime divisor of n^2+1.
  • A252158 (program): Triangle read by rows, 1 <= k <= n, T(n,k) = number of arrangements of n circles in the affine plane having k solid regions in which the union of solid circles is connected.
  • A252169 (program): Beatty sequence for sqrt(Pi*phi) where phi is the golden ratio A001622.
  • 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.
  • A252230 (program): Triangular array T read by rows: for j = k+1..2*k, k >=1, T(j,k) = least number of iterations of (h,i) -> (i,h-i) needed to take (k,j) to (k’,j’) satisfying k’ <= j’.
  • A252233 (program): Characteristic function for the integers that are the product of an odd number of primes each with multiplicity one.
  • A252284 (program): Exponential generating function exp(-x-x^2-x^3/3).
  • A252355 (program): a(n) = sum_{k = 0..n-1} (-1)^k*C(2*n-1,k)*C(n-1,k), n>0.
  • A252359 (program): Numbers n such that the sum of the heptagonal numbers H(n) and H(n+1) is equal to the pentagonal number P(m) for some m.
  • A252360 (program): Numbers n such that the pentagonal number P(n) is equal to the sum of the heptagonal numbers H(m) and H(m+1) for some m.
  • A252372 (program): Characteristic function for A251726: a(n) = 1 if n > 1 and gpf(n) < spf(n)^2, otherwise 0; here spf(n) and gpf(n) (smallest and greatest prime factor of n) are sequences A020639(n) and A006530(n).
  • A252373 (program): Partial sums of A252372, inverse function for A251726.
  • A252424 (program): Numbers k such that sum of odd divisors of k equals sum of squares of primes dividing k.
  • A252461 (program): Shift one instance of the smallest prime one step towards smaller primes: a(1) = 1, a(2n) = n, and for odd numbers > 1: a(n) = (n / prime(s)) * prime(s-1), where s = A055396(n), index of the smallest prime dividing n.
  • A252462 (program): Shift one instance of the largest prime one step towards smaller primes: a(1) = 1, a(2^n) = 2^(n-1), and for other numbers: a(n) = (n / prime(g)) * prime(g-1), where g = A061395(n), index of the greatest prime dividing n.
  • A252463 (program): Hybrid shift: a(1) = 1, a(2n) = n, a(2n+1) = A064989(2n+1); shift the even numbers one bit right, shift the prime factorization of odd numbers one step towards smaller primes.
  • A252464 (program): a(1) = 0, a(2n) = 1 + a(n), a(2n+1) = 1 + a(A064989(2n+1)); also binary width of terms of A156552 and A243071.
  • A252480 (program): Numbers whose decimal representation has at least one ‘0’ digit in a position other than the final digit.
  • A252482 (program): Exponents n such that the decimal expansion of the power 12^n contains no zeros.
  • 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).
  • A252501 (program): Triangle T read by rows: T(n,k) = binomial(2*n+1,k)*binomial(n,k), n>=0, 0<=k<=n.
  • A252502 (program): Number of digits of Phi_n(10), or number of digits in base b of Phi_n(b), where Phi is the cyclotomic polynomial.
  • A252505 (program): Number of biquadratefree (4th power free) divisors of n.
  • A252585 (program): Numbers n such that the sum of the pentagonal numbers P(n) and P(n+1) is equal to the heptagonal number H(m) for some m.
  • A252586 (program): Numbers n such that the heptagonal number H(n) is equal to the sum of the pentagonal numbers P(m) and P(m+1) for some m.
  • A252630 (program): Numbers n such that the sum of the hexagonal numbers X(n), X(n+1), X(n+2) and X(n+3) is equal to the heptagonal number H(m) for some m.
  • A252631 (program): Numbers n such that the heptagonal number H(n) is equal to the sum of the hexagonal numbers X(m), X(m+1), X(m+2) and X(m+3) for some m.
  • A252649 (program): The number of positive integers that are less than or equal to n that have a primitive root.
  • A252650 (program): Expansion of (eta(q) * eta(q^2) * eta(q^3) / eta(q^6))^2 in powers of q.
  • A252651 (program): Expansion of q^(-1/2) * (eta(q) * eta(q^2) * eta(q^6) / eta(q^3))^2 in powers of q.
  • A252669 (program): a(n) is the smallest integer k such that n*k mod (n+k) = 1, or -1 if no such k exists.
  • A252696 (program): Number of strings of length n over a 3-letter alphabet that do not begin with a nontrivial palindrome.
  • A252697 (program): Number of strings of length n over a 4-letter alphabet that do not begin with a palindrome.
  • A252706 (program): Expansion of phi(-q) / phi(-q^3) in powers of q where phi() is a Ramanujan theta function.
  • A252709 (program): Sum_{k=0..n} k^(n+k)*(n-k)^k.
  • A252710 (program): Sum_{k=0..n} k^(n-k)*(n+k)^k.
  • A252722 (program): Number of (3+2) X (n+2) 0..3 arrays with every consecutive three elements in every row and diagonal having exactly two distinct values, and in every column and antidiagonal not having exactly two distinct values, and new values 0 upwards introduced in row major order.
  • A252727 (program): a(n) = n-th number of the n-th iteration of the hyperbinomial transform on sequence A001858 (number of forests of trees on n labeled nodes).
  • 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) > 2*n, then a(n) = 1, otherwise 0 (when A003961(n) < 2*n) [where A003961(n) shifts the prime factorization of n one step towards larger primes].
  • A252743 (program): a(n) = A252742(A005940(1+n)).
  • A252747 (program): Numbers n such that the hexagonal number H(n) is equal to the sum of four consecutive squares.
  • A252748 (program): a(n) = A003961(n) - 2*n.
  • A252749 (program): Partial sums of A252748: a(0) = 0, a(n) = A252748(n) + a(n-1).
  • A252759 (program): Manhattan distance of n in array A246278 from the top left corner: a(1) = 0; for n>1: a(n) = A055396(n) + A246277(n) - 1.
  • A252762 (program): Numbers n such that the sum of the pentagonal numbers P(n), P(n+1), P(n+2) and P(n+3) is equal to the hexagonal number H(m) for some m.
  • A252763 (program): Numbers n such that the hexagonal number H(n) is equal to the sum of the pentagonal numbers P(m), P(m+1), P(m+2) and P(m+3) for some m.
  • A252769 (program): Numbers n such that the sum of the pentagonal numbers P(n), P(n+1), P(n+2) and P(n+3) is equal to the heptagonal number H(m) for some m.
  • A252770 (program): Numbers n such that the heptagonal number H(n) is equal to the sum of the pentagonal numbers P(m), P(m+1), P(m+2) and P(m+3) for some m.
  • A252801 (program): Primes whose trajectories under the map x -> A039951(x) enter the cycle {2, 1093}.
  • 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.
  • A252815 (program): Number of n X 3 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.
  • A252822 (program): Number of n X 2 nonnegative integer arrays with upper left 0 and every value within 3 of its city block distance from the upper left and every value increasing by 0 or 1 with every step right or down.
  • A252840 (program): Coefficients of G_i(x) with G_0 = 1, G_1 = 1+x, G_n = (1-2*x)*G_{n-1}+(x-x^2)*G_{n-2}.
  • A252849 (program): Numbers with an even number of square divisors.
  • A252854 (program): Number of (n+2) X (1+2) 0..2 arrays with every consecutive three elements in every row, column, diagonal and antidiagonal having exactly two distinct values, and new values 0 upwards introduced in row major order.
  • A252863 (program): Number of Eulerian paths in a lattice graph bounded by the four equations x+y=1, x+y=2n, x-y=2, and x-y=-2.
  • 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.
  • A252871 (program): Number of nX3 nonnegative integer arrays with upper left 0 and lower right n+3-4 and value increasing by 0 or 1 with every step right or down
  • A252893 (program): Primes congruent to 11 mod 111.
  • A252895 (program): Numbers with an odd number of square divisors.
  • A252922 (program): a(n) = sigma(n-1) + sigma(n-2) + sigma(n-3), with a(1)=0, a(2)=1, a(3)=4.
  • A252924 (program): Number of n X 2 nonnegative integer arrays with upper left 0 and lower right n+2-6 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.
  • A252970 (program): Number of nX2 nonnegative integer arrays with upper left 0 and lower right n+2-5 and value increasing by 0 or 1 with every step right or down
  • A252994 (program): Multiples of 26.
  • A252995 (program): Numbers n such that the n-th odd composite number is 3n.
  • A253012 (program): a(n) = ceiling( (n+1) * (n+2) / 12).
  • A253029 (program): Number of (n+2) X (1+2) 0..2 arrays with every consecutive three elements in every row and column having exactly two distinct values, and new values 0 upwards introduced in row major order.
  • A253062 (program): Largest order of a rooted tree that does not contain a rooted caterpillar subtree of order n.
  • A253064 (program): Number of odd terms in f^n, where f = 1/x+1+x+y.
  • A253066 (program): Number of odd terms in f^n, where f = 1/x+1+x+1/y+y/x+x*y.
  • A253068 (program): The subsequence A253066(2^n-1).
  • A253077 (program): Bisection of A136704 (divided by 2).
  • A253081 (program): Partial sums of A246029.
  • A253082 (program): Partial sums of A246595.
  • A253083 (program): Partial sums of A227349.
  • A253084 (program): Triangle read by rows: T(n,k) = {binomial(n+k,n-k)*binomial(n,k)} mod 2, 0 <= k <= n.
  • A253091 (program): List of ternary words obtained by expanding (1+2x)^n mod 3 and reading the coefficients starting with the constant term.
  • A253092 (program): Log_3(A133579(n)).
  • A253093 (program): Related to residues of poles of moment function for random walks in 4 dimensions.
  • A253098 (program): Partial sums of A169707.
  • A253101 (program): a(n) = A253100(2^n-1).
  • A253102 (program): a(n) = A071053(n)^3.
  • A253103 (program): A001045(n)^3.
  • A253106 (program): Semiprimes with smallest factor <= 3.
  • A253109 (program): a(n) = n ^ (Fibonacci(n) mod n).
  • A253120 (program): Numbers n such that the sum of the octagonal numbers O(n), O(n+1), O(n+2) and O(n+3) is equal to the hexagonal number H(m) for some m.
  • A253121 (program): Numbers n such that the hexagonal number H(n) is equal to the sum of the octagonal numbers O(m), O(m+1), O(m+2) and O(m+3) for some m.
  • 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.
  • A253139 (program): a(n) = lcm_{d|n} tau(d), where tau(d) represents the number of divisors of d (A000005(d)).
  • A253141 (program): If n is a prime power, then a(n) = lambda(tau(n)) = A014963(A000005(n)); otherwise, a(n) = 1.
  • A253145 (program): Triangular numbers (A000217) omitting the term 1.
  • A253146 (program): A fractal tree, read by rows: for n > 2, T(n,1) = T(n-1,1)+2, T(n,n) = T(n-1,1)+3, and for k=2..n-1, T(n,k) = T(n-2,k-1).
  • A253151 (program): Number of (n+1)X(n+1) 0..1 arrays with every 2X2 subblock diagonal minus antidiagonal sum nondecreasing horizontally and vertically
  • A253152 (program): Number of (n+1) X (1+1) 0..1 arrays with every 2 X 2 subblock diagonal minus antidiagonal sum nondecreasing horizontally and vertically.
  • A253153 (program): Number of (n+1) X (2+1) 0..1 arrays with every 2 X 2 subblock diagonal minus antidiagonal sum nondecreasing horizontally and vertically.
  • A253154 (program): Number of (n+1) X (3+1) 0..1 arrays with every 2 X 2 subblock diagonal minus antidiagonal sum nondecreasing horizontally and vertically.
  • A253155 (program): Number of (n+1) X (4+1) 0..1 arrays with every 2 X 2 subblock diagonal minus antidiagonal sum nondecreasing horizontally and vertically.
  • A253156 (program): Number of (n+1) X (5+1) 0..1 arrays with every 2 X 2 subblock diagonal minus antidiagonal sum nondecreasing horizontally and vertically.
  • A253157 (program): Number of (n+1) X (6+1) 0..1 arrays with every 2 X 2 subblock diagonal minus antidiagonal sum nondecreasing horizontally and vertically.
  • A253158 (program): Number of (n+1) X (7+1) 0..1 arrays with every 2 X 2 subblock diagonal minus antidiagonal sum nondecreasing horizontally and vertically.
  • A253165 (program): a(n) = (-1)^n*2^(6*n+3)*(zeta(-2*n-1,1/2) - zeta(-2*n-1,1)), where zeta(a,z) is the generalized Riemann zeta function.
  • A253167 (program): Numbers n such that the sum of the pentagonal numbers P(n), P(n+1), P(n+2) and P(n+3) is equal to the octagonal number O(m) for some m.
  • A253168 (program): Numbers n such that the octagonal number O(n) is equal to the sum of the pentagonal numbers P(m), P(m+1), P(m+2) and P(m+3) for some m.
  • A253169 (program): Smallest m such that A256188(m) = n.
  • A253171 (program): a(n) = number of permutations of (1,2,…,n) producible by an ordered triple of distinct transpositions.
  • 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.
  • A253187 (program): Number of ordered ways to write n as the sum of a pentagonal number, a second pentagonal number and a generalized decagonal number.
  • A253191 (program): Decimal expansion of log(2)^2.
  • A253192 (program): Number of ways to place nonintersecting diagonals in convex (n+3)-gon so as to create exactly one triangle.
  • 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.
  • A253198 (program): a(n) = a(n-1) + a(n-2) - (-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.
  • A253205 (program): Natural numbers n such that n-1 is divisible by the sum of the decimal digits of n.
  • A253206 (program): Coefficients of the Dirichlet series for zeta(5s)/zeta(s).
  • 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.
  • A253243 (program): Expansion of phi(-x^2) * psi(x^3) * chi(x^3) in powers of x where phi(), psi(), chi() are Ramanujan theta functions.
  • A253246 (program): Pisano period of A006190 to mod prime(n).
  • A253249 (program): Number of nonempty chains in the divides relation on the divisors of n.
  • A253251 (program): a(1) = 1, and for n > 0, a(n+1) = a(n) + floor(10^k/a(n)), where k is the least integer such that 10^k >= a(n).
  • A253254 (program): Largest prime factor of the n-th 11-gonal number.
  • A253255 (program): G.f. satisfies: A(x) = (1 - x^3*A(x)^3)^2 / (1 - x*A(x))^4.
  • A253256 (program): G.f. satisfies: A(x) = (1 - x^3*A(x)^6) / (1 - x*A(x)^2)^2.
  • A253262 (program): Expansion of (x + x^2 + x^3) / (1 - x + x^2 - x^3 + x^4) in powers of x.
  • A253265 (program): The number of tilings of 2 X n boards with squares of 2 colors and dominoes of 3 colors.
  • A253268 (program): Product_{k=1..n} Fibonacci(k)^k.
  • A253273 (program): Triangle T(n,k) = Sum_{j=0..n-k+1} binomial(k+j,k-j+1)*binomial(n-k,j-1), read by rows.
  • A253275 (program): a(n) = Sum_{i=1..floor(n/2)} d( i*(n-i) ), where d(n) = the number of divisors of n.
  • A253283 (program): Triangle read by rows: coefficients of the partial fraction decomposition of [d^n/dx^n] (x/(1-x))^n/n!.
  • A253284 (program): Triangle read by rows, T(n,k) = (k+1)*(n+1)!*(n+k)!/((k+1)!^2*(n-k)!) with n >= 0 and 0 <= k <= n.
  • A253285 (program): a(n) = RF(n+1,3)*C(n+2,n-1), where RF(a,n) is the rising factorial.
  • A253289 (program): G.f.: Product_{k>=1} 1/(1-x^k)^(2*k-1).
  • A253298 (program): Digital root for the following sequences, F(4*n)/F(4); F(12*n)/F(12); F(20*n)/F(20), where the pattern increases by 8, ad infinitum, with the Fibonacci numbers F = A000045.
  • A253301 (program): Complement of the Beatty sequence for sqrt(Pi*phi), where phi is the golden ratio.
  • A253304 (program): Numbers n such that the sum of the heptagonal numbers H(n) and H(n+1) is equal to the octagonal number O(m) for some m.
  • A253305 (program): Numbers n such that the octagonal number O(n) is equal to the sum of the heptagonal numbers H(m) and H(m+1) for some m.
  • A253317 (program): Indices in A253315 where records occur.
  • A253368 (program): a(n) = F(12*n)/(12^2) with the Fibonacci numbers F = A000045.
  • A253388 (program): Numbers n such that the number of divisors of n is the product of two distinct primes.
  • A253408 (program): Values of difference z-y that solve equation x^2 + y^2 = z^2 + 2.
  • A253410 (program): Indices of centered pentagonal numbers (A005891) which are also centered octagonal numbers (A016754).
  • A253411 (program): Indices of centered octagonal numbers (A016754) which are also centered pentagonal numbers (A005891).
  • A253412 (program): Number of n-bit legal binary words with maximal set of 1s.
  • A253414 (program): G.f. satisfies (1+x^2)*g(x) = 1 + x*g(x^2).
  • A253428 (program): Number of (n+1)X(n+1) 0..1 arrays with every 2X2 subblock diagonal minus antidiagonal sum nondecreasing horizontally, vertically and ne-to-sw antidiagonally
  • A253429 (program): Number of (n+1) X (2+1) 0..1 arrays with every 2 X 2 subblock diagonal minus antidiagonal sum nondecreasing horizontally, vertically and ne-to-sw antidiagonally.
  • 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.
  • A253436 (program): Number of (2+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.
  • 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.
  • A253438 (program): Number of (4+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.
  • A253439 (program): Number of (5+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.
  • A253440 (program): Number of (6+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.
  • A253441 (program): Number of (7+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.
  • A253442 (program): Expansion of x * (96 - 816*x) / ((1 - x) * (1 - 1442*x + x^2)) in powers of x.
  • A253445 (program): a(n) = concatenation of n^2 with itself.
  • A253446 (program): Indices of centered heptagonal numbers (A069099) which are also centered octagonal numbers (A016754).
  • A253447 (program): Indices of centered octagonal numbers (A016754) which are also centered heptagonal numbers (A069099).
  • A253457 (program): Indices of centered hexagonal numbers (A003215) which are also centered heptagonal numbers (A069099).
  • A253458 (program): Indices of centered heptagonal numbers (A069099) which are also centered hexagonal numbers (A003215).
  • A253459 (program): Indices of centered square numbers (A001844) which are also centered heptagonal numbers (A069099).
  • A253460 (program): Indices of centered heptagonal numbers (A069099) which are also centered square numbers (A001844).
  • 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.
  • A253473 (program): a(n) = phi(c(n)) - tau(phi(c(n))), where c(n) is the n-th composite number.
  • A253475 (program): Indices of centered square numbers (A001844) which are also centered hexagonal numbers (A003215).
  • A253476 (program): Indices of centered triangular numbers (A005448) which are also centered heptagonal numbers (A069099).
  • A253477 (program): Indices of centered heptagonal numbers (A069099) which are also centered triangular numbers (A005448).
  • 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.
  • A253511 (program): Number of n-bit binary strings in which the length of any run of ones is a power of two.
  • A253512 (program): a(n) = (2^n - 1) * (3^(n+2) - 1) / 2.
  • 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 2*k 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).
  • A253547 (program): The total number of star-shaped dodecagons appearing in a variant of hexagon expansion after n iterations.
  • A253550 (program): Shift one instance of the largest prime one step towards larger primes: a(1) = 1, for n>1: a(n) = (n / prime(g)) * prime(g+1), where g = A061395(n), index of the greatest prime dividing n.
  • A253560 (program): Multiply n by its largest prime factor: a(n) = A006530(n) * n.
  • A253563 (program): Permutation of natural numbers: a(0) = 1, a(1) = 2; after which, a(2n) = A253560(a(n)), a(2n+1) = A253550(a(n)).
  • A253564 (program): Permutation of natural numbers: a(n) = A156552(A122111(n)).
  • A253565 (program): Permutation of natural numbers: a(0) = 1, a(1) = 2; after which, a(2n) = A253550(a(n)), a(2n+1) = A253560(a(n)).
  • A253566 (program): Permutation of natural numbers: a(n) = A243071(A122111(n)).
  • A253567 (program): Noncomposites together with such composites n = p_i * p_j * p_k * … * p_u, p_i <= p_j <= p_k <= … <= p_u, where there is at least one such pair of successive prime factors (when sorted into a nondecreasing order) that the square of the former is larger than the latter: (p_i)^2 > p_j or (p_j)^2 > p_k, etc.
  • A253568 (program): Even bisection of A122111: a(n) = A122111(2*n).
  • A253570 (program): Maximum number of circles of radius 1 that can be packed into a regular n-gon with side length 2 (conjectured).
  • A253571 (program): Total number of even outdegree nodes among all labeled rooted trees on n nodes.
  • A253579 (program): Centered pentagonal numbers (A005891) which are also centered octagonal numbers (A016754).
  • A253580 (program): A fractal tree, read by rows: for n > 1: T(n,0) = T(n-1,0)+2, T(n,2*n) = T(n-1,0)+3, and for k=1..2*n-1: T(n,k) = T(n-1,k-1).
  • A253583 (program): Decimal expansion of cube root of 2 multiplied by square root of 3.
  • A253585 (program): Numbers whose binary expansion equals the first n digits of the binary sequence A252488 whose run lengths are given by A001511 (the ruler function).
  • A253588 (program): Upward antidiagonals of array of all multiples of primorial(n), for each n>0.
  • A253599 (program): Centered square numbers (A001844) which are also centered heptagonal numbers (A069099).
  • A253607 (program): First differences of A253580, when the tree is seen as flattened list.
  • A253608 (program): The binary representation of a(n) is the concatenation of n and the binary complement of n, A035327(n).
  • A253610 (program): Numbers n with property that the sum of n and the digital root of n is prime.
  • 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).
  • A253623 (program): Expansion of phi(q) * f(q, q^2)^2 / f(q^2, q^4) in powers of q where phi(), f() are Ramanujan theta functions.
  • A253625 (program): Expansion of psi(q^2) * f(-q, q^2)^2 / f(-q, -q^5) in powers of q where psi(), f() are Ramanujan theta functions.
  • A253626 (program): Expansion of psi(q^2) * f(q, q^2)^2 / f(q, q^5) in powers of q where psi(), f() are Ramanujan theta functions.
  • A253628 (program): Psi(n) mod n, where Psi is the Dedekind psi function (A001615).
  • A253629 (program): Multiplicative function defined for prime powers by a(p^e) = p^(e-1)(p+1) if p > 2 and a(2^e) = 2^(e-1).
  • A253630 (program): Number of iterations of A253629 needed for n to reach 2.
  • 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)).
  • A253665 (program): a(n) = 2^n*n!/(floor(n/2)!)^2.
  • A253666 (program): Triangle read by rows, T(n,k) = C(n,k)*n!/(floor(n/2)!)^2, n>=0, 0<=k<=n.
  • A253667 (program): Square array read by ascending antidiagonals, T(n, k) = k!*x^k, n>=0, k>=0.
  • A253668 (program): Square array read by ascending antidiagonals, T(n, k) = k!*x^k, n>=0, k>=0.
  • A253671 (program): a(n) = floor(A000111(n)/A000111(n-1)).
  • A253673 (program): Indices of centered triangular numbers (A005448) that are also centered octagonal numbers (A016754).
  • A253674 (program): Indices of centered octagonal numbers (A016754) which are also centered triangular numbers (A005448).
  • A253675 (program): Centered triangular numbers (A005448) which are also centered octagonal numbers (A016754).
  • A253679 (program): Numbers that begin a run of an odd number of consecutive integers whose cubes sum to a square.
  • A253680 (program): Numbers c(n) whose square are equal to the sum of an odd number M of consecutive cubed integers b^3 + (b+1)^3 + … + (b+M-1)^3 = c(n)^2, starting at b(n) (A253679).
  • A253681 (program): Integer squares c^2 that are equal to the sum of an odd number M of consecutive cubed integers b^3 + (b+1)^3 + … + (b+M-1)^3 = c^2 starting at b(n) (A253679).
  • A253689 (program): Centered triangular numbers (A005448) which are also centered heptagonal numbers (A069099).
  • 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).
  • A253708 (program): Numbers c(n) whose squares are equal to the sums of consecutive cubed integers b^3 + (b+1)^3 + … + (b+M-1)^3 = c^2, for a first term b(n) being an odd squared integer (A016754).
  • A253709 (program): Integer squares c^2 that are equal to the sums of M (A253707) 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).
  • A253711 (program): Second partial sums of 11th powers (A008455).
  • A253712 (program): Second partial sums of 12th powers (A008456).
  • A253713 (program): Second partial sums of 13th powers (A010801).
  • A253714 (program): Indices of hexagonal numbers (A000384) which are also centered heptagonal numbers (A069099).
  • A253715 (program): Indices of centered heptagonal numbers (A069099) which are also hexagonal numbers (A000384).
  • A253716 (program): Hexagonal numbers (A000384) which are also centered heptagonal numbers (A069099).
  • 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.
  • A253720 (program): a(n) = length of row n in A253676 and A254068, assuming the 3x+1 (or Collatz) conjecture.
  • A253721 (program): Triprimes modulo 10.
  • A253723 (program): Length of shortest addition chain corresponding to maximum of A003313(k)/log_2(k) in interval 2^n < k < 2^(n+1).
  • 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).
  • A253742 (program): Number of (n+1) X (1+1) 0..2 arrays with every 2 X 2 subblock ne-sw antidiagonal difference nondecreasing horizontally and nw+se diagonal sum nondecreasing vertically.
  • A253767 (program): Partial sums of A247666.
  • A253769 (program): Sum of number of divisors of all positive integers <= prime(n).
  • A253779 (program): Numbers c whose cubes are equal to the sum of m^3 consecutive cubes for m^3 not divisible by 3 (A118719).
  • A253780 (program): Cubes c^3 that are equal to the sum of m^3 consecutive cubes starting at b^3 with b (A253778) for m^3 not divisible by 3 (A118719).
  • A253786 (program): a(3n) = 0, a(3n+1) = 0, a(3n+2) = 1 + a(n+1).
  • A253791 (program): Permutation of natural numbers: a(n) = A244153(A005940(n+1)).
  • A253792 (program): Permutation of natural numbers: a(n) = A156552(A244154(n)).
  • A253807 (program): Primitive part of A006190(n), n >= 1.
  • A253811 (program): Part of the y solutions of the Pell equation x^2 - 2*y^2 = +7.
  • A253821 (program): Indices of octagonal numbers (A000567) which are also centered triangular numbers (A005448).
  • A253822 (program): Indices of centered triangular numbers (A005448) which are also octagonal numbers (A000567).
  • A253823 (program): Octagonal numbers (A000567) which are also centered triangular numbers (A005448).
  • A253826 (program): Indices of centered octagonal numbers (A016754) which are also triangular numbers (A000217).
  • A253827 (program): a(n) is the number of primes of the form x^2 + x + prime(n) for 0 <= x <=prime(n).
  • A253828 (program): Digit of Pi raised to the power of the next digit of Pi.
  • A253831 (program): Number of 2-Motzkin paths with no level steps at height 1.
  • A253832 (program): a(n) = a(n-1) * (1 + a(n-2)/a(n-4)), a(0) = a(1) = a(2) = a(3) = 1.
  • A253852 (program): a(n) = a(n-4) * (a(n-3) + a(n-1)) / a(n-3), with a(0) = a(1) = a(2) = a(3) = 1.
  • A253853 (program): a(n) = 1 + a(n-2)*a(n-3), with a(0) = a(1) = a(2) = 1.
  • A253878 (program): Indices of triangular numbers (A000217) which are also centered heptagonal numbers (A069099).
  • A253879 (program): Indices of centered heptagonal numbers (A069099) which are also triangular numbers (A000217).
  • A253880 (program): Triangular numbers (A000217) that are also centered heptagonal numbers (A069099).
  • A253883 (program): Permutation of natural numbers: a(n) = A243505(A122111(n)).
  • A253884 (program): Permutation of natural numbers: a(n) = A122111(A243506(n)).
  • 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).
  • A253891 (program): Permutation of natural numbers: a(n) = A245611(A163511(n)).
  • A253892 (program): Permutation of natural numbers: a(n) = A243071(A245612(n)).
  • 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.
  • A253908 (program): Partial sums of A072272.
  • A253909 (program): 1 together with the positive squares.
  • A253910 (program): Concatenation of n-th prime and n-th nonprime.
  • A253911 (program): Concatenation of n-th nonprime and n-th prime.
  • A253918 (program): Number of Motzkin n-paths with two kinds of level steps both of which are final steps.
  • A253920 (program): Indices of centered octagonal numbers (A016754) which are also heptagonal numbers (A000566).
  • A253921 (program): Indices of octagonal numbers (A000567) which are also centered pentagonal numbers (A005891).
  • A253922 (program): Indices of centered pentagonal numbers (A005891) which are also octagonal numbers (A000567).
  • A253923 (program): Octagonal numbers (A000567) which are also centered pentagonal numbers (A005891).
  • A253926 (program): a(n) is the excess of the number of Collatz permutations of length n (with first index 15) over the n-th Fibonacci number.
  • A253936 (program): a(n) = prime(n + (prime(n) mod 10)).
  • 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).
  • A253969 (program): Primes p such that p + nextprime(p) is divisible by 6.
  • A254006 (program): a(0) = 1, a(n) = 3*a(n-2) if n mod 2 = 0, otherwise a(n) = 0.
  • A254007 (program): Cardinality of the set of equivalence classes of the set X_n of finite integer sequences {x_1 = 0, x_2, …, x_n} satisfying |x_k - x_{k+1}| = 1, where two such sequences are deemed equivalent if they are permutations of each other.
  • A254010 (program): Numbers n such that 4n+1 and 4(n+1)+1 are primes.
  • A254011 (program): Expansion of (1 - x^18) / ((1 - x^5) * (1 - x^6) * (1 - x^9)) in powers of x.
  • A254027 (program): Table T(n,k) = 3^n - 2^k read by antidiagonals.
  • 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.
  • A254030 (program): a(n) = 1*4^n + 2*3^n + 3*2^n + 4*1^n.
  • A254031 (program): a(n) = 1*5^n + 2*4^n + 3*3^n + 4*2^n + 5*1^n.
  • 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).
  • A254048 (program): a(n) = A126760(A007494(n)).
  • 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)).
  • A254051 (program): Square array A by downward antidiagonals: A(n,k) = (3 + 3^n*(2*floor(3*k/2) - 1))/6, n,k >= 1; read as A(1,1), A(1,2), A(2,1), A(1,3), A(2,2), A(3,1), …
  • A254053 (program): Square array: A(row,col) = 2^(row-1) * ((2*A249745(col))-1) = A064216(A254051(row,col)), read by antidiagonals A(1,1), A(1,2), A(2,1), A(1,3), A(2,2), A(3,1), …
  • A254055 (program): Square array: A(row,col) = A003602(A254051(row,col)), read by antidiagonals A(1,1), A(1,2), A(2,1), A(1,3), A(2,2), A(3,1), …
  • A254056 (program): Sum two last digits of the sequence to get next term, starting with 1,2.
  • A254064 (program): Positive integers whose square is expressible in exactly one way as x^2 + 6xy + y^2, with 0 < x < y.
  • A254065 (program): Vulgar fractions whose denominators are numbers ending with nine, the case 1/19.
  • A254076 (program): a(n) = 2*a(n-1) + a(n-2) - 2*a(n-3) for n>2, a(0)=-1, a(1)=-2, a(2)=-4.
  • A254078 (program): a(n) is the number of steps after which n variables with increasing value ranges all have equal values when the values of all variables are decreased by 1 at each step and the value is set to the maximum value again when the resulting value would be 0.
  • A254101 (program): Square array A(row,col) = A000265(A254051(row,col)).
  • A254102 (program): Square array A(row,col) = A253887(A254055(row,col)) = A126760(A254101(row,col)).
  • A254104 (program): Permutation of natural numbers: a(0) = 0, a(3n) = 1 + 2*a(2n - 1), a(3n+1) = 1 + 2*a(2n), a(3n+2) = 2*a(n+1).
  • A254110 (program): Zero-based column index of n in A254105: if A234017(n) = 0, then a(n) = 0, otherwise a(n) = 1 + a(A234017(n)).
  • A254111 (program): One-based column index of n in A254105: If A234017(n) = 0, then a(n) = 1, otherwise a(n) = 1 + a(A234017(n)).
  • A254112 (program): Row index of n in A254105: If A234017(n) = 0, then a(n) = A213714(n), otherwise a(n) = a(A234017(n)).
  • A254115 (program): Permutation of natural numbers: a(n) = A254104(A048673(n)).
  • A254117 (program): Permutation of natural numbers: a(n) = A254104(A249746(1+n)-1).
  • A254124 (program): The number of tilings of a 3 X n rectangle using integer length rectangles with at least one side of length 1, i.e., tiles are 1X1, 1X2, …, 1Xn, 2X1, 3X1.
  • A254128 (program): Number of binary strings of length n that begin with an odd-length palindrome.
  • 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.
  • A254136 (program): Indices of pentagonal numbers (A000326) which are also centered hexagonal numbers (A003215).
  • A254137 (program): Indices of centered hexagonal numbers (A003215) which are also pentagonal numbers (A000326).
  • A254138 (program): Pentagonal numbers (A000326) which are also centered hexagonal numbers (A003215).
  • A254142 (program): a(n) = (9*n+10)*binomial(n+9,9)/10.
  • A254144 (program): a(n) = 1*6^n + 2*5^n + 3*4^n + 4*3^n + 5*2^n + 6*1^n.
  • A254145 (program): a(n) = 1*7^n + 2*6^n + 3*5^n + 4*4^n + 5*3^n + 6*2^n + 7*1^n.
  • A254146 (program): a(n) = 1*8^n + 2*7^n + 3*6^n + 4*5^n + 5*4^n + 6*3^n + 7*2^n + 8*1^n.
  • A254147 (program): a(n) = 1*9^n + 2*8^n + 3*7^n + 4*6^n + 5*5^n + 6*4^n + 7*3^n + 8*2^n + 9*1^n.
  • A254148 (program): a(n) = 9*2^n + 7*4^n + 3*8^n + 8*3^n + 2*9^n + 6*5^n + 5*6^n + 4*7^n + 10^n + 10.
  • A254150 (program): Number of independent sets in the generalized Aztec diamond E(L_5,L_{2n-1}).
  • A254156 (program): Decimal expansion of alpha particle mass in u.
  • A254157 (program): a(n) = binomial(3*n,n)^n.
  • A254179 (program): Decimal expansion of atomic unit of time in s.
  • A254196 (program): a(n) is the numerator of Product_{i=1..n} (1/(1-1/prime(i))) - 1.
  • A254228 (program): Indices of heptagonal numbers (A000566) which are also centered square numbers (A001844).
  • A254229 (program): Indices of centered square numbers (A001844) which are also heptagonal numbers (A000566).
  • A254230 (program): Heptagonal numbers (A000566) which are also centered square numbers (A001844).
  • A254231 (program): Product of tribonacci numbers A000073(2) * … * A000073(n).
  • A254232 (program): Product of Perrin numbers A001608(2) * … * A001608(n).
  • A254269 (program): Largest prime factor of the strict partition numbers Q(n) (partitions into distinct parts, A000009).
  • A254281 (program): Decimal expansion of deuteron mass in u.
  • A254282 (program): Expansion of (1 - (1 - 27*x)^(1/3)) / (9*x).
  • A254283 (program): Indices of hexagonal numbers (A000384) which are also centered triangular numbers (A005448).
  • A254284 (program): Indices of centered triangular numbers (A005448) which are also hexagonal numbers (A000384).
  • A254285 (program): Hexagonal numbers (A000384) which are also centered triangular numbers (A005448).
  • A254286 (program): Expansion of (1 - (1-256*x)^(1/4)) / (64*x).
  • A254287 (program): Expansion of (1 - (1 - 3125*x)^(1/5)) / (625*x).
  • A254308 (program): a(n) = a(n-1) + (if a(n-1) is odd a(n-2) else a(n-3)) with a(0) = 0, a(1) = 1.
  • A254314 (program): Hankel transform of a(n) is A006720(n). Hankel transform of a(n+1) is A006720(n+2).
  • A254316 (program): Hankel transform of a(n) is A006720(n+1). Hankel transform of a(n+1) is A006720(n+3).
  • A254322 (program): Expansion of e.g.f.: (1-11*x)^(-10/11).
  • A254332 (program): Indices of centered pentagonal numbers (A005891) which are also squares (A000290).
  • A254333 (program): Squares (A000290) which are also centered pentagonal numbers (A005891).
  • A254340 (program): Sum of the distinct prime factors of n plus n+1: a(n) = A008472(n) + n + 1.
  • A254346 (program): Expansion of f(x, x^5) * f(-x^6) / f(x)^2 in powers of x where f() is a Ramanujan theta function.
  • A254362 (program): a(n) = 3*2^n + 3^n + 6.
  • A254363 (program): a(n) = 4^n + 6*2^n + 3^(n+1) + 10.
  • A254364 (program): a(n) = 3*4^n + 10*2^n + 6*3^n + 5^n + 15.
  • A254365 (program): a(n) = 2^(n+2) + 3^n + 10.
  • A254366 (program): a(n) = 4^n + 10*2^n + 4*3^n + 20.
  • A254367 (program): a(n) = 5*2^(n+2) + 2^(2n+2) + 10*3^n + 5^n + 35.
  • A254368 (program): a(n) = 5*2^n + 3^n + 15.
  • A254369 (program): a(n) = 15*2^n + 4^n + 5*3^n + 35.
  • A254370 (program): a(n) = 35*2^n + 5*4^n + 15*3^n + 5^n + 70.
  • 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*(2*n + 1)!/n!.
  • A254382 (program): Number of rooted labeled trees on n nodes such that every nonroot node is the child of a branching node or of the root.
  • A254397 (program): Initial digits of A237424 in decimal representation.
  • A254398 (program): Final digits of A237424 in decimal representation.
  • A254407 (program): a(n) = n*(n+1)*(11*n +10)/6.
  • A254408 (program): a(n) = 2*n^2*binomial(2*n,n)^2, a closed form for a double binomial sum involving absolute values.
  • A254443 (program): Numbers n such that T(n) + T(n+1) + … + T(n+21) is a square, where T(m) = A000217(m) is the m-th triangular number.
  • 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.
  • A254463 (program): a(n) = 15*2^n + 6*4^n + 10*3^n + 3*5^n + 6^n + 21.
  • A254464 (program): a(n) = 21*2^n + 10*4^n + 15*3^n + 3*6^n + 6*5^n + 7^n + 28.
  • A254465 (program): a(n) = 35*2^n + 10*4^n + 20*3^n + 4*5^n + 6^n + 56.
  • A254466 (program): a(n) = 56*2^n + 20*4^n + 35*3^n + 4*6^n + 10*5^n + 7^n + 84.
  • A254467 (program): a(n) = 15*4^n + 70*2^n + 35*3^n + 5^(n+1) + 6^n + 126.
  • A254468 (program): a(n) = 35*4^n + 126*2^n + 70*3^n + 15*5^n + 5*6^n + 7^n + 210.
  • A254469 (program): Sixth partial sums of cubes (A000578).
  • A254470 (program): Sixth partial sums of fourth powers (A000583).
  • A254471 (program): Sixth partial sums of fifth powers (A000584).
  • A254472 (program): Sixth partial sums of sixth powers (A001014).
  • A254473 (program): 24-hedral numbers: a(n) = (2*n + 1)*(8*n^2 + 14*n + 7).
  • A254474 (program): 30-gonal numbers: a(n) = n*(14*n-13).
  • A254503 (program): Möbius transform of A034448.
  • A254520 (program): Möbius transform of A034676.
  • A254522 (program): Numerators of (2^n - 1 + (-1)^n)/(2*n), n > 0.
  • A254525 (program): Expansion of f(-x^2)^2 * f(-x, x^2) / f(x^3)^3 in powers of x where f(,) is Ramanujan’s general theta function.
  • 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.
  • A254571 (program): Least multiplier k such that k*n is abundant or perfect (A023196).
  • A254572 (program): Least multiple of n that is abundant or perfect (A023196).
  • A254573 (program): Number of ways to write n = x*(x+1) + y*(3*y+1)/2 + z*(3*z-1)/2 with x,y,z nonnegative integers
  • A254574 (program): Number of ways to write n = x*(x+1)/2 + y*(3*y+1)/2 + z*(3*z-1)/2 with x,y,z nonnegative integers
  • A254594 (program): Expansion of 1 / ((1 - x^2)^2 * (1 - x^3) * (1 - x^4)) in powers of x.
  • A254598 (program): Numbers of n-length words on alphabet {0,1,…,8} with no subwords ii, for i from {0,1}.
  • A254599 (program): Numbers of words on alphabet {0,1,…,9} with no subwords ii, for i from {0,1}.
  • A254600 (program): Numbers of words on alphabet {0,1,…,10} with no subwords ii, for i from {0,1}.
  • A254601 (program): Numbers of n-length words on alphabet {0,1,…,6} with no subwords ii, where i is from {0,1,2}.
  • A254602 (program): Numbers of n-length words on alphabet {0..7} with no subwords ii, where i is from {0..2}.
  • A254605 (program): The minimum absolute difference between k*m1 and m2 (m1<m2), where m1*m2 is the n-th term of A075362.
  • A254609 (program): Triangle read by rows: T(n,k) = A243757(n)/(A243757(k)*A243757(n-k)).
  • A254614 (program): Union of odd odious (A092246) and evil (A001969) numbers.
  • A254619 (program): a(n) = 4^n*(2*n + 1)!/n!.
  • A254620 (program): a(n) = 9^n*(2*n + 1)!/n!.
  • A254623 (program): Number of ways to write n as x^2 + y*(3*y+1)/2 + z*(5*z+3)/2 with x,y,z nonnegative integers.
  • 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).
  • A254629 (program): Number of ways to write n as x^2 + y*(y+1) + z*(4*z+1) with x,y,z nonnegative integers.
  • A254632 (program): Triangle read by rows, T(n, k) = 4^n*[x^k]hypergeometric([3/2, -n], [3], -x), n>=0, 0<=k<=n.
  • A254633 (program): a(n) = 16^n*[x^n]hypergeometric([3/2, -2*n], [3], -x).
  • A254636 (program): Numbers that cannot be represented as x*y + x + y, where x>=y>1.
  • 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).
  • A254644 (program): Fourth partial sums of fifth powers (A000584).
  • A254645 (program): Fourth partial sums of sixth powers (A001014).
  • A254646 (program): Fourth partial sums of seventh powers (A001015).
  • A254647 (program): Fourth partial sums of eighth powers (A001016).
  • A254651 (program): Characteristic function of A254614, numbers that are either odd or evil (or both).
  • A254652 (program): Indices of pentagonal numbers (A000326) which are also centered heptagonal numbers (A069099).
  • A254653 (program): Indices of centered heptagonal numbers (A069099) which are also pentagonal numbers (A000326).
  • A254654 (program): Pentagonal numbers (A000326) which are also centered heptagonal numbers (A069099).
  • A254655 (program): Run lengths of A254379 (Characteristic function of the even odious numbers).
  • A254657 (program): Numbers of words on alphabet {0,1,…,8} with no subwords ii, where i is from {0,1,2}.
  • A254658 (program): Numbers of words on alphabet {0,1,…,7} with no subwords ii, where i is from {0,1,2,3}.
  • A254659 (program): Numbers of words on alphabet {0,1,…,8} with no subwords ii, where i is from {0,1,2,3}.
  • A254660 (program): Numbers of words on alphabet {0,1,…,6} with no subwords ii, where i is from {0,1,…,4}.
  • A254661 (program): Number of ways to write n as the sum of a triangular number, an even square and a second pentagonal number.
  • A254662 (program): Numbers of words on alphabet {0,1,…,7} with no subwords ii, where i is from {0,1,…,4}.
  • A254663 (program): Numbers of n-length words on alphabet {0,1,…,7} with no subwords ii, where i is from {0,1,…,5}.
  • A254664 (program): Numbers of words on alphabet {0,1,…,8} with no subwords ii, where i is from {0,1,…,5}.
  • A254667 (program): The nonnegative numbers with 2 instead of 1.
  • A254668 (program): Number of ways to write n as the sum of a square, a second pentagonal number, and a hexagonal number.
  • A254671 (program): Numbers that can be represented as x * y + x + y, where x >= y > 1.
  • A254674 (program): Indices of heptagonal numbers (A000566) which are also centered triangular numbers (A005448).
  • A254675 (program): Indices of centered triangular numbers (A005448) which are also heptagonal numbers (A000566).
  • A254676 (program): Heptagonal numbers (A000566) which are also centered triangular numbers (A005448).
  • A254681 (program): Fifth partial sums of fourth powers (A000583).
  • A254682 (program): Fifth partial sums of fifth powers (A000584).
  • A254683 (program): Fifth partial sums of sixth powers (A001014).
  • A254684 (program): Fifth partial sums of seventh powers (A001015).
  • A254685 (program): Number of partially ordered partitions of n into parts less than or equal to 3, in which the order of adjacent 2’s and 3’s is unimportant.
  • A254699 (program): Number of length 1+4 0..n arrays with every five consecutive terms having the maximum of some two terms equal to the minimum of the remaining three terms.
  • A254706 (program): a(n) = Catalan(2*n) mod prime(n).
  • A254707 (program): Expansion of (1 + 2*x^2) / ((1 - x^2)^2 * (1 - x^3) * (1 - x^4)) in powers of x.
  • A254708 (program): Expansion of (1 + 2*x^2) / (1 - 2*x^2 - x^3 + 2*x^5 + 2*x^6 - x^8 - 2*x^9 + x^11) in powers of x.
  • A254709 (program): Indices of pentagonal numbers (A000326) which are also centered square numbers (A001844).
  • 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 + k*sqrt(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 -> x*sqrt(2).
  • A254732 (program): a(n) is the least k > n such that n divides k^2.
  • A254733 (program): a(n) is the least k > n such that n divides k^3.
  • A254734 (program): a(n) is the least k > n such that n divides k^4.
  • A254745 (program): Chebyshev polynomials of the second kind, U(n,x)^2, evaluated at x = sqrt(3)/2.
  • A254747 (program): a(n) = (1 + Sum_{j=0..n} (C(n,j)*C(3*j-1,j))) / 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).
  • A254784 (program): Apply partial sum operator 5 times to primes.
  • A254795 (program): Numerators of the convergents of the generalized continued fraction 2 + 1^2/(4 + 3^2/(4 + 5^2/(4 + … ))).
  • A254796 (program): Denominators of the convergents of the generalized continued fraction 2 + 1^2/(4 + 3^2/(4 + 5^2/(4 + … ))).
  • A254828 (program): Number of length 1 1..(n+1) arrays with every leading partial sum divisible by 2, 3 or 5.
  • A254847 (program): Number of (n+2) X (1+2) 0..1 arrays with no 3 x 3 subblock diagonal sum one and no antidiagonal sum two.
  • A254855 (program): Indices of octagonal numbers (A000567) that are also centered heptagonal numbers (A069099).
  • A254856 (program): Indices of centered heptagonal numbers (A069099) that are also octagonal numbers (A000567).
  • A254857 (program): Octagonal numbers (A000567) that are also centered heptagonal numbers (A069099).
  • A254858 (program): Iterated partial sums of prime numbers, square array read by diagonals.
  • 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).
  • A254870 (program): Seventh partial sums of fourth powers (A000583).
  • A254871 (program): Seventh partial sums of fifth powers (A000584).
  • A254872 (program): Seventh partial sums of sixth powers (A001014).
  • A254874 (program): a(n) = floor((10*n^3 + 63*n^2 + 126*n + 89) / 72).
  • A254875 (program): a(n) = floor((10*n^3 + 57*n^2 + 102*n + 72) / 72).
  • A254877 (program): Expansion of (1 - x^5) / ((1 - x) * (1 - x^2)^2 * (1 - x^3) * (1 - x^4)) in powers of x.
  • A254883 (program): Triangle read by rows, T(n,k) = sum(j=0..2*(n-k), A254882(n-k,j)*k^j /(n-k)!), n>=0, 0<=k<=n.
  • A254884 (program): a(n) = Fibonacci(2*n) + ((-1)^n-1)*Fibonacci(n).
  • A254885 (program): Number of ways to write n as the sum of two squares and a positive triangular number.
  • A254895 (program): Indices of octagonal numbers (A000567) that are also centered square numbers (A001844).
  • A254896 (program): Octagonal numbers (A000567) that are also centered square numbers (A001844).
  • A254898 (program): Read the first n decimal digits of Pi-3 backwards.
  • A254923 (program): The slowest increasing sequence of semiprimes with alternating parity.
  • A254926 (program): There are a(n) numbers m such that 1 <= m <= n and gcd(m,n) is cubefree.
  • A254948 (program): Number of length 1 1..(n+1) arrays with every leading partial sum divisible by 2, 3, 5, 7 or 11
  • A254955 (program): Prime numbers indexed by oblong numbers.
  • A254962 (program): Indices of hexagonal numbers (A000384) that are also centered pentagonal numbers (A005891).
  • A254963 (program): a(n) = n*(11*n + 3)/2.
  • A254964 (program): Indices of heptagonal numbers (A000566) that are also centered hexagonal numbers (A003215).
  • A254965 (program): Indices of centered hexagonal numbers (A003215) that are also heptagonal numbers (A000566).
  • A254966 (program): Heptagonal numbers (A000566) that are also centered hexagonal numbers (A003215).
  • A254981 (program): a(n) is the sum of the divisors d of n such that n/d is cubefree.
  • A255000 (program): Prime(n + d(n)), with d(n) = prime(n+1) - prime(n), for n >= 1.
  • A255005 (program): a(n) = the digit sum of prime(n) + the digit product of prime(n).
  • A255006 (program): a(n) is the numerator of polygamma(2n+1, 1) / Pi^(2n+2).
  • A255007 (program): a(n) is the denominator of polygamma(2n+1, 1) / Pi^(2n+2).
  • A255043 (program): a(n) = (5*9^n - 1)/2.
  • A255044 (program): Array A read by upward antidiagonals: A(n,k) = ((2*n+1)*9^k-1)/2, n,k >= 0.
  • A255045 (program): a(n) = (1 + A160552(n))/2.
  • A255046 (program): a(n) = (1 + A151548(n))/2.
  • A255047 (program): 1 together with the positive terms of A000225.
  • A255049 (program): a(n) = 2*A160552(n).
  • A255051 (program): a(1)=1, a(n+1) = a(n)/gcd(a(n),n) if this GCD is > 1, else a(n+1) = a(n) + n + 1.
  • A255053 (program): Least inverse of A255072; a(n) = smallest k such that A255072(k) = n.
  • A255054 (program): Run lengths in A255072.
  • A255055 (program): Greatest inverse of A255072; a(n) = largest k such that A255072(k) = n.
  • A255068 (program): a(n) is the largest k such that A255070(k) = n.
  • 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.
  • A255109 (program): Number of length n+2 0..2 arrays with at most one downstep in every n consecutive neighbor pairs.
  • A255115 (program): Number of n-length words on {0,1,2} in which 0 appears only in runs of length 2.
  • A255116 (program): Number of n-length words on {0,1,2,3} in which 0 appears only in runs of length 2.
  • A255117 (program): Number of n-length words on {0,1,2,3,4} in which 0 appears only in runs of length 2.
  • A255118 (program): Number of n-length words on {0,1,2,3,4,5} in which 0 appears only in runs of length 2.
  • A255119 (program): Number of n-length words on {0,1,2,3,4,5,6} in which 0 appears only in runs of length 2.
  • A255120 (program): After the first zero, numbers from 0 to A255071(n)-1 followed by numbers from 0 to A255071(n+1)-1, etc.
  • A255121 (program): After zero, each n occurs A255071(n) times.
  • A255138 (program): a(n) = (1 + 2^n*(3 + 2*(-1)^n))/3.
  • A255139 (program): a(n) = n! - Fibonacci(n).
  • A255162 (program): Rational part of circle radii in nested circles and hexagons (see comment).
  • A255163 (program): Irrational parts of circle radii in nested circles and hexagons (see comment).
  • A255165 (program): a(n) = Sum_{k=2..n} floor(log(n)/log(k)), n >= 1.
  • A255171 (program): First differences of A072473.
  • A255174 (program): a(n) = prime(3*n) - prime(2*n).
  • 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).
  • A255179 (program): Second differences of ninth powers (A001017).
  • A255181 (program): Third differences of seventh powers (A001015).
  • A255182 (program): Third differences of eighth powers (A001016).
  • A255183 (program): Third differences of ninth powers (A001017).
  • A255184 (program): 25-gonal numbers: a(n) = n*(23*n-21)/2.
  • A255185 (program): 26-gonal numbers: a(n) = n*(12*n-11).
  • A255186 (program): 27-gonal numbers: a(n) = n*(25*n-23)/2.
  • A255187 (program): 29-gonal numbers: a(n) = n*(27*n-25)/2.
  • A255201 (program): Number of prime factors of n^2.
  • A255211 (program): a(n) = n*(n+1)*(7*n+2)/6.
  • A255216 (program): a(n) = floor((3/sqrt(5))^n).
  • A255217 (program): Primorial mod sum-of-primes.
  • A255220 (program): Number of (n+2)X(n+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
  • 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
  • A255229 (program): Integers n such that n^2 - 1 is the difference of the squares of twin primes.
  • A255236 (program): All positive solutions x of the second class of the Pell equation x^2 - 2*y^2 = -7.
  • A255238 (program): Triangle T(n, m) of numbers of points of a square lattice covered by a circular disk of radius n (centered at any lattice point taken as origin) with ordinate y = m in the first quadrant.
  • A255239 (program): Alternating row sums of triangle A255238.
  • A255240 (program): Decimal expansion of 1/(2*cos(Pi/7)).
  • A255241 (program): Decimal expansion of 2*cos(3*Pi/7).
  • A255242 (program): Calculate the aliquot parts of a number n and take their sum. Then repeat the process calculating the aliquot parts of all the previous aliquot parts and add their sum to the previous one. Repeat the process until the sum to be added is zero. Sequence lists these sums.
  • A255249 (program): Decimal expansion of -2*cos(5*Pi/7).
  • A255252 (program): Expansion of psi(x) * psi(-x)^2 in powers of x where psi() is a Ramanujan theta function.
  • A255257 (program): Expansion of psi(x) * phi(-x^2)^2 in powers of x where phi(), psi() are Ramanujan theta functions.
  • A255258 (program): Expansion of q^2 * phi(q) * psi(q^16) in powers of q where phi(), psi() are Ramanujan theta functions.
  • A255260 (program): a(n) = a(n-1) + sum of the pentagonal numbers which are among the first (n-1) terms of the sequence, with a(1)=1.
  • A255261 (program): a(n) = a(n-1) + sum of the hexagonal numbers which are among the first (n-1) terms of the sequence, with a(1)=1.
  • 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.
  • A255274 (program): From Goldbach conjecture: Consider the pairs (2n-+1, 3), (2n-1, 5), (2n-3, 7), …, (3, 2n+1) of odd numbers having sum 2n+4; a(n) is the index of the first pair of primes (p, q) on the list.
  • A255284 (program): a(n) = A255283(2^n-1).
  • A255285 (program): List of ternary words obtained by expanding (2+x)^n mod 3 and reading the coefficients starting with the constant term.
  • A255286 (program): Set x=3 in polynomial corresponding to A253091(n).
  • A255295 (program): Number of ON cells after n generations of the odd-rule cellular automaton defined by OddRule 527 when started with a single ON cell.
  • A255296 (program): a(n) = A255295(2^n-1).
  • A255297 (program): Number of ON cells after n generations of the odd-rule cellular automaton defined by OddRule 035 when started with a single ON cell.
  • A255301 (program): a(n) = A255300(2^k-1).
  • A255303 (program): a(n) = A255302(2^n - 1).
  • A255307 (program): Concatenation of the first n entries of the difference sequence of prime numbers (see A001223).
  • 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.
  • A255314 (program): Prime numbers of the form n*(n + 1) + (n*(n + 1))^2 + 1.
  • A255317 (program): Expansion of psi(-x^3)^2 / chi(-x) in powers of x where psi(), chi() are Ramanujan theta functions.
  • A255318 (program): Expansion of psi(x^3) * f(x^2, x^4) in powers of x where psi(), f() are Ramanujan theta functions.
  • A255319 (program): Expansion of psi(x^3) * f(x, x^5) in powers of x where psi(), f() are Ramanujan theta functions.
  • A255320 (program): Expansion of chi(-x) * psi(x^3) * psi(x^48) in powers of x where chi(), psi() are Ramanujan theta functions.
  • A255326 (program): a(n) gives the number of steps needed to reach zero, when we start from x = n and repeatedly subtract x’s squarefree kernel (A007947(x)) from it.
  • A255341 (program): Numbers n such that there is exactly one 1 in their factorial base representation (A007623).
  • A255342 (program): Numbers n such that there are exactly two 1’s in their factorial base representation (A007623).
  • A255343 (program): Numbers n such that there are exactly three 1’s in their factorial base representation (A007623).
  • A255346 (program): Numbers n such that n and n+1 both have at least two distinct prime factors.
  • A255347 (program): a(n) = n * (1 - (-1)^(n/4) / 4) if n divisible by 4, a(n) = n otherwise.
  • A255353 (program): Denominators in an expansion of 3 - sqrt(5) as a sum of fractions +-1/d.
  • A255361 (program): Number of ways n can be represented as x*y+x+y where x>=y>1.
  • A255362 (program): Numbers n such that neither n nor n+1 is representable as x*y+x+y, where x>=y>1.
  • A255365 (program): Expansion of phi(-x^3) * phi(-x^48) / chi(-x^16) in powers of x where phi(), chi() are Ramanujan theta functions.
  • A255368 (program): a(n) = -(-1)^n * 2 * n / 3 if n divisible by 3, a(n) = -(-1)^n * n otherwise.
  • A255369 (program): a(n) = (sigma(n)-n-1)*(2-mu(n)), where sigma(n) is the sum of the divisors of n and mu(n) is the Möbius function.
  • A255381 (program): Number of strings of k+n decimal digits that contain one string of exactly k consecutive “0” digits, where k >= n.
  • A255383 (program): Compositorial mod sum-of-composites.
  • A255384 (program): a(n) = sopfr(n)^2 - 2n, where sopfr(n) is the sum of the prime factors of n with multiplicity.
  • A255385 (program): a(n) = sigma(n) + phi(n) - tau(n).
  • A255386 (program): Number of binary words of length n with exactly one occurrence of subword 010 and exactly one occurrence of subword 101.
  • A255398 (program): Numbers n such that n^2 lacks the digit 1 in its decimal expansion.
  • A255406 (program): Expansion of the hyperbolic arc lemniscate tangent function.
  • A255411 (program): Shift factorial base representation of n one digit left (with 0 added to right), increment all nonzero digits by one, then convert back to decimal; Numbers with no digit 1 in their factorial base representation.
  • A255413 (program): Row 3 of Ludic array A255127: a(n) = A007310((5*n)-3).
  • A255414 (program): Row 4 of Ludic array A255127.
  • A255415 (program): Row 5 of Ludic array A255127.
  • A255429 (program): Numbers n which have a proper number of divisors which is prime
  • 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).
  • A255442 (program): a(n) = A255304(2^n-1).
  • A255445 (program): Number of ON cells after n generations of the odd-rule cellular automaton defined by OddRule 037 when started with a single ON cell.
  • A255451 (program): A255450(2^n-1).
  • A255453 (program): A255452(2^n-1).
  • A255459 (program): a(n) = A255458(2^n-1).
  • A255460 (program): Number of ON cells after n generations of the odd-rule cellular automaton defined by OddRule 517 when started with a single ON cell.
  • A255462 (program): Number of ON cells after n generations of the odd-rule cellular automaton defined by OddRule 365 when started with a single ON cell.
  • A255463 (program): a(n) = 3*4^n-2*3^n.
  • A255464 (program): Number of ON cells after n generations of the odd-rule cellular automaton defined by OddRule 137 when started with a single ON cell.
  • A255465 (program): a(n) = A255464(2^n-1).
  • A255466 (program): Number of ON cells after n generations of the odd-rule cellular automaton defined by OddRule 167 when started with a single ON cell.
  • A255467 (program): a(n) = A255466(2^n-1).
  • A255470 (program): Number of ON cells after n generations of the odd-rule cellular automaton defined by OddRule 176 when started with a single ON cell.
  • A255471 (program): a(n) = A255470(2^n-1).
  • A255473 (program): Number of ON cells after n generations of the odd-rule cellular automaton defined by OddRule 257 when started with a single ON cell.
  • A255474 (program): a(n) = A255473(2^n-1).
  • A255484 (program): a(n) = Product_{k=0..n} (prime(k+1)*(binomial(n,k) mod 2).
  • A255490 (program): The subsequence A247649(2^n-1).
  • A255491 (program): Numbers k such that 90*k+1 is composite.
  • A255499 (program): a(n) = (n^4 + 2*n^3 - n^2)/2.
  • A255505 (program): Numerator of Bernoulli(2n)/(2n!).
  • A255506 (program): Denominator of Bernoulli(2n)/(2n!).
  • A255527 (program): Where records occur in A255437.
  • A255528 (program): G.f.: Product_{k>=1} 1/(1+x^k)^k.
  • A255559 (program): One-based column index of n in array A255555.
  • A255563 (program): a(n) = -3 * n/4 if n divisible by 4, a(n) = -(-1)^n * n otherwise.
  • A255568 (program): Numbers in whose binary representation there are six 1-bits more than there are nonleading 0-bits.
  • A255584 (program): Semiprimes of the form (4*n + 1)*(6*n + 1) = 24*n^2 + 10*n + 1.
  • A255588 (program): Convert n to base 3, move the least significant digit to the most significant one and convert back to base 10.
  • A255589 (program): Convert n to base 4, move the least significant digit to the most significant one and convert back to base 10.
  • A255592 (program): Convert n to base 7, move least significant digit to most significant digit and convert back to base 10.
  • A255595 (program): Sylvester’s sequence modulo 109.
  • A255598 (program): a(n) is the minimal number q>1 such that n(q+1)-1 is prime, or -1 if no such q exists.
  • A255602 (program): Numbers k which are odd and squarefree and have the property that k is either a prime number or for every prime p dividing k, p+1 is not divisible by any of the other prime factors of k.
  • A255606 (program): Integer part of the area of a hexagon with side length n.
  • A255607 (program): Numbers n such that both 4*n+1 and 6*n+1 are primes.
  • A255610 (program): G.f.: Product_{k>=1} 1/(1-x^k)^(3*k).
  • A255611 (program): G.f.: Product_{k>=1} 1/(1-x^k)^(4*k).
  • A255612 (program): G.f.: Product_{k>=1} 1/(1-x^k)^(5*k).
  • A255613 (program): G.f.: Product_{k>=1} 1/(1-x^k)^(6*k).
  • A255614 (program): G.f.: Product_{k>=1} 1/(1-x^k)^(7*k).
  • A255616 (program): Table read by antidiagonals, T(n,k) = floor(sqrt(k^n)), n >= 0, k >=1.
  • A255630 (program): Number of n-length ternary words avoiding runs of zeros of length 1 (mod 3).
  • A255631 (program): Number of n-length words on {0,1,2,3} avoiding runs of zeros of length 1 (mod 3).
  • A255632 (program): Number of n-length words on {0,1,2,3,4} avoiding runs of zeros of length 1 (mod 3).
  • A255633 (program): Number of n-length words on {0,1,2,3,4,5} avoiding runs of zeros of length 1 (mod 3).
  • A255634 (program): Numbers n such that 1 + 16n^2 is prime.
  • A255645 (program): Partial sums of A134660.
  • A255646 (program): Odd triprimes modulo 10.
  • A255647 (program): Expansion of (phi(q) * phi(q^22) + phi(q^2) * phi(q^11)) / 2 in powers of q where phi() is a Ramanujan theta function.
  • A255648 (program): Expansion of (a(q) + a(q^2) + a(q^3) + a(q^6) - 4) / 6 in powers of q where a() is a cubic AGM theta function.
  • A255655 (program): The sum of the odd terms in row n of A050873.
  • A255670 (program): Number of the column of the Wythoff array (A035513) that contains L(n), where L = A000201, the lower Wythoff sequence.
  • A255671 (program): Number of the column of the Wythoff array (A035513) that contains U(n), where U = A001950, the upper Wythoff sequence.
  • A255673 (program): Coefficients of A(x), which satisfies: A(x) = 1 + x*A(x)^3 + x^2*A(x)^6.
  • A255675 (program): Least integer k such that the n-th prime of form m^2+1 divides the composite number k^2+1.
  • A255680 (program): a(n) = n*(n mod 3)*(n mod 5).
  • A255683 (program): Sum of the binary numbers whose digits are cyclic permutations of the binary expansion of n
  • A255687 (program): a(n) = n*(n + 1)*(7*n + 11)/6.
  • A255688 (program): G.f.: (2*x+1)/(2*sqrt(4*x^2-8*x+1)) + 1/2.
  • A255689 (program): Convert n to base 4, move the most significant digit to the least significant one and convert back to base 10.
  • A255690 (program): Convert n to base 5, move the most significant digit to the least significant one and convert back to base 10.
  • A255692 (program): Convert n to base 7, move the most significant digit to the least significant one and convert back to base 10.
  • A255737 (program): Total number of toothpicks in the toothpick structure of A153000 that are parallel to the initial toothpick, after n odd rounds.
  • 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}.
  • A255747 (program): Partial sums of A160552.
  • 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).
  • A255763 (program): Odd numbers that are not twin primes.
  • 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).
  • A255773 (program): Tree of lower Wythoff numbers (A000201) generated as the 1-component of the graph described at A095903.
  • A255774 (program): Tree of upper Wythoff numbers (A001950) generated as the 2-component of the graph described at A095903.
  • A255805 (program): Numbers with no zeros in base-8 representation.
  • A255806 (program): Expansion of e.g.f.: exp(Sum_{k>=1} 3*x^k).
  • A255807 (program): E.g.f.: exp(Sum_{k>=1} k^2 * x^k).
  • A255808 (program): Numbers with no zeros in base-9 representation.
  • A255813 (program): Numbers of words on {0,1,2,3} having no isolated zeros.
  • A255814 (program): Numbers of words on {0,1,2,3,4,} having no isolated zeros.
  • A255815 (program): Numbers of words on {0,1,2,3,4,5} having no isolated zeros.
  • A255817 (program): Parity of A000788, which is the total number of ones in 0..n in binary.
  • A255819 (program): E.g.f.: exp(Sum_{k>=1} k^3 * x^k).
  • A255821 (program): Numbers of words on {0,1,…,36} having no isolated zeros.
  • 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.
  • A255826 (program): a(n) = n for n < 6; a(6n) = a(n); if every 6th term (a(6), a(12), a(18),…) 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.
  • A255828 (program): a(n) = n for n < 8; a(8n) = a(n); if every 8th term (a(8), a(16), a(24),…) 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) = (4*n^2 - 4*n + 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.
  • A255870 (program): a(n) is the total number of pentagrams in a pentagram fractal after n iterations.
  • A255873 (program): The first nonzero digit of n/7.
  • A255875 (program): a(n) = Fibonacci(n+2) + n - 2.
  • A255876 (program): a(n) = (4*n^2 + 4*n - 3 - 3*(-1)^n)/2.
  • A255877 (program): a(n) = (2n-2)^3 + (2n-2) - 1.
  • A255878 (program): First differences of A256188.
  • A255879 (program): Partial sums of A256188.
  • A255881 (program): Expansion of exp( Sum_{n >= 1} A000364(n)*x^n/n ).
  • A255882 (program): Expansion of exp( Sum_{n >= 1} A210657(n)*(-x)^n/n ).
  • A255883 (program): Expansion of exp( Sum_{n >= 1} A000281(n)*x^n/n ).
  • A255884 (program): Expansion of exp( Sum_{n >= 1} A002438(n)*x^n/n ).
  • A255887 (program): a(n) = 1 if the n-th prime is the sum of three squares, otherwise a(n) = 0.
  • A255894 (program): Polyiamond Family Planners: a(n) is the least number of children of a polyiamond of size n.
  • A255895 (program): O.g.f.: exp( Sum_{n>=1} A000364(n+1)*x^n/n ), where A000364 is the Euler numbers.
  • A255900 (program): Expansion of exp( Sum_{n >= 1} A000464(n-1)*x^n/n ).
  • A255908 (program): Triangle read by rows: T(n,L) = number of rho-labeled graphs with n edges whose labeling is bipartite with boundary value L.
  • A255910 (program): Decimal expansion of 16/9.
  • A255912 (program): O.g.f.: exp( Sum_{n>=1} A000364(2*n)*x^n/n ), where A000364 is the Euler numbers.
  • A255919 (program): Gray code of Fibonacci(n).
  • A255926 (program): Expansion of exp( Sum_{n >= 1} A210676(n)*x^n/n ).
  • A255927 (program): a(n) = (3/4) * Sum_{k>=0} (3*k)^n/4^k.
  • A255928 (program): Expansion of exp( Sum_{n >= 1} A094088(n)*x^n/n ).
  • A255929 (program): Expansion of exp( Sum_{n >= 1} A210672(n)*x^n/n ).
  • A255930 (program): Expansion of exp( Sum_{n >= 1} A210674(n)*x^n/n ).
  • A255931 (program): a(n) is the numerator of Gamma(n+1/2)^2/(2*n*Pi), the value of an integral with sinh in the denominator.
  • A255932 (program): a(n) is the denominator of Gamma(n+1/2)^2/(2*n*Pi), the value of an integral with sinh in the denominator.
  • A255935 (program): Triangle read by rows: a(n) = Pascal’s triangle A007318(n) + A197870(n+1).
  • A255941 (program): Decimal expansion of A such that y = A*x^2 cuts the triangle with vertices (0,0), (1,0), (0,1) into two equal areas.
  • A255951 (program): Number of collections of nonempty multisets with a total of n+1 objects of exactly n colors.
  • A255975 (program): Rectangular array T(i,j) read by downwards antidiagonals: an interspersion associated with the fractal sequence A022328.
  • 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.
  • A255984 (program): Decimal expansion of sqrt(3*Pi/2), the value of an oscillatory integral.
  • A255986 (program): Decimal expansion of Sum_{m,n >= 1} (-1)^(m + n)/(m*n*(m + n)).
  • A255988 (program): Number of length n+4 0..1 arrays with at most one downstep in every 4 consecutive neighbor pairs.
  • 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.
  • A256003 (program): a(n) = 0 followed by numerators of 2*A176327(n)/A176289(n).
  • A256006 (program): Recurrence: a(n) = Sum_{k=0..n-1} a(k)*C(n+1,k), a(0)=1.
  • A256007 (program): Numbers k satisfying |k + 1 - 2F| <= 1 for some positive Fibonacci number F.
  • A256008 (program): Self-inverse permutation of positive integers: 4k+1 is swapped with 4k+3, and 4k+2 with 4k+4.
  • A256010 (program): Product of n and the total number of parts in all partitions of n. Also, product of n and the sum of largest parts of all partitions of n.
  • A256014 (program): Expansion of phi(-q^3)^4 / (phi(-q) * phi(-q^9)) in powers of q where phi() is a Ramanujan theta function.
  • A256016 (program): a(n) = n! * Sum_{k=0..n} k^n/k!.
  • 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.
  • A256032 (program): Number of idempotents in partial Brauer monoid PB_n.
  • A256037 (program): Triangle read by rows: number of R-class idempotents of rank k in Brauer monoid B_n.
  • A256061 (program): Number T(n,k) of 2n-length strings of balanced parentheses of exactly k different types; triangle T(n,k), n>=0, 0<=k<=n, read by rows.
  • 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).
  • A256092 (program): G.f.: (2*x)/((1-(1-8*x)^(1/4))*(1-8*x)^(3/4)).
  • A256095 (program): Triangle of greatest common divisors of two triangular numbers (A000217).
  • A256096 (program): Expansion of (4+3*x)/(1+3*x).
  • A256098 (program): Denominators for the numerators A256097.
  • A256099 (program): Decimal expansion of the real root of a cubic used by Omar Khayyám in a geometrical problem.
  • A256101 (program): The broken eggs problem.
  • A256105 (program): a(n) = [x^n] 2^(2*n) / Product_{k>=1} (1-x^k)^(2^(-k)).
  • A256108 (program): Positions of nonzero digits in binary expansion of Pi.
  • A256122 (program): Number of iterations needed to reach 0 or 1 under the map n-> n-sopf(n), where sopf(n) is the sum of the distinct primes dividing n (A008472).
  • 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).
  • A256169 (program): Expansion of (1-sqrt(1-4*(x+x^2)^2))/(2*(x+x^2)^2).
  • A256173 (program): Numbers k such that ceiling(sqrt(k))^2 - k is a square.
  • A256178 (program): Expansion of exp( Sum_{n >= 1} L(2*n)*L(4*n)*x^n/n ), where L(n) = A000032(n) is a Lucas number.
  • A256184 (program): First of two variations by Per Nørgård of his “infinity sequence”, cf. A004718: u(0) = 0; u(3*n) = -u(n); u(3*n+1) = u(n) - 2; u(3*n+2) = u(n) - 1.
  • A256187 (program): First differences of Per Nørgård’s “infinity sequence” A004718.
  • A256188 (program): In positive integers: replace k*(k+1)/2 with the first k numbers.
  • A256215 (program): Triangle read by rows: T(n,k) = (n-1)!*n^(k-1)*binomial(n,k)/(k-1)!.
  • A256216 (program): a(n) = A053656(n) - A000011(n).
  • A256217 (program): a(n) = A000011(n) - A256216(n).
  • A256225 (program): Number of partitions of 5n into 5 parts.
  • A256229 (program): Powering the decimal digits of n (right-associative) with 0^0 = 1 by convention.
  • A256232 (program): Multiplicative with a(2^e) = 1-e, a(3^e) = 1, a(p^e) = e+1 if p>3.
  • 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.
  • A256239 (program): Sum of all the parts in the partitions of 6n into 6 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.
  • A256252 (program): Number of successive odd noncomposite numbers A006005 and number of successive odd composite numbers A071904, interleaved.
  • A256253 (program): Number of successive odd nonprimes A014076 and number of successive odd primes A065091, interleaved.
  • 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.
  • A256258 (program): Triangle read by rows in which the row lengths are the terms of A011782 and row n lists the terms of A016969 except for the right border which gives the positive terms of A000225.
  • A256266 (program): Total number of ON states after n generations of cellular automaton based on triangles (see Comments lines for definition).
  • A256268 (program): Table of k-fold factorials, read by antidiagonals.
  • A256269 (program): Expansion of psi(-q) * chi(q^3) * phi(q^9) in powers of q where phi(), psi(), chi() are Ramanujan theta functions.
  • A256272 (program): G.f.: Sum_{n>=1} Pell(n+1) * x^n / (1 - x^n), where Pell(n) = A000129(n).
  • A256275 (program): Decimal equivalent of the binary string generated by the negation of the n X n identity matrix.
  • A256276 (program): Expansion of q * phi(q) * chi(q^3) * psi(-q^9) in powers of q where phi(), psi(), chi() are Ramanujan theta functions.
  • A256277 (program): C(2*n,n) mod 2*n+1.
  • A256278 (program): a(0)=1, a(1)=2, a(n)=31a(n-1)-29a(n-2).
  • A256279 (program): Expansion of psi(q) * chi(-q^3) * phi(-q^9) in powers of q where phi(), psi(), chi() are Ramanujan theta functions.
  • A256280 (program): Expansion of phi(q^3)^4 / (phi(q) * phi(q^9)) in powers of q where phi() is a Ramanujan theta function.
  • A256281 (program): Inverse Moebius transform of Pell numbers.
  • A256282 (program): Expansion of f(-q^3) * psi(q^3)^3 / (psi(q) * psi(q^9)) in powers of q where psi(), f() are Ramanujan theta functions.
  • A256287 (program): Number of partitions of 7n into 7 parts.
  • A256288 (program): Sum of all the parts in the partitions of 7n into 7 parts.
  • A256289 (program): Apply the transformation 0 -> 1 -> 2 -> 3 -> 4 -> 5 -> 6 -> 7 -> 8 -> 0 to the digits of n written in base 9; do not convert back to base 10.
  • A256290 (program): Numbers which have only digits 4 and 5 in base 10.
  • A256291 (program): Numbers which have only digits 5 and 6 in base 10.
  • A256292 (program): Numbers which have only digits 6 and 7 in base 10.
  • A256293 (program): Apply the transformation 0 -> 1 -> 2 -> 0 to the digits of n written in base 3, then convert back to base 10.
  • A256294 (program): Apply the transformation 0 -> 1 -> 2 -> 3 -> 0 to the digits of n written in base 4, then convert back to base 10.
  • A256295 (program): Apply the transformation 0 -> 1 -> 2 -> 3 -> 4 -> 0 to the digits of n written in base 5, then convert back to base 10.
  • A256296 (program): Apply the transformation 0 -> 1 -> 2 -> 3 -> 4 -> 5 -> 0 to the digits of n written in base 6, then convert back to base 10.
  • A256297 (program): Apply the transformation 0 -> 1 -> 2 -> 3 -> 4 -> 5 -> 6 -> 0 to the digits of n written in base 7, then convert back to base 10.
  • A256298 (program): Apply the transformation 0 -> 1 -> 2 -> 3 -> 4 -> 5 -> 6 -> 7 -> 0 to the digits of n written in base 8, then convert back to base 10.
  • A256299 (program): Apply the transformation 0 -> 1 -> 2 -> 3 -> 4 -> 5 -> 6 -> 7 -> 8 -> 0 to the digits of n written in base 9, then convert back to base 10.
  • A256302 (program): Least prime p such that p+3*k*(k+1) is prime for all k=0,…,n.
  • A256303 (program): Apply the transformation 0 -> 1 -> 2 -> 0 to the digits of n written in base 3; do not convert back to base 10.
  • A256304 (program): Apply the transformation 0 -> 1 -> 2 -> 3 -> 0 to the digits of n written in base 4; do not convert back to base 10.
  • A256305 (program): Apply the transformation 0 -> 1 -> 2 -> 3 -> 4 -> 0 to the digits of n written in base 5; do not convert back to base 10.
  • A256306 (program): Apply the transformation 0 -> 1 -> 2 -> 3 -> 4 -> 5 -> 0 to the digits of n written in base 6; do not convert back to base 10.
  • A256307 (program): Apply the transformation 0 -> 1 -> 2 -> 3 -> 4 -> 5 -> 6 -> 0 to the digits of n written in base 7; do not convert back to base 10.
  • A256308 (program): Apply the transformation 0 -> 1 -> 2 -> 3 -> 4 -> 5 -> 6 -> 7 -> 0 to the digits of n written in base 8; do not convert back to base 10.
  • A256309 (program): Number of partitions of 2n into exactly 5 parts.
  • A256310 (program): Number of partitions of 2n into exactly 6 parts.
  • A256313 (program): Number of partitions of 3n into exactly 4 parts.
  • A256314 (program): Number of partitions of 3n into exactly 5 parts.
  • A256315 (program): Number of partitions of 3n into exactly 6 parts.
  • A256316 (program): Number of partitions of 4n into exactly 5 parts.
  • A256317 (program): Number of partitions of 4n into exactly 6 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.
  • A256331 (program): Number of Largest Hairpin Family matchings on n edges.
  • A256340 (program): Numbers which have only digits 7 and 8 in base 10.
  • A256341 (program): Numbers which have only digits 8 and 9 in base 10.
  • A256357 (program): L.g.f.: log( 1 + Sum_{n>=1} x^(n^2) + x^(2*n^2) ).
  • A256374 (program): Primes of the form 7*k^2 + 7*k + 17.
  • A256376 (program): Primes of the form 10n^2 - 90n + 163.
  • A256378 (program): Primes of the form 3m^4-4.
  • A256381 (program): Numbers n such that n-3 and n+3 are semiprimes.
  • A256382 (program): Numbers n such that n-4 and n+4 are semiprimes.
  • A256383 (program): Numbers n such that n-5 and n+5 are semiprimes.
  • A256387 (program): Numbers n such that no prime can be the arithmetic mean of 2 semiprimes whose difference is 2*n.
  • A256388 (program): Numbers n such that a single prime is the arithmetic mean of 2 semiprimes whose difference is 2*n.
  • A256389 (program): Numbers n such that one or more primes can be the arithmetic mean of 2 semiprimes whose difference is 2*n.
  • A256397 (program): Primes congruent to {17, 23} mod 24.
  • A256400 (program): Numerators of coefficients of expansion of exp( Sum_{k=0..oo} x^(2^k)/2^k ) in powers of x.
  • A256421 (program): Odd numbers and twice primes, sorted.
  • A256428 (program): G.f.: x^2*(1-2*x)/(1-8*x+22*x^2-26*x^3+14*x^4-5*x^5+x^6).
  • A256429 (program): a(n) is the total number of pentagrams in a variant of pentagram fractal after n iterations.
  • A256432 (program): Characteristic function of octahedral numbers.
  • A256435 (program): First differences of sums of two squares.
  • A256436 (program): Characteristic function of pentatope numbers.
  • A256442 (program): Denominators of sqrt(2) * Integral_{x=0..sqrt(1/3)} 1/(1-x^2)^(n+3/2) dx.
  • A256450 (program): Numbers that have at least one 1-digit in their factorial base representation (A007623).
  • A256452 (program): Number of integer solutions to n^2 = x^2 + y^2 with x>0, y>=0.
  • A256455 (program): Numbers that appear at least once in a Pythagorean triple (a, b, b+1).
  • A256462 (program): Double sum of the product of two binomials with even arguments.
  • A256465 (program): Number of points in a circle of squared radius n, points on the circle counted half.
  • A256467 (program): Inverse Lah transform of the squares.
  • A256478 (program): a(0) = 0; and for n >= 1, if A079559(n) = 1, then a(n) = 1 + a(A213714(n)-1), otherwise a(n) = a(A234017(n)).
  • A256479 (program): a(1) = 0, and for n > 1, if A079559(n) = 0, then a(n) = 1 + a(A234017(n)), otherwise a(n) = a(A213714(n)-1).
  • A256490 (program): First differences of A257512: a(n) = A257512(n+1) - A257512(n).
  • A256491 (program): a(n) = prime(prime(n) + n - 2).
  • A256493 (program): Number of factorizations of m^3 into at most 3 factors, where m is a product of exactly n distinct primes.
  • A256494 (program): Expansion of -x^2*(x^3+x-1) / ((x-1)*(x+1)*(2*x-1)*(x^2+1)).
  • A256497 (program): Triangle read by rows, sums of 2 distinct nonzero cubes: T(n,k) = (n+1)^3+k^3, 1 <= k <= n.
  • A256502 (program): Largest integer not exceeding the harmonic mean of the first n squares.
  • A256505 (program): Expansion of phi(x^3) * phi(-x^48) / chi(-x^16) in powers of x where phi(), chi() are Ramanujan theta functions.
  • A256506 (program): a(n) = (2*n+3)*a(n-1) + a(n-2), a(0)=0, a(1)=1.
  • A256512 (program): n*(1+(2*n)^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.
  • A256530 (program): Number of ON cells at n-th stage in simple 2-dimensional cellular automaton (see Comments lines for definition).
  • A256531 (program): First differences of A256530.
  • 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.
  • A256540 (program): Number of partitions of 4n into at most 6 parts.
  • A256558 (program): Number of ways to write n = p + floor(k*(k+1)/4), where p is a prime and k is a positive integer.
  • A256562 (program): Number of deficient numbers <= n.
  • A256574 (program): Expansion of chi(x) * psi(-x^3) * psi(x^48) in powers of x where psi(), chi() are Ramanujan theta functions
  • A256585 (program): Primes of the form 3n^2 + 39n + 37.
  • A256593 (program): Decimal expansion of 1/Pi*Integral_{0..Pi} x^2*log(2*cos(x/2))^2 dx, one of the log-cosine integrals related to zeta(4).
  • A256595 (program): Triangle A074909(n) with 0’s as second column.
  • A256602 (program): Primes of form 12*k + 1 and not a twin prime.
  • A256608 (program): Least common eventual period of a^(2^k) mod n for all a.
  • A256626 (program): Expansion of psi(x) / psi(x^3) in powers of x where psi() is a Ramanujan theta function.
  • A256636 (program): Expansion of phi(-x^3) / f(-x^2) in powers of x where phi(), f() are Ramanujan theta functions.
  • A256644 (program): Numbers of alternating permutations where numbers at odd positions and even positions are monotone respectively.
  • 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.
  • A256656 (program): Numbers for which the minimal alternating Fibonacci representation has positive trace.
  • A256657 (program): Numbers for which the minimal alternating Fibonacci representation has negative trace.
  • A256660 (program): Number of terms in the minimal alternating Fibonacci representation of n.
  • A256662 (program): Sum of absolute values of terms in the minimal alternating Fibonacci representation of n.
  • A256663 (program): Nonnegative part of the minimal alternating Fibonacci representation of n.
  • A256664 (program): Nonpositive part of the minimal alternating Fibonacci representation of n.
  • A256666 (program): a(n) = ( 2*n*(2*n^2 + 11*n + 26) - (-1)^n + 1 )/16.
  • A256673 (program): Odd numbers with prime arithmetic derivative A003415.
  • A256676 (program): Digital roots of centered 11-gonal numbers (A069125).
  • A256680 (program): Minimal most likely sum for a roll of n 4-sided dice.
  • A256689 (program): From third root of Riemann zeta function: form Dirichlet series Sum b(n)/n^x whose cube is zeta function; sequence gives denominator of b(n).
  • A256691 (program): From fourth root of Riemann zeta function: form Dirichlet series Sum b(n)/n^x whose fourth power is zeta function; sequence gives denominator of b(n).
  • A256693 (program): From fifth root of Riemann zeta function: form Dirichlet series Sum b(n)/n^x whose fifth power is zeta function; sequence gives denominator of b(n).
  • A256698 (program): Numbers with positive triangular trace.
  • A256699 (program): Numbers with negative triangular trace.
  • 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).
  • A256704 (program): Palindromes of the form 4n + 1 that are divisible by 5.
  • A256710 (program): a(n) = (2*n-3)*a(n-1) - 2*a(n-2), a(0)=0, a(1)=1.
  • 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.
  • A256720 (program): Decimal expansion of the location of the far 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.
  • A256754 (program): a(n) = bitwise AND of n and the reverse of n.
  • A256756 (program): a(n) = bitwise XOR of n and the reverse of n.
  • A256757 (program): Number of iterations of A007733 required to reach 1.
  • A256759 (program): Nonpositive part of the minimal alternating triangular-number representation of n (defined at A255974).
  • A256764 (program): Number of (n+2)X(1+2) 0..1 arrays with no 3x3 subblock diagonal sum less than the antidiagonal sum
  • A256765 (program): Number of (n+2)X(2+2) 0..1 arrays with no 3x3 subblock diagonal sum less than the antidiagonal sum
  • A256775 (program): Primes of the form n^2 + 81.
  • A256776 (program): Primes of form n^2 + 256.
  • A256777 (program): Primes of form n^2 + 625.
  • A256785 (program): Numbers n such that digitsum(n) is a whole number when n is represented in the fractional base 1.5 = 3/2.
  • A256790 (program): Number of terms in the minimal alternating squares representation of n.
  • A256792 (program): Numbers whose minimal alternating squares representation has positive trace.
  • A256793 (program): Numbers whose minimal alternating squares representation has positive trace.
  • A256794 (program): First differences of A256792.
  • A256795 (program): Difference sequence of A256793.
  • A256796 (program): Positive part of the minimal alternating squares representation of n.
  • A256797 (program): Nonpositive part of the minimal alternating squares representation of n.
  • A256813 (program): Number of length n+5 0..1 arrays with at most two downsteps in every 5 consecutive neighbor pairs.
  • 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.
  • A256827 (program): a(n) = maximum number of minus balls for which it is better not to quit when you have n plus balls in the Shepp Urn game.
  • A256832 (program): Product of first n Pell numbers Pell(1), … , Pell(n).
  • A256833 (program): a(n) = (4*n+3)*(4*n+2).
  • A256834 (program): Primes of form n^2 + 1296.
  • A256838 (program): Primes of form n^2 + 10000.
  • A256840 (program): Primes of form n^2 + 20736.
  • A256855 (program): Number of ordered ways to write n as x*(3*x-1)/2 + y*(3*y+1)/2 + z*(3*z+1), where x and y are nonnegative integers and z is an integer.
  • A256857 (program): a(n) = n*(n^2 + 3*n - 2)/2.
  • A256859 (program): a(n) = n*(n + 1)*(n + 2)*(n^2 - n + 4)/24.
  • A256860 (program): a(n) = n*(n + 1)*(n + 2)*(n + 3)*(n^2 - n + 5)/120.
  • A256861 (program): a(n) = n*(n + 1)*(n + 2)*(n + 3)*(n + 4)*(n^2 - n + 6)/720.
  • A256862 (program): a(1)=1, then a(n) = least number > a(n-1) such that 2*a(n-1)+a(n) is prime.
  • A256871 (program): a(n) = 2^(n-1)*(2^n+11).
  • A256873 (program): a(n) = 2^(n-1)*(2^n+5).
  • A256880 (program): n*n!/round(n/2).
  • A256881 (program): a(n) = n!/ceiling(n/2).
  • 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.
  • A256914 (program): Trace of the enhanced squares representation of n.
  • A256915 (program): Length of the enhanced squares representation of n.
  • A256944 (program): Squares which are not the sums of two consecutive nonsquares.
  • A256956 (program): a(n) = pi(n) * pi(n+1), where pi(n) is the number of primes <= n.
  • A256958 (program): The integers (shown from -50 on).
  • A256959 (program): a(0)=1, a(1)=4; thereafter a(n) = 13*4^n/8-2^(n+1)+1.
  • A256960 (program): a(0)=1, a(1)=4; thereafter a(n) = a(n-2)+2*A055099(n-1)+2^(n-1).
  • A256963 (program): Partial sums of A005210.
  • A256965 (program): Decimal expansion of sqrt(2) + sqrt(3/2).
  • 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.
  • A256989 (program): One-based column index of n in array A256995.
  • A256991 (program): If A079559(n) = 1, a(n) = A213714(n) - 1, otherwise a(n) = A234017(n).
  • A256992 (program): Position of n in either of the complementary sequences, A005187 or A055938: a(n) = A213714(n) + A234017(n).
  • A256993 (program): a(1) = 0; for n > 1, a(n) = 1 + a(A256992(n)).
  • 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.
  • A257007 (program): Number of Zagier-reduced binary quadratic forms of discriminant n^2-4.
  • A257008 (program): Number of Zagier-reduced binary quadratic forms of discriminant n^2+4.
  • A257014 (program): Number of (n+2)X(1+2) 0..2 arrays with no 3x3 subblock diagonal sum equal to the antidiagonal sum
  • A257015 (program): Number of (n+2)X(2+2) 0..2 arrays with no 3x3 subblock diagonal sum equal to the antidiagonal sum
  • A257019 (program): Numbers whose quarter-square representation consists of two terms.
  • A257020 (program): Numbers whose quarter-square representation consists of three terms.
  • A257021 (program): Numbers whose quarter-square representation consists of four terms.
  • A257022 (program): Trace of n in the quarter-sum representation of n.
  • A257023 (program): Number of terms in the quarter-sum representation of n.
  • A257024 (program): Number of squares in the quarter-sum representation of n.
  • A257042 (program): a(n) = (3*n+7)*n^2.
  • A257046 (program): Numbers having trace 1 in their enhanced squares representation, see A256913.
  • A257047 (program): Numbers not having trace 1 in their enhanced squares representation, see A256913.
  • 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.
  • A257060 (program): Number of length n 1..(6+1) arrays with every leading partial sum divisible by 2 or 3.
  • A257063 (program): Number of length 1 1..(n+1) arrays with every leading partial sum divisible by 2 or 3.
  • A257070 (program): Traces of primes in enhanced squares representation, cf. A256913.
  • A257071 (program): Length of enhanced squares representation of n-th prime, cf. A256913.
  • A257075 (program): a(n) = (-1)^(n mod 3).
  • A257076 (program): Expansion of (1 - x^3) / (1 - x + x^2) in powers of x.
  • A257077 (program): a(n) = prime(n)-prime(1)-prime(2)-…-prime(k), while the result > 0.
  • A257079 (program): The least nonzero digit missing from the factorial representation (A007623) of n.
  • A257080 (program): n multiplied by the least nonzero digit missing from its factorial base representation: a(n) = n * A257079(n).
  • A257083 (program): Partial sums of A257088.
  • A257088 (program): a(2*n) = 4*n if n>0, a(2*n + 1) = 2*n + 1, a(0) = 1.
  • A257089 (program): a(n) = log_3 (A256689(n)).
  • A257090 (program): a(n) = log_2 (A256691(n)).
  • A257091 (program): a(n) = log_5 (A256693(n)).
  • A257113 (program): a(1) = 2, a(2) = 3; thereafter a(n) is the sum of all the previous terms.
  • A257126 (program): a(n) = A055938(n) - A005187(n).
  • A257132 (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.
  • A257133 (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.
  • A257134 (program): Decimal expansion of Pi^4/45.
  • A257136 (program): Decimal expansion of 2*Pi^6/945.
  • A257143 (program): a(2*n) = 3*n if n>0, a(2*n + 1) = 2*n + 1, a(0) = 1.
  • A257145 (program): a(n) = 5 * floor( (n+2) / 5) - n with a(0) = 1.
  • A257163 (program): Primes of the form 3n^2 + 2.
  • 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) = 4*n/3 if n = 3*k 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.
  • A257176 (program): The decimal expansion of the Integral_x=0..1 _y=0..x sin(x*y).
  • A257178 (program): Number of 3-Motzkin paths of length n with no level steps at odd level.
  • A257179 (program): Expansion of (1 + x^5) / ((1 - x) * (1 + x^4)) in powers of x.
  • A257181 (program): Expansion of (1 - x) * (1 + x^4) / (1 + x^5) in powers of x.
  • A257196 (program): Expansion of (1 + x) * (1 + x^5) / ((1 + x^2) * (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+2*n+17)/120.
  • A257200 (program): a(n) = n*(n+1)*(n+2)*(n+3)*(n^2+3*n+26)/720.
  • A257201 (program): a(n) = n*(n+1)*(n+2)*(n+3)*(n+4)*(n^2+4*n+37)/5040.
  • 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)).
  • A257226 (program): Numbers that have at least one divisor containing the digit 9 in base 10.
  • A257230 (program): Floor(sqrt(q)-(q-p)), where p and q are consecutive primes.
  • A257231 (program): a(n) = n^2 mod p where p is the least prime greater than n.
  • A257232 (program): Triangle T(n, k) with the natural numbers in columns with nonprime k and the nonnegative numbers in columns with prime k, for 1 <= k <= n.
  • A257233 (program): Multiplicity sequence for the alternating row sums of triangle A257232.
  • A257235 (program): Decimal expansion of the real root of x^3 + x - 6.
  • A257236 (program): Decimal expansion of the real root of 4*x^3 + 3*x - 40.
  • A257238 (program): Triangle T(n, k) = n^3 - k^3, 0 <= k < = n.
  • A257239 (program): Decimal expansion of the real root of x^3 + 4*x - 13.
  • A257240 (program): Decimal expansion of the real root of x^3 - 3*x - 10.
  • A257241 (program): Irregular triangle read by rows: Stifel’s version of the arithmetical triangle.
  • A257242 (program): Random Fibonacci tree defined with the pair(1,1).
  • A257248 (program): a(1) = 0; and for n > 1, if A079559(n) = 1, then a(n) = 1 + a(A213714(n)-1), otherwise a(n) = a(A234017(n)).
  • A257249 (program): a(0) = 1, and for n >= 1, if A079559(n) = 0, then a(n) = 1 + a(A234017(n)), otherwise a(n) = a(A213714(n)-1).
  • A257260 (program): One-based position of the rightmost zero in the factorial base representation of n (A007623), 0 if no nonleading zeros present.
  • A257261 (program): One-based position of the rightmost one in the factorial base representation (A007623) of n, 0 if no one is present.
  • A257262 (program): Numbers such that the least missing nonzero digit (A257079) in their factorial base representation is 2.
  • A257263 (program): Numbers such that the least missing nonzero digit (A257079) in their factorial base representation is 3.
  • A257272 (program): a(n) = 2^(n-1)*(2^n+7).
  • A257273 (program): a(n) = 2^(n-1)*(2^n+3).
  • A257282 (program): Numbers whose square is not the sum of two consecutive nonsquares.
  • A257285 (program): a(n) = 4*5^n - 3*4^n.
  • A257286 (program): a(n) = 5*6^n-4*5^n.
  • A257287 (program): a(n) = 6*7^n - 5*6^n.
  • A257288 (program): a(n) = 7*8^n-6*7^n.
  • A257289 (program): a(n) = 8*9^n - 7*8^n.
  • A257290 (program): Number of 3-Motzkin paths of length n with no level steps at even level.
  • A257292 (program): Numbers whose square can be written as the sum of two consecutive nonsquares.
  • A257295 (program): Arithmetic mean of the digits of n, rounded to the nearest integer.
  • A257300 (program): Number of Motzkin paths of length n with no peaks at level 2.
  • A257319 (program): Numbers n such that the n-th generation of Sawtooth 201 has minimum population in Conway’s Game of Life.
  • A257346 (program): Numbers not of the form x^2+xy+2y^2.
  • A257352 (program): G.f.: (1-2*x+51*x^2)/(1-x)^3.
  • A257365 (program): Triangle, read by rows, T(n,k) = Sum_{m=0..(n-k)/2} C(k,m)*C(n-2*m,k).
  • A257388 (program): Number of 4-Motzkin paths of length n with no level steps at odd level.
  • A257389 (program): Number of 3-generalized Motzkin paths of length n with no level steps H=(3,0) at odd level.
  • A257390 (program): Number of 4-Motzkin paths of length n with no level steps at even level.
  • A257391 (program): Numbers of the form 4^p*(4^p+1)*(2^p-1) with p an odd prime.
  • A257398 (program): Expansion of phi(-x^6)^2 / chi(-x) in powers of x where phi(), chi() are Ramanujan theta functions.
  • A257399 (program): Expansion of phi(x^3) * phi(-x^12) / chi(-x^4) in powers of x where phi(), chi() are Ramanujan theta functions.
  • A257402 (program): Expansion of chi(x) * psi(-x^3) * psi(x^12) in powers of x where psi(), chi() are Ramanujan theta functions.
  • A257408 (program): Values of n such that there is exactly 1 solution to x^2 - y^2 = n with x > y >= 0.
  • A257409 (program): Values of n such that there are exactly 2 solutions to x^2 - y^2 = n, with x > y >= 0.
  • A257410 (program): Values of n such that there are exactly 3 solutions to x^2 - y^2 = n with x > y >= 0.
  • A257411 (program): Values of n such that there are exactly 4 solutions to x^2 - y^2 = n with x > y >= 0.
  • A257412 (program): Values of n such that there are exactly 5 solutions to x^2 - y^2 = n with x > y >= 0.
  • A257413 (program): Values of n such that there are exactly 6 solutions to x^2 - y^2 = n with x > y >= 0.
  • A257415 (program): Values of n such that there are exactly 8 solutions to x^2 - y^2 = n with x > y >= 0.
  • A257416 (program): Values of n such that there are exactly 9 solutions to x^2 - y^2 = n with x > y >= 0.
  • A257417 (program): Values of n such that there are exactly 10 solutions to x^2 - y^2 = n with x > y >= 0.
  • A257418 (program): Number of pieces after a sheet of paper is folded n times and cut diagonally.
  • A257436 (program): Decimal expansion of G(1/3), a generalized Catalan constant.
  • A257439 (program): Number of (n+2)X(n+2) 0..1 arrays with no 3x3 subblock diagonal sum 0 and no antidiagonal sum 3 and no row sum 1 and no column sum 1
  • A257442 (program): Number of (n+2) X (3+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.
  • A257443 (program): Number of (n+2) X (4+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.
  • 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) - 3*n^2 - 9*n.
  • A257449 (program): a(n) = 75*(2^n - 1) - 4*n^3 - 18*n^2 - 52*n.
  • A257450 (program): a(n) = 541*(2^n - 1) - 5*n^4 - 30*n^3 - 130*n^2 - 375*n.
  • A257464 (program): Number of factorizations of m^n into 3 factors, where m is a product of exactly 3 distinct primes and each factor is a product of n primes (counted with multiplicity).
  • A257469 (program): Expansion of f(-x) * psi(x^6) in powers of x where psi(), f() are Ramanujan theta functions.
  • 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+15*x-8*x^2 ) / ( (x-1)*(x^2-4*x+1) ).
  • A257499 (program): Array A read by upward antidiagonals in which the entry in row n and column k is defined by A(n,k) = (1 + 2^n*(6*k-3+2*(-1)^n))/3, n,k >= 1.
  • A257501 (program): Triangle, read by rows, T(n,k) = 2*k*C(2*(n+k),n-k)/(n+k).
  • A257507 (program): Row 2 of A257264: a(n) = A011371(A055938(n)).
  • A257510 (program): Number of nonleading zeros in factorial base representation of n (A007623).
  • A257511 (program): Number of 1’s in factorial base representation of n (A007623).
  • A257512 (program): Those vertices of the binary beanstalk whose children are both leaves.
  • A257516 (program): Number of 3-generalized Motzkin paths of length n with no level steps H=(3,0) at even level.
  • A257520 (program): Number of factorizations of m^2 into 2 factors, where m is a product of exactly n distinct primes and each factor is a product of n primes (counted with multiplicity).
  • A257522 (program): Table T(i,j) = denominator of (1/i + 1/j) = i*j/gcd(i*j,i+j) read by antidiagonals (i >= 1, j >= 1).
  • A257531 (program): If 2^(n-1) mod n = 1, then 1 else 0.
  • A257532 (program): Triangle, read by rows, T(n,k)=k/n*Sum_{i=0..n-k} C(2*n,n-k-i)*C(2*n+i-1,i).
  • A257533 (program): Sum of the proper divisors of the n-th semiprime.
  • A257541 (program): The rank of the partition with Heinz number n.
  • 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.
  • A257543 (program): Expansion of 1 / (1 - x^5 - x^8 + x^9) in powers of x.
  • A257546 (program): Number of permutations of length n such that numbers at odd positions are monotone and numbers at even positions are also monotone.
  • A257548 (program): a(1) = 1, a(2) = 2, a(3) = 5, a(4) = 8 and a(5) = 15, a(n) = sum of previous terms.
  • A257556 (program): Triangle, read by rows, T(n,k)= Sum_{i=0..(n-k)/2} C(2*k,i)*C(n-2*i-1,k-1).
  • A257557 (program): Expansion (x-1)/(x^5+2*x^3+2*x-1).
  • 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)=8*n*(2*n-1)*a(n-1).
  • A257587 (program): If n = abcd… in decimal, a(n) = a^2 - b^2 + c^2 - d^2 + …
  • A257588 (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.
  • A257597 (program): Irregular triangle read by rows: coefficients of polynomials V_n(x), highest degree terms first.
  • A257600 (program): Expansion of (4 + 15*x - 35*x^2 + 20*x^3 - 2*x^5)/(1 - x)^5.
  • A257601 (program): a(n) = (n^4 + 20*n^3 + 125*n^2 + 250*n + 24)/12.
  • A257602 (program): Expansion of (1 + x + 21*x^2 + x^3 + x^4)/(1 - x)^5.
  • A257609 (program): Triangle read by rows: T(n,k) = t(n-k, k); t(n,m) = f(m)*t(n-1,m) + f(n)*t(n,m-1), where f(x) = 2*x + 2.
  • A257612 (program): Triangle read by rows: T(n,k) = t(n-k, k); t(n,m) = f(m)*t(n-1,m) + f(n)*t(n,m-1), where f(x) = 4*x + 2.
  • A257620 (program): Triangle read by rows: T(n, k) = t(n-k, k), where t(0,0) = 1, t(n,m) = 0 if n < 0 or m < 0, else t(n,m) = f(m)*t(n-1,m) + f(n)*t(n,m-1), and f(n) = 3*n + 3.
  • A257625 (program): Triangle read by rows: T(n, k) = t(n-k, k), where t(0,0) = 1, t(n,m) = 0 if n < 0 or m < 0, else t(n,m) = f(m)*t(n-1,m) + f(n)*t(n,m-1), and f(n) = 6*n + 3.
  • A257628 (program): Expansion of 1 - f(-x) in powers of x where f() is a Ramanujan theta function.
  • 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.
  • A257639 (program): a(n) is the minimal position at which the maximal value of row n appears in row n of triangle A008289.
  • A257644 (program): First differences of A264100.
  • A257645 (program): a(n) = 15*n + 14.
  • A257651 (program): Expansion of chi(x)^2 * f(-x^6)^3 in powers of x where chi(), f() are Ramanujan theta functions.
  • A257656 (program): Expansion of f(x) * f(x^3) * f(-x^4)^2 * chi(-x^6)^2 in powers of x where chi(), f() are Ramanujan theta functions.
  • A257667 (program): Primes containing a digit 5.
  • A257668 (program): Primes containing a digit 7.
  • A257679 (program): The smallest nonzero digit present in the factorial base representation (A007623) of n, 0 if no nonzero digits present.
  • A257680 (program): Characteristic function for A256450: 1 if there is at least one 1-digit present in the factorial representation of n (A007623), otherwise 0.
  • A257682 (program): Partial sums of A257680: a(0) = 0; for n >= 1, a(n) = A257680(n) + a(n-1).
  • 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).
  • A257692 (program): Numbers such that the smallest nonzero digit present (A257679) in their factorial base representation is 2.
  • A257694 (program): a(0) = 1; for n >= 1, a(n) = A060130(n) * a(A257684(n)).
  • A257696 (program): a(0) = 0; for n >= 1, a(n) = gcd(A060130(n), a(A257684(n))).
  • A257708 (program): Numbers n such that T(n) + T(n+1) + … + T(n+24) is a square, where T = A000217 (triangular numbers).
  • A257721 (program): Hexagonal numbers (A000384) that are the sum of two consecutive hexagonal numbers.
  • A257765 (program): Positive integers whose square is the sum of 26 consecutive squares.
  • A257772 (program): Numbers n>=0 such that (n+1)^3 - n^3 = 3*n^2+3*n+1 is not prime.
  • A257775 (program): Decimal expansion of (e/2)^2.
  • A257791 (program): Rectangular array A read by upward antidiagonals in which the entry in row n and column k is defined by A(n,k) = 2^(n+1)*(2*k - 1), n,k >= 1.
  • A257792 (program): Expansion of 1/(1-x-x^2-x^3-x^5+x^8-x^9).
  • A257799 (program): Parity of binary weight of each term in the infinite trunk of inverted binary beanstalk: a(n) = A010060(A233271(n)).
  • A257800 (program): Sequence A233271 reduced modulo 2: a(n) = A000035(A233271(n)); the parity of each term in the infinite trunk of inverted binary beanstalk.
  • A257803 (program): Positions of odd numbers in A233271, the infinite trunk of inverted binary beanstalk.
  • A257804 (program): Positions of even numbers in A233271, the infinite trunk of inverted binary beanstalk.
  • A257806 (program): a(n) = A257808(n) - A257807(n).
  • A257807 (program): a(n) = number of odd numbers in range 0 .. n of A233271, the infinite trunk of inverted binary beanstalk.
  • A257808 (program): a(n) = number of nonzero even numbers in range 0 .. n of A233271, the infinite trunk of inverted binary beanstalk.
  • 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.
  • A257838 (program): Main diagonal of iterated partial sums array of Fibonacci numbers (starting with the first partial sums).
  • 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).
  • A257852 (program): Array A read by upward antidiagonals in which the entry A(n,k) in row n and column k is defined by A(n,k) = (2^n*(6*k - 3 - 2*(-1)^n) - 1)/3, n,k >= 1.
  • A257853 (program): a(n) = 2*n^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.
  • A257859 (program): a(n) = (2*n-1)*a(n-1) - a(n-2) with a(0)=2, a(1)=1.
  • A257863 (program): Expansion of 1/(1 - x - x^2 + x^5 - x^6).
  • 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^2-3*x+3)/(x-1)^6.
  • A257900 (program): Expansion of 1/2 - (phi(-q)^2 + phi(-q^9)^2) / 4 in powers of q where phi() is a Ramanujan theta function.
  • A257920 (program): Expansion of phi(x) * psi(x^3) in powers of x where phi(), psi() are Ramanujan theta functions.
  • A257921 (program): Expansion of f(x^2, -x^4) * f(-x, -x^5)^2 / f(-x^12, -x^12) in powers of x where f(, ) is Ramanujan’s general theta functions.
  • 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).
  • A257931 (program): Period length 24 sequence [0, 1, 1, 0, -2, -1, 0, 1, 0, 0, -1, -1, 0, 1, 1, 0, 0, -1, 0, 1, 2, 0, -1, -1].
  • A257932 (program): Expansion of 1/(1-x-x^2-x^3+x^5+x^7).
  • A257933 (program): Prime p such that sqrt(p+2) is semiprime (A001358).
  • 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).
  • A257943 (program): Array A read by upward antidiagonals in which the entry in row n and column k is defined by A(n,k) = (1 + 3^(n-1)*(2*k - 1))/2, n,k >= 1.
  • A257956 (program): Row sums of A232642, when seen as a triangle read by rows.
  • A257961 (program): List of permutations of the intervals of numbers [0,F(n)) defined by x -> x*F(n-1) mod F(n), where F(n) is the n-th Fibonacci number A000045.
  • A257970 (program): a(1) = 1, a(2) = 2, a(3) = 5; thereafter a(n) = 2 * Sum_{k=1..n-1} a(k).
  • A257971 (program): First differences of A006921.
  • A257984 (program): Nonhomogeneous Beatty sequence: ceiling((n - 1/2)*Pi))
  • A257990 (program): The side-length of the Durfee square of the partition having Heinz number n.
  • A257991 (program): Number of odd parts in the partition having Heinz number n.
  • A257992 (program): Number of even parts in the partition having Heinz number n.
  • A257993 (program): Least gap in the partition having Heinz number n; index of the least prime not dividing n.
  • A257994 (program): Number of prime parts in the partition having Heinz number n.
  • A257998 (program): Partial sums of A188967.
  • A258000 (program): Expansion of 1/(1-x-x^2-x^3-x^4+x^5+x^6+x^7-x^9).
  • A258011 (program): Numbers remaining after the third stage of Lucky sieve.
  • A258016 (program): Unlucky numbers removed at the stage three of Lucky sieve.
  • A258021 (program): Eventual fixed point of map x -> floor(tan(x)) when starting the iteration with the initial value x = n.
  • A258022 (program): Nonnegative integers n with property that when starting from x=n, the map x -> floor(tan(x)) reaches [the fixed point] 0 (or any other integer less than 1 if such negative fixed points exist).
  • A258025 (program): Numbers k such that prime(k+2) - 2*prime(k+1) + prime(k) > 0.
  • A258026 (program): Numbers k such that prime(k+2) - 2*prime(k+1) + prime(k) < 0.
  • A258034 (program): Expansion of phi(q) * phi(q^9) in powers of q where phi() is a Ramanujan theta function.
  • A258048 (program): Nonhomogeneous Beatty sequence: ceiling((n + 1/2)*Pi/(Pi- 1))
  • 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.
  • A258056 (program): 3x + 1 sequence starting at 75.
  • A258057 (program): First differences of the arithmetic derivative sequence A003415.
  • 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,… .
  • A258089 (program): a(n) = n for n = 0..3; for n>3, a(n) = 4*a(n-1) + 3*a(n-2) + 2*a(n-3) + a(n-4).
  • A258090 (program): Expansion of q^(-5/6) * (eta(q) * eta(q^6)^2 / eta(q^3))^2 in powers of q.
  • A258091 (program): Smallest prime factor of 1+78557*2^n, cf. A258073.
  • A258093 (program): Expansion of q^(-1) * psi(q) / psi(q^3)^3 in powers of q where psi() is a Ramanujan theta function.
  • A258094 (program): McKay-Thompson series of class 6E for the Monster group with a(0) = 7.
  • A258096 (program): Expansion of psi(x^4) * phi(-x^4)^4 / phi(-x) in powers of x where phi(), psi() are Ramanujan theta function.
  • A258098 (program): 3x + 1 sequence starting at 79.
  • A258099 (program): Expansion of ( psi(x^3) * phi(-x^3) / (psi(x) * f(-x^2)) )^2 in powers of x where phi(), psi(), f() are Ramanujan theta functions.
  • A258100 (program): Expansion of c(q) * c(q^3) / c(q^2)^2 in powers of q where c() is a cubic AGM theta function.
  • A258109 (program): Number of balanced parenthesis expressions of length 2n and depth 3.
  • A258114 (program): E.g.f.: Sum_{n>=0} x^n * cosh(n*x).
  • A258115 (program): a(n) = A208570(n)/n.
  • A258121 (program): Number of vertices of degree n in all Lucas cubes.
  • A258122 (program): The multiplicative Wiener index of the cycle graph C_n (n>=3).
  • A258125 (program): a(1) = a(2) = 2; a(n) = a(n-1) + gpf(a(n-2)), where gpf is greatest prime factor.
  • A258128 (program): Octagonal numbers (A000567) that are the sum of two consecutive octagonal numbers.
  • A258130 (program): Octagonal numbers (A000567) that are the sum of ten consecutive octagonal numbers.
  • A258133 (program): Expansion of tri-digit zeros interlaced with an arithmetic progression of positive and negative numbers.
  • A258143 (program): Row sums of A257241, Stifel’s version of the arithmetical triangle.
  • A258144 (program): Alternating row sums of A257241, Stifel’s version of the arithmetical triangle.
  • A258145 (program): Row lengths of the irregular array in A256598.
  • A258146 (program): Decimal expansion of (1 - 2/Pi)/2: ratio of the area of a circular segment with central angle Pi/2 and the area of the corresponding circular half-disk.
  • A258147 (program): Decimal expansion of (4 - 3*sqrt(3)/Pi)/6: ratio of the area of a circular segment with central angle 2*Pi/3 and the area of the corresponding circular half-disk.
  • A258148 (program): Decimal expansion of (2 - 3*sqrt(3)/Pi)/6: ratio of the area of a circular segment with central angle Pi/3 and the area of the corresponding circular half-disk
  • A258149 (program): Triangle of the absolute difference of the two legs (catheti) of primitive Pythagorean triangles.
  • A258150 (program): Triangle of Fibonacci’s congruum (congruous) numbers divided by 24 based on primitive Pythagorean triangles. Areas divided by 6 of these triangles.
  • A258155 (program): Products of squares of three successive primes.
  • A258160 (program): a(n) = 8*Lucas(n).
  • A258171 (program): a(n) = Sum_{d|n} phi(d)*Bell(n/d) for n>0, a(0) = 0.
  • A258172 (program): Sum over all Dyck paths of semilength n of products over all peaks p of x_p, where x_p is the x-coordinate of peak p.
  • A258187 (program): Numbers n such that either n^k - 1 or n^k - 2 is prime for some positive k, but not both.
  • A258196 (program): Expansion of f(-x^2) * phi(-x^3) in powers of x where phi(), f() are Ramanujan theta functions.
  • A258197 (program): Arithmetic derivative of Pascal’s triangle.
  • A258198 (program): a(n) = largest k for which A001563(k) = k*k! <= n.
  • A258199 (program): a(n) = largest term of A001563 <= n.
  • A258210 (program): Expansion of f(-q) * f(-q^2) * chi(-q^3) in powers of q where chi(), f() are Ramanujan theta functions.
  • A258211 (program): Nonsquarefree numbers of the form 4*k + 2.
  • A258213 (program): Number of permutations of {1,2,3,…,n} such that no even numbers are adjacent.
  • A258216 (program): Number of permutations of {1,2,3,…,n} such that no multiples of 3 are adjacent.
  • A258228 (program): Expansion of f(q) * f(-q^2) * chi(q^3) in powers of q where chi(), f() are Ramanujan theta functions.
  • A258256 (program): Expansion of f(q^3) * psi(-q^3)^3 / (psi(-q) * psi(-q^9)) in powers of q where psi(), f() are Ramanujan theta functions.
  • A258261 (program): Primes p such that 3p - 4 is also prime.
  • A258272 (program): The smallest amount which cannot be made with fewer than n British coins.
  • A258277 (program): Expansion of chi(-q) * phi(-q^3) * psi(q^3) in powers of q where chi(), phi(), psi() are Ramanujan theta functions.
  • A258278 (program): Expansion of f(-x, -x^5)^2 in powers of x where f(,) is Ramanujan’s general theta function.
  • A258279 (program): Expansion of psi(q)^2 * chi(-q^3)^2 in powers of q where psi(), chi() are Ramanujan theta functions.
  • A258290 (program): Arithmetic derivative of central binomial coefficients, cf. A000984.
  • A258291 (program): Expansion of q^(-1/4) * eta(q) * eta(q^2) * eta(q^6) / eta(q^3) in powers of q.
  • A258292 (program): Expansion of psi(-q)^2 * chi(q^3)^2 in powers of q where psi(), f() are Ramanujan theta functions.
  • A258314 (program): G.f. B(x) satisfies: B(x) = 1 + x*A(x)*C(x) where A(x) = B(x)*C(x) and C(x) = 1 + 2*x*A(x)*B(x).
  • A258315 (program): G.f. C(x) satisfies: C(x) = 1 + 2*x*A(x)*B(x) where A(x) = B(x)*C(x) and B(x) = 1 + x*A(x)*C(x).
  • A258317 (program): Row sums of triangle A258197.
  • A258321 (program): a(n) = Fibonacci(n) + n*Lucas(n).
  • A258322 (program): Expansion of phi(-q) * phi(-q^9) in powers of q where phi() is a Ramanujan theta function.
  • A258325 (program): a(n) = Product_{k=1..n} (1 + p(k)), where p(k) is the partition function A000041.
  • A258326 (program): a(1) = 3; for n > 1, a(n) = a(n-1) + prime(n+2) - 2*prime(n+1) + 2*prime(n) - prime(n-1).
  • A258327 (program): Expansion of phi(x^3) / f(-x^2) in powers of x where phi(), f() are Ramanujan theta functions.
  • A258328 (program): L.g.f.: log(1 + Sum_{n>=1} x^(n^2) + x^(3*n^2) ).
  • A258331 (program): Sum of the cubes of the divisors of n^3.
  • A258340 (program): a(n) = (7^n + 3^n - 2)/8.
  • A258347 (program): Expansion of Product_{k>=1} 1/(1-x^k)^(k*(k+1)).
  • A258348 (program): Expansion of Product_{k>=1} 1/(1-x^k)^(k*(k-1)).
  • A258349 (program): Expansion of Product_{k>=1} 1/(1-x^k)^(k*(k-1)/2).
  • A258350 (program): Expansion of Product_{k>=1} 1/(1-x^k)^(k*(k+1)*(k+2)).
  • A258369 (program): Stirling-Bernoulli transform of A027656.
  • 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.
  • A258377 (program): O.g.f. satisfies A^2(z) = 1/(1 - z)*( BINOMIAL(BINOMIAL(A(z))) ).
  • 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.
  • A258389 (program): a(n) = (n^(n+1)-(n-1)^n) + ((n+1)^n-n^(n-1)).
  • A258390 (program): Number of 2n-length strings of balanced parentheses of exactly 2 different types that are introduced in ascending order.
  • A258391 (program): Number of 2n-length strings of balanced parentheses of exactly 3 different types that are introduced in ascending order.
  • A258392 (program): Number of 2n-length strings of balanced parentheses of exactly 4 different types that are introduced in ascending order.
  • A258394 (program): Number of 2n-length strings of balanced parentheses of exactly 6 different types that are introduced in ascending order.
  • A258399 (program): Number of 4n-length strings of balanced parentheses of exactly n different types that are introduced in ascending order.
  • A258402 (program): a(n) = (n^2 + 4*n + 6) * n^2.
  • A258403 (program): Decimal expansion of the area of the regular 10-gon (decagon) of circumradius = 1.
  • A258409 (program): Greatest common divisor of all (d-1)’s, where the d’s are the positive divisors of n.
  • A258410 (program): Nonnegative integers with an equal number of occurrences of all digits in bijective base-2 numeration.
  • A258415 (program): Array A read by upward antidiagonals in which the entry in row n and column k is defined by A(n,k) = (2 + 2^(n-1)*(6*k - 3 + 2*(-1)^n))/3, n,k >= 1.
  • A258430 (program): Primes in A088580.
  • A258431 (program): Sum over all peaks of Dyck paths of semilength n of the arithmetic mean of the x and y coordinates.
  • A258434 (program): n^2 - phi(n).
  • A258435 (program): Primes of form x^2 - phi(x) in increasing order.
  • A258439 (program): Powers of 3 alternating with powers of 2.
  • A258440 (program): Number of squares of all sizes in 3*n*(n+1)/2-ominoes in form of three-quarters of Aztec diamonds.
  • A258445 (program): Irregular triangle related to Pascal’s triangle.
  • A258451 (program): a(n) = 1 + a(n-1)/gcd(a(n-1),n) with a(0)=3.
  • A258453 (program): G.f.: Sum_{k>0} x^((k^2 + k)/2) / (1 + x^k).
  • A258456 (program): Product of divisors of n is not a square.
  • A258457 (program): Number of partitions of n into parts of exactly 2 sorts which are introduced in ascending order.
  • A258468 (program): a(n) = lcm(n, n - tau(n)).
  • A258471 (program): Number of partitions of 2n into two sorts of parts having exactly n parts of the second sort.
  • 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
  • A258565 (program): Arithmetic derivative of powerful numbers, cf. A001694.
  • A258566 (program): Triangle in which n-th row contains all possible products of n-1 of the first n primes in descending order.
  • A258567 (program): Smallest prime factors of 2-full numbers.
  • A258578 (program): Primes p such that difference between p and next prime after p is multiple of 6.
  • A258582 (program): a(n) = n*(2*n + 1)*(4*n + 1)/3.
  • A258587 (program): Expansion of f(-x, -x) * f(x^2, x^10) in powers of x where f(, ) is Ramanujan’s general theta function.
  • 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.
  • A258590 (program): Expansion of psi(-x) * psi(-x^6)^2 / f(-x^3) in powers of x where psi(), f() are Ramanujan theta functions.
  • A258594 (program): Number of prime factors of the number of partitions of n into distinct parts, a(n) = A001222(A000009(n)).
  • A258595 (program): Number of distinct primes dividing the number of partitions of n into distinct parts, a(n) = A001221(A000009(n)).
  • A258596 (program): Number of divisors of the number of partitions of n into distinct parts, a(n) = A000005(A000009(n)).
  • A258597 (program): a(n) = 13*3^n.
  • A258598 (program): a(n) = 17*3^n.
  • A258613 (program): Numbers m that are coprime to the largest square <= m, cf. A048760.
  • A258614 (program): Numbers m having with the largest square <= m a common divisor > 1.
  • A258617 (program): a(n) = (4*n+8)*n^2.
  • A258618 (program): a(n) = (4*n+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.
  • A258655 (program): a(n) = A256357(n^2), where exp( Sum_{n>=1} A256357(n)*x^n/n ) = 1 + Sum_{n>=1} x^(n^2) + x^(2*n^2).
  • A258663 (program): Numbers n such that 9n-1 is prime.
  • A258664 (program): A total of n married couples, including a mathematician M and his wife, are to be seated at the 2n chairs around a circular table, with no man seated next to his wife. After the ladies are seated at every other chair, M is the first man allowed to choose one of the remaining chairs. The sequence gives the number of ways of seating the other men, with no man seated next to his wife, if M chooses the chair that is 3 seats clockwise from his wife’s chair.
  • A258674 (program): Number of (n+2) X (1+2) 0..1 arrays with no 3 x 3 subblock diagonal sum equal to the antidiagonal sum.
  • A258675 (program): Number of (n+2) X (2+2) 0..1 arrays with no 3 x 3 subblock diagonal sum equal to the antidiagonal sum.
  • A258684 (program): a(n) = A041105(4n+1).
  • A258703 (program): a(n) = floor(n/sqrt(2) - 1/2).
  • A258710 (program): Motzkin numbers A001006 read mod 11.
  • A258711 (program): Motzkin numbers A001006 read mod 7.
  • A258712 (program): Motzkin numbers A001006 read mod 5.
  • A258717 (program): If n even then 2*n^2-4*n else 2*n^2-4*n-3.
  • A258721 (program): a(n) = 24*n^2 + 52*n + 29.
  • A258723 (program): Expansion of 1/(1-12*x+48*x^2)^(1/2).
  • A258731 (program): Number of length n+1 0..3 arrays with at most one downstep in every n consecutive neighbor pairs.
  • A258741 (program): Expansion of f(x^3, x^5) / f(x, x^3) in powers of x where f(, ) is Ramanujan’s general theta function.
  • A258745 (program): Order of general affine group AGL(n,2) (=A028365(n)) divided by (n+1).
  • A258746 (program): Permutation of the positive integers: this permutation transforms the enumeration system of positive irreducible fractions A007305/A047679 (Stern-Brocot) into the enumeration system A162909/A162910 (Bird), and vice versa.
  • A258747 (program): Expansion of chi(-x) * f(x^3) * f(-x^6) in powers of x where chi(), f() are Ramanujan theta functions.
  • A258749 (program): Decimal expansion of Ls_3(Pi), the value of the 3rd basic generalized log-sine integral at Pi (negated).
  • A258758 (program): Triangle T(n,k) = C(n+k-1,k)*C(2*n-1,n-k).
  • A258759 (program): Decimal expansion of Ls_3(Pi/3), the value of the 3rd basic generalized log-sine integral at Pi/3 (negated).
  • A258764 (program): Expansion of chi(-x^2) * psi(-x^3)^2 in powers of x where psi(), chi() are Ramanujan theta functions.
  • A258774 (program): a(n) = 1 + sigma(n) + sigma(n)^2.
  • A258775 (program): Numbers n such that 1 + sigma(n)+ sigma(n)^2 is prime.
  • A258776 (program): Primes in A258774.
  • A258779 (program): Expansion of (f(-x) * phi(x))^2 in powers of x where phi(), f() are Ramanujan theta functions.
  • A258781 (program): a(n) is the greatest positive integer k such that lambda(k) <= n where lambda is the Carmichael lambda function (A002322).
  • A258782 (program): Nearest integer to log_2(n!).
  • A258800 (program): The number of zeroless decimal numbers whose digital sum is n.
  • 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.
  • A258817 (program): a(n) = (!0 + !1 +… + !(n-1)) mod n.
  • A258820 (program): Reversed rows of A178252 presented as diagonals of an irregular triangle.
  • A258831 (program): Expansion of (psi(-x^3) * f(-x, x^2))^2 in powers of x where psi(), f(,) are Ramanujan theta functions.
  • A258832 (program): Expansion of psi(-x^3) * f(-x, x^2) in powers of x where psi(), f(,) are Ramanujan theta functions.
  • A258833 (program): Nonhomogeneous Beatty sequence: ceiling((n + 1/4)*sqrt(2)).
  • A258834 (program): Nonhomogeneous Beatty sequence: ceiling((n - 1/4)*(2 + 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) = 9*n^2 - 237*n + 1927.
  • A258867 (program): Positions n where A185653(n) = 0.
  • A258869 (program): Expansion of 1 to the basis 1.880000478655… (A127583).
  • A258875 (program): a(1) = a(2) = a(3) = 1; for n > 3, a(n) = ceiling((a(n-1) + a(n-2) + a(n-3))/2).
  • A258877 (program): Primes p=prime(m) such that both p and m have the same digital root.
  • A258881 (program): a(n) = n + the sum of the squared digits of n.
  • A258916 (program): n*a(n+1) = (2*n^2+2*n+1)*a(n)+(n+1)*a(n-1); a(0)=1, a(1)=0.
  • A258929 (program): a(n) is the unique even-valued residue modulo 5^n of a number m such that m^2+1 is divisible by 5^n.
  • A258934 (program): Half the difference between the 2n-th prime and the n-th prime, starting from n=2.
  • A258935 (program): Independence number of Keller graphs.
  • A258939 (program): Expansion of f(-x^3, -x^5) * f(x^3, x^13) / (f(-x, -x^2) * f(-x^8, -x^16)) in powers of x where f(, ) is Ramanujan’s general theta function.
  • A258943 (program): Exponential reversion of Fibonacci numbers A000045.
  • A258945 (program): Decimal expansion of Dickman’s constant C_4.
  • 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).
  • A258972 (program): Number of other odd numbers between the twin primes, with a(1) = 1.
  • A258973 (program): The number of plain lambda terms presented by de Bruijn indices, see Bendkowski et al. where zeros have no weight.
  • A258974 (program): a(n) = 1 + sigma(n)^2.
  • A258976 (program): Numbers n such that 1 + sigma(n)^2 is prime.
  • A258977 (program): Primes in A258974.
  • A258978 (program): a(n) = 1 + sigma(n) + sigma(n)^2 + sigma(n)^3 + sigma(n)^4.
  • A258991 (program): Decimal expansion of the multiple zeta value (Euler sum) zetamult(4,4).
  • A258992 (program): Primes p such that p^2 - 8 is also prime.
  • A258993 (program): Triangle read by rows: T(n,k) = binomial(n+k,n-k), k = 0..n-1.
  • A258996 (program): Permutation of the positive integers: this permutation transforms the enumeration system of positive irreducible fractions A002487/A002487’ (Calkin-Wilf) into the enumeration system A162911/A162912 (Drib), and vice versa.
  • A258998 (program): a(n) = -(-1)^n if n = k^2 for positive integer k, otherwise 0.
  • A259022 (program): Period 9 sequence [ 1, -1, -1, 1, 0, -1, 1, 1, -1, …].
  • A259031 (program): Smallest m such that |A259029(m)| = n.
  • 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, …].
  • A259048 (program): u(1) = v(1) = 1, u(n) = u(n-1) + v(n-1), v(n) = u(n-1)^2 + v(n-1)^2, a(n) = u(n).
  • A259054 (program): a(n) = 4*n^2 - 4*n + 19, n >= 1.
  • A259055 (program): a(n) = 9*n^2 + 18*n + 7.
  • A259056 (program): a(n) gives the determinant of a bisymmetric n X n matrix involving the entries 1, 2, …, A002620(n+1).
  • A259057 (program): One-third of the even-indexed entries of A259056.
  • 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.
  • A259074 (program): Triangle T(n,k) = Sum_{j=0..(n-k)/3} C(n-3*j-1,k-1)*C(n-k-3*j,j).
  • A259076 (program): Powers of 80.
  • A259098 (program): Row sums of A146565.
  • A259104 (program): A000522(n+2)-A000522(n).
  • A259108 (program): a(n) = 2 * A000538(n).
  • A259109 (program): 2*A000540.
  • A259110 (program): 2*A000447(n).
  • A259111 (program): a(n) = least number k > 1 such that 1^k + 2^k + … + k^k == n (mod k).
  • A259131 (program): Numbers n such that 13*n^2 + 52 is a square.
  • A259145 (program): Numbers k such that k^2 - phi(k) is prime, where phi() is A000010.
  • A259156 (program): Positive triangular numbers (A000217) that are pentagonal numbers (A000326) divided by 2.
  • 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.
  • A259162 (program): Positive hexagonal numbers (A000384) that are pentagonal numbers (A000326) 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).
  • A259179 (program): Number of Dyck paths described in A237593 that contain the point (n,n) in the diagram of the symmetric representation of sigma.
  • A259181 (program): a(n) = n*(n+1)*(n+2)*(n+3)*(2*n^2+6*n+7)/360.
  • A259182 (program): a(n) = prime(n) if n prime otherwise 1.
  • A259184 (program): a(n) = 1 - sigma(n) + sigma(n)^2.
  • A259185 (program): Numbers n such that 1 - sigma(n) + sigma(n)^2 is prime.
  • A259186 (program): Primes in A259184.
  • A259189 (program): Semiprimes of the form n^3 + 2.
  • A259190 (program): Primes of the form sigma(n) + sigma(n)^2 - 1.
  • A259207 (program): 5x + 1 sequence beginning at 5.
  • A259210 (program): Positive hexagonal numbers (A000384) that are other hexagonal numbers divided by 3.
  • A259212 (program): A total of n married couples, including a mathematician M and his wife W, are to be seated at the 2n chairs around a circular table. M and W are the first couple allowed to choose chairs, and they choose two chairs next to each other. The sequence gives the number of ways of seating the remaining couples so that women and men are in alternate chairs but M and W are the only couple seated next to each other.
  • A259214 (program): Number of (n+1)X(n+1) 0..1 arrays with each 2X2 subblock having clockwise pattern 0000 0011 or 0101
  • 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.
  • A259216 (program): Number of (n+1) X (2+1) 0..1 arrays with each 2 X 2 subblock having clockwise pattern 0000 0011 or 0101.
  • A259217 (program): Number of (n+1) X (3+1) 0..1 arrays with each 2 X 2 subblock having clockwise pattern 0000 0011 or 0101.
  • A259218 (program): Number of (n+1) X (4+1) 0..1 arrays with each 2 X 2 subblock having clockwise pattern 0000 0011 or 0101.
  • A259219 (program): Number of (n+1) X (5+1) 0..1 arrays with each 2 X 2 subblock having clockwise pattern 0000 0011 or 0101.
  • A259220 (program): Number of (n+1) X (6+1) 0..1 arrays with each 2 X 2 subblock having clockwise pattern 0000 0011 or 0101.
  • A259221 (program): Number of (n+1) X (7+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.
  • A259227 (program): Hydropronic numbers: numbers n that can be written as a product of 2 integers whose sum is equal to ceiling(n/ceiling(sqrt(n))) + ceiling(sqrt(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!).
  • A259266 (program): a(n) is the unique odd-valued residue modulo 5^n of a number m such that m^2+1 is divisible by 5^n.
  • A259278 (program): Number of compositions of n into parts 1, 6, and 7.
  • A259279 (program): a(n) = Sum_{k=0..n} k^2 * A000041(k).
  • 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.
  • A259284 (program): Decimal expansion of log(2) + 1/3.
  • 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.
  • A259291 (program): Number of (n+1) X (2+1) 0..1 arrays with each 2 X 2 subblock having clockwise pattern 0001 0101 or 0111.
  • A259301 (program): Taken over all those prime-partitionable numbers m for which there exists a 2-partition of the set of primes < m that has one subset containing two primes only, a(n) is the frequency with which the smaller prime occurs, where n is the prime index.
  • A259308 (program): a(n) = 1 + sigma(n)^4.
  • A259309 (program): Numbers n such that 1 + sigma(n)^4 is prime.
  • A259310 (program): Primes of the form: 1 + sigma(n)^4.
  • A259311 (program): First differences of A098058.
  • A259315 (program): Nonprimes containing no zeros in decimal representation.
  • A259317 (program): a(n) = 2*(2*n+1)*A000538(n) - 4*A000330(n)^2.
  • A259318 (program): a(n) = A259109(n)*A006331(n) - A259108(n)^2.
  • A259319 (program): a(n) = 2*A002309(n).
  • A259320 (program): a(n) = 2*n*A259319(n) - A259110(n)^2.
  • A259321 (program): a(n) = A259110(n)*A259323(n) - A259319(n)^2.
  • A259322 (program): Sum of sixth powers of odd numbers.
  • A259323 (program): 2*A259322(n).
  • A259334 (program): Triangle read by rows: T(n,k) = k*(n-1)!*n^(n-k-1)/(n-k)!, 1 <= k <= n.
  • A259335 (program): a(n) = Sum(b(2*n, k)^2*(b(2*n, k + 1) - b(2*n, k - 1)), k = 0 .. n)/(n*b(2*n, n)), where b denotes a binomial coefficient.
  • A259343 (program): A001116(n) + 1.
  • 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.
  • A259373 (program): a(n) = Product_{k=0..n} p(k)^k, where p(k) is the partition function A000041.
  • A259399 (program): a(n) = Sum_{k=0..n} p(k)^2, where p(k) is the partition function A000041.
  • A259400 (program): a(n) = Sum_{k=0..n} 2^k*p(k), where p(k) is the partition function A000041.
  • A259401 (program): a(n) = Sum_{k=0..n} 2^(n-k)*p(k), where p(k) is the partition function A000041.
  • A259410 (program): a(n) = 1 - sigma(n) + sigma(n)^2 - sigma(n)^3 + sigma(n)^4.
  • A259417 (program): Even powers of the odd primes listed in increasing order.
  • A259431 (program): Inverse of permutation in A183209.
  • A259436 (program): a(n) = Sum_{k=0..n} p(k)^k, where p(k) is the partition function A000041.
  • A259437 (program): a(n) = Sum_{k=0..n} p(k)^n, where p(k) is the partition function A000041.
  • A259438 (program): a(n) = Sum_{k=0..n} p(k)^(n-k), where p(k) is the partition function A000041.
  • A259444 (program): a(1)=2. For n>1, a(n) = smallest number > a(n-1) which is different from all the numbers a(i)^a(j) for 1 <= i < n, 1 <= j < n.
  • 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.
  • A259457 (program): From higher-order arithmetic progressions.
  • A259458 (program): From higher-order arithmetic progressions.
  • A259459 (program): From higher-order arithmetic progressions.
  • A259462 (program): From higher-order arithmetic progressions.
  • A259468 (program): Digits of an idempotent 12-adic number.
  • A259469 (program): Digits of an idempotent 12-adic number.
  • A259472 (program): Coefficients in an asymptotic expansion of A003319(n)/n! in falling factorials.
  • A259476 (program): Cayley’s triangle of V numbers; triangle V(n,k), n >= 4, n <= k <= 2*n-4, read by rows.
  • A259477 (program): Triangle of numbers where T(n,k) is the number of k-dimensional faces on a partially truncated n-dimensional simplex, 0 <= k <= n.
  • A259486 (program): a(n) = 3*n^2 - 3*n + 1 + 6*floor((n-1)*(n-2)/6).
  • A259508 (program): Number of (n+1) X (1+1) 0..1 arrays with each 2 X 2 subblock having clockwise pattern 0000 0001 0101 0111.
  • A259517 (program): Number of (n+1) X (1+1) 0..1 arrays with each 2 X 2 subblock having clockwise pattern 0000 0001 0011 0101 or 1111.
  • A259525 (program): First differences of A007318, when Pascal’s triangle is seen as flattened list.
  • A259533 (program): Number of restricted barred preferential arrangements of an n-set having 3 bars in which 3 fixed sections are restricted sections and 1 section is a free section.
  • 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(5*n-1,2*n)/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.
  • A259554 (program): a(n) = Sum_{i=0..n} (2^(i)*(-1)^(i+n)*C(n,i)*C(2*n+i-1,n-1)).
  • A259555 (program): a(n) = 2*n^2 - 2*n + 17.
  • A259557 (program): a(n) = binomial(4*n-1, 2*n).
  • 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.
  • A259569 (program): Triangle of numbers where T(n,k) is the number of k-dimensional faces on the polytope that is the convex hull of all permutations of the list (0,1,…,1,2), where there are n - 1 ones, for n > 0. T(0,0) is 1.
  • A259572 (program): Reciprocity array of 0; rectangular, read by antidiagonals.
  • A259574 (program): Sum of numbers in the n-th antidiagonal of the reciprocity array of 0.
  • A259575 (program): Reciprocity array of 1; rectangular, read by antidiagonals.
  • A259577 (program): Sum of numbers in the n-th antidiagonal of the reciprocity array of 1.
  • A259578 (program): Reciprocity array of 2; rectangular, read by antidiagonals.
  • A259581 (program): Reciprocity array of 3; rectangular, read by antidiagonals.
  • A259588 (program): Denominators of the other-side convergents to e.
  • A259589 (program): Numerators of the other-side convergents to e.
  • A259592 (program): Denominators of the other-side convergents to sqrt(3).
  • A259593 (program): Numerators of the other-side convergents to sqrt(3).
  • A259594 (program): Denominators of the other-side convergents to sqrt(6).
  • A259595 (program): Numerators of the other-side convergents to sqrt(6).
  • A259596 (program): Denominators of the other-side convergents to sqrt(7).
  • A259597 (program): Numerators of the other-side convergents to sqrt(7).
  • 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(6*n,2*n)/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.
  • A259627 (program): List of numbers L - 1, L, and L+1, where L = A000032, the Lucas numbers, sorted into increasing order and duplicates removed.
  • A259649 (program): Smallest prime factor of the n-th pentagonal number (A000326).
  • 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.
  • A259655 (program): Expansion of psi(x^2) * f(-x^3)^3 / f(-x) in powers of x where psi(), f() are Ramanujan theta functions.
  • A259659 (program): Expansion of phi(x^6) * f(-x)^3 / f(-x^3) in powers of x where phi(), f() are Ramanujan theta functions.
  • A259661 (program): Binary representation of the middle column of the “Rule 54” elementary cellular automaton starting with a single ON cell.
  • A259662 (program): Expansion of phi(-q^3) / phi(-q)^3 in powers of q where phi() is a Ramanujan theta function.
  • 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.
  • A259668 (program): Expansion of psi(-x)^2 * psi(x^3)^2 / (phi(-x^4) * psi(-x^6)) in power of x where phi(), psi() are Ramanujan theta functions.
  • A259669 (program): a(0)=0, a(1)=1, a(n) = min{5 a(k) + (5^(n-k)-1)/4, k=0..(n-1)} for n>=2.
  • A259676 (program): Heptagonal numbers (A000566) that are semiprimes (A001358).
  • A259677 (program): Octagonal numbers (A000567) that are semiprimes (A001358).
  • A259691 (program): Triangle read by rows: T(n,k) number of arrangements of non-attacking rooks on an n X n right triangular board where the top rook is in row k (n >= 0, 1 <= k <= n+1).
  • A259692 (program): a(n) = Sum(k^4*sigma(k)*sigma(n-k),k=1..n-1).
  • A259693 (program): a(n) = Sum(k^5*sigma(k)*sigma(n-k),k=1..n-1).
  • A259694 (program): a(n) = Sum(k^6*sigma(k)*sigma(n-k),k=1..n-1).
  • A259695 (program): a(n) = Sum_{k=1..n-1} k^7 * sigma(k) * sigma(n-k).
  • A259696 (program): a(n) = Sum_{k=1..n-1} k^8*sigma(k)*sigma(n-k).
  • A259709 (program): a(n) = A259708(n,n-1).
  • A259713 (program): a(n) = 3*2^n - 2*(-1)^n.
  • A259714 (program): a(n) = Sum_{k=1..n-1}((k mod 5)*a(n-k)), a(1) = 1.
  • A259736 (program): Number of (n+2) X (2+2) 0..1 arrays with each 3 X 3 subblock having clockwise perimeter pattern 00010101 or 01010101.
  • A259743 (program): Expansion of f(-x)^3 * psi(x^4) in powers of x where psi(), f() are Ramanujan theta functions.
  • A259748 (program): a(n) = (Sum_{0<x<y<n} x*y) mod n.
  • A259749 (program): Numbers that are congruent to {1,2,5,7,10,11,13,17,19,23} mod 24.
  • 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.
  • A259757 (program): G.f. A(x) satisfies: A(x)^2 = 1+x + x*A(x)^5.
  • A259760 (program): Triangle read by rows: T(n,k) is the number of partial idempotent mappings (of an n-chain) with breadth exactly k.
  • A259761 (program): Expansion of (phi(x)^2 + phi(x^9)^2) / 2 in powers of x where phi() is a Ramanujan theta function.
  • A259773 (program): Product of the digits of the n-th Lucas number.
  • A259774 (program): Expansion of f(x, x^7) / f(x, x^3) in powers of x where f(, ) is Ramanujan’s general theta function.
  • A259775 (program): Stepped path in P(k,n) array of k-th partial sums of squares (A000290).
  • A259788 (program): Greatest prime factor of phi(binomial(2*n,n)).
  • A259790 (program): Expansion of f(-x)^3 * phi(x^2) in powers of x where phi(), f() are Ramanujan theta functions.
  • A259791 (program): Number of connected D-integral graphs on n vertices.
  • A259796 (program): Number of partitions of 3^n into n-th powers.
  • A259821 (program): a(n) = floor( (3^n+1)^2/3^n ).
  • A259823 (program): a(0)=0, a(1)=1, a(n)=min{3 a(k) + 2^(n-k)-1, k=0..(n-1)} for n>=2.
  • A259826 (program): Numbers n such that n is a multiple of 6 and both n-1 and n+1 are composite.
  • A259827 (program): Expansion of phi(x) * f(-x^12)^3 / f(-x^4) in powers of x where phi(), f() are Ramanujan theta functions.
  • A259829 (program): a(n) = (-1)^floor(n/2) * A035185(n).
  • A259830 (program): Decimal expansion of the length of the “double egg” curve (length of one egg with diameter a = 1).
  • A259834 (program): Number of permutations of [n] with no fixed points where the maximal displacement of an element equals n-1.
  • A259845 (program): a(0)=1, a(1)=3, and the INVERT transform of the sequence deletes the 3.
  • A259852 (program): Numerators of the terms of Lehmer’s series S_2(2), where S_k(x) = Sum_{n>=1} n^k*x^n/binomial(2*n, n).
  • A259853 (program): Denominators of the terms of Lehmer’s series S_2(2), where S_k(x) = Sum_{n>=1} n^k*x^n/binomial(2*n, n).
  • A259858 (program): A bisection of A002083.
  • A259859 (program): a(0)=0; thereafter A003470(n-1) + A003470(n) - 1.
  • A259860 (program): a(n+8)+34*a(n+4)+a(n)=0 with a(0)-a(7) as shown.
  • A259861 (program): a(n+8)+34*a(n+4)+a(n)=0 with a(0)-a(7) as shown.
  • A259868 (program): a(n) = n*A004141(n).
  • A259869 (program): a(0) = -1; for n > 0, number of indecomposable derangements, i.e., no fixed points, and not fixing [1..j] for any 1 <= j < n.
  • A259870 (program): a(0)=0, a(1)=1; a(n) = n*a(n-1) + (n-2)*a(n-2) - Sum_{j=1..n-1} a(j)*a(n-j).
  • A259871 (program): a(0)=1/2, a(1)=1; a(n) = n*a(n-1) + (n-2)*a(n-2) - 2*Sum_{j=1..n-1} a(j)*a(n-j) + 2*Sum_{j=0..n-1} a(j)*a(n-1-j).
  • A259872 (program): a(0)=-1, a(1)=1; a(n) = n*a(n-1) + (n-2)*a(n-2) + Sum_{j=1..n-1} a(j)*a(n-j) + 2*Sum_{j=0..n-1} a(j)*a(n-1-j).
  • A259877 (program): If n is even then a(n) = n!/( 2^(n/2)*(n/2)! ), otherwise a(n) = n!/( 3*2^((n-1)/2)*((n-3)/2)! ).
  • A259884 (program): Expansion of phi(x) * f(-x^3)^3 / f(-x) in powers of x where phi(), f() are Ramanujan theta functions.
  • A259895 (program): Expansion of psi(x^2) * psi(x^3) in powers of x where psi() is a Ramanujan theta function.
  • A259896 (program): Expansion of psi(x) * psi(x^6) in powers of x where phi() is a Ramanujan theta function.
  • A259900 (program): n*a(n+1) = (2*n^2 + 3*n + 2)*a(n) - (n^2 - n - 2)*a(n-1) with n>1, a(0)=0, a(1)=1.
  • A259901 (program): n*a(n+1) = (2*n^2+3*n+2)*a(n)-(n^2-n-2)*a(n-1); a(0)=1, a(1)=0.
  • A259902 (program): n*a(n+1) = (2*n^2+3n-1)*a(n)-(n^2-n-2)*a(n-1); a(0)=0, a(1)=1.
  • A259903 (program): n*a(n+1) = (2*n^2+3*n-1)*a(n)-(n^2-n-2)*a(n-1); a(0)=1, a(1)=3.
  • A259904 (program): n*a(n+1) = (2*n^2+2n-1)*a(n)+(n+1)*a(n-1); a(0)=0, a(1)=1.
  • A259905 (program): n*a(n+1) = (2*n^2+2n-1)*a(n)+(n+1)*a(n-1); a(0)=1, a(1)=2.
  • A259906 (program): n*a(n+1) = (2*n^2+2n-1)*a(n) + (n+1)*a(n-1); a(0)=0, a(1)=1.
  • A259907 (program): Fifth differences of 7th powers (A001015).
  • A259911 (program): Triangular array; row k shows the discriminant of the field of the number having purely periodic continued fraction with period (j,k), for j=1..k+1-j.
  • A259912 (program): Discriminant of the field of the number having constant continued fraction [n,n,n,…].
  • A259913 (program): Discriminant of the number field containing the number with periodic continued fraction [1,n,1,n,1,n,…].
  • A259914 (program): Staircase path through the array P(n,k) of the k-th partial sums of cubes (A000578).
  • A259923 (program): a(n) = prime(n)^pi(n).
  • A259925 (program): a(n) = (n^2 - n - 1)^n.
  • A259926 (program): a(n) = n^(2*n) - n^(2*n - 1).
  • A259928 (program): Decimal expansion of the infinite double sum S = Sum_{m>=1} (Sum_{n>=1} 1/(m^2*n*(m+n)^3)).
  • A259936 (program): Number of ways to express the integer n as a product of its unitary divisors (A034444).
  • A259937 (program): Concatenation of the numbers from 1 to n with numbers from n down to 1.
  • A259966 (program): Total binary weight (cf. A000120) of all A005251(n) binary sequences of length n not containing any isolated 1’s.
  • A259967 (program): a(n) = a(n-1) + a(n-2) + a(n-4).
  • 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).
  • A259977 (program): Number of proper divisors of A005381(n).
  • A259978 (program): Terms in A053177 that are relatively prime to 3.
  • A259979 (program): Numbers that are both 1 + square of a prime and twice a prime.
  • A259982 (program): Decimal expansion of 1/2^20.
  • A259986 (program): This sequence and A259987 are base-6 analogs of A007185 and A016090, written in base 10.
  • A259987 (program): This sequence and A259986 are base 6 analogs of A007185 and A016090, written in base 10.
  • A259988 (program): This sequence and A259989 are base-6 analogs of A007185 and A016090, written in base 6.
  • A259989 (program): This sequence and A259988 are base-6 analogs of A007185 and A016090, written in base 6.
  • A259990 (program): This sequence and A259991 are base-14 analogs of A007185 and A016090, written in base 10.
  • A259991 (program): This sequence and A259990 are base-14 analogs of A007185 and A016090, written in base 10.
  • A260006 (program): a(n) = f(1,n,n), where f is the Sudan function defined in A260002.
  • A260022 (program): A bisection of A006921.
  • A260023 (program): a(1)=77; thereafter form the product of the digits of the previous term.
  • A260033 (program): Number of configurations of the general monomer-dimer model for a 2 X 2n square lattice.
  • A260056 (program): Irregular triangle read by rows: coefficients T(n, k) of certain polynomials p(n, x) with exponents in increasing order, n >= 0 and 0 <= k <= 2*n.
  • A260057 (program): Expansion of f(-x, -x^5)^3 / (f(x, x^5) * f(-x^2, -x^2)^2) in powers of x where f(, ) is Ramanujan’s general theta function.
  • A260058 (program): Expansion of f(x^2, x^4) * f(x^3, x^3) / f(-x, -x^2)^2 in power of x where f(, ) is Ramanujan’s general theta function.
  • A260076 (program): Cyclotomic polynomial value Phi(9,n!).
  • A260077 (program): Cyclotomic polynomial value Phi(10,n!).
  • A260089 (program): Expansion of psi(x^2) * f(x, x^2) in powers of x where psi(), f() are Ramanujan theta functions.
  • A260090 (program): Maximum number of kings on an n X n chessboard such that no king attacks more than one other king.
  • A260107 (program): Lexicographically first increasing sequence of positive integers such that there are exactly a(k) terms less than or equal to 3*a(k), for each k.
  • A260109 (program): Expansion of f(x^3) * f(-x^3)^2 * psi(x)^2 / psi(-x) in powers of x where psi(), f() are Ramanujan theta functions.
  • A260110 (program): Expansion of f(-x, -x) * f(x^4, x^8) in powers of x where f(,) is Ramanujan’s general theta function.
  • 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.
  • A260114 (program): Expansion of f(x)^4 * phi(-x^3) / phi(-x) in powers of x where phi(), f() are Ramanujan theta functions.
  • A260118 (program): Expansion of f(-x, -x^5) * psi(x^4) in powers of x where psi(), f() are Ramanujan theta functions.
  • A260122 (program): a(n) = floor( Product_{k = 1..n} k^(k/2) ).
  • A260145 (program): Expansion of x * (psi(x^4) / phi(x))^2 in powers of x where phi(), psi() are Ramanujan theta functions.
  • A260150 (program): Expansion of f(x, x^5)^3 / (f(-x, -x^5) * f(-x^2, -x^2)^2) in powers of x where f(, ) is Ramanujan’s general theta function.
  • A260158 (program): Expansion of psi(x)^4 * psi(-x^3) / f(x) in powers of x where psi, f() are Ramanujan theta functions.
  • 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.
  • A260163 (program): Expansion of f(x^2)^2 / f(-x) in powers of x where f() is a Ramanujan theta function.
  • A260164 (program): Expansion of f(-x^8)^2 / f(-x) in powers of x where f() is a Ramanujan theta function.
  • A260165 (program): Expansion of f(x, x^2) * f(x, x^3)^3 in powers of x where f(, ) is Ramanujan’s general theta function.
  • A260166 (program): Expansion of phi(x^2) * f(-x^3)^3 / chi(-x)^2 in powers of x where phi(), chi(), f() are Ramanujan theta functions.
  • A260167 (program): Expansion of psi(x^4) * f(-x^3)^3 / chi(-x)^2 in powers of x where psi(), chi(), f() are Ramanujan theta functions.
  • A260178 (program): a(n) = hyperfactorial(prime(n)-1) mod prime(n).
  • A260180 (program): G.f.: Sum_{n>=0} x^n * (1 - x^n)^n.
  • A260181 (program): Numbers whose last digit is prime.
  • A260183 (program): Expansion of f(x, x^2) * f(x^4, x^8) / f(-x^3, -x^6)^2 in powers of x where f(, ) is Ramanujan’s general theta function.
  • A260187 (program): a(n) = n modulo the greatest primorial <= n.
  • A260188 (program): Greatest primorial less than or equal to n.
  • A260190 (program): Kronecker symbol(-6 / 2*n + 1).
  • A260191 (program): Numbers m such that there exists no square whose base-m digit sum is binomial(m,2).
  • A260192 (program): Kronecker symbol(-6 / 2*n + 7).
  • A260194 (program): a(n+1) = a(n) + gcd(a(n),a(n-2)), with a(1) = a(2) = a(3) = 1
  • A260196 (program): 1, -3, followed by -1’s.
  • A260209 (program): Values A such that p=prime(n) satisfies binomial(2p-1, p-1) == 1 + A*p (mod p^4).
  • A260210 (program): A034602(n) modulo prime(n).
  • A260211 (program): Irregular triangle read by rows, T(n,k) is the decimal number conversion from an n-bit symmetric binary table arranged in ascending order for n > 1.
  • A260215 (program): Expansion of chi(-q) * chi(q^9) / (chi(q) * chi(-q^9)) in powers of q where chi() is a Ramanujan theta function.
  • 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).
  • A260222 (program): a(n)=gcd(n,F(n-1)), where F(n) is the n-th Fibonacci number.
  • A260228 (program): a(n) = max(gcd(n,F(n-1)),gcd(n,F(n+1))), where F(n) is the n-th Fibonacci number.
  • A260231 (program): a(n) = Product_{k=1..n} (1 + k^k).
  • 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).
  • A260253 (program): Number of symmetry-allowed, linearly-independent terms at n-th order in the expansion of E x (e+a) rovibrational perturbation matrix H(Jx,Jy,Jz).
  • A260254 (program): Number of ways to write n as sum of two palindromes in decimal representation.
  • A260259 (program): a(n) = F(n)*F(n+1) - (-1)^n, where F = A000045.
  • A260260 (program): a(n) = n*(16*n^2 - 21*n + 7)/2.
  • A260263 (program): a(n+1) = a(n) + largest digit not in a(n), starting with a(1) = 1.
  • A260264 (program): a(n+1) = a(n) + largest digit not in a(n), starting with a(0) = 0.
  • A260271 (program): Primes that contain only the digits (1, 4, 9).
  • A260295 (program): Expansion of f(-x^2)^3 * f(-x^6)^3 / f(-x)^2 in powers of x where f() is a Ramanujan theta function.
  • A260297 (program): a(n) = prime(n) - (hyperfactorial(prime(n)-1) mod prime(n)).
  • A260300 (program): Bisection of A258409: a(n) = A258409(2n+1).
  • A260302 (program): Maximum water retention of a number octagon of order n.
  • A260304 (program): a(n) = 5*a(n-1) - 5*a(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.
  • A260308 (program): Expansion of psi(x) * phi(x^3) in powers of x where phi(), psi() are Ramanujan theta functions.
  • A260313 (program): Expansion of phi(x)^2 / psi(x) in powers of x where phi(), psi() are Ramanujan theta functions.
  • A260314 (program): Expansion of phi(x)^2 / phi(-x^2) in powers of x where phi() is a Ramanujan theta function.
  • A260316 (program): n/3 if 3 divides n, else n-1.
  • A260326 (program): Common denominator of coefficients in Nörlund’s polynomial D_{2n}(x).
  • A260331 (program): Labelings of n diamond-shaped posets with 4 vertices per diamond where the labels follow the poset relations.
  • A260341 (program): A002107 with the zero terms omitted.
  • A260360 (program): The absolute difference between the largest prime factors of prime(n)-1 and prime(n+1)-1.
  • A260373 (program): The nearest perfect square to n!
  • A260375 (program): Numbers k such that A260374(k) is a perfect square.
  • 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.
  • A260391 (program): Positions of 0 in the infinite palindromic word at A260390.
  • A260392 (program): Positions of 1 in the infinite palindromic word at A260390.
  • 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.
  • A260394 (program): Infinite palindromic word (a(1),a(2),a(3),…) with initial word w(1) = (0,1,1) and midword sequence (a(n)); see Comments.
  • A260395 (program): Positions of 0 in the infinite palindromic word at A260394.
  • A260396 (program): Positions of 1 in the infinite palindromic word at A260394.
  • 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.
  • A260398 (program): Positions of 0 in the infinite palindromic word at A260397.
  • A260399 (program): Positions of 1 in the infinite palindromic word at A260397.
  • A260400 (program): Positions of 0 in the infinite palindromic word at A259599.
  • A260401 (program): Positions of 1 in the infinite palindromic word at A259599.
  • A260411 (program): Number of ways n can be represented as a sum of a positive cube, a positive square, and a positive triangular number.
  • A260415 (program): Expansion of f(x, x^2) * f(x^4, x^8) in powers of x where f(,) is Ramanujan’s general theta function.
  • A260416 (program): The smallest prime that is greater than prime(n) and congruent to n mod prime(n).
  • 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.
  • A260449 (program): Infinite palindromic word (a(1),a(2),a(3),…) with initial word w(1) = (1,2,3) and midword sequence (a(n)); see Comments.
  • A260450 (program): Infinite palindromic word (a(1),a(2),a(3),…) with initial word w(1) = (1,3,2) and midword sequence (a(n)); see Comments.
  • A260451 (program): Infinite palindromic word (a(1),a(2),a(3),…) with initial word w(1) = (2,3,1) and midword sequence (a(n)); see Comments.
  • A260452 (program): Infinite palindromic word (a(1),a(2),a(3),…) with initial word w(1) = (2,1,3) and midword sequence (a(n)); see Comments.
  • A260453 (program): Infinite palindromic word (a(1),a(2),a(3),…) with initial word w(1) = (3,1,2) and midword sequence (a(n)); see Comments.
  • A260454 (program): Infinite palindromic word (a(1),a(2),a(3),…) with initial word w(1) = (3,2,1) and midword sequence (a(n)); see Comments.
  • A260455 (program): Infinite palindromic word (a(1),a(2),a(3),…) with initial word w(1) = 0 and midword sequence (1,null,1,null,1,null,…); see Comments.
  • A260456 (program): Infinite palindromic word (a(1),a(2),a(3),…) with initial word w(1) = 1 and midword sequence (0,null,0,null,0,null,…); see Comments.
  • A260458 (program): Limit of gcd(PP(n) - k, PP(n) + k) as k -> oo, where PP(n) is the product of the first n primes.
  • A260464 (program): Number of chains in the poset of even-sized subsets of {1,2,…,n} ordered by inclusion.
  • A260478 (program): Cyclotomic polynomial value Phi(8,n!).
  • A260479 (program): Positions of 0 in the infinite palindromic word at A260455.
  • A260480 (program): Positions of 0 in the infinite palindromic word at A260455.
  • A260483 (program): Beatty sequence for e^(1/Pi) = A179706.
  • A260484 (program): Complement of the Beatty sequence for e^(1/Pi) = A179706.
  • A260488 (program): Numbers of the form 2^m * (6k + 1) for m, k >= 0, and 0.
  • A260489 (program): a(n) = 3n - A260488(n).
  • A260492 (program): Pascal’s triangle aerated with columns of zeros.
  • A260504 (program): Number of chains in the poset of all odd-sized subsets of {1,2,…,n} ordered by inclusion.
  • A260505 (program): Number of binary words of length n with exactly one occurrence of subword 010 and exactly two occurrences of subword 101.
  • A260509 (program): Number of graphs on labeled vertices {x, y, 1, 2, …, n}, such that there is a partition of the vertices into V_1 and V_2 with x in V_1, y in V_2, every v in V_1 adjacent to an even number of vertices in V_2, and every v in V_2 adjacent to an even number of vertices in V_1.
  • A260513 (program): a(n) = (8*n+13*n^3+3*n^5)/24; also the sum of triangular numbers taken in successive groups of increasing size (see Example).
  • A260516 (program): Expansion of f(x, x^2) * f(x^2, x^10) in powers of x where f(,) is Ramanujan’s general theta function.
  • A260518 (program): Expansion of psi(x)^2 * f(-x^3)^3 / f(-x) in powers of x where psi(), f() are Ramanujan theta functions.
  • A260523 (program): Numbers n such that (sum of digits of n) + (product of digits of n) is semiprime.
  • A260545 (program): Expansion of phi(-x^6)^2 / (chi(x) * phi(-x)^2) in powers of x where phi(), chi() are Ramanujan theta functions.
  • A260546 (program): Expansion of phi(-x^3) * psi(-x^3) / phi(-x)^2 in powers of x where phi(), psi() are Ramanujan theta functions
  • A260547 (program): Expansion of psi(x^3) * psi(-x^3) * chi(-x) / phi(-x)^2 in powers of x where phi(), psi(), chi() are Ramanujan theta functions.
  • A260552 (program): Triangle read by rows giving successive states of cellular automaton generated by “Rule 17” initiated with a single ON (black) cell.
  • A260577 (program): Numbers n for which d(n+d(n)) < d(n), where d(n) is the number of divisors of n.
  • A260581 (program): Numbers n for which d(n+d(n)) > d(n), where d(n) is the number of divisors of n.
  • A260585 (program): Number of ways to place 2n rooks on an n X n board, with 2 rooks in each row and each column, multiple rooks in a cell allowed, and exactly 2 rooks below the main diagonal.
  • A260596 (program): Array A read by upward antidiagonals in which the entry A(n,k) in row n and column k is defined by A(n,k) = (8 + (3*floor((4*n + 1)/3) - 2)*4^k)/12, n,k >= 1.
  • A260599 (program): Expansion of psi(x^4) / chi(-x)^2 in powers of x where psi(), chi() are Ramanujan theta functions.
  • A260610 (program): Suprafactorials: Product of first n hyperfactorials divided by the product of the first n superfactorials.
  • A260611 (program): a(n) = superfactorial(prime(n)-1) mod prime(n).
  • A260619 (program): Arithmetic derivative of hyperfactorial(n).
  • A260620 (program): Arithmetic derivative of superfactorial(n).
  • A260622 (program): a(n) is the sum of the positive divisors of A003266(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.
  • A260640 (program): Numbers n such that binomial(3*n,n) == 0 (mod n).
  • A260644 (program): Four steps forward, three steps back.
  • A260647 (program): Numbers that are the sum of two distinct nonzero triangular numbers.
  • A260649 (program): Expansion of (phi(q^3) * phi(q^5) + phi(q) * phi(q^15)) / 2 - 1 in powers of q where phi(q) is a Ramanujan theta function.
  • A260655 (program): a(n) = 4*36^n*Gamma(n+3/2)/(sqrt(Pi)*(n+2)!).
  • A260658 (program): Numerators of a BBP-like formula for 4*Pi/sqrt(27).
  • A260671 (program): Expansion of theta_3(q) * theta_3(q^15) in powers of q.
  • A260675 (program): Expansion of psi(x^2) * phi(x^15) in powers of x where phi(), psi() are Ramanujan theta functions.
  • A260678 (program): Numbers n>0 for which n+(17-n)^2 is not prime.
  • A260679 (program): a(n) = n+(17-n)^2.
  • A260682 (program): Löschian numbers (A003136) of the form 6*k+1.
  • A260683 (program): Number of 2’s in the expansion of 2^n in base 3.
  • A260684 (program): Irregular triangular array read by rows. Row n gives the primes in the prime factorization of n! that have exponent of 1.
  • A260686 (program): Period 6 zigzag sequence, repeat [0, 1, 2, 3, 2, 1].
  • A260688 (program): a(n) = the least number of pieces of currency of denominations .01, .05, .10, .25, 1, 5, 10, 20, 50, 100 that the greedy algorithm uses to make n times .01 (n “cents”) in change.
  • A260699 (program): a(2n+6) = a(2n) + 12*n + 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*(2*n+1), a(2n+7) = a(2n+1) + 12*n + 28, with a(1)=1, a(3)=6, a(5)=16.
  • A260710 (program): Expansion of 1/(1 - x - x^2 - x^4 + x^5 + x^7).
  • 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.
  • A260715 (program): Row 5 of A260717.
  • A260736 (program): a(0) = 0; for n >= 1, a(n) = A000035(n) + a(A257684(n)); in the factorial representation of n the number of digits with maximal possible value allowed in its location.
  • A260740 (program): a(n) = n minus the number of positive squares needed to sum to n using the greedy algorithm: a(n) = n - A053610(n).
  • A260751 (program): 25 primes in arithmetic progression: a(n) = 6171054912832631 + (n-1)*81737658082080 for n = 1, 2, …, 25.
  • A260754 (program): a(n) = prime(n+1)! / prime(n).
  • A260769 (program): Certain directed lattice paths.
  • A260770 (program): Certain directed lattice paths.
  • A260771 (program): Certain directed lattice paths.
  • A260772 (program): Certain directed lattice paths.
  • A260773 (program): Certain directed lattice paths.
  • A260774 (program): Certain directed lattice paths.
  • A260775 (program): Certain directed lattice paths.
  • A260776 (program): Certain directed lattice paths.
  • A260786 (program): Twice the Euler or up/down numbers A000111.
  • A260794 (program): Number of steps required by R. L. Graham’s generalized binary merging algorithm.
  • A260810 (program): a(n) = n^2*(3*n^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.
  • A260814 (program): Powers of 2 with distinct digits.
  • A260815 (program): a(2) = 3; for n >= 3, a(n) = a(n-1) + gcd(n, a(n-1))^2.
  • A260820 (program): Nonnegative integers n such that n^3-3 is divisible by n-3.
  • A260832 (program): a(n) = numerator(Jtilde2(n)).
  • A260846 (program): a(n) = (-3 - 28*3^n + 73*15^n)/21.
  • A260851 (program): a(n) in base n is the concatenation of the base n expansions of (1, 2, 3, …, n-1, n, n-1, …, 3, 2, 1).
  • A260854 (program): Base-4 representation of a(n) is the concatenation of the base-4 representations of 1, 2, …, n, n-1, …, 1.
  • A260855 (program): Base-5 representation of a(n) is the concatenation of the base-5 representations of 1, 2, …, n, n-1, …, 1.
  • A260856 (program): Base-6 representation is the concatenation of the base-6 representations of 1, 2, …, n, n-1, …, 1.
  • A260857 (program): Base-7 representation of a(n) is the concatenation of the base-7 representations of 1, 2, …, n, n-1, …, 1.
  • A260858 (program): Base-8 representation of a(n) is the concatenation of the base-8 representations of 1, 2, …, n, n-1, …, 1.
  • A260859 (program): Base-9 representation of a(n) is the concatenation of the base-9 representations of 1, 2, …, n, n-1, …, 1.
  • A260860 (program): Base-60 representation of a(n) is the concatenation of the base-60 representations of 1, 2, …, n, n-1, …, 1.
  • A260861 (program): Base-11 representation of a(n) is the concatenation of the base-11 representations of 1, 2, …, n, n-1, …, 1.
  • A260862 (program): Base-12 representation of a(n) is the concatenation of the base-12 representations of 1, 2, …, n, n-1, …, 1.
  • A260864 (program): Base-14 representation of a(n) is the concatenation of the base-14 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]}.
  • A260881 (program): Number of trapezoidal words of length n.
  • A260884 (program): Number of set partitions of a 2n-set into even blocks which have even length minus the number of partitions into even blocks which have odd length.
  • A260905 (program): Totients of the Blum integers.
  • A260907 (program): Numbers n such that prime(n) + prime(n+1) + prime(n+2) is not a prime.
  • A260917 (program): Expansion of 1/(1 - x - x^2 - x^3 + x^6 + x^7).
  • A260918 (program): Number of squares of all sizes in polyominoes obtained by union of two pyramidal figures (A092498) with intersection equals A002623.
  • A260930 (program): Differences between the numbers n such that n^2 + 2 is prime.
  • A260931 (program): a(n) = A260930(n)/6 for n > 2.
  • A260934 (program): Sum of evil divisors of n. For evil numbers see A001969.
  • A260937 (program): Indices i of pentagonal numbers P(i) such that (P(i)-1)/2 is also a pentagonal number.
  • 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)).
  • A260941 (program): Expansion of phi(-x) * phi(x^6) / chi(-x^3) in powers of x where phi(), chi() are Ramanujan theta functions.
  • A260942 (program): Expansion of x * phi(-x) * psi(x^12) / chi(-x^3) in powers of x where phi(), psi(), chi() are Ramanujan theta functions.
  • A260943 (program): Expansion of psi(-x^2) * chi(x^3) * f(x^6) in powers of x where psi(), chi(), f() are Ramanujan theta functions.
  • A260945 (program): Expansion of (2*b(q^4) - b(q) - b(q^2)) / 3 in powers of q where b() is a cubic AGM theta function.
  • A260955 (program): Differences of the increasing arithmetic progression a^2+a, b^2+b, c^2+c, where b = 5*a+2, c = 7*a+3 and a >= 0.
  • A260963 (program): Numbers n such that gcd(sigma(n), n*(n+1)/2 - sigma(n)) = 1, where sigma(n) is sum of positive divisors of n.
  • A261004 (program): Expansion of (-3-164*x-x^2)/(1-99*x+99*x^2-x^3).
  • A261009 (program): Write 2^n in base 3, add up the “digits”.
  • A261010 (program): Write 5^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.
  • A261024 (program): Decimal expansion of Cl_2(2*Pi/3), where Cl_2 is the Clausen function of order 2.
  • A261032 (program): a(n) = (-1)^n*(n^8 + 4*n^7 - 14*n^5 + 28*n^3 - 17*n)/2.
  • A261034 (program): Numbers k such that 3k is squarefree.
  • A261040 (program): Values of c such that the Diophantine equation 5*a + 3*b = c has no solutions in positive integers.
  • A261042 (program): Generating function g(0) where g(k) = 1 - x*2*(k+1)*(k+2)/(x*2*(k+1)*(k+2) - 1/g(k+1)).
  • A261043 (program): Number of multisets of nonempty words with a total of n letters over binary alphabet such that all letters occur at least once in the multiset.
  • A261046 (program): Irregular triangle read by rows: the first column consists of the odd numbers repeated but without the first 1. Row n (n>=0) contains floor(n/2)=1 terms. Every row contains successive odd numbers.
  • A261053 (program): Expansion of Product_{k>=1} (1+x^k)^(k^k).
  • A261054 (program): Expansion of ( 2+x-x^2+x^3 ) / (1-x^2-x)^3 .
  • A261055 (program): Expansion of ( -1-2*x+x^2+x^3 ) / (x^2+x-1)^3 .
  • A261056 (program): Expansion of ( 2-x^2 ) / (x^2+2*x-1)^2 .
  • A261058 (program): Column k=1 of A213221.
  • A261064 (program): a(n) = (3^n-1)*(n+1)/4.
  • A261065 (program): Second column of A086872.
  • A261070 (program): Irregular triangle read by rows: T(n,k) is the number of arrangements of n circles with 2k intersections (using the same rules as A250001).
  • 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).
  • A261088 (program): Number of steps needed to reach zero when starting from k = n^2 and repeatedly applying the map that replaces k with k - d(k), where d(k) is the number of divisors of k (A000005).
  • A261092 (program): First differences of A261093; characteristic function for A219640.
  • A261093 (program): a(n) = number of nonzero terms of A219640 <= n.
  • A261094 (program): Left inverse of A219640: If n = A219640(k) for some k, then a(n) = k, otherwise zero.
  • A261095 (program): First differences of A219640: a(n) = A219640(n+1) - A219640(n).
  • A261100 (program): a(n) is the greatest m for which A002182(m) <= n; the least monotonic left inverse for highly composite numbers A002182.
  • A261104 (program): a(0)=0; for n >= 1, a(n) = 1 + a(n-A070319(n)), where A070319(n) is the maximum value for A000005 (number of divisors) in range 1 .. n.
  • A261115 (program): Expansion of f(x, x) * f(x^4, x^8) in powers of x where f(,) is Ramanujan’s general theta function.
  • A261116 (program): Pairs of integers (a,b) such a^2 + (a+1)^2 = b^2.
  • A261118 (program): Expansion of psi(x)^2 * psi(-x^3)^2 / (phi(-x^4) * psi(-x^6)) in power of x where phi(), psi() are Ramanujan theta functions.
  • A261119 (program): Expansion of f(x^2, -x^4) * f(x, x^5)^2 / f(-x^12, -x^12) in powers of x where f(, ) is Ramanujan’s general theta function.
  • A261120 (program): The number of distinct triple points in the set of function values FLSN(m/6/7^n), m in 0, 1, 2… 6*7^n, where FLSN:[0,1] is the “flowsnake” plane filling curve.
  • A261122 (program): Expansion of f(-x) * f(x^4, x^8)^2 / f(-x^3, -x^9) in powers of x where f(,) is Ramanujan’s general theta function.
  • A261128 (program): Cyclotomic polynomial value Phi(7,n!).
  • A261130 (program): a(n) = Product(p prime | n < p <= 2*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.
  • A261154 (program): Expansion of psi(q^6) * f(-q^12) / (psi(-q) * psi(q^9)) in powers of q where psi(), f() are Ramanujan theta functions.
  • A261156 (program): Expansion of chi(q) * chi(-q^9) / (chi(-q) * chi(q^9)) in powers of q where chi() is a Ramanujan theta function.
  • 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)).
  • A261185 (program): Flowsnake parity pattern: a(n) = (A261180(n) mod 2).
  • A261186 (program): binomial(3*n-2,n+1).
  • A261188 (program): Integers such that no subsequence of decimal representation is divisible by 3.
  • A261189 (program): Integers such that no subsequence of decimal representation is divisible by 5.
  • A261190 (program): Leap years in Symmetry454 calendar, starting year AD 1.
  • A261191 (program): 40-gonal numbers: a(n) = 38*n*(n-1)/2 + n.
  • A261193 (program): a(n) = n! - 2.
  • A261196 (program): Expansion of sqrt(8*x + sqrt(1 + 64*x^2)).
  • A261197 (program): Cubes of the successive terms of the decimal expansion of Pi.
  • A261202 (program): Expansion of phi(-x) * phi(-x^9) / f(-x^6)^2 in powers of x where phi(), f() are Ramanujan theta functions.
  • A261203 (program): Expansion of f(-x^6)^2 / (phi(-x) * phi(-x^9)) in powers of x where phi(), f() are Ramanujan theta functions.
  • A261207 (program): Expansion of (x-1)/8 - (x^2-4*x-1)/(8*sqrt(x^2-6*x+1)).
  • A261210 (program): a(n) = gpf(1 + Product_{k=0..4} prime(n+k)), where gpf is greatest prime factor and prime(i) is the i-th prime.
  • A261221 (program): a(n) = number of steps to reach 0 when starting from k = n and repeatedly applying the map that replaces k with k - A053610(k), where A053610(k) = the number of positive squares needed to sum to k using the greedy algorithm.
  • A261222 (program): a(n) = number of steps to reach 0 when starting from k = n*n and repeatedly applying the map that replaces k with k - A053610(k), where A053610(k) = the number of positive squares that sum to k using the greedy algorithm.
  • A261223 (program): a(n) = number of steps to reach 0 when starting from k = (n*n)-1 and repeatedly applying the map that replaces k with k - A053610(k), where A053610(k) = the number of positive squares that sum to k using the greedy algorithm.
  • A261224 (program): a(n) = number of steps needed to reach (n^2)-1 when starting from k = ((n+1)^2)-1 and repeatedly applying the map that replaces k with k - A053610(k), where A053610(k) = the number of positive squares that sum to k using the greedy algorithm.
  • 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.
  • A261252 (program): Expansion of f(-x^3) * f(-x^6) / (f(x) * f(-x^4)) in powers of x where f() is a Ramanujan theta function.
  • A261266 (program): Expansion of ((x-1/2)*(1/sqrt(8*x^2-8*x+1)+1)-x)/(x-1).
  • 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.
  • A261273 (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) = denominator of R(prime(n)).
  • A261276 (program): 100-gonal numbers: a(n) = 98*n*(n-1)/2 + n.
  • A261299 (program): Binary representation of the middle column of the “Rule 30” elementary cellular automaton starting with a single ON cell.
  • A261300 (program): Concatenate successive run lengths of 0’s in the binary expansion of n, each increased by 1.
  • A261301 (program): a(n+1) = abs(a(n) - gcd(a(n), n)), a(1) = 1.
  • A261302 (program): a(n+1) = abs(a(n) - gcd(a(n), 2n+1)), a(1) = 1.
  • A261303 (program): a(n+1) = abs(a(n) - gcd(a(n), 3n+2)), a(1) = 1.
  • A261304 (program): a(n+1) = abs(a(n) - gcd(a(n), 4n+3)), a(1) = 1.
  • A261305 (program): a(n+1) = abs(a(n) - gcd(a(n), 5*n+4)), u(1) = 1.
  • A261306 (program): a(n+1) = abs((n) - gcd(a(n), 6*n+5)), a(1) = 1.
  • A261307 (program): a(n+1) = abs(a(n) - gcd(a(n), 7*n+6)), a(1) = 1.
  • A261308 (program): a(n+1) = abs(a(n) - gcd(a(n), 8n+7)), a(1) = 1.
  • A261309 (program): a(n+1) = abs(a(n) - gcd(a(n), 9n+8)), u(1) = 1.
  • A261310 (program): a(n+1) = abs(a(n) - gcd(a(n), 10n+9)), a(1) = 1.
  • A261317 (program): Number of permutations sigma of [n] without fixed points such that sigma^6 = Id.
  • A261320 (program): Expansion of (phi(q^3) / phi(q))^2 in powers of q where phi() is a Ramanujan theta function.
  • A261321 (program): Expansion of (phi(q) / phi(q^3))^2 in powers of q where phi() is a Ramanujan theta function.
  • A261325 (program): Expansion of f(x^3, x^3) * f(x, x^5) / f(x, x)^2 in powers of x where f(,) is Ramanujan’s general theta function.
  • A261326 (program): Expansion of f(-x^2, -x^4)^2 / (f(x^3, -x^6) * f(-x, x^2)) in powers of x where f(,) is Ramanujan’s general theta function.
  • A261327 (program): a(n) = (n^2 + 4) / 4^((n + 1) mod 2).
  • 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) = 48*n*(n-1)/2 + n.
  • A261345 (program): Number of distinct prime divisors among the numbers k^2 + 1 for k in 1 <= k <= n.
  • A261348 (program): a(1)=0; a(2)=0; for n>2: a(n) = A237591(n,2) = A237593(n,2).
  • A261363 (program): Triangle read by rows: partial row sums of Sierpinski’s triangle.
  • A261365 (program): Prime-numbered rows of Pascal’s triangle.
  • A261366 (program): a(n) = number of even terms in row n of triangle A261363.
  • A261368 (program): Number of sequences F such that F(k) = F(k-1) + F(k-2), F(1), F(2) are positive integers, and there exists some integer x>2 such that F(x) = n.
  • A261369 (program): Expansion of (psi(-x^3) / f(x))^2 in powers of x where psi(), f() are Ramanujan theta functions.
  • A261386 (program): Expansion of Product_{k>=1} ((1+x^k)/(1-x^k))^(2*k).
  • A261389 (program): Expansion of Product_{k>=1} ((1+x^k)/(1-x^k))^(3*k).
  • A261391 (program): a(n) = n^5 + 5*n^3 + 5*n.
  • A261393 (program): Additive terms of the rational Collatz tree.
  • A261394 (program): Expansion of phi(q)^4 / phi(q^3) in powers of q where phi() is a Ramanujan theta function.
  • A261397 (program): a(n) = 3^n*Fibonacci(n).
  • A261398 (program): Integer coefficients arising from a formula for Sum_{m>=1} sin(Pi*m/3)^2/m^2.
  • A261399 (program): a(1)=1; thereafter a(n) = (2/5)*(9*6^(n-2)+1).
  • A261415 (program): The maximal midpoint-free set Z_7^{+}{0,1,3}.
  • A261421 (program): Numerators of coefficients in Taylor series expansion of sqrt(m(x)) where m(x) is g.f. for Motzkin numbers A001006.
  • A261423 (program): Largest palindrome <= n.
  • A261424 (program): Difference between n and the largest palindrome <= n.
  • A261426 (program): Expansion of f(-x^3)^3 * phi(x^6) / f(-x) in powers of x where phi(), f() are Ramanujan theta functions.
  • A261428 (program): Number of permutations p of [2n] without fixed points such that p^8 = Id.
  • A261429 (program): Number of permutations p of [3n] without fixed points such that p^9 = Id.
  • A261441 (program): Number of binary strings of length n+3 such that the smallest number whose binary representation is not visible in the string is 5.
  • A261444 (program): Expansion of f(x^3)^2 * f(-x^6)^2 / f(-x^2) in powers of x where f() is a Ramanujan theta function.
  • A261445 (program): Expansion of f(x, x^3) * f(x, x^2)^3 in powers of x where f(, ) is Ramanujan’s general theta function.
  • A261446 (program): Expansion of f(-x^3, -x^3) * f(-x, -x^5) / f(-x, -x)^2 in powers of x where f(,) is Ramanujan’s general theta function.
  • A261465 (program): a(n) = prime(n+1)^2 - prime(n).
  • A261466 (program): Records in A261461.
  • A261468 (program): a(n) = prime(n+2) mod prime(n).
  • A261469 (program): a(n) = prime(n+3) mod prime(n).
  • A261470 (program): a(n) = prime(n+3) - prime(n+2) - prime(n+1) + prime(n).
  • A261471 (program): Cyclotomic polynomial value Phi(6,n!).
  • A261491 (program): a(n) = ceiling(2 + sqrt(8*n-4)).
  • A261492 (program): Number of partitions of subsets of {1,…,n}, where consecutive integers are required to be in the same part and the elements of {1, n} are required to be in the same part if they are both members of a subset.
  • A261507 (program): Fibonacci-numbered rows of Pascal’s triangle. Triangle read by rows: T(n,k)= binomial(Fibonacci(n), k).
  • A261521 (program): a(n) = n^2 + 2*n + 29.
  • A261540 (program): a(n) = n^7 + 7*n^5 + 14*n^3 + 7*n.
  • A261543 (program): Numbers of the form (prime(k) + Fibonacci(k))/2.
  • 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).
  • A261574 (program): a(n) = n*(n^2 + 3)*(n^6 + 6*n^4 + 9*n^2 + 3).
  • A261576 (program): Expansion of 3 * b(q^2) * c(q^2) / c(q)^2 in powers of q where b(), c() are cubic AGM theta functions.
  • A261586 (program): Odd numbers n such that the sum of the binary digits of n equals the sum of the binary digits of n^2.
  • A261589 (program): 6-Modular Catalan Numbers C_{n,6}.
  • A261591 (program): 8-Modular Catalan Numbers C_{n,8}.
  • A261606 (program): a(n) = Fibonacci(n) mod 60.
  • A261607 (program): Initial digit of Fibonacci number F(n) in base 60.
  • A261609 (program): Number of composite divisors of n^2+1.
  • A261614 (program): Numbers that are neither prime (A000040) nor practical (A005153).
  • A261616 (program): Expansion of Product_{k>=0} 1/(1 - x^(3*k+1))^2.
  • A261618 (program): Concatenation of n, n+1 and n.
  • A261619 (program): a(n) = floor(prime(n^2) / prime(n)).
  • A261629 (program): Expansion of Product_{k>=0} 1/(1-x^(4*k+1))^2.
  • A261630 (program): Expansion of Product_{k>=0} (1+x^(4*k+1))^2.
  • A261631 (program): Expansion of Product_{k>=0} 1/(1-x^(3*k+1))^3.
  • A261632 (program): Expansion of Product_{k>=0} 1/(1-x^(4*k+1))^3.
  • A261634 (program): Expansion of Product_{k>=0} (1+x^(4*k+1))^3.
  • A261635 (program): Expansion of Product_{k>=0} 1/(1-x^(3*k+1))^4.
  • A261636 (program): Expansion of Product_{k>=0} 1/(1-x^(4*k+1))^4.
  • A261638 (program): Expansion of Product_{k>=0} (1+x^(4*k+1))^4.
  • A261642 (program): Triangle, read by rows, where T(n,k) = (k^2 + k)^(n-k) for k=1..n and n>=1.
  • A261643 (program): a(n) = Sum_{k=1..n} (k^2 + k)^(n-k).
  • A261663 (program): Number of equivalence classes of permutations avoiding the pattern {123}.
  • A261664 (program): Number of equivalence classes of permutations avoiding the pattern {231}.
  • A261667 (program): Dimension of a certain space of duality relations arising in study of q-analogs of multiple zeta values.
  • A261668 (program): Number of admissible words of Type G arising in study of q-analogs of multiple zeta values.
  • 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.
  • A261682 (program): a(n) = 2^n+(1+(n mod 2)/2)*C(n+1,floor((n+(n mod 2))/2))-1.
  • A261687 (program): Values of g-hat_2(n), a sum involving Stirling numbers of the first kind.
  • A261691 (program): Change of base from fractional base 3/2 to base 3.
  • 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.
  • A261711 (program): Triangle read by rows: T(n,k) is the number of words over alphabet {0,1,2,3} having exactly k occurrences of the string 01, where n>=0 and k>=0.
  • A261720 (program): Array of pyramidal (3-dimensional figurate numbers) read by antidiagonals.
  • A261721 (program): Fourth-dimensional figurate numbers.
  • A261723 (program): Interleave 2^n + 2 and 2^n + 1.
  • A261726 (program): a(n) = binomial(prime(n+1)-1, prime(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.
  • A261775 (program): Expansion of Product_{k>=1} (1 - x^(8*k))/(1 - x^k).
  • A261776 (program): Expansion of Product_{k>=1} (1 - x^(10*k))/(1 - x^k).
  • A261779 (program): a(n) = ceiling((n-1)! / n).
  • A261783 (program): Number of compositions of n where each part i is marked with a word of length i over an n-ary alphabet whose letters appear in alphabetical order.
  • A261791 (program): The integer part of the surface area of the 4-dimensional sphere of radius n.
  • A261792 (program): Primes of the form k*pi(k) - 1, where pi(k) is the number of primes <= k.
  • A261793 (program): Successively add the smallest number that is not a substring in decimal representation.
  • A261794 (program): a(n) is the smallest nonzero number that is not a substring of n in decimal representation.
  • A261795 (program): First differences of A261793.
  • A261799 (program): Number of 7-compositions of n: matrices with 7 rows of nonnegative integers with positive column sums and total element sum n.
  • A261800 (program): Number of 8-compositions of n: matrices with 8 rows of nonnegative integers with positive column sums and total element sum n.
  • A261801 (program): Number of 9-compositions of n: matrices with 9 rows of nonnegative integers with positive column sums and total element sum n.
  • A261802 (program): Number of 10-compositions of n: matrices with 10 rows of nonnegative integers with positive column sums and total element sum n.
  • A261807 (program): a(n) = n XOR n^3.
  • A261809 (program): a(n) = n! - prime(n).
  • A261812 (program): First differences of A098842.
  • A261869 (program): First differences of A055615.
  • A261871 (program): Numbers of the form (2*j-1)*(2^k-1); j>=1, k>=2.
  • A261872 (program): a(n) = phi(n) mod 5, where phi is the Euler totient function.
  • A261874 (program): Numbers n such that the sum of digits of n is divisible by at least one prime divisor of n.
  • A261879 (program): Decimal expansion of BesselI(3,2).
  • A261880 (program): Array of higher-order differences of the sequence (-1)^n*A000111(n) read by downward antidiagonals.
  • A261882 (program): Decimal expansion of 32/27.
  • A261883 (program): Decimal expansion of 1 - 2^(-1/3).
  • A261884 (program): Expansion of (a(q) - a(q^2) - 2*a(q^3) + 2*a(q^6)) / 6 in powers of q where a() is a cubic AGM function.
  • A261890 (program): Second differences of A055615, first differences of A261869.
  • A261893 (program): a(n) = (n+1)^3 - n^2.
  • A261895 (program): Decimal expansion of the lower limit of A162795(i)/i^2.
  • A261898 (program): Values of |G-hat_1(n)|, a sum involving Stirling numbers of the second kind.
  • A261899 (program): Values of |G-hat_2(n)|, a sum involving Stirling numbers of the second kind.
  • A261914 (program): Largest palindrome < n (or 0 if n=0).
  • A261927 (program): Sum of the larger parts of the partitions of n into two squarefree parts.
  • A261928 (program): a(n) is the number of different pairs (x*y,x+y) mod n.
  • A261929 (program): a(n) is the number of different pairs (p,q) mod n not of the form (x*y,x+y) mod n for any (x,y).
  • A261952 (program): Start with a single equilateral triangle for n=0; for the odd n-th generation add a triangle at each expandable vertex of the triangles of the (n-1)-th generation (this is the “vertex to vertex” version); for the even n-th generation use the “side to side” version; a(n) is the number of triangles added in the n-th generation.
  • 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.
  • A261954 (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 “side 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.
  • A261973 (program): The first of three consecutive positive integers the sum of the squares of which is equal to the sum of the squares of eleven consecutive positive integers.
  • A261974 (program): The first of eleven consecutive positive integers the sum of the squares of which is equal to the sum of the squares of three consecutive positive integers.
  • A261983 (program): Number of compositions of n such that at least two adjacent parts are equal.
  • A261985 (program): Sum of the smaller parts of the partitions of n into two squarefree parts.
  • A261988 (program): Expansion of phi(q^9) / phi(q) in powers of q where phi() is a Ramanujan theta function.
  • A261992 (program): Expansion of psi(x) * f(-x^18)^3 / (phi(-x^3) * f(-x^3)^3) in powers of x where phi(), psi(), f() are Ramanujan theta functions.
  • A261993 (program): Number of distinct fractional parts of the numbers 1/(prime(j)-1)+…+1/(prime(k)-1) with 1 <= j <= k <= n, where the fractional part of x is given by x - floor(x).
  • A261998 (program): Expansion of Product_{k>=1} (1-x^k)*(1+x^k)^4.
  • A262000 (program): a(n) = n^2*(7*n - 5)/2.
  • A262003 (program): L.g.f.: log( Sum_{n>=0} x^n/n! * Product_{k=1..n} (k^3 + 1) ).
  • 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.
  • A262018 (program): The first of five consecutive positive integers the sum of the squares of which is equal to the sum of the squares of eleven consecutive positive integers.
  • A262019 (program): The first of eleven consecutive positive integers the sum of the squares of which is equal to the sum of the squares of five consecutive positive integers.
  • A262020 (program): Inverse binomial transform of double factorial n!! = A006882(n).
  • 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.
  • A262038 (program): Least palindrome >= n.
  • A262039 (program): Nearest palindrome to n; in case of a tie choose the larger palindrome.
  • A262041 (program): Decimal expansion of 3/(8 - 6*sqrt(3)/Pi).
  • A262044 (program): Partial sum of the first n odd composite numbers.
  • A262049 (program): Sum of the palindromic primes dividing n (with repetition).
  • 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.
  • A262063 (program): The first of seven consecutive positive integers the sum of the squares of which is equal to the sum of the squares of six consecutive positive integers.
  • A262064 (program): Expansion of f(x^9, x^15) / f(-x^2, -x^4) in powers of x where f(, ) is the Ramanujan general theta function
  • 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.
  • A262075 (program): The first of eight consecutive positive integers the sum of the squares of which is equal to the sum of the squares of seven consecutive positive integers.
  • A262080 (program): Decimal expansion of 3*Pi/(2*Pi + sqrt(27)).
  • A262088 (program): a(0)=0, a(1)=1, a(n) = -a(n-2)^2 - a(n-1)^3.
  • A262090 (program): Expansion of f(x^3, x^21) / f(-x^2, -x^4) where f(, ) is the Ramanujan general theta function.
  • A262095 (program): Number of non-semiprime divisors of n.
  • 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).
  • A262138 (program): Interleaved first and second differences of the prime numbers.
  • 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.
  • A262145 (program): O.g.f.: exp( Sum_{n >= 1} A000182(n+1)*x^n/n ), where A000182 is the sequence of tangent numbers.
  • A262146 (program): Expansion of f(-x, -x^5) * f(x, x^7) / f(-x, -x^2)^2 in powers of x where f(, ) is Ramanujan’s general theta function.
  • A262160 (program): Expansion of psi(x^6) / psi(x) in powers of x where psi() is a Ramanujan theta function.
  • A262161 (program): a(n) is the largest term in the continued fraction for a(n-1) + n^2/a(n-1), where a(1)=1.
  • A262183 (program): a(0) = 0, a(n) = 10*a(n-1) + n*(n+1)*(n+2)/6.
  • A262184 (program): a(n) = Fibonacci(n)^2 - Fibonacci(n) + 1.
  • A262186 (program): a(n) = prime(n)^3 - n^3.
  • A262202 (program): Number of divisors d | n such that d^2 < n and d^2 does not divide n.
  • A262203 (program): Primes of the form k*(k+2)/3 - 3, k>2.
  • A262204 (program): a(n) = (2*prime(n))! / prime(n)!.
  • A262206 (program): Product of prime(n) consecutive numbers starting from n.
  • A262207 (program): a(n) = prime(n)^n mod n^n.
  • A262208 (program): a(n) = prime(n)^prime(n) mod n^n.
  • A262209 (program): Inverse Mobius Transform of A002654.
  • A262211 (program): Minimum number of 12’s such that n*[n; 12, …, 12, n] = [x; …, x] for some x, where […] denotes simple continued fractions.
  • A262212 (program): Minimum number of 2’s such that n*[n; 2, …, 2, n] = [x; …, x] for some x, where […] denotes simple continued fractions.
  • A262213 (program): Minimum number of 3’s such that n*[n; 3, …, 3, n] = [x; …, x] for some x, where […] denotes simple continued fractions.
  • A262214 (program): Minimum number of 4’s such that n*[n; 4, …, 4, n] = [x; …, x] for some x, where […] denotes simple continued fractions.
  • A262215 (program): Minimum number of 5’s such that n*[n; 5, …, 5, n] = [x; …, x] for some x, where […] denotes simple continued fractions.
  • A262216 (program): Minimum number of 6’s such that n*[n; 6, …, 6, n] = [x; …, x] for some x, where […] denotes simple continued fractions.
  • A262217 (program): Minimum number of 7’s such that n*[n; 7, …, 7, n] = [x; …, x] for some x, where […] denotes simple continued fractions.
  • A262218 (program): Minimum number of 8’s such that n*[n; 8, …, 8, n] = [x; …, x] for some x, where […] denotes simple continued fractions.
  • A262219 (program): Minimum number of 9’s such that n*[n; 9, …, 9, n] = [x; …, x] for some x, where […] denotes simple continued fractions.
  • A262220 (program): Minimum number of 10’s such that n*[n; 10, …, 10, n] = [x; …, x] for some x, where […] denotes simple continued fractions.
  • A262221 (program): a(n) = 25*n*(n + 1)/2 + 1.
  • A262226 (program): Eulerian numbers of type D, the primary type.
  • A262227 (program): Eulerian numbers of type D, the complementary type.
  • A262232 (program): Number of black and white n-bead necklaces with at least 3 white beads (turning over is not allowed); also number of clockwise arrangements of reflex and non-reflex angles that can form an n-gon.
  • 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.
  • A262258 (program): a(n) = the number of hills (arch length of 1 with no covering arches) for semi-meander solutions with n arches and floor((n+2)/2) arch group returns to the x axis.
  • A262260 (program): Number of triangles formed by the positions of odd numbers in the first n rows of Pascal’s triangle, also known as Tartaglia’s triangle.
  • A262261 (program): a(n) = Product_{k=0..n} binomial(4*k,k).
  • 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.
  • A262275 (program): Prime numbers with an even number of steps in their prime index chain.
  • A262284 (program): Primes whose binary expansion begins 101.
  • A262285 (program): Primes whose binary expansion begins 111.
  • A262286 (program): Primes whose binary expansion begins 100.
  • A262287 (program): Primes whose binary expansion begins 110.
  • A262288 (program): a(0)=0; thereafter add the smallest positive number that is not a substring.
  • 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.
  • A262308 (program): Bisection of A008705.
  • A262309 (program): Bisection of A008705.
  • A262310 (program): a(n) = coefficient of x^(2n) in the expansion of the modular form Product_{k>=1} (1-x^k)^n.
  • A262326 (program): Number of (n+1) X (2+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.
  • 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.
  • A262341 (program): Largest primitive prime factor of Fibonacci number F(n), or 1 if no primitive.
  • 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.
  • A262344 (program): Centered 11-gonal (or hendecagonal) primes.
  • A262351 (program): Sum of the parts in the partitions of n into exactly two squarefree parts.
  • A262353 (program): a(n) = ceiling((3-sqrt(5))*10^(2*n+1)).
  • 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.
  • A262368 (program): Expansion of f(x^2, x^2) * f(x, x^2)^2 in powers of x where f(, ) is Ramanujan’s general theta function.
  • 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) = (1/n)*Sum_{k=1..n} k*binomial(n,k-1)*binomial(2*n,n-k).
  • 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.
  • A262407 (program): a(n) = Sum_{k=0..n-1} C(n,k+1)*C(n,k)*C(n-1,k).
  • 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.
  • A262415 (program): Number of (n+1) X (3+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.
  • A262428 (program): Concatenate the n-th prime with the n-th semiprime.
  • A262438 (program): Number of digits of hexadecimal representation of n.
  • A262439 (program): Number of primes not exceeding 1+n*(n+1)/2.
  • A262440 (program): a(n) = Sum_{k=0..n}(binomial(n,k)*binomial(n+k-1,n-k)).
  • A262441 (program): a(n) = Sum_{k=0..n+1}(binomial(n-1,k)/(k+1)*binomial(n+k+1,n-k)).
  • A262442 (program): a(n) = Sum_{k=0..n}(binomial(n-1,n-k)*binomial(n+k-1,n-k)).
  • A262444 (program): Number of 3-colored integer partitions such that no adjacent parts have the same color.
  • A262445 (program): Number of exact 3-colored partitions such that no adjacent parts have the same color.
  • 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.
  • A262480 (program): Number of trivial c-Wilf equivalence classes in the symmetric group S_n.
  • 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.
  • A262489 (program): The index of the first of two consecutive positive triangular numbers (A000217) the sum of which is equal to the sum of three consecutive positive triangular numbers.
  • 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.
  • A262493 (program): Centered 13-gonal (or tridecagonal) primes.
  • A262518 (program): Even bisection of A155043.
  • A262519 (program): Odd bisection of A155043.
  • A262520 (program): a(n) = A262519(n) - A262518(n).
  • A262523 (program): a(n+3) = a(n) + 6*n + 13, a(0)=0, a(1)=2, a(2)=7.
  • A262537 (program): Bisection of A262310.
  • A262538 (program): Bisection of A262310.
  • A262539 (program): a(n) = coefficient of x^n in the expansion of Product_{k>=1} (1-x^k)^(3*n).
  • A262540 (program): Bisection of A262539.
  • A262541 (program): Bisection of A262539.
  • A262543 (program): Number of rooted asymmetrical polyenoids of type U_n* having n edges.
  • A262557 (program): Numbers with digits in strictly decreasing order, sorted lexicographically.
  • 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?”.
  • A262570 (program): a(n) = A002704(n)/2.
  • A262571 (program): Concatenation of the numbers from 2 to n.
  • A262572 (program): Concatenation of the numbers from 1 to n but omitting 2.
  • A262573 (program): Concatenation of the numbers from 1 to n but omitting 3.
  • A262574 (program): Concatenation of the numbers from 1 to n but omitting 4.
  • A262575 (program): Concatenation of the numbers from 1 to n but omitting 5.
  • A262576 (program): Concatenation of the numbers from 1 to n but omitting 6.
  • A262577 (program): Concatenation of the numbers from 1 to n but omitting 7.
  • A262578 (program): Concatenation of the numbers from 1 to n but omitting 8.
  • A262579 (program): Concatenation of the numbers from 1 to n but omitting 9.
  • A262580 (program): Concatenation of the numbers from 1 to n but omitting 10.
  • A262581 (program): Concatenation of the numbers from 1 to n but omitting 11.
  • A262582 (program): Concatenation of the numbers from 1 to n but omitting 12.
  • A262583 (program): a(n) = A002704(n)-2.
  • A262584 (program): (A002704(n)-2)/2.
  • A262585 (program): a(0)=0; thereafter a(n) = A002705(n)-2.
  • A262588 (program): Duplicate of A193140.
  • A262590 (program): Sets with a congruence property.
  • A262591 (program): Sets with a congruence property.
  • A262592 (program): a(n) = (3^(n+1) - 2n^2 + 4n + 5) / 8..
  • A262593 (program): Expansion of (1-3*x)^3/((1-x)^4*(1-4*x)).
  • A262594 (program): Expansion of (1-2*x)^2/((1-x)^4*(1-4*x)).
  • A262600 (program): Number of Dyck paths of semilength n and height exactly 4.
  • A262601 (program): a(n) = n!*(e*Gamma(n,1)*(n-1)+1).
  • A262602 (program): a(n) = a(n-7) + a(n-4) + a(n-1) for n>1 and a(n)=1 for n<=1.
  • A262607 (program): Sum_{k=0..n} ((k+1)*binomial(n+1,k)*binomial(2*n-k,n))/(n+1).
  • A262609 (program): Divisors of 1728.
  • A262610 (program): The values of sigma function (A000203) and the positive integers interleaved.
  • 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.
  • A262618 (program): Number of parts in the asymmetric representation of sigma(n) in an octant.
  • A262619 (program): Number of parts in the symmetric representation of sigma(n) in two successive octants of two quadrants.
  • 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.
  • A262664 (program): Expansion of (1-2*x)/((2-x)*sqrt(5*x^2-6*x+1))+1/(2-x).
  • A262672 (program): Expansion of (3-x-x^3) / ((x-1)^2*(1+x+x^2+x^3)).
  • A262674 (program): Decimal expansion of the real root of x^3 - 6x^2 + 4x - 2.
  • A262676 (program): Number of nonzero even numbers encountered when iterating A049820 starting from n: a(0) = 0 and for n >= 1, a(n) = (1-A000035(n)) + a(A049820(n)).
  • A262677 (program): Number of odd numbers encountered when iterating A049820 starting from n: a(0) = 0 and for n >= 1, a(n) = A000035(n) + a(A049820(n)).
  • A262680 (program): Number of squares encountered before zero is reached when iterating A049820 starting from n: a(0) = 0 and for n >= 1, a(n) = A010052(n) + a(A049820(n)).
  • A262682 (program): Even bisection of A262680.
  • 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.
  • A262708 (program): a(n) = p-(p/5) where p = prime(n) and (p/5) is a Legendre symbol.
  • A262710 (program): Powers of -4.
  • A262712 (program): Numbers n such that sum of digits on n^2 is 9.
  • 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).
  • A262717 (program): a(n) = (n-1)*binomial(3*n-2,n)/(2*n-1)+(n+1)*binomial(3*n,n)/(2*n+1)-binomial(3*n-1,n).
  • A262718 (program): a(n) = (n+1)^n - 2*(n^n) + (n-1)^n.
  • A262720 (program): a(n) = Sum_{k=0..n/2} binomial(n+3,k)*binomial(n+1-k,k+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!.
  • A262726 (program): Expansion of phi(-x) * psi(x^6) in powers of x where phi(), psi() are Ramanujan theta functions.
  • A262732 (program): a(n) = (1/n!) * (5*n)!/(5*n/2)! * (3*n/2)!/(3*n)!.
  • A262733 (program): a(n) = (1/n!) * (7*n)!/(7*n/2)! * (5*n/2)!/(5*n)!.
  • 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)).
  • A262736 (program): Expansion of Product_{k>=1} (1 + x^(2*k-1))^(2*k-1).
  • A262737 (program): O.g.f. exp( Sum_{n >= 1} A262732(n)*x^n/n ).
  • A262738 (program): O.g.f. exp( Sum_{n >= 1} A211419(n)*x^n/n ).
  • A262739 (program): O.g.f. exp( Sum_{n >= 1} A262733(n)*x^n/n ).
  • A262740 (program): O.g.f. exp( Sum_{n >= 1} A211421(n)*x^n/n ).
  • A262744 (program): Remainder when sum of first n primes is divided by n-th triangular number.
  • A262745 (program): Number of permutations of [n] with an odd number of rises.
  • A262749 (program): Numbers that are the sum of two distinct nonzero triangular numbers in more than one way.
  • 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.
  • A262768 (program): a(n) = binomial(2*n+2,n)-2*binomial(2*n,n)+binomial(2*n-2,n).
  • A262770 (program): A Beatty sequence: a(n)=floor(n*p) where p=2*cos(Pi/7)=A160389.
  • A262773 (program): A Beatty sequence: a(n)=floor(q*n) where q=A231187.
  • A262774 (program): Expansion of psi(x^2) * phi(-x^3) in powers of x where phi(), psi() are Ramanujan theta functions.
  • A262777 (program): a(n) = 10^n - prime(n).
  • A262778 (program): a(n) = 10^n + prime(n).
  • A262779 (program): Binary representation of the n-th iteration of the “Rule 175” elementary cellular automaton starting with a single ON (black) cell.
  • A262780 (program): Expansion of phi(-x^6) * psi(x^4) + x * phi(-x^2) * psi(x^12) in powers of x where phi(), psi() are Ramanujan theta functions.
  • 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.
  • A262807 (program): a(n) = (Product_{k=1..n} prime(k+1)) mod (Sum_{k=1..n} prime(k+1)) where prime(k) is the k-th prime number.
  • A262808 (program): Triangle read by rows giving successive states of cellular automaton generated by “Rule 147” initiated with a single ON (black) cell.
  • A262811 (program): Expansion of Product_{k>=1} 1/(1-x^(2*k-1))^(2*k-1).
  • A262813 (program): Number of ordered ways to write n as x^3 + y^2 + z*(z+1)/2 with x >= 0, y >=0 and z > 0.
  • A262815 (program): Number of ordered ways to write n as x^3 + y*(y+1)/2 + z*(3*z+1)/2, where x, y and z are nonnegative integers.
  • A262816 (program): Number of ordered ways to write n as x^3 + y^2 + z*(3*z-1)/2, where x and y are nonnegative integers, and z is a nonzero integer.
  • A262817 (program): Number of (n+3)X(3+3) 0..1 arrays with each row divisible by 9 and column not divisible by 9, read as a binary number with top and left being the most significant bits.
  • A262826 (program): a(n) = Sum_{d|n} -(-1)^d * 2^(n^2/d) * d.
  • A262842 (program): G.f.: Product_{k>=1} (1 - x^k)^(-k^(k-2)).
  • 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.
  • A262857 (program): Number of ordered ways to write n as w^3 + 2*x^3 + y^2 + 2*z^2, where w, x, y and z are nonnegative integers.
  • A262861 (program): Binary representation of the n-th iteration of the “Rule 147” elementary cellular automaton starting with a single ON (black) cell.
  • A262862 (program): Decimal representation of the n-th iteration of the “Rule 147” elementary cellular automaton starting with a single ON (black) cell.
  • A262863 (program): Binary representation of the middle column of the “Rule 147” elementary cellular automaton starting 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.
  • A262865 (program): Binary representation of the n-th iteration of the “Rule 153” elementary cellular automaton starting with a single ON (black) cell.
  • A262866 (program): Decimal representation of the n-th iteration of the “Rule 153” 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.
  • A262868 (program): Number of squarefree numbers appearing among the larger parts of the partitions of n into two parts.
  • A262869 (program): Number of squarefree numbers appearing among the smaller parts of the partitions of n into two parts.
  • A262870 (program): Sum of the squarefree numbers appearing among the larger parts of the partitions of n into two parts.
  • A262871 (program): Sum of the squarefree numbers appearing among the smaller parts of the partitions of n into two parts.
  • A262882 (program): Right diagonal of A262881.
  • A262910 (program): a(n) = Sum_{k=0..n} binomial(k+n-1,k)*binomial(k+n,2*k).
  • A262922 (program): a(1)=1; for n>1, a(n) = a(n-1) + n + 2 if a(n-1) and n are coprime, otherwise a(n) = a(n-1)/gcd(a(n-1),n).
  • A262925 (program): Sum of n consecutive fourth powers starting with n^4.
  • A262926 (program): Sum of n consecutive n-th powers starting with n^n.
  • A262927 (program): a(n+9) = a(n) + 10*(n+4) + 9. a(0)=0, a(1)=1, a(2)=3, a(3)=6, a(4)=10, a(5)=15, a(6)=23, a(7)=30, a(8)=39.
  • A262930 (program): Expansion of (psi(-q) / f(q^3))^2 in powers of q where psi(), f() are Ramanujan theta functions.
  • A262946 (program): Expansion of Product_{k>=1} 1/(1-x^(3*k-1))^(3*k-1).
  • A262947 (program): Expansion of Product_{k>=1} 1/(1-x^(3*k-2))^(3*k-2).
  • A262957 (program): Numerators of the n-th iteration of the alternating continued fraction formed from the positive integers, starting with (1 - …).
  • A262970 (program): Total cycle length of all iteration trajectories of all elements of random mappings from [n] to [n].
  • A262973 (program): Total tail length of all iteration trajectories of all elements of random mappings from [n] to [n].
  • A262977 (program): a(n) = binomial(4*n-1,n).
  • A262986 (program): Start of first run of length n in Golomb’s sequence A001462.
  • A262987 (program): Expansion of f(-x, -x^5) * f(x^3, x^5) / f(-x, -x^2)^2 in powers of x where f(, ) is Ramanujan’s general theta function.
  • A262997 (program): a(n+3) = a(n) + 24*n + 40, a(0)=0, a(1)=5, a(2)=19.
  • A263002 (program): Expansion of (f(-x^5) / f(-x))^2 in powers of x where f() is a Ramanujan theta function.
  • A263013 (program): a(0) = -a(1) = a(2) = 1, a(n) = 0 for n>2.
  • A263017 (program): n is the a(n)-th positive integer having its binary weight.
  • A263021 (program): Expansion of f(-x^3)^6 / (phi(-x) * phi(-x^3)) in powers of x where phi(), f() are Ramanujan theta functions.
  • A263022 (program): a(n) = gcd(n, 1^(n-1) + 2^(n-1) + … + (n-1)^(n-1)) for n > 1.
  • A263044 (program): a(1) = a(2) = a(3) = 1; for n>3, a(n) = (a(n-3) + a(n-1))*(a(n-2) + a(n-3)).
  • A263045 (program): a(1)=a(2)=1, a(3)=2; for n>3, a(n) = (a(n-1) + a(n-2))*a(n-3) - a(n-1).
  • A263047 (program): a(1)=0, a(2)=1, a(3)=2; for n>3, a(n) = a(n-3)*a(n-1) - a(n-2).
  • A263050 (program): Expansion of f(-x) * f(x^4, x^8) / f(-x^3)^2 in powers of x where f(, ) is Ramanujan’s general theta function.
  • A263051 (program): Expansion of f(-x) * f(x^2, x^10) / f(-x^3)^2 in powers of x where f(, ) is Ramanujan’s general theta function.
  • A263053 (program): Number of (n+1) X 2 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.
  • A263064 (program): Number of lattice paths from (n,n,n,n) to (0,0,0,0) using steps that decrement one or more components by one.
  • A263065 (program): Number of lattice paths from {n}^5 to {0}^5 using steps that decrement one or more components by one.
  • A263066 (program): Number of lattice paths from {n}^6 to {0}^6 using steps that decrement one or more components by one.
  • 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.
  • A263089 (program): Least monotonic left inverse for A261089; a(n) = largest k for which A261089(k) <= n.
  • A263098 (program): a(n) = Max( tau(k) : k=1,2,3,…,n^2 ) where tau(k) = A000005(k) is the number of divisors of k.
  • A263102 (program): Number of distinct cycles without repeated edges on the multigraph with 2 vertices connected by n edges.
  • 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.
  • A263132 (program): Positive values of m, arranged in order, such that binomial(4*m - 1, m) is odd.
  • A263133 (program): Numbers m such that binomial(4*m + 3, m) is odd.
  • 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.
  • A263170 (program): a(n) = (Sum_{k=1..n} prime(k))^3 - (Sum_{k=1..n} prime(k)^3).
  • A263199 (program): Expansion of Product_{k>=1} 1/(1 - x^(2*k+1))^(2*k+1).
  • A263200 (program): Number of perfect matchings on a Möbius strip of width 3 and length 2n.
  • A263226 (program): a(n) = 15*n^2 - 13*n.
  • A263227 (program): a(n) = n*(67*n - 89)/2.
  • A263228 (program): a(n) = 2*n*(16*n - 13).
  • A263229 (program): a(n) = 4*n*(21*n - 26).
  • A263231 (program): a(n) = n*(25*n - 39)/2.
  • A263232 (program): Triangle read by rows: T(n,k) is the number of partitions of n having exactly k parts equal to 3 (n >= 0, 0 <= k <= floor(n/3)).
  • A263243 (program): Triangle read by rows giving successive states of cellular automaton generated by “Rule 155” initiated with a single ON (black) cell.
  • A263244 (program): Binary representation of the n-th iteration of the “Rule 155” elementary cellular automaton starting with a single ON (black) cell.
  • A263245 (program): Decimal representation of the n-th iteration of the “Rule 155” elementary cellular automaton starting with a single ON (black) cell.
  • A263272 (program): Self-inverse permutation of nonnegative integers: a(n) = A263273(2*n) / 2.
  • A263273 (program): Bijective base-3 reverse: a(0) = 0; for n >= 1, a(n) = A030102(A038502(n)) * A038500(n).
  • A263295 (program): Denominators of the n-th iteration of the alternating continued fraction formed from the positive integers, starting with (1 - …).
  • A263297 (program): The greater of bigomega(n) and maximal prime index in the prime factorization of n.
  • A263309 (program): Numbers n such that p=6n+1 and q=6p+1 are primes.
  • A263313 (program): Permutation of the nonnegative integers: [4k+3, 4k, 4k+1, 4k+2, …].
  • A263319 (program): a(n) = pi(n^2)*phi(n)/2, where pi(x) denotes the number of primes not exceeding x, and phi(.) is Euler’s totient function given by A000010.
  • A263323 (program): The greater of maximal exponent and maximal prime index in the prime factorization of n.
  • A263325 (program): a(n) = sigma(n)*pi(n^2), where sigma(n) is the sum of all (positive) divisors of n, and pi(x) is the number of primes not exceeding x.
  • 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.
  • A263353 (program): Decimal expansion of the generalized hypergeometric function 3F2(1/2,1/2,1/2; 3/2,3/2; x) at x=1/2.
  • 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.
  • A263384 (program): Fourth column of the matrix of polynomial coefficients of the rational approximation to Mill’s ratio.
  • A263385 (program): Number of (n+1)X(1+1) arrays of permutations of 0..n*1-1 with each element moved a city block distance of exactly 2.
  • A263390 (program): a(3n) = n, otherwise a(n) = a(floor(2n/3)).
  • A263394 (program): a(n) = Product_{i=1..n} (3^i - 2^i).
  • A263408 (program): Triangle read by rows: T(n>=1, k>=0) is the number of standard tableaux of size n and (Haglund and Stevens) inversion number k.
  • A263416 (program): a(n) = Product_{k=0..n} (3*k+1)^(n-k).
  • A263417 (program): a(n) = Product_{k=0..n} (3*k+2)^(n-k).
  • A263418 (program): a(n) is the total number of pentagrams in a variant of pentagram fractal after n iterations.
  • A263419 (program): a(n) is the total number of pentagrams in a variant of pentagram fractal after n iterations.
  • A263420 (program): Number of nX2 arrays of permutations of 0..n*2-1 with each element moved a city block distance of 0 or 2.
  • A263426 (program): Permutation of the nonnegative integers: [4k+2, 4k+1, 4k, 4k+3, …].
  • A263428 (program): Triangle read by rows giving successive states of cellular automaton generated by “Rule 3” initiated with a single ON (black) cell.
  • A263430 (program): a(n) = Product_{k=0..n} (4*k+1)^(n-k).
  • A263433 (program): Expansion of f(x, x) * f(x^2, x^4)^2 in powers of x where f(, ) is Ramanujan’s general theta function.
  • A263445 (program): a(n) = (2n+1)*(n+1)!*Bernoulli(2n).
  • A263449 (program): Permutation of the natural numbers: [4k+1, 4k+4, 4k+3, 4k+2, …].
  • A263451 (program): a(n) is the largest anagram of 2*a(n-1), a(1)=1.
  • A263452 (program): Expansion of f(-q^3)^3 * psi(q^12) / f(-q) in powers of q where ps(), f() are Ramanujan theta functions.
  • A263458 (program): Deal a pack of n cards into two piles and gather them up, n/2 times. All n such that this reverses the order of the deck.
  • 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).
  • A263490 (program): Decimal expansion of the generalized hypergeometric function 3F2(1/2,1/2,1/2 ; 1,1; x) at x=1/4.
  • A263491 (program): Decimal expansion of the generalized hypergeometric function 3F2(1/2,1/2,3/2; 1,1;x) at x=1/4.
  • A263492 (program): Decimal expansion of the generalized hypergeometric function 3F2(1/2,1/2,3/2 ; 1,2 ; x) at x=1/4.
  • A263493 (program): Decimal expansion of the generalized hypergeometric function 3F2(1/2, 3/2, 5/2; 2, 2;x) at x=1/4.
  • A263494 (program): Decimal expansion of the generalized hypergeometric function 3F2(3/2, 3/2, 3/2; 1, 2; x) at x=1/4.
  • A263495 (program): Decimal expansion of the generalized hypergeometric function 3F2(3/2, 3/2, 3/2; 2, 2; x) at x=1/4.
  • A263496 (program): Decimal expansion of the generalized hypergeometric function 3F2(3/2, 3/2, 5/2; 2, 2; x) at x=1/4.
  • 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.
  • A263501 (program): Expansion of phi(-x) * f(-x^2)^3 / f(-x^3) in powers of x where phi(), f() are Ramanujan theta functions.
  • 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.
  • A263526 (program): Expansion of f(x, x)^2 / (f(x^3, x^3) * f(x, x^5)) in powers of x where f(, ) is Ramanujan’s general theta function.
  • A263527 (program): Expansion of phi(-x^3) * f(-x^6)^3 / f(-x^2) in powers of x where phi(), f() are Ramanujan theta functions.
  • A263528 (program): Expansion of (psi(x) * psi(x^3) / f(-x^3)^2)^2 in powers of x where psi(), f() are Ramanujan theta functions.
  • A263529 (program): Binomial transform of double factorial n!! (A006882).
  • 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).
  • A263538 (program): Expansion of 3 * a(q^2) * b(q^2) * c(q^2) / (b(q) * c(q)^2) in powers of q where a(), b(), c() are cubic AGM theta functions.
  • A263548 (program): Expansion of f(x, x) * f(x^2, x^10) in powers of x where f(, ) is Ramanujan’s general theta function.
  • A263551 (program): Number of (n+1) X (1+1) 0..4 arrays with each row and column divisible by 7, read as a base-5 number with top and left being the most significant digits.
  • A263566 (program): Number of (n+2)X(2+2) arrays of permutations of 0..n*4+7 with each element moved 0 or 1 knight moves and no more than 1 element left unmoved.
  • A263569 (program): Number of distinct prime divisors p of 2*n such that lpf(2*n - p) = p, where lpf = least prime factor (A020639).
  • A263571 (program): Expansion of f(x^2, x^2) * f(x, x^5) in powers of x where f(, ) is Ramanujan’s general theta function.
  • A263574 (program): Beatty sequence for 1/sqrt(3) - log(phi)/3575 where phi is the golden ratio, A001622.
  • A263576 (program): Stirling transform of Fibonacci numbers (A000045).
  • A263598 (program): Number of (n+1) X (1+1) arrays of permutations of 0..n*2+1 filled by rows with each element moved a city block distance of 0 or 2, and rows and columns in increasing lexicographic order.
  • A263613 (program): Palindromic numbers in base 4 that are cubes.
  • A263614 (program): a(2n) = A000125(n), a(2n+1) = 2*a(2n).
  • A263615 (program): Partial sums of A263614 starting at n=2.
  • A263622 (program): a(n) = (3^(n+1)-2^(n+2)+2*n+1)/4.
  • A263624 (program): Number of Seidel matrices of order n with exactly three distinct eigenvalues, up to switching equivalence.
  • A263636 (program): Numbers n such that A263635(n)=2.
  • A263646 (program): Coefficients for an expansion of the Schwarzian derivative of a power series.
  • A263647 (program): Numbers n such that 2^n-1 and 3^n-1 are coprime.
  • A263651 (program): Numbers n such that the difference between n and the largest square less than n is a nonzero square.
  • A263653 (program): a(n) = bigomega(n)^omega(n).
  • A263656 (program): Number of length-2n central circular binary strings without zigzags (see reference for precise definition).
  • A263658 (program): Number of (0, 1)-necklaces with n zeros and n ones without zigzags (see reference for precise definition).
  • A263660 (program): Number of length n arrays of permutations of 0..n-1 with each element moved by -2 to 2 places and with no two consecutive increases or two consecutive decreases.
  • A263673 (program): a(n) = lcm{1,2,…,n} / binomial(n,floor(n/2)).
  • A263687 (program): b(n) in (sqrt(2))_n = b(n) + c(n)*sqrt(2), where (x)_n is the Pochhammer symbol, b(n) and c(n) are integers.
  • A263688 (program): c(n) in (sqrt(2))_n = b(n) + c(n)*sqrt(2), where (x)_n is the Pochhammer symbol, b(n) and c(n) are integers.
  • A263689 (program): a(n) = (2*n^6 - 6*n^5 + 5*n^4 - n^2 + 12)/12.
  • A263694 (program): Expansion of (1 + x + x^2 + x^3 + 4*x^4 - x^5 - x^6 - x^7 + 3*x^8)/((1 - x)^2*(1 + x + x^2 + x^3 + x^4 + x^5 + x^6 + x^7)).
  • A263710 (program): Number of length n arrays of permutations of 0..n-1 with each element moved by -1 to 1 places and every four consecutive elements having its maximum within 4 of its minimum.
  • A263715 (program): Nonnegative integers that are the sum or difference of two squares.
  • A263719 (program): Decimal expansion of the real root r of r^3 + r - 1 = 0.
  • A263722 (program): Integers k > 0 such that k^2 + p^2 is composite for all primes p.
  • A263727 (program): Largest square number less than or equal to the n-th Fibonacci number.
  • A263730 (program): Irregular triangle read by rows in which row n > 1 lists k such that (k^2 + k*n)/(k + 1) is an integer.
  • A263766 (program): a(n) = Product_{k=1..n} (k^2 - 2).
  • A263768 (program): Number of necklaces with n beads colored white or red, where the number of white beads is odd and at least three and turning over is allowed.
  • A263769 (program): Smallest prime q such that q == -1 (mod prime(n)-1).
  • 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.
  • A263773 (program): Expansion of b(-q)^2 in powers of q where b() is a cubic AGM theta function.
  • A263790 (program): The number of length-n permutations avoiding the patterns 1234, 1324 and 2143.
  • 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.
  • A263805 (program): Binary representation of the n-th iteration of the “Rule 157” elementary cellular automaton starting with a single ON (black) cell.
  • A263806 (program): Decimal representation of the n-th iteration of the “Rule 157” elementary cellular automaton starting 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.
  • A263823 (program): a(n) = n!*Sum_{k=0..n} Fibonacci(k-1)/k!, where Fibonacci(-1) = 1, Fibonacci(n) = A000045(n) for n>=0.
  • A263824 (program): Permutation of the nonnegative integers: [6k+3, 6k+4, 6k+5, 6k, 6k+1, 6k+2, …].
  • A263827 (program): The number c_{Cc pi_1(B_1)}(2n) of the second amphicosm 2n-coverings over the first amphicosm.
  • A263828 (program): The number c_{P c pi_1(B_1)}(n) of the first amphicosm n-coverings over the first amphicosm.
  • A263832 (program): The number c_{Cc,pi_1(B_2)}(n) of the second amphicosm n-coverings over the second amphicosm.
  • A263837 (program): Non-abundant numbers (or nonabundant numbers): complement of A005101; numbers k for which sigma(k) <= 2*k.
  • A263841 (program): Expansion of (1-2*x-x^2)/(sqrt(1+x)*(1-3*x)^(3/2)*2*x)-1/(2*x).
  • A263843 (program): Reversion of g.f. for A162395 (squares with signs).
  • A263844 (program): Constant term in expansion of n in Fraenkel’s exotic ternary representation.
  • A263845 (program): A258059(n)+1.
  • A263846 (program): Floor of cube root of n-th prime.
  • A263847 (program): a(n) = p(2*n)-p(2*n-2)-p(n) where p(n) are the partition numbers A000041(n).
  • A263878 (program): a(n) = Sum_{k=0..n} (-1)^k*k*Fibonacci(k), where Fibonacci(k) = A000045(k).
  • A263882 (program): Babbage quotients b_p = (binomial(2p-1, p-1) - 1)/p^2 with p = prime(n).
  • A263883 (program): Ivanov’s number a(n) = i*(n+2-i) where i = min{j > 0 | j*(j+1) >= 2*(n-1)}.
  • A263895 (program): Expansion of e.g.f.: exp(-x)*x/(1-2*x)^2.
  • A263907 (program): Number of (2n+2) X (2+2) 0..1 arrays with each row and column modulo 3 equal to 1, read as a binary number with top and left being the most significant bits.
  • A263919 (program): Triangle read by rows giving successive states of cellular automaton generated by “Rule 163” initiated with a single ON (black) cell.
  • A263922 (program): Highest exponent in prime factorization of n-th central binomial coefficient.
  • A263923 (program): Expansion of psi(-x^3)^2 * f(-x^2)^3 / f(-x)^2 in powers of x where psi(), f() are Ramanujan theta functions.
  • A263931 (program): a(n) = binomial(2*n, n) / Product(p prime | n < p <= 2*n).
  • 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.
  • A263943 (program): Positive integers n such that (n+21)^3 - n^3 is a square.
  • A263944 (program): Positive integers n such that (n+28)^3 - n^3 is a square.
  • A263945 (program): Positive integers n such that (n+39)^3 - n^3 is a square.
  • A263946 (program): Positive integers n such that (n+52)^3 - n^3 is a square.
  • A263948 (program): Positive integers n such that (n+61)^3 - n^3 is a square.
  • A263949 (program): Positive integers n such that (n+84)^3 - n^3 is a square.
  • A263951 (program): Square numbers in A070552.
  • A263977 (program): Integers k > 0 such that k^2 + p^2 is prime for some prime p.
  • A263981 (program): Least even k such that phi(k) >= n.
  • A263982 (program): Number of partitions of n with a palindromicity of 3.
  • A263986 (program): Difference between Catalan numbers and Fibonacci numbers: a(n) = C(n) - F(n).
  • A263991 (program): a(n) is the number of uniform consecutive subintervals of the unit interval each of size 2^(-ceiling(log_2(n))) that are completely covered by one of the n uniform consecutive subintervals (of size 1/n each) of the unit interval.
  • A263997 (program): Sequence of block lengths in a block spiral of width 1.
  • A264000 (program): Number of (n+1) X (3+1) arrays of permutations of 0..n*4+3 with each element having index change (+-,+-) 0,0 1,2 or 1,0.
  • A264004 (program): Number of (1+1) X (n+1) arrays of permutations of 0..n*2+1 with each element having index change (+-,+-) 0,0 1,2 or 1,0.
  • A264008 (program): Index of the smallest Fibonacci number divisible by prime(n)^2.
  • 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.
  • A264026 (program): Expansion of (f(x^3) / f(x))^6 in powers of x where f() is a Ramanujan theta function.
  • A264027 (program): Triangle read by rows: T(n, k) = Sum_{t=k..n-2} (-1)^(t-k)*(n-t)!*binomial(t,k)*binomial(n-2,t).
  • A264028 (program): Triangle read by rows: T(n, k) = Sum_{t=k..n-3} (-1)^(t-k)*(n-t)!*binomial(t,k)*binomial(n-3,t).
  • A264029 (program): T(n,k)=Number of (n+1)X(k+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 lexicographically nondecreasing and columns lexicographically nonincreasing.
  • A264036 (program): Stirling transform of A077957 (aerated powers of 2).
  • A264037 (program): Stirling transform of A077957 (aerated powers of 2) with 0 prepended [0, 1, 0, 2, 0, 4, 0, 8, …].
  • A264038 (program): Convolution of Lucas and Jacobsthal numbers.
  • 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.
  • A264054 (program): Number of (n+1) X (2+1) arrays of permutations of 0..n*3+2 with each element having index change +-(.,.) 0,0 1,2 or 2,-2.
  • A264055 (program): Number of (n+1)X(3+1) arrays of permutations of 0..n*4+3 with each element having index change +-(.,.) 0,0 1,2 or 2,-2.
  • 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.
  • A264079 (program): Expansion of b(2)*b(6)/(1 - 2*x + x^3 - x^4 - x^5 + 2*x^6), where b(k) = (1-x^k)/(1-x).
  • A264080 (program): a(n) = 6*F(n)*F(n+1) + (-1)^n, where F = A000045.
  • A264081 (program): The sum of the 2 X 2 idempotent matrices over Z/nZ is congruent to {{a(n),0}, {0,a(n)}} (mod n).
  • A264085 (program): Number of (n+1) X (2+1) arrays of permutations of 0..n*3+2 with each element having index change +-(.,.) 0,0 0,1 or 2,-2.
  • 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.
  • A264102 (program): Numbers n with the property that the symmetric representation of sigma(n) has four parts, each of width one.
  • A264104 (program): Numbers n with the property that the symmetric representation of sigma(n) has four parts, each of width one and two regions meet at the center of the Dyck path.
  • A264105 (program): a(n) = smallest k such that n divides Sum_{i=1..k} Fibonacci(i).
  • A264106 (program): Number of (n+1) X (2+1) arrays of permutations of 0..n*3+2 with each element having index change +-(.,.) 0,0 0,2 or 1,1.
  • 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.
  • A264132 (program): Number of (1+1)X(n+1) arrays of permutations of 0..n*2+1 with each element having index change +-(.,.) 0,0 0,2 or 1,2.
  • A264147 (program): a(n) = n*F(n+1) - (n+1)*F(n), where F = A000045.
  • A264152 (program): a(n) = (2^floor(n+n/2)/sqrt(Pi)^mod(n+1,2))*Gamma(n+1/2)/Gamma(n/2+1).
  • A264153 (program): a(n) = ((2*n)!)^2 / 2^n.
  • A264166 (program): Number of (n+1) X (1+1) arrays of permutations of 0..n*2+1 with each element having directed index change 0,0 0,1 1,0 -2,-1 or -1,-2.
  • A264184 (program): Number of (n+1)X(2+1) arrays of permutations of 0..n*3+2 with each element having index change +-(.,.) 0,0 1,-1 or 2,2.
  • A264200 (program): Numerator of sum of numbers in set g(n) generated as in Comments
  • A264203 (program): Number of (n+1) X (3+1) arrays of permutations of 0..n*4+3 with each element having index change +-(.,.) 0,0 0,2 or 1,0.
  • A264234 (program): Numerators of the coefficients in the expansion of 1/W(x) - 1/x where W(x) is the Lambert W function.
  • A264235 (program): Denominator of the coefficients in the expansion of 1/W(x) - 1/x where W(x) is the Lambert W function.
  • A264238 (program): Number of (n+1) X (2+1) arrays of permutations of 0..n*3+2 with each element having directed index change 0,0 1,1 0,-1 -1,1 or 0,-2.
  • A264245 (program): Number of (1+1) X (n+1) arrays of permutations of 0..n*2+1 with each element having directed index change 0,0 1,1 0,-1 -1,1 or 0,-2.
  • 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.
  • A264264 (program): The length of the shortest nontrivial integral cevian of an isosceles triangle, with base of length 1 and legs of length n, that divides 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.
  • A264273 (program): Number of (2+1) X (n+1) arrays of permutations of 0..n*3+2 with each element having index change +-(.,.) 0,0 1,0 or 1,2.
  • A264280 (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 0,1 1,0 or -1,-2.
  • A264307 (program): Number of (n+1) X (2+1) arrays of permutations of 0..n*3+2 with each element having directed index change 0,0 0,1 1,0 -1,-2 or 0,2.
  • A264357 (program): Array A(r, n) of number of independent components of a symmetric traceless tensor of rank r and dimension n, written as triangle T(n, r) = A(r, n-r+2), n >= 1, r = 2..n+1.
  • 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.
  • A264361 (program): Number of (n+1) X (5+1) arrays of permutations of 0..n*6+5 with each element having directed index change 0,0 0,2 1,0 or -1,-2.
  • A264365 (program): Number of (1+1) X (n+1) arrays of permutations of 0..n*2+1 with each element having directed index change 0,0 0,2 1,0 or -1,-2.
  • A264366 (program): Number of (2+1) X (n+1) arrays of permutations of 0..n*3+2 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.
  • A264387 (program): 2*(1+2*a(n)) is the n-th even squarefree number A039956(n), n >= 1.
  • 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).
  • A264390 (program): Partial sums of A267326.
  • A264409 (program): a(n) = Sum_{k=0..n} binomial(n, k) * binomial((n-k)*k, k).
  • A264411 (program): a(n) = binomial(2*n^2, n).
  • A264416 (program): G.f.: Sum_{n>=0} x^n * (d/dx)^(n^2) x^(n^2) * (1+x)^n / (n^2)!, where (d/dx)^k denotes the k-th derivative operator.
  • 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).
  • A264441 (program): Length of row n of the irregular triangle A133995 (positive integers <= n which are neither divisors of n nor coprime to n).
  • 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.
  • A264491 (program): Number of (2+1) X (n+1) arrays of permutations of 0..n*3+2 with each element having directed index change 2,-1 1,0 2,1 0,-1 -2,-2 or -1,0.
  • A264507 (program): Number of (1+1) X (n+1) arrays of permutations of 0..n*2+1 with each element having directed index change -1,1 0,-1 0,1 or 1,0.
  • A264514 (program): Number of (2n) X (2+1) arrays of permutations of 0..n*6-1 with each element having directed index change -1,0 0,2 -1,-2 or 1,0.
  • A264515 (program): Number of (n+1)X(3+1) arrays of permutations of 0..n*4+3 with each element having directed index change -1,0 0,2 -1,-2 or 1,0.
  • A264526 (program): Smallest number m such that both 2*n-m and 2*n+m are primes.
  • A264527 (program): Largest number m such that (2*n-m, 2*n+m) is a prime pair.
  • A264544 (program): Number of (n+1) X (2+1) arrays of permutations of 0..n*3+2 with each element having directed index change -1,1 -1,2 1,0 or 0,-1.
  • A264551 (program): Number of (2+1) X (n+1) arrays of permutations of 0..n*3+2 with each element having directed index change -1,1 -1,2 1,0 or 0,-1.
  • 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.
  • A264570 (program): Number of (2+1) X (n+1) arrays of permutations of 0..n*3+2 with each element having directed index change 1,0 1,1 0,-1 or -1,1.
  • 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.
  • A264598 (program): Row sums of triangle in A264597.
  • A264599 (program): Partial sums of A257007.
  • A264608 (program): Degeneracies of entanglement witness eigenstates for spin 3 particles.
  • 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.
  • A264622 (program): Number of (n+1) X (1+1) arrays of permutations of 0..n*2+1 with each element having directed index change -2,0 -1,0 0,-1 or 1,1.
  • A264635 (program): Number of n X 1 arrays of permutations of 0..n*1-1 with rows nondecreasing modulo 2 and columns nondecreasing modulo 4.
  • A264656 (program): Number of n X 1 arrays of permutations of 0..n*1-1 with rows nondecreasing modulo 2 and columns nondecreasing modulo 5.
  • A264663 (program): Catalan numbers written in base 2.
  • A264668 (program): a(n) = A264600(n) - A061486(n).
  • A264689 (program): Minimum of the Kamae-Xue measure of randomness for binary strings of length n.
  • A264701 (program): Number of n X 1 arrays of permutations of 0..n-1 with rows nondecreasing modulo 2 and columns nondecreasing modulo 6.
  • A264717 (program): Central terms of triangle A100326.
  • A264719 (program): Numbers that are greater than the average of their closest flanking primes.
  • A264720 (program): Numbers that are less than the average of their closest flanking primes.
  • A264721 (program): Composite numbers that are greater than the average of their closest flanking primes.
  • A264722 (program): Composite numbers that are less than the average of their closest flanking primes.
  • A264724 (program): a(n) = n^2 + phi(n).
  • A264731 (program): Rectangular array A read by upward antidiagonals in which the entry in row n and column k is defined by A(n,k) = prime(2^(n-1)*(2*k-1)), n,k >= 1.
  • A264740 (program): Sum of odd parts of divisors of n.
  • A264744 (program): Exponent of the prime power A264734(n).
  • A264745 (program): Rectangular array A read by upward antidiagonals in which the entry in row n and column k is defined by A(n,k) = Fibonacci(2^(n-1)*(2*k-1) + 1), n,k >= 1.
  • A264748 (program): a(n) = Sum_{k = 1..n} (k^n - n^k).
  • 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.
  • A264751 (program): Triangle read by rows: T(n,k) is the number of sequences of k <= n 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 k-th throw.
  • A264754 (program): Expansion of (1 + 2*x - 2*x^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).
  • A264771 (program): Primes of the form n^2 + phi(n).
  • A264772 (program): Triangle T(n,k) = binomial(3*n - 2*k, 2*n - k), 0 <= k <= n.
  • A264773 (program): Triangle T(n,k) = binomial(4*n - 3*k, 3*n - 2*k), 0 <= k <= n.
  • A264774 (program): Triangle T(n,k) = binomial(5*n - 4*k, 4*n - 3*k), 0 <= k <= n.
  • A264782 (program): a(n) = Sum_{d|n} möbius(d)^(n/d).
  • A264786 (program): Let { d_1, d_2, …, d_k } be the divisors of n. Then a(n) = d_k^1 + d_(k-1)^2 + … + d_1^k.
  • A264788 (program): a(n) is the number of circles added at n-th iteration of the pattern starting with 2 circles. (See comment.)
  • A264790 (program): Numbers k such that k^2 + 17 is prime.
  • A264791 (program): Number of n X 1 arrays of permutations of 0..n*1-1 with rows nondecreasing modulo 2 and columns nondecreasing modulo 7.
  • A264797 (program): Number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by “Rule 342”, based on the 5-celled von Neumann neighborhood.
  • A264798 (program): Irregular triangle read by rows: odd-valued terms of A094728(n+1).
  • A264800 (program): Nearly-Fibonacci sequence.
  • A264802 (program): Position of the n largest occurrences of a shortest addition chain of length n in A003313, written as a triangle.
  • A264821 (program): Centered 14-gonal (or tetradecagonal) primes.
  • A264822 (program): Centered 15-gonal (or pentadecagonal) primes.
  • A264823 (program): Centered 16-gonal (or hexadecagonal) primes.
  • A264824 (program): Centered 17-gonal (or heptadecagonal) primes.
  • A264825 (program): Centered 18-gonal (or octadecagonal) primes.
  • A264828 (program): Nonprimes that are not twice a prime.
  • A264844 (program): Centered 19-gonal (or nonadecagonal) primes.
  • A264845 (program): Centered 20-gonal (or icosagonal) primes.
  • A264847 (program): Pluritriangular numbers: a(0) = 0; a(n+1) = a(n) + the number of digits in terms a(0)..a(n).
  • A264850 (program): a(n) = n*(n + 1)*(n + 2)*(7*n - 5)/12.
  • A264851 (program): a(n) = n*(n + 1)*(n + 2)*(4*n - 3)/6.
  • A264852 (program): a(n) = n*(n + 1)*(n + 2)*(9*n - 7)/12.
  • A264853 (program): a(n) = n*(n + 1)*(5*n^2 + 5*n - 4)/12.
  • A264854 (program): a(n) = n*(n + 1)*(11*n^2 + 11*n - 10)/24.
  • A264871 (program): Array read by antidiagonals: T(n,m) = (1+2^n)^m; n,m>=0.
  • A264872 (program): Array read by antidiagonals: T(n,m) = 2^n*(1+2^n)^m; n,m >= 0.
  • A264888 (program): a(n) = n*(n + 1)*(13*n^2 + 13*n - 14)/24.
  • A264889 (program): Partial sums of hyperfactorials (A002109).
  • A264891 (program): a(n) = n*(5*n - 3)*(25*n^2 - 15*n - 6)/8.
  • A264892 (program): a(n) = n*(3*n - 2)*(9*n^2 - 6*n - 2).
  • A264893 (program): First differences of A155043.
  • A264894 (program): a(n) = n*(7*n - 5)*(49*n^2 - 35*n - 10)/8.
  • A264895 (program): a(n) = n*(4*n - 3)*(16*n^2 - 12*n - 3).
  • A264906 (program): a(n) is the denominator of the 2nd term of the power series which is the loop length in a regular n-gon. (See comment.)
  • A264908 (program): Primes of the form 2^i + 2^j + 2^k - 1, i > j > k > 0.
  • A264928 (program): G.f.: exp( Sum_{n>=1} x^n/n * (1 - 3*x^n)/(1 - x^n) ).
  • A264938 (program): a(n) = n*(2*n-1) + floor(n/3).
  • A264960 (program): Half-convolution of the central binomial coefficients A000984 with itself.
  • A264966 (program): Permutation of nonnegative integers: a(n) = A057889(A263273(n)).
  • A264968 (program): Permutation of nonnegative integers: a(n) = A246200(A263272(n)).
  • A264974 (program): Self-inverse permutation of natural numbers: a(n) = A263273(4*n) / 4.
  • A264975 (program): Permutation of nonnegative integers: a(n) = A264974(A263272(n)).
  • A264976 (program): Permutation of nonnegative integers: a(n) = A263272(A264974(n)).
  • A264978 (program): Self-inverse permutation of nonnegative integers: a(n) = A263273(8*n)/8.
  • A264980 (program): Base-3 reversal of 2^n: a(n) = A030102(A000079(n)).
  • A264981 (program): Highest power of 9 dividing n.
  • A264983 (program): Odd bisection of A263273.
  • A264984 (program): Even bisection of A263273; terms of A263262 doubled.
  • A264985 (program): Self-inverse permutation of nonnegative integers: a(n) = (A264983(n)-1) / 2.
  • A264986 (program): Even bisection of A263272; terms of A264974 doubled.
  • A264987 (program): Odd bisection of A263272.
  • A264989 (program): Self-inverse permutation of nonnegative integers: a(n) = (A264987(n)-1) / 2.
  • A264990 (program): a(n) = number of occurrences of a most frequent nonzero digit in factorial base representation (A007623) of n.
  • A264991 (program): Permutation of nonnegative integers: a(n) = A264989(A264985(n)).
  • A264996 (program): Self-inverse permutation of natural numbers: a(n) = (1/2) * (1+A263273(2n -1)) = 1 + A264985(n-1).
  • A265006 (program): Twin prime pairs of the form (k^2 + k - 1, k^2 + k + 1).
  • A265012 (program): a(n) = 10^(prime(n)-1) mod prime(n)^2.
  • A265014 (program): Triangle read by rows: T(n,k) = number of neighbors in n-dimensional lattice for generalized neighborhood given with parameter k.
  • A265015 (program): a(n) = A015128(n)^n.
  • A265021 (program): Sum of fifth powers of the first n even numbers.
  • A265024 (program): a(n) = n! * Sum_{d in D(n+1)} (-1)^(d+1)*(n+1)/d, D(n) the divisors of n.
  • 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.
  • A265031 (program): Denominator of Kirchhoff index of ladder graph L_n.
  • A265035 (program): Coordination sequence of 2-uniform tiling {3.4.6.4, 4.6.12} with respect to a point of type 4.6.12.
  • A265037 (program): G.f.: (1 + 22*x - 34*x^2 + 14*x^3)/((1 - x)^2*(1 - 6*x + 8*x^2)).
  • 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).
  • A265050 (program): Poincaré series for hyperbolic reflection group with Coxeter diagram shown in Comments.
  • A265051 (program): Poincaré series for hyperbolic reflection group with Coxeter diagram shown in Comments.
  • A265056 (program): Partial sums of A234275.
  • A265064 (program): Coordination sequence for (2,5,5) tiling of hyperbolic plane.
  • A265068 (program): Coordination sequence for (2,5,infinity) tiling of hyperbolic plane.
  • A265069 (program): Coordination sequence for (2,6,6) tiling of hyperbolic plane.
  • A265070 (program): Coordination sequence for (2,6,infinity) tiling of hyperbolic plane.
  • A265071 (program): Coordination sequence for (3,3,4) tiling of hyperbolic plane.
  • A265072 (program): Coordination sequence for (3,3,5) tiling of hyperbolic plane.
  • A265073 (program): Coordination sequence for (3,3,6) tiling of hyperbolic plane.
  • A265075 (program): Coordination sequence for (3,4,4) tiling of hyperbolic plane.
  • A265076 (program): Coordination sequence for (3,5,5) tiling of hyperbolic plane.
  • A265077 (program): Coordination sequence for (3,6,8) tiling of hyperbolic plane.
  • A265078 (program): Partial sums of A072154.
  • A265093 (program): a(n) = Sum_{k=0..n} q(k)^2, where q(k) = partition numbers into distinct parts (A000009).
  • A265094 (program): a(n) = q(n)^n, where q(n) = partition numbers into distinct parts (A000009).
  • A265095 (program): a(n) = Sum_{k=0..n} q(k)^k, where q(k) = partition numbers into distinct parts (A000009).
  • A265096 (program): a(n) = Sum_{k=0..n} p(k)*q(k), where p(k) = partition numbers (A000041) and q(k) = partition numbers into distinct parts (A000009).
  • A265097 (program): a(n) = Product_{k=0..n} q(k)^k, where q(k) = partition numbers into distinct parts (A000009).
  • A265100 (program): a(n) = 9*A005836(n) + 5, n >= 1.
  • A265101 (program): a(n) = binomial(6*n + 5, 3*n + 1)/(6*n + 5).
  • A265102 (program): a(n) = binomial(8*n + 6, 4*n + 1)/(8*n + 6).
  • A265103 (program): a(n) = binomial(10*n + 7, 5*n + 1)/(10*n + 7).
  • A265104 (program): a(n) = A265100(n+1) - 6, n >= 1.
  • A265106 (program): Expansion of (x^5-x^4-2*x^3+x^2-x)/(-x^4+x^3-2*x^2+3*x-1).
  • A265107 (program): Expansion of (2*x^4+x^3+x)/(-x^2-2*x+1).
  • A265112 (program): a(n) = A023360(A000040(n)): number of compositions of prime(n) into prime parts.
  • 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.
  • A265130 (program): Total sum of number of lambda-parking functions, where lambda ranges over all partitions of k into distinct parts with largest part n and n<=k<=n*(n+1)/2.
  • A265132 (program): Number of nonintersecting (or self-avoiding) rook paths joining opposite corners of an n X n grid that move in 3 or fewer cardinal directions.
  • A265133 (program): Beatty sequence for log(2).
  • A265134 (program): Numbers that are the sum of two distinct nonzero triangular numbers in exactly two ways.
  • A265135 (program): Numbers that are the sum of two distinct nonzero triangular numbers in more than two ways.
  • A265136 (program): Numbers that are the sum of two distinct nonzero triangular numbers in exactly three ways.
  • A265137 (program): Numbers that are the sum of two distinct nonzero triangular numbers in more than three ways.
  • A265140 (program): Numbers that are the sum of two distinct nonzero triangular numbers in exactly one way.
  • A265155 (program): Integers which are unique starting points for the algorithm described in A090566.
  • A265157 (program): Number of 2’s in the base-3 representation of 2^n - 1.
  • A265159 (program): Rectangular array A read by upward antidiagonals in which the entry in row n and column k is defined by A(n,k) = 5 + 9*A005836(2^(k - 1)*(2 n - 1)), n,k >= 1.
  • A265160 (program): a(n) = 2^n + prime(n).
  • A265161 (program): Array A read by upward antidiagonals in which the entry in row n and column k is defined by A(n,k) = (3/2)*(3^k - 1) + A265159(n,k), n,k >= 1.
  • A265165 (program): a(n) = sum of the n-th column of the array A265163(n,k). See Comments for more details.
  • A265166 (program): Numbers n such that 2^n-1 and 5^n-1 are coprime.
  • A265172 (program): Binary representation of the n-th iteration of the “Rule 90” elementary cellular automaton starting with a single ON cell.
  • A265184 (program): a(n) = Sum_{k = 0..n} (-1)^k*prime(k)#, where prime(k)# is the prime factorial function.
  • 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 2*floor(m^2/11) = floor(2*m^2/11).
  • A265188 (program): Nonnegative m for which 3*floor(m^2/11) = floor(3*m^2/11).
  • A265204 (program): Sum of phi(i) over squarefree numbers i <= n.
  • 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.
  • A265211 (program): Squares that become prime when their rightmost digit is removed.
  • A265223 (program): Total number of OFF (white) cells after n iterations of the “Rule 150” elementary cellular automaton starting with a single ON (black) cell.
  • A265224 (program): Total number of OFF (white) cells after n iterations of the “Rule 30” elementary cellular automaton starting with a single ON (black) cell.
  • 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 k*floor(m^2/9) = floor(k*m^2/9), with 2 < k < 9.
  • A265228 (program): Interleave the even numbers with the numbers that are congruent to {1, 3, 7} mod 8.
  • A265229 (program): Number of nX2 arrays containing 2 copies of 0..n-1 with no equal vertical neighbors and new values introduced sequentially from 0.
  • A265233 (program): Number of 3Xn arrays containing n copies of 0..3-1 with no equal vertical neighbors and new values introduced sequentially from 0.
  • A265250 (program): Number of partitions of n having no parts strictly between the smallest and the largest part (n>=1).
  • A265263 (program): Change every other 1 bit in binary expansion of n to 0.
  • A265278 (program): Expansion of (x^4+x^3-x^2+x)/(x^3+x^2-3*x+1).
  • A265280 (program): Binary representation of the n-th iteration of the “Rule 86” elementary cellular automaton starting with a single ON (black) cell.
  • A265281 (program): Decimal representation of the n-th iteration of the “Rule 86” elementary cellular automaton starting with a single ON (black) cell.
  • A265282 (program): Number of triangles in a certain geometric structure: see “Illustration of initial terms” link for precise definition.
  • 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.
  • A265310 (program): Least positive k such that the product of divisors of n (A007955) divides k!.
  • A265316 (program): First row of A262057.
  • A265319 (program): Binary representation of the n-th iteration of the “Rule 102” elementary cellular automaton starting with a single ON (black) cell.
  • A265320 (program): Binary representation of the n-th iteration of the “Rule 110” elementary cellular automaton starting with a single ON (black) cell.
  • A265321 (program): Total number of ON (black) cells after n iterations of the “Rule 110” elementary cellular automaton starting with a single ON (black) cell.
  • A265322 (program): Number of OFF (white) cells in the n-th iteration of the “Rule 110” elementary cellular automaton starting with a single ON (black) cell.
  • A265323 (program): Total number of OFF (white) cells after n iterations of the “Rule 110” elementary cellular automaton starting with a single ON (black) cell.
  • A265326 (program): n-th prime minus its binary reversal.
  • A265330 (program): Zero-based row index to A265345; 2-adic valuation of bijective base-3 reversal of n: a(n) = A007814(A263273(n)).
  • A265331 (program): One-based row index to A265345.
  • A265332 (program): a(n) is the index of the column in A265901 where n appears; also the index of the row in A265903 where n appears.
  • 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”.
  • A265336 (program): Number of nonleading 0-bits in bijective base-3 reversal of n: a(n) = A080791(A263273(n)).
  • A265337 (program): Number of 1-bits in base-3 reversal of n: a(n) = A000120(A263273(n)).
  • A265340 (program): Number of iterations of A265339 needed to reach zero; a(0) = 0; for n >= 1, a(n) = 1 + a(A265339(n)).
  • A265341 (program): Permutation of odd numbers: a(n) = 1 + (2*A265353(n)).
  • A265342 (program): Permutation of even numbers: a(n) = 2 * A265351(n).
  • A265343 (program): Permutation of nonnegative integers: a(n) = A264978(A263272(n).
  • A265344 (program): Permutation of nonnegative integers: a(n) = A263272(A264978(n).
  • A265349 (program): Numbers in whose factorial base representation (A007623) no digit > 0 occurs more than once.
  • A265350 (program): Numbers in whose factorial base representation (A007623) at least one of the nonzero digits occurs more than once (although not necessarily in adjacent positions).
  • A265351 (program): Permutation of nonnegative integers: a(n) = A263272(A263273(n)).
  • A265352 (program): Permutation of nonnegative integers: a(n) = A263273(A263272(n)).
  • A265353 (program): Permutation of nonnegative integers: a(n) = A264985(A263273(n)).
  • A265354 (program): Permutation of nonnegative integers: a(n) = A263273(A264985(n)).
  • A265355 (program): Permutation of nonnegative integers: a(n) = A263272(A264985(n)).
  • A265356 (program): Permutation of nonnegative integers: a(n) = A264985(A263272(n)).
  • A265357 (program): Permutation of nonnegative integers: a(n) = A264989(A263272(n)).
  • A265358 (program): Permutation of nonnegative integers: a(n) = A263272(A264989(n)).
  • 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).
  • A265361 (program): Permutation of nonnegative integers: a(n) = A264974(A264989(n)).
  • A265362 (program): Permutation of nonnegative integers: a(n) = A264989(A264974(n)).
  • A265363 (program): Permutation of nonnegative integers: a(n) = A264974(A263273(n)).
  • A265364 (program): Permutation of nonnegative integers: a(n) = A263273(A264974(n)).
  • A265365 (program): Permutation of nonnegative integers: a(n) = A264978(A263273(n)).
  • A265366 (program): Permutation of nonnegative integers: a(n) = A263273(A264978(n)).
  • A265367 (program): Permutation of nonnegative integers: a(n) = A264974(A263272(A263273(n))).
  • A265376 (program): a(1) = 1 and a(n) = Sum_{i=1..n-1} (-1)^i*i*a(i).
  • A265379 (program): Binary representation of the n-th iteration of the “Rule 158” elementary cellular automaton starting with a single ON (black) cell.
  • A265380 (program): Binary representation of the middle column of the “Rule 158” elementary cellular automaton starting with a single ON (black) cell.
  • 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).
  • A265385 (program): Sequence defined by a(1)=a(2)=1 and a(n) = gray(a(n-1) + a(n-2)), with gray(m) = A003188(m).
  • A265386 (program): Sequence defined by a(1)=a(2)=1 and a(n) = gray(gray(a(n-1)) + gray(a(n-2))), with gray(m) = A003188(m).
  • A265387 (program): Sequence defined by a(1)=a(2)=1 and a(n) = gray(a(n-1)) + gray(a(n-2)), with gray(m) = A003188(m).
  • A265388 (program): a(n) = gcd{k=1..n-1} binomial(2*n, 2*k), a(1) = 0.
  • A265389 (program): The sums from the following procedure: from the list of positive integers, repeatedly remove the first three numbers and their sum.
  • A265401 (program): Numbers n for which gcd{k=1..n-1} binomial(2*n, 2*k) = 1.
  • A265402 (program): Fixed points of A265388: numbers n for which gcd{k=1..n-1} binomial(2*n, 2*k) = n.
  • A265403 (program): Numbers n for which gcd{k=1..n-1} binomial(2*n, 2*k) = 2n-1.
  • A265409 (program): a(n) = index to the nearest inner neighbor in Ulam-style square-spirals using zero-based indexing.
  • A265410 (program): a(n) = one-based index to the nearest horizontally or vertically adjacent inner neighbor in square-grid spirals, and to the nearest diagonally adjacent inner neighbor when n is one of the corner cases A033638.
  • 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).
  • A265423 (program): (-1)^n + 50*floor(3n/2) - 100*floor(n/4).
  • A265424 (program): a(n) = ((-1)^n - 1)/2 + 25*floor(3*n/2) - 50*floor(n/4).
  • A265427 (program): Binary representation of the n-th iteration of the “Rule 188” elementary cellular automaton starting with a single ON (black) cell.
  • 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.
  • A265435 (program): Riordan array (1, x*f(x)) where f(x) is the g.f. of A007564.
  • 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.
  • A265509 (program): a(n) = largest base-2 palindrome m <= 2n+1 such that every base-2 digit of m is <= the corresponding digit of 2n+1; m is written in base 10.
  • A265510 (program): a(n) = largest base-2 palindrome m <= 2n+1 such that every base-2 digit of m is <= the corresponding digit of 2n+1; m is written in base 2.
  • 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.
  • A265529 (program): Largest base-3 palindrome m <= n, written in base 10.
  • A265530 (program): Largest base-3 palindrome m <= n, written in base 3.
  • A265531 (program): Largest base-4 palindrome m <= n, written in base 10.
  • A265532 (program): Largest base-4 palindrome m <= n, written in base 4.
  • A265533 (program): Largest base-5 palindrome m <= n, written in base 10.
  • A265534 (program): Largest base-5 palindrome m <= n, written in base 5.
  • A265535 (program): Largest base-6 palindrome m <= n, written in base 10.
  • A265536 (program): Largest base-6 palindrome m <= n, written in base 6.
  • A265537 (program): Largest base-7 palindrome m <= n, written in base 10.
  • A265538 (program): Largest base-7 palindrome m <= n, written in base 7.
  • A265539 (program): Largest base-8 palindrome m <= n, written in base 10.
  • A265540 (program): Largest base-8 palindrome m <= n, written in base 8.
  • A265541 (program): Largest base-9 palindrome m <= n, written in base 10.
  • A265542 (program): Largest base-9 palindrome m <= n, written in base 9.
  • A265543 (program): a(n) = smallest base-2 palindrome m >= n such that every base-2 digit of n is <= the corresponding digit of m; m is written in base 2.
  • A265559 (program): Smallest base-2 palindrome m >= n, written in base 2.
  • A265560 (program): Smallest base-3 palindrome m >= n, written in base 10.
  • A265561 (program): Smallest base-3 palindrome m >= n, written in base 3.
  • A265562 (program): Smallest base-4 palindrome m >= n, written in base 10.
  • A265563 (program): Smallest base-4 palindrome m >= n, written in base 4.
  • A265564 (program): Smallest base-5 palindrome m >= n, written in base 10.
  • A265565 (program): Smallest base-5 palindrome m >= n, written in base 5.
  • A265566 (program): Smallest base-6 palindrome m >= n, written in base 10.
  • A265567 (program): Smallest base-6 palindrome m >= n, written in base 6.
  • A265568 (program): Smallest base-7 palindrome m >= n, written in base 10.
  • A265569 (program): Smallest base-7 palindrome m >= n, written in base 7.
  • A265570 (program): Smallest base-8 palindrome m >= n, written in base 10.
  • A265571 (program): Smallest base-8 palindrome m >= n, written in base 8.
  • A265572 (program): Smallest base-9 palindrome m >= n, written in base 10.
  • A265573 (program): Smallest base-9 palindrome m >= n, written in base 9.
  • A265574 (program): LCM-transform of triangular numbers.
  • A265583 (program): Array T(n,k) = k*(k-1)^(n-1) read by ascending antidiagonals; k,n >= 1.
  • A265584 (program): Array T(n,k) counting words with n letters drawn from a k-letter alphabet with no letter appearing thrice in a 3-letter subword.
  • A265609 (program): Array read by ascending antidiagonals: A(n,k) the rising factorial, also known as Pochhammer symbol, for n >= 0 and k >= 0.
  • A265610 (program): a(n) = rf(n, n+2)/(n+2)! - rf(n, n)/n!, rf the rising factorial A265609.
  • A265611 (program): a(n) = a(n-1) + floor((n-1)/2) - (-1)^n + 2 for n>=2, a(0)=1, a(1)=3.
  • A265612 (program): a(n) = CatalanNumber(n+1)*n*(1+3*n)/(6+2*n).
  • A265613 (program): a(n) = CatalanNumber(n+1)*n*(3*n^2+5*n+2)/((4+n)*(3+n)).
  • A265640 (program): Prime factorization palindromes (see comments for definition).
  • A265643 (program): a(n) = +-1 == ((p - 1)/2)! (mod p), where p is the n-th prime number == 3 (mod 4).
  • A265644 (program): Triangle read by rows: T(n,m) is the number of quaternary words of length n with m strictly increasing runs (0 <= m <= n).
  • A265645 (program): a(n) = n^2 * floor(n/2).
  • A265647 (program): Smallest k such that n divides k*(k+1)*(k+2)/6.
  • A265667 (program): Permutation of nonnegative integers: a(n) = n + floor(n/3)*(-1)^(n mod 3).
  • A265673 (program): Area A under the trajectory of each odd number in the “3x+1” problem.
  • A265676 (program): a(n) is the total number of petals of the Flower of Life at the n-th iteration.
  • A265688 (program): Binary representation of the n-th iteration of the “Rule 190” elementary cellular automaton starting with a single ON (black) cell.
  • A265694 (program): a(n) = n!! mod n^2 where n!! is a double factorial number (A006882).
  • A265698 (program): Middle column of the “Rule 135” elementary cellular automaton starting with a single ON (black) cell.
  • A265699 (program): Binary representation of the middle column of the “Rule 135” elementary cellular automaton starting with a single ON (black) cell.
  • A265700 (program): Decimal representation of the middle column of the “Rule 135” elementary cellular automaton starting with a single ON (black) cell.
  • A265701 (program): Number of ON (black) cells in the n-th iteration of the “Rule 135” elementary cellular automaton starting with a single ON (black) cell.
  • A265702 (program): Total number of ON (black) cells after n iterations of the “Rule 135” elementary cellular automaton starting with a single ON (black) cell.
  • A265703 (program): Number of OFF (white) cells in the n-th iteration of the “Rule 135” elementary cellular automaton starting with a single ON (black) cell.
  • A265704 (program): Total number of OFF (white) cells after n iterations of the “Rule 135” elementary cellular automaton starting with a single ON (black) cell.
  • A265705 (program): Triangle read by rows: T(n,k) = k IMPL n, 0 <= k <= n, bitwise logical IMPL.
  • A265716 (program): a(n) = n IMPL (2*n), where IMPL is the bitwise logical implication.
  • A265718 (program): Triangle read by rows giving successive states of cellular automaton generated by “Rule 1” initiated with a single ON (black) cell.
  • A265720 (program): Binary representation of the n-th iteration of the “Rule 1” elementary cellular automaton starting with a single ON (black) cell.
  • A265721 (program): Decimal representation of the n-th iteration of the “Rule 1” elementary cellular automaton starting with a single ON (black) cell.
  • 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.
  • A265725 (program): Number of binary strings of length n having at least one run of length at least 4.
  • A265729 (program): Decimal expansion of 32*Pi.
  • A265734 (program): Permutation of nonnegative integers: a(n) = n + floor(n/5)*(-1)^(n mod 5).
  • A265736 (program): Row sums of triangle A265705.
  • A265743 (program): a(n) = number of terms of A005187 needed to sum to n using the greedy algorithm.
  • A265744 (program): a(n) is the number of Pell numbers (A000129) needed to sum to n using the greedy algorithm (A317204).
  • A265745 (program): a(n) is the number of Jacobsthal numbers (A001045) needed to sum to n using the greedy algorithm.
  • A265746 (program): Jacobsthal greedy base (A265747) interpreted as base-3 numbers, then shown in decimal.
  • A265747 (program): Numbers written in Jacobsthal greedy base.
  • A265754 (program): Reduced frequency counts for A004001: a(n) = A265332(n+1) - A036987(n).
  • A265755 (program): a(n) = a(n-1) + a(n-2) if n is even and a(n) = a(n-3) + a(n-4) if n is odd, with a(0) = a(1) = a(2) = 0 and a(3) = 1.
  • A265760 (program): Denominators of primes-only best approximates (POBAs) to 1; see Comments.
  • A265762 (program): Coefficient of x in minimal polynomial of the continued fraction [1^n,2,1,1,1,…], where 1^n means n ones.
  • A265767 (program): Numerators of upper primes-only best approximates (POBAs) to 5; see Comments.
  • A265771 (program): Denominators of primes-only best approximates (POBAs) to 6; see Comments.
  • A265802 (program): Coefficient of x^2 in minimal polynomial of the continued fraction [1^n,4,1,1,1,…], where 1^n means n ones.
  • A265803 (program): Coefficient of x in minimal polynomial of the continued fraction [1^n,4,1,1,1,…], where 1^n means n ones.
  • A265804 (program): Coefficient of x^2 in minimal polynomial of the continued fraction [1^n,5,1,1,1,…], where 1^n means n ones.
  • A265805 (program): Coefficient of x in minimal polynomial of the continued fraction [1^n,5,1,1,1,…], where 1^n means n ones.
  • A265848 (program): Pascal’s triangle, right and left halves interchanged.
  • A265852 (program): n such that A261807(n) = n^3 - n.
  • A265888 (program): a(n) = n + floor(n/4)*(-1)^(n mod 4).
  • A265893 (program): a(n) = A084558(n) - A230403(n); the length of factorial base representation of n without its trailing zeros.
  • A265904 (program): Self-inverse permutation of nonnegative integers: a(n) = A263272(A263273(A263272(n))).
  • A265905 (program): a(1) = 1; for n > 1, a(n) = a(n-1) + A153880(a(n-1)).
  • A265906 (program): a(n) = A153880(A265905(n)); also the first differences of A265905.
  • A265917 (program): a(n) = floor(A070939(n)/A000120(n)) where A070939(n) is the binary length of n and A000120(n) is the binary weight of n.
  • A265918 (program): a(n) = A070939(n) mod A000120(n), where A070939(n) is the binary length of n and A000120(n) is the binary weight of n.
  • A265936 (program): G.f.: Sum_{n>=0} (1 + x)^(n^2) / 2^n.
  • A265937 (program): G.f.: Sum_{n>=0} (1 + x)^(n*(n+1)/2) / 2^n.
  • A265939 (program): Central terms of triangle A102363.
  • 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.
  • A266007 (program): Number of n X 3 integer arrays with each element equal to the number of horizontal and antidiagonal neighbors equal to itself.
  • A266008 (program): Number of n X 4 integer arrays with each element equal to the number of horizontal and antidiagonal neighbors equal to itself.
  • A266027 (program): Number of n X 2 integer arrays with each element equal to the number of horizontal and antidiagonal neighbors less than itself.
  • A266046 (program): Real part of Q^n, where Q is the quaternion 2 + j + k.
  • A266049 (program): Number of n X 2 integer arrays with each element equal to the number of horizontal and antidiagonal neighbors less than or equal to itself.
  • A266050 (program): Number of n X 3 integer arrays with each element equal to the number of horizontal and antidiagonal neighbors less than or equal to itself.
  • A266070 (program): Middle column of the “Rule 3” elementary cellular automaton starting with a single ON (black) cell.
  • A266071 (program): Binary representation of the 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.
  • A266174 (program): Triangle read by rows giving successive states of cellular automaton generated by “Rule 5” initiated with a single ON (black) cell.
  • A266175 (program): Binary representation of the n-th iteration of the “Rule 5” elementary cellular automaton starting with a single ON (black) cell.
  • A266176 (program): Decimal representation of the n-th iteration of the “Rule 5” elementary cellular automaton starting 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.
  • A266188 (program): a(n) = A004001(A087686(n)).
  • A266189 (program): Self-inverse permutation of nonnegative integers: a(n) = A263273(A264985(A263273(n))).
  • A266213 (program): Square array A(n,r), the number of neighbors at a sharp Manhattan distance r in a finite n-hypercube lattice, read by upwards antidiagonals; A(n,r) = Sum_{k=0..min(n,r)} binomial(r-1,k-1)*binomial(n,k)* 2^k.
  • A266214 (program): Numbers n that are not coprime to the numerator of zeta(2*n)/(Pi^(2*n)).
  • A266216 (program): Triangle read by rows giving successive states of cellular automaton generated by “Rule 7” initiated with a single ON (black) cell.
  • A266217 (program): Binary representation of the n-th iteration of the “Rule 7” elementary cellular automaton starting 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.
  • A266219 (program): Binary representation of the middle column 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.
  • A266225 (program): Least x>1 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.
  • A266238 (program): a(n+1) = 2^(2*n - 1) + (-1)^n * a(n), a(1) = 1.
  • A266246 (program): Middle column of the “Rule 9” elementary cellular automaton starting with a single ON (black) cell.
  • A266247 (program): Binary representation of the middle column of the “Rule 9” elementary cellular automaton starting with a single ON (black) cell.
  • A266248 (program): Decimal representation of the 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.
  • A266254 (program): Binary representation of the n-th iteration of the “Rule 11” elementary cellular automaton starting with a single ON (black) cell.
  • A266255 (program): Decimal representation of the n-th iteration of the “Rule 11” elementary cellular automaton starting 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.
  • A266265 (program): Product of products of divisors of divisors of n.
  • A266282 (program): Triangle read by rows giving successive states of cellular automaton generated by “Rule 13” initiated with a single ON (black) cell.
  • A266283 (program): Binary representation of the n-th iteration of the “Rule 13” elementary cellular automaton starting with a single ON (black) cell.
  • A266284 (program): Decimal representation of the n-th iteration of the “Rule 13” elementary cellular automaton starting 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.
  • A266288 (program): Expansion of a(q)^2 * (c(q)/3)^3 in powers of q where a(), c() are cubic AGM theta functions.
  • 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.
  • A266301 (program): Binary representation of the n-th iteration of the “Rule 15” elementary cellular automaton starting 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].
  • A266323 (program): Binary representation of the n-th iteration of the “Rule 19” elementary cellular automaton starting with a single ON (black) cell.
  • A266324 (program): Decimal representation of the n-th iteration of the “Rule 19” elementary cellular automaton starting with a single ON (black) cell.
  • 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.
  • A266335 (program): G.f. = b(2)^2*b(6)/(x^7+x^6-x^5-x^2-x+1), where b(k) = (1-x^k)/(1-x).
  • A266336 (program): G.f. = b(2)*b(6)/(x^6-x^4+x^2-2*x+1), where b(k) = (1-x^k)/(1-x).
  • A266337 (program): Expansion of b(3)*b(4)/(1 - 2*x + x^5), where b(k) = (1-x^k)/(1-x).
  • A266339 (program): G.f. = b(2)^2*b(4)/(x^5+x^4-x^3-x^2-x+1), where b(k) = (1-x^k)/(1-x).
  • A266340 (program): G.f. = b(2)*b(4)*b(6)/(x^8+x^6-x^5+x^4-2*x^3-x+1), where b(k) = (1-x^k)/(1-x).
  • A266341 (program): If A036987(n) = 1, a(n) = n - A053644(n), otherwise a(n) = n - A053644(n) + 2^(A063250(n)-1).
  • A266353 (program): Expansion of b(3)*b(4)/(1 - 2*x + x^2 - x^3 + x^4), where b(k) = (1-x^k)/(1-x).
  • A266365 (program): Number of possible plugboard settings for a WWII German Enigma Cipher Machine with n cables.
  • A266367 (program): Expansion of b(2)*b(4)/(1 - 2*x - 2*x^3 + 3*x^4), where b(k) = (1-x^k)/(1-x).
  • A266370 (program): G.f. = b(2)^2*b(4)/(2*x^5+x^4-2*x^3-x^2-x+1), where b(k) = (1-x^k)/(1-x).
  • A266372 (program): G.f. = b(2)*b(4)*b(6)/(x^9+x^8+x^7+x^6-x^5-x^4-x^3-x^2-x+1), where b(k) = (1-x^k)/(1-x).
  • A266374 (program): G.f. = b(2)*b(6)/(3*x^6-2*x^5-2*x+1), where b(k) = (1-x^k)/(1-x).
  • A266375 (program): G.f. = b(2)*b(4)*b(6)/(x^8+x^7-x^3-x^2-x+1), where b(k) = (1-x^k)/(1-x).
  • A266376 (program): G.f. = b(2)*b(4)*b(6)/(x^9+x^8+x^7-2*x^3-x^2-x+1), where b(k) = (1-x^k)/(1-x).
  • 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.
  • A266381 (program): Binary representation of the n-th iteration of the “Rule 22” elementary cellular automaton starting with a single ON (black) cell.
  • A266382 (program): Decimal representation of the n-th iteration of the “Rule 22” elementary cellular automaton starting with a single ON (black) cell.
  • A266383 (program): Total number of ON (black) cells after n iterations of the “Rule 22” elementary cellular automaton starting with a single ON (black) cell.
  • A266384 (program): Total number of OFF (white) cells after n iterations of the “Rule 22” 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.
  • A266393 (program): Number of permutations of n letters that contain exactly 3 distinguishable A’s, 2 distinguishable B’s and n-5 distinguishable other letters, where no A’s are adjacent and no B’s are adjacent.
  • 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.
  • A266400 (program): Indices of primes in A005097.
  • A266407 (program): Permutation of natural numbers: a(n) = A064989(A263273((2*n)-1)).
  • A266429 (program): Number of 3 X n binary arrays with rows and columns lexicographically nondecreasing and column sums nondecreasing.
  • 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.
  • A266445 (program): Binary representation of the middle column of the “Rule 25” elementary cellular automaton starting with a single ON (black) cell.
  • A266446 (program): Decimal representation of the 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.
  • A266459 (program): Triangle read by rows giving successive states of cellular automaton generated by “Rule 27” initiated 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.
  • A266471 (program): Number of 4 X n binary arrays with rows and columns lexicographically nondecreasing and column sums nonincreasing.
  • A266475 (program): Sum of the parts i_1 + i_2 + … + i_{A001222(n)} of the unique strict partition with encoding n = Product_{j=1..A001222(n)} prime(i_j-j+1).
  • A266491 (program): a(n) = n*A130658(n).
  • A266497 (program): Binomial transform of A015128.
  • A266498 (program): Index of the smallest triangular number greater than 3^n.
  • A266502 (program): Triangle read by rows giving successive states of cellular automaton generated by “Rule 28” initiated with a single ON (black) cell.
  • A266504 (program): a(n) = 2*a(n - 2) + a(n - 4) with a(0) = a(1) = 2, a(2) = 1, a(3) = 3.
  • A266505 (program): a(n) = 2*a(n - 2) + a(n - 4) with a(0) = -1, a(1) = 1, a(2) = 3, a(3) = 5.
  • A266506 (program): a(2n) = a(2n - 4) + a(2n - 3) and a(2n + 1) = 2*a(2n - 4) + a(2n - 3), with a(0) = 2, a(1) = -1, a(2) = 2, a(3) = 1. Alternatively, interleave denominators (A266504) and numerators (A266505) of convergents to sqrt(2).
  • 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.
  • A266514 (program): Triangle read by rows giving successive states of cellular automaton generated by “Rule 29” initiated with a single ON (black) cell.
  • A266515 (program): Binary representation of the n-th iteration of the “Rule 29” elementary cellular automaton starting with a single ON (black) cell.
  • A266516 (program): Decimal representation of the n-th iteration of the “Rule 29” elementary cellular automaton starting with a single ON (black) cell.
  • A266529 (program): Terms of A160552 repeated.
  • A266530 (program): Partial sums of A266529.
  • 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.
  • A266551 (program): Image of n under the 3p+1 map, which is a variation of the 3x+1 (Collatz) map.
  • A266561 (program): 12-dimensional square numbers.
  • A266575 (program): Expansion of q * f(-q^4)^6 / phi(-q) in powers of q where phi(), f() are Ramanujan theta functions.
  • A266577 (program): Square array read by descending antidiagonals: T(n,k) = ((2^(n+1) + 1)^(k-1) + 1)/2.
  • A266587 (program): Smallest index of a Lucas number (A000032) that is divisible by prime(n), if it exists, or 0 if it does not exist (for n > 1).
  • A266591 (program): Middle column of the “Rule 37” elementary cellular automaton starting with a single ON (black) cell.
  • A266592 (program): Binary representation of the 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.
  • A266605 (program): Triangle read by rows giving successive states of cellular automaton generated by “Rule 39” initiated with a single ON (black) cell.
  • A266611 (program): Middle column of the “Rule 41” elementary cellular automaton starting with a single ON (black) cell.
  • A266612 (program): Binary representation of the 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.
  • A266614 (program): Number of ON (black) cells in the n-th iteration of the “Rule 41” elementary cellular automaton starting with a single ON (black) cell.
  • A266615 (program): Total number of ON (black) cells after n iterations of the “Rule 41” elementary cellular automaton starting with a single ON (black) cell.
  • A266616 (program): Number of OFF (white) cells in the n-th iteration of the “Rule 41” elementary cellular automaton starting with a single ON (black) cell.
  • A266617 (program): Total number of OFF (white) cells after n iterations of the “Rule 41” elementary cellular automaton starting with a single ON (black) cell.
  • A266620 (program): a(n) = least non-divisor of n!.
  • A266640 (program): Reversed reduced frequency counts for A004001: a(n) = A265754(A054429(n)).
  • A266642 (program): Permutation of nonnegative integers: a(n) = A264966(2*n) / 2.
  • A266644 (program): Permutation of nonnegative integers: a(n) = A264966(3*n) / 3.
  • A266659 (program): Triangle read by rows giving successive states of cellular automaton generated by “Rule 47” initiated with a single ON (black) cell.
  • A266660 (program): Binary representation of the n-th iteration of the “Rule 47” elementary cellular automaton starting with a single ON (black) cell.
  • A266661 (program): Decimal representation of the n-th iteration of the “Rule 47” elementary cellular automaton starting 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.
  • A266667 (program): Binary representation of the n-th iteration of the “Rule 51” elementary cellular automaton starting with a single ON (black) cell.
  • A266668 (program): Decimal representation of the n-th iteration of the “Rule 51” elementary cellular automaton starting with a single ON (black) cell.
  • A266669 (program): Triangle read by rows giving successive states of cellular automaton generated by “Rule 53” initiated with a single ON (black) cell.
  • A266677 (program): Alternating sum of hexagonal pyramidal numbers.
  • A266678 (program): Middle column of the “Rule 175” elementary cellular automaton starting with a single ON (black) cell.
  • A266679 (program): Positive integers not shotgun (or Schrotschuss) numbers, in order of the first number to be permuted forward by the transformations T[k] where k = 2 or k is odd.
  • A266680 (program): Binary representation of the middle column of the “Rule 175” elementary cellular automaton starting with a single ON (black) cell.
  • A266685 (program): T(n,k) is the number of loops appearing in pattern of circular arc connecting two vertices of regular polygons. (See Comments.)
  • A266697 (program): Multiplicative order of 2^n mod 2*n+1.
  • A266698 (program): x-values of solutions to the Diophantine equation x^2 - 7*y^2 = 2.
  • A266699 (program): Coefficient of x^2 in minimal polynomial of the continued fraction [1^n,1/2,1,1,1,…], where 1^n means n ones.
  • A266700 (program): Coefficient of x in minimal polynomial of the continued fraction [1^n,1/2,1,1,1,…], where 1^n means n ones.
  • A266701 (program): Coefficient of x^2 in minimal polynomial of the continued fraction [1^n,1/3,1,1,1,…], where 1^n means n ones.
  • A266703 (program): Coefficient of x^2 in minimal polynomial of the continued fraction [1^n,2/3,1,1,1,…], where 1^n means n ones.
  • A266705 (program): Coefficient of x^2 in minimal polynomial of the continued fraction [1^n,sqrt(5),1,1,1,…], where 1^n means n ones.
  • A266706 (program): Coefficient of x in minimal polynomial of the continued fraction [1^n,sqrt(5),1,1,1,…], where 1^n means n ones.
  • A266707 (program): Coefficient of x^2 in minimal polynomial of the continued fraction [1^n,tau,1,1,1,…], where 1^n means n ones and tau = golden ratio = (1 + sqrt(5))/2.
  • A266708 (program): Coefficient of x in minimal polynomial of the continued fraction [1^n,tau,1,1,1,…], where 1^n means n ones and tau = golden ratio = (1 + sqrt(5))/2.
  • A266709 (program): Coefficient of x in minimal polynomial of the continued fraction [2,1^n,2,1,1,…], where 1^n means n ones.
  • A266714 (program): Number of k <= n such that (n mod k) is prime.
  • A266716 (program): Triangle read by rows giving successive states of cellular automaton generated by “Rule 59” initiated with a single ON (black) cell.
  • A266719 (program): Middle column of the “Rule 59” elementary cellular automaton starting with a single ON (black) cell.
  • A266720 (program): Binary representation of the 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).
  • A266744 (program): G.f.: 1/((1-t^4)*(1-t)*(1-t^3)*(1-t^5)*(1-t^7)).
  • A266745 (program): Expansion of 1/((1-t^5)^2*(1-t)*(1-t^3)*(1-t^7)*(1-t^9)).
  • A266746 (program): G.f.: 1/((1-t^6)*(1-t)*(1-t^3)*(1-t^5)*(1-t^7)*(1-t^9)*(1-t^11)).
  • A266747 (program): G.f.: 1/((1-t^7)^2*(1-t)*(1-t^3)*(1-t^5)*(1-t^9)*(1-t^11)*(1-t^13)).
  • A266748 (program): G.f.: 1/((1-t^8)*(1-t)*(1-t^3)*(1-t^5)*(1-t^7)*(1-t^9)*(1-t^11)*(1-t^13)*(1-t^15)).
  • A266749 (program): G.f.: 1/((1-t^9)^2*(1-t)*(1-t^3)*(1-t^5)*(1-t^7)*(1-t^11)*(1-t^13)*(1-t^15)*(1-t^17)).
  • A266750 (program): G.f.: 1/((1-t^10)*(1-t)*(1-t^3)*(1-t^5)*(1-t^7)*(1-t^9)*(1-t^11)*(1-t^13)*(1-t^15)*(1-t^17)*(1-t^19)).
  • A266752 (program): Binary representation of the n-th iteration of the “Rule 163” elementary cellular automaton starting with a single ON (black) cell.
  • 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)).
  • A266758 (program): E.g.f.: x*(1+x-(x^2-6*x+1)^(1/2))/8 + x^2/2.
  • A266768 (program): Molien series for invariants of finite Coxeter group D_5.
  • A266769 (program): Expansion of 1/((1-x)*(1-x^2)^2*(1-x^3)).
  • A266771 (program): Molien series for invariants of finite Coxeter group D_8 (bisected).
  • A266776 (program): Molien series for invariants of finite Coxeter group A_7.
  • A266777 (program): Molien series for invariants of finite Coxeter group A_8.
  • A266789 (program): Middle column of the “Rule 61” elementary cellular automaton starting with a single ON (black) cell.
  • A266790 (program): Binary representation of the middle column of the “Rule 61” elementary cellular automaton starting with a single ON (black) cell.
  • A266791 (program): Decimal representation of the middle column of the “Rule 61” elementary cellular automaton starting with a single ON (black) cell.
  • A266792 (program): Number of ON (black) cells in the n-th iteration of the “Rule 61” elementary cellular automaton starting with a single ON (black) cell.
  • A266793 (program): Total number of ON (black) cells after n iterations of the “Rule 61” elementary cellular automaton starting with a single ON (black) cell.
  • A266794 (program): Number of OFF (white) cells in the n-th iteration of the “Rule 61” elementary cellular automaton starting with a single ON (black) cell.
  • A266795 (program): Total number of OFF (white) cells after n iterations 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.
  • A266811 (program): Total number of ON (black) cells after n iterations of the “Rule 62” elementary cellular automaton starting with a single ON (black) cell.
  • A266813 (program): Total number of OFF (white) cells after n iterations of the “Rule 62” elementary cellular automaton starting with a single ON (black) cell.
  • A266814 (program): Decimal expansion of -sqrt(2)*arctan(sqrt(2)/5) + Pi*sqrt(2)/4.
  • A266836 (program): Odd Löschian numbers.
  • A266840 (program): Triangle read by rows giving successive states of cellular automaton generated by “Rule 69” initiated with a single ON (black) cell.
  • A266841 (program): Binary representation of the n-th iteration of the “Rule 69” elementary cellular automaton starting with a single ON (black) cell.
  • A266842 (program): Decimal representation of the n-th iteration of the “Rule 69” elementary cellular automaton starting 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.
  • A266844 (program): Binary representation of the n-th iteration of the “Rule 70” elementary cellular automaton starting with a single ON (black) cell.
  • A266846 (program): Decimal representation of the n-th iteration of the “Rule 70” elementary cellular automaton starting with a single ON (black) cell.
  • A266848 (program): Triangle read by rows giving successive states of cellular automaton generated by “Rule 71” initiated with a single ON (black) cell.
  • A266849 (program): Binary representation of the n-th iteration of the “Rule 71” elementary cellular automaton starting with a single ON (black) cell.
  • A266850 (program): Decimal representation of the n-th iteration of the “Rule 71” elementary cellular automaton starting with a single ON (black) cell.
  • A266872 (program): Binary representation of the n-th iteration of the “Rule 77” elementary cellular automaton starting 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.
  • A266875 (program): Number of partially ordered sets (“posets”) with n labeled elements, modulo n.
  • A266883 (program): Numbers of the form m*(4*m+1)+1, where m = 0,-1,1,-2,2,-3,3,…
  • A266910 (program): Number of size 2 subsets of S_n that generate a transitive subgroup of S_n.
  • A266911 (program): GCD of A002443(n) and A002444(n), numerator and denominator in Feinler’s formula for the Bernoulli number B_{2n}.
  • A266912 (program): Numbers n which are anagrams of n+18.
  • A266913 (program): Denominator of the volume of d dimensional symmetric convex cuboid with constraints |x1 + x2 + … xd| <= 1 and |x1|, |x2|, …, |xd| <= 1.
  • 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.
  • A266941 (program): Expansion of Product_{k>=1} 1 / (1 - k*x^k)^k.
  • A266943 (program): Expansion of Product_{k>=1} 1 / (1 - 2*x^k))^2.
  • A266945 (program): Expansion of Product_{k>=1} 1 / (1 - 2*x^k))^3.
  • 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.
  • A266964 (program): Expansion of Product_{k>=1} (1 - k*x^k)^k.
  • A266973 (program): a(n) = 4^n mod 17.
  • A266975 (program): Binary representation of the n-th iteration of the “Rule 78” elementary cellular automaton starting with a single ON (black) cell.
  • A266976 (program): Decimal representation of the n-th iteration of the “Rule 78” elementary cellular automaton starting with a single ON (black) cell.
  • 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.
  • A266979 (program): Binary representation of the n-th iteration of the “Rule 79” elementary cellular automaton starting with a single ON (black) cell.
  • A266980 (program): Decimal representation of the n-th iteration of the “Rule 79” elementary cellular automaton starting 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.
  • A266983 (program): Binary representation of the n-th iteration of the “Rule 81” elementary cellular automaton starting 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.
  • A267001 (program): Triangle read by rows giving successive states of cellular automaton generated by “Rule 83” initiated 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) = (32*n^3 - 2*n)/3.
  • A267034 (program): Triangle read by rows giving successive states of cellular automaton generated by “Rule 85” initiated with a single ON (black) cell.
  • A267035 (program): Binary representation of the n-th iteration of the “Rule 85” elementary cellular automaton starting 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.
  • A267040 (program): Decimal expansion of sqrt(8)*arctan(sqrt(2)/5).
  • A267043 (program): Middle column of the “Rule 91” elementary cellular automaton starting with a single ON (black) cell.
  • A267044 (program): Binary representation of the 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.
  • A267046 (program): Number of ON (black) cells in the n-th iteration 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.
  • A267050 (program): Triangle read by rows giving successive states of cellular automaton generated by “Rule 92” initiated 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.
  • A267054 (program): Binary representation of the n-th iteration of the “Rule 93” elementary cellular automaton starting with a single ON (black) cell.
  • A267055 (program): Decimal representation of the n-th iteration of the “Rule 93” elementary cellular automaton starting with a single ON (black) cell.
  • A267067 (program): Primes p such that mu(p-2) = 1; that is, p-2 is squarefree and has an even number of prime factors, where mu is the Moebius function (A008683).
  • A267068 (program): a(n) = (n+1) / A189733(n).
  • A267084 (program): a(n) = ceiling(A007504(n)/n) - floor(A007504(n)/n); a(n) is 0 if n divides the sum of first n primes, 1 otherwise.
  • A267089 (program): T(n,k) is decimal conversion of 1’s in an n X n table that lie on its principal diagonals.
  • A267090 (program): Triangle read by rows: Fill an n X n square with 1’s, except for 0’s on the two main diagonals. Then T(n,k) is decimal equivalent of the k-th row (0<=k<=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.
  • A267114 (program): Numbers n for which A001222(n) = A267115(n) + A267116(n).
  • A267133 (program): a(n) = (1/n)(2/n)(3/n)…((n-1)/n) where (k/n) is the Kronecker symbol, n >= 1.
  • A267134 (program): a(n) = n minus the number of primes of form 6m + 1 that are less than n-th prime of form 6m - 1.
  • A267135 (program): a(n) = n minus the number of primes of form 4m + 1 that are less than n-th prime of form 4m + 3.
  • A267137 (program): Numbers of the form x^2 + x + x*y + y + y^2 where x and y are integers.
  • 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.
  • A267145 (program): Triangle read by rows giving successive states of cellular automaton generated by “Rule 105” initiated with a single ON (black) cell.
  • A267146 (program): Binary representation of the n-th iteration of the “Rule 105” elementary cellular automaton starting with a single ON (black) cell.
  • A267147 (program): Decimal representation of the n-th iteration of the “Rule 105” elementary cellular automaton starting with a single ON (black) cell.
  • A267148 (program): Number of ON (black) cells in the n-th iteration of the “Rule 105” elementary cellular automaton starting with a single ON (black) cell.
  • A267149 (program): Total number of ON (black) cells after n iterations of the “Rule 105” elementary cellular automaton starting with a single ON (black) cell.
  • A267150 (program): Number of OFF (white) cells in the n-th iteration of the “Rule 105” elementary cellular automaton starting with a single ON (black) cell.
  • A267151 (program): Total number of OFF (white) cells after n iterations of the “Rule 105” elementary cellular automaton starting with a single ON (black) cell.
  • A267155 (program): Middle column of the “Rule 107” elementary cellular automaton starting with a single ON (black) cell.
  • A267156 (program): Binary representation of the middle column of the “Rule 107” elementary cellular automaton starting with a single ON (black) cell.
  • A267157 (program): Decimal representation of the 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.
  • A267183 (program): Row 3 of the square array in A267181.
  • A267184 (program): Row 4 of the square array in A267181.
  • A267185 (program): Column 2 of the square array in A267181.
  • A267196 (program): Labeled graded semiorders.
  • A267208 (program): Middle column of the “Rule 109” elementary cellular automaton starting with a single ON (black) cell.
  • A267209 (program): Binary representation of the 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.
  • A267220 (program): Expansion of exp( Sum_{n >= 1} A005259(n)*x^n/n ).
  • A267226 (program): Number of length-n 0..2 arrays with no following elements greater than or equal to the first repeated value.
  • A267227 (program): Number of length-n 0..3 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.
  • A267240 (program): Number of n X 3 binary arrays with row sums nondecreasing and columns lexicographically nondecreasing.
  • A267246 (program): Binary representation of the n-th iteration of the “Rule 165” elementary cellular automaton starting with a single ON (black) cell.
  • A267247 (program): Decimal representation of the n-th iteration of the “Rule 165” elementary cellular automaton starting with a single ON (black) cell.
  • A267256 (program): Middle column of the “Rule 111” elementary cellular automaton starting with a single ON (black) cell.
  • A267257 (program): Binary representation of the middle column of the “Rule 111” elementary cellular automaton starting with a single ON (black) cell.
  • A267258 (program): Decimal representation of the middle column of the “Rule 111” elementary cellular automaton starting with a single ON (black) cell.
  • A267259 (program): Number of ON (black) cells in the n-th iteration of the “Rule 111” elementary cellular automaton starting with a single ON (black) cell.
  • A267260 (program): Total number of ON (black) cells after n iterations of the “Rule 111” elementary cellular automaton starting with a single ON (black) cell.
  • A267261 (program): Number of OFF (white) cells in the n-th iteration of the “Rule 111” elementary cellular automaton starting with a single ON (black) cell.
  • A267262 (program): Total number of OFF (white) cells after n iterations 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.
  • A267269 (program): Triangle read by rows giving successive states of cellular automaton generated by “Rule 115” initiated with a single ON (black) cell.
  • A267272 (program): Triangle read by rows giving successive states of cellular automaton generated by “Rule 117” initiated with a single ON (black) cell.
  • A267273 (program): Binary representation of the n-th iteration of the “Rule 117” elementary cellular automaton starting with a single ON (black) cell.
  • A267274 (program): Decimal representation of the n-th iteration of the “Rule 117” elementary cellular automaton starting with a single ON (black) cell.
  • A267290 (program): Primes of the form 11*k^2-11*k+7.
  • A267295 (program): Circulant Ramsey numbers RC_2(3,n) of the second kind.
  • A267296 (program): Circulant Ramsey numbers RC_1(3,n) of the first kind.
  • A267297 (program): Square triangular numbers that are the sum of 2 nonzero nonconsecutive triangular numbers.
  • A267309 (program): Number of discrete vectors with integral components and integral length <= n in a 3-dimensional vectorspace (Partial sums of A267651).
  • A267313 (program): Expansion of x*(-1 + 2*x + 3*x^2 - 2*x^3 + x^4)/((1 - x)^3*(1 + x + x^2)^2).
  • A267314 (program): Expansion of 2*x*(1 + 2*x - x^2)/((1 - x)*(1 + x^2)^2).
  • A267315 (program): Decimal expansion of the Dirichlet eta function at 4.
  • 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.
  • A267322 (program): Expansion of (1 + x + x^2 + x^4 + 2*x^5)/(1 - x^3)^3.
  • A267326 (program): Number of ways writing n^2 as a sum of four squares: a(n) = A000118(n^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.
  • A267348 (program): Decimal equivalents of terms of A266926 interpreted as binary numbers.
  • A267349 (program): Triangle read by rows giving successive states of cellular automaton generated by “Rule 123” initiated with a single ON (black) cell.
  • A267350 (program): Binary representation of the n-th iteration of the “Rule 123” elementary cellular automaton starting with a single ON (black) cell.
  • A267351 (program): Decimal representation of the n-th iteration of the “Rule 123” elementary cellular automaton starting with a single ON (black) cell.
  • 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.
  • A267356 (program): Binary representation of the n-th iteration of the “Rule 124” elementary cellular automaton starting with a single ON (black) cell.
  • A267357 (program): Decimal representation of the n-th iteration of the “Rule 124” elementary cellular automaton starting with a single ON (black) cell.
  • A267364 (program): Binary representation of the n-th iteration of the “Rule 126” elementary cellular automaton starting with a single ON (black) cell.
  • A267365 (program): Decimal representation of the n-th iteration of the “Rule 126” elementary cellular automaton starting with a single ON (black) cell.
  • A267366 (program): Binary representation of the middle column of the “Rule 126” elementary cellular automaton starting with a single ON (black) cell.
  • A267367 (program): Decimal representation of the middle column of the “Rule 126” 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.
  • A267379 (program): Positions of 1’s in A094186
  • A267380 (program): First differences of A267379
  • A267414 (program): Integers n such that n! = x^3 + y^3 + z^3 where x, y and z are nonnegative integers, is soluble.
  • A267417 (program): Triangle read by rows giving successive states of cellular automaton generated by “Rule 129” initiated with a single ON (black) cell.
  • A267423 (program): Triangle read by rows giving successive states of cellular automaton generated by “Rule 133” initiated with a single ON (black) cell.
  • A267424 (program): Fibonacci numbers that are not of the form x^2 + y^2 + z^2 where x, y and z are integers.
  • A267430 (program): Squares whose digit sum is not a prime.
  • A267437 (program): A linear recurrence related to the elliptic curves y^2 = x^3 -35*a^2*x - 98*a^3 with a = -1, -5, -6, -17, or -111.
  • A267442 (program): Middle column of the “Rule 129” elementary cellular automaton starting with a single ON (black) cell.
  • A267443 (program): Binary representation of the middle column of the “Rule 129” elementary cellular automaton starting with a single ON (black) cell.
  • A267444 (program): Decimal representation of the 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.
  • A267451 (program): Number of ON (black) cells in the n-th iteration of the “Rule 131” elementary cellular automaton starting with a single ON (black) cell.
  • A267452 (program): Total number of ON (black) cells after n iterations of the “Rule 131” elementary cellular automaton starting with a single ON (black) cell.
  • A267453 (program): Number of OFF (white) cells in the n-th iteration of the “Rule 131” elementary cellular automaton starting with a single ON (black) cell.
  • A267454 (program): Total number of OFF (white) cells after n iterations of the “Rule 131” elementary cellular automaton starting with a single ON (black) cell.
  • A267456 (program): Binary representation of the n-th iteration of the “Rule 133” elementary cellular automaton starting with a single ON (black) cell.
  • A267457 (program): Decimal representation of the n-th iteration of the “Rule 133” 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.
  • A267465 (program): Number of length-n 0..2 arrays with no following elements larger than the first repeated value.
  • A267466 (program): Number of length-n 0..3 arrays with no following elements larger than the first repeated value.
  • A267472 (program): Number of length-4 0..n arrays with no following elements larger than the first repeated value.
  • A267481 (program): Primes which are squares (mod 31).
  • A267482 (program): Triangle of coefficients of Gaussian polynomials [2n+1,1]_q represented as finite sum of terms (1+q^2)^k*q^(g-k), where k = 0,1,…,g with g=n.
  • A267483 (program): Triangle of coefficients of Gaussian polynomials [2n+3,2]_q represented as finite sum of terms (1+q^2)^k*q^(g-k), where k = 0,1,…,g with g=2n+1.
  • A267488 (program): Smallest b > 1 such that there exists an odd prime p with p < b such that b^(p-1) == 1 (mod p^n).
  • A267489 (program): a(n) = n^2 - 4*floor(n^2/6).
  • A267499 (program): Number of fixed points of autobiographical numbers (A267491 … A267498) in base n.
  • A267513 (program): Middle column of the “Rule 137” elementary cellular automaton starting with a single ON (black) cell.
  • A267514 (program): Binary representation of the middle column of the “Rule 137” elementary cellular automaton starting with a single ON (black) cell.
  • A267515 (program): Decimal representation of the middle column of the “Rule 137” elementary cellular automaton starting with a single ON (black) cell.
  • A267516 (program): Number of ON (black) cells in the n-th iteration of the “Rule 137” elementary cellular automaton starting with a single ON (black) cell.
  • A267517 (program): Total number of ON (black) cells after n iterations of the “Rule 137” elementary cellular automaton starting with a single ON (black) cell.
  • A267518 (program): Number of OFF (white) cells in the n-th iteration of the “Rule 137” elementary cellular automaton starting with a single ON (black) cell.
  • A267519 (program): Total number of OFF (white) cells after n iterations of the “Rule 137” elementary cellular automaton starting with a single ON (black) cell.
  • 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)*(4*n + 3)/3.
  • A267523 (program): Binary representation of the n-th iteration of the “Rule 139” elementary cellular automaton starting with a single ON (black) cell.
  • A267524 (program): Binary representation of the middle column of the “Rule 139” elementary cellular automaton starting with a single ON (black) cell.
  • A267526 (program): Binary representation of the n-th iteration of the “Rule 141” elementary cellular automaton starting with a single ON (black) cell.
  • A267527 (program): Decimal representation of the n-th iteration of the “Rule 141” elementary cellular automaton starting with a single ON (black) cell.
  • 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.
  • A267535 (program): Binary representation of the n-th iteration of the “Rule 143” elementary cellular automaton starting 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.
  • A267538 (program): Binary representation of the 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.
  • A267540 (program): Primes p such that p (mod 3) = p (mod 5).
  • A267541 (program): Expansion of (2 + 4*x + x^2 + x^3 + 2*x^4 + x^5)/(1 - x - x^5 + x^6).
  • A267550 (program): Primes p such that p (mod 3) = p (mod 5) = p (mod 7).
  • 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.
  • A267577 (program): Binary representation of the n-th iteration of the “Rule 167” elementary cellular automaton starting with a single ON (black) cell.
  • A267578 (program): Decimal representation of the n-th iteration of the “Rule 167” elementary cellular automaton starting with a single ON (black) cell.
  • A267579 (program): Middle column of the “Rule 167” elementary cellular automaton starting with a single ON (black) cell.
  • A267580 (program): Binary representation of the middle column of the “Rule 167” elementary cellular automaton starting with a single ON (black) cell.
  • A267581 (program): Decimal representation of the 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.
  • A267588 (program): Binary representation of the 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.
  • 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.
  • A267606 (program): Binary representation of the n-th iteration of the “Rule 181” elementary cellular automaton starting with a single ON (black) cell.
  • A267607 (program): Decimal representation of the n-th iteration of the “Rule 181” elementary cellular automaton starting with a single ON (black) cell.
  • A267608 (program): Binary representation of the n-th iteration of the “Rule 182” elementary cellular automaton starting with a single ON (black) cell.
  • A267609 (program): Decimal representation of the n-th iteration of the “Rule 182” elementary cellular automaton starting 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.
  • A267625 (program): Number of nX2 arrays containing 2 copies of 0..n-1 with every element equal to or 1 greater than any west neighbor modulo n and the upper left element equal to 0.
  • 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.
  • A267651 (program): Number of ways to write n^2 as a sum of three squares: a(n) = A005875(n^2).
  • A267652 (program): a(n) = 4*a(n - 1) + 4*a(n - 2) for n>1, a(0)=2, a(1)=3.
  • A267654 (program): Irregular triangle of palindromic subsequences. Every row has 2*n+1 terms. From the second row, there are only two alternated numbers: 2*n+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.
  • A267674 (program): Binary representation of the n-th iteration of the “Rule 195” elementary cellular automaton starting with a single ON (black) cell.
  • A267675 (program): Decimal representation of the n-th iteration of the “Rule 195” elementary cellular automaton starting with a single ON (black) cell.
  • A267676 (program): Triangle read by rows giving successive states of cellular automaton generated by “Rule 197” initiated with a single ON (black) cell.
  • A267679 (program): Triangle read by rows giving successive states of cellular automaton generated by “Rule 201” initiated with a single ON (black) cell.
  • A267680 (program): Binary representation of the n-th iteration of the “Rule 201” elementary cellular automaton starting with a single ON (black) cell.
  • A267681 (program): Decimal representation of the n-th iteration of the “Rule 201” elementary cellular automaton starting with a single ON (black) cell.
  • A267682 (program): a(n) = 2*a(n-1) - 2*a(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.
  • A267684 (program): Binary representation of the n-th iteration of the “Rule 203” elementary cellular automaton starting 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.
  • A267688 (program): Binary representation of the n-th iteration of the “Rule 199” elementary cellular automaton starting with a single ON (black) cell.
  • A267689 (program): Decimal representation of the n-th iteration of the “Rule 199” elementary cellular automaton starting with a single ON (black) cell.
  • A267691 (program): a(n) = (n + 1)*(6*n^4 - 21*n^3 + 31*n^2 - 31*n + 30)/30.
  • A267694 (program): Q-toothpick sequence in the first quadrant starting with two Q-toothpicks centered at (1,1). The endpoints of the left hand Q-toothpick are at (0,1) and (1,2). The endpoints of the right hand Q-toothpick are at (1,0) and (2,1). With a(0) = 0.
  • A267695 (program): First differences of A267694.
  • 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.
  • A267722 (program): Number of nX5 arrays of permutations of 5 copies of 0..n-1 with every element equal to at least one horizontal neighbor and the top left element equal to 0.
  • 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.
  • A267737 (program): Number of nX3 arrays containing 3 copies of 0..n-1 with every element equal to or 1 greater than any west or northeast neighbors modulo n and the upper left element equal to 0.
  • A267747 (program): Numbers k such that k mod 2 = k mod 3 = k mod 5.
  • A267755 (program): Expansion of (1 + 2*x + x^2 + x^3 + 4*x^4 + 2*x^5)/(1 - x - x^5 + x^6).
  • A267756 (program): Indices of Euclid numbers (A006862) of the form x^2 + y^2 + z^2 where x, y and z are integers.
  • 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.
  • A267779 (program): Binary representation of the n-th iteration of the “Rule 211” elementary cellular automaton starting 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.
  • A267801 (program): Binary representation of the n-th iteration of the “Rule 213” elementary cellular automaton starting 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.
  • A267804 (program): Binary representation of the n-th iteration of the “Rule 214” elementary cellular automaton starting with a single ON (black) cell.
  • A267805 (program): Decimal representation of the n-th iteration of the “Rule 214” 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.
  • A267817 (program): Numbers n with property that n is divisible by A268336(n).
  • A267825 (program): Index of largest primorial factor of binomial(2n,n).
  • A267831 (program): Expansion of (1 + 5*x - 7*x^2 - 3*x^3)/((1 - x)*(1 + x^2)^2).
  • A267832 (program): Number of nX2 arrays containing 2 copies of 0..n-1 with every element equal to or 1 greater than any northeast neighbor modulo n and the upper left element equal to 0.
  • A267844 (program): a(n) = Catalan(n)^2*(4n + 3).
  • A267845 (program): Triangle read by rows giving successive states of cellular automaton generated by “Rule 227” initiated with a single ON (black) cell.
  • A267846 (program): Binary representation of the n-th iteration of the “Rule 227” elementary cellular automaton starting 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.
  • A267849 (program): Triangular array: T(n,k) is the 2-row creation rook number to place k rooks on a 3 x n board.
  • 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.
  • A267854 (program): Binary representation of the n-th iteration of the “Rule 230” elementary cellular automaton starting with a single ON (black) cell.
  • A267855 (program): Decimal representation of the n-th iteration of the “Rule 230” 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).
  • A267863 (program): Numerators of the rational number triangle R(m, a) = (m - 2*a)/(2*m), m >= 1, a = 1, …, m. This is a regularized Sum_{j >= 0} (a + m*j)^(-s) for s = 0 defined by analytic continuation of a generalized Hurwitz Zeta function.
  • A267864 (program): Denominator triangle for A267863: T(m, a) = denominator((m - 2*a)/(2*m)), m >= 1, a = 1, …, m.
  • 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.
  • A267879 (program): Binary representation of the 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.
  • A267885 (program): Binary representation of the n-th iteration of the “Rule 235” 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.
  • A267887 (program): Binary representation of the n-th iteration of the “Rule 237” 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.
  • A267889 (program): Binary representation of the n-th iteration of the “Rule 239” 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.
  • A267891 (program): Numbers with 8 odd divisors.
  • A267892 (program): Numbers with 9 odd divisors.
  • A267893 (program): Numbers with 10 odd divisors.
  • A267894 (program): Numbers whose number of odd divisors is nonprime.
  • A267895 (program): Numbers whose number of odd divisors is prime.
  • 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).
  • A267899 (program): Number of nX3 arrays containing 3 copies of 0..n-1 with every element equal to at least one horizontal or vertical neighbor and the top left element equal to 0.
  • 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.
  • A267912 (program): Number of 1 X n 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.
  • A267913 (program): Number of 2 X n 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.
  • A267914 (program): Number of 3Xn 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.
  • A267923 (program): Binary representation of the n-th iteration of the “Rule 245” elementary cellular automaton starting 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.
  • A267934 (program): Binary representation of the n-th iteration of the “Rule 249” elementary cellular automaton starting 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.
  • A267944 (program): Primes that are a prime power minus two.
  • A267945 (program): Primes that are a prime power plus two.
  • A267946 (program): Number of n X 1 0..2 arrays with every repeated value in every row and column one larger mod 3 than the previous repeated value, and upper left element zero.
  • A267947 (program): Number of n X 2 0..2 arrays with every repeated value in every row and column one larger mod 3 than the previous repeated value, and upper left element zero.
  • A267958 (program): 4 times A042965.
  • A267968 (program): a(n) = Product_{k = 1..n} k^(k + 1).
  • A267980 (program): a(n) = Catalan(n)^2*(4n + 1).
  • A267981 (program): a(n) = Catalan(n)^2*(4n + 2).
  • A267982 (program): a(n) = 4*n*Catalan(n)^2.
  • A267983 (program): Integers n such that n^3 = (x^2 + y^2 + z^2) / 3 where x > y > z > 0, is soluble.
  • 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).
  • A267991 (program): Number of 2Xn arrays containing n copies of 0..2-1 with row sums and column sums nondecreasing.
  • A267999 (program): Numbers n > 1 such that gcd(n, 2^n - 2) = 1.
  • A268013 (program): Number of n X 1 0..2 arrays with every repeated value in every row and column greater than or equal to the previous repeated value.
  • A268014 (program): Number of n X 2 0..2 arrays with every repeated value in every row and column greater than or equal to the previous repeated value.
  • A268015 (program): Number of nX3 0..2 arrays with every repeated value in every row and column greater than or equal to the previous repeated value.
  • A268021 (program): a(1) = a(2) = 1; if n > 2 then a(n) = a(n-1)*a(n-2) - a(n-2) - a(n-1).
  • A268032 (program): Run lengths in the parity of A233312.
  • A268034 (program): A268032 with repeated 1’s removed.
  • A268038 (program): List of y-coordinates of point moving in clockwise square spiral.
  • A268040 (program): Array y AND NOT x, read by antidiagonals.
  • A268044 (program): The odd numbers congruent to {3, 4} mod 5.
  • A268063 (program): Primes of the form (k^3 - k^2 - k - 1)/2 for some integer k > 0.
  • A268066 (program): Even numbers coprime to the number of their divisors.
  • A268082 (program): Numbers n such that gcd(binomial(2*n-1,n), n) is equal to 1.
  • A268085 (program): a(n) = Catalan(n)^2*n.
  • A268087 (program): a(n) = A162909(n) + A162910(n).
  • A268088 (program): Number of nX3 0..2 arrays with every repeated value in every row not one larger and in every column one larger mod 3 than the previous repeated value, and upper left element zero.
  • A268093 (program): Number of 1 X n 0..2 arrays with every repeated value in every row not one larger and in every column one larger mod 3 than the previous repeated value, and upper left element zero.
  • A268094 (program): Number of 2 X n 0..2 arrays with every repeated value in every row not one larger and in every column one larger mod 3 than the previous repeated value, and upper left element zero.
  • A268099 (program): a(n) = 2^(n mod 2)*5*10^floor(n/2) - 1.
  • A268100 (program): a(n) = 2^((n-1) mod 2)*5*10^floor((n-1)/2).
  • A268145 (program): Twin prime pairs concatenated to their average in decimal representation (with the lesser twin prepended and the greater twin appended).
  • A268146 (program): Twin prime pairs concatenated to their average in decimal representation (the greater twin prepended, the lesser appended).
  • 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.
  • A268164 (program): Number of n X 1 0..3 arrays with every repeated value in every row and column one larger mod 4 than the previous repeated value, and upper left element zero.
  • A268165 (program): Number of n X 2 0..3 arrays with every repeated value in every row and column one larger mod 4 than the previous repeated value, and upper left element zero.
  • A268173 (program): a(n) = Sum_{k=0..n} (-1)^k*floor(sqrt(k)).
  • A268174 (program): Integers m such that m^(m+1) == 1 (modulo (m+2)).
  • A268185 (program): a(n) = prime(n) + last digit of prime(n).
  • A268196 (program): a(n) = Product_{k=0..n} binomial(3*k,k).
  • A268201 (program): a(n) = 4*n^3 - 6*n^2 + 3*n - 1.
  • A268208 (program): Number of paths from (0,0) to (n,n) using only steps North, Northeast and East (i.e., steps E(1,0), D(1,1), and N(0,1)) that do not cross y=x “vertically”.
  • 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).
  • A268221 (program): Triangle read by rows: T(n,k) (n>=4, k=3..n+1) is the number of topologies t on n points having exactly k open sets such that t contains exactly one open set of size m for each m in {0,3,4,5,…,s,n} where s is the size of the largest proper open set in t.
  • A268223 (program): Triangle read by rows: T(n,k) (n>=6, k=3..n+1) is the number of topologies t on n points having exactly k open sets such that t contains exactly one open set of size m for each m in {0,5,6,7,…,s,n} where s is the size of the largest proper open set in t.
  • 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.
  • A268229 (program): Rotate the Sierpinski triangle A047999 counterclockwise by 45 degrees to get a square array; a(n) = period of row n.
  • A268230 (program): Decimal equivalents of A268229.
  • A268231 (program): Indices of 1’s in A047999.
  • A268232 (program): Indices of 0’s in A047999.
  • 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).
  • A268255 (program): Number of length-(n+1) 0..2 arrays with new repeated values introduced in sequential order starting with zero.
  • 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).
  • A268286 (program): a(n) = Bell(prime(n)).
  • 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.
  • A268316 (program): a(n) is the number of Dyck paths of length 4n and height n.
  • A268317 (program): Irregular triangle read by rows: T(n,k) gives the columns sum in the table Fib(n+1) X Fib(n), where k = 1..Fib(n), and 1’s are assigned to cells on the longest diagonal path.
  • A268318 (program): Irregular triangle read by rows: T(n,k) gives the row sums in the table Fib(n+1) X Fib(n), where k = 1..Fib(n+1), and 1’s are assigned to cells on the longest diagonal path.
  • A268319 (program): Numbers that are the mean of two distinct positive cubes.
  • A268328 (program): Integers of the form (prime(m) + prime(m+1)/10 for some m.
  • A268329 (program): Expansion of (1 - sqrt(1 - 4*x))^5/16.
  • A268335 (program): Exponentially odd numbers.
  • A268336 (program): a(n) = A174824(n)/n, where A174824(n) = lcm(A002322(n), n) and A002322(n) is the Carmichael lambda function (also known as the reduced totient function or the universal exponent of n).
  • A268340 (program): Characteristic function of the prime powers p^k, k >= 2.
  • A268342 (program): Number of edges in the unitary addition Cayley graph Gn.
  • A268344 (program): a(n) = 11*a(n - 1) - 3*a(n - 2) for n>1, a(0)=0, a(1)=1.
  • A268345 (program): Number of partitions of (2, n) into a sum of distinct pairs.
  • A268349 (program): Expansion of (1 + x - x^2 - 6*x^3)/(1 - x - 2*x^2 - 3*x^3 - 4*x^4).
  • A268351 (program): a(n) = 3*n*(9*n - 1)/2.
  • A268353 (program): a(n) is the exponent of 2 corresponding to the n-th Proth prime.
  • A268354 (program): Highest power of 7 dividing n.
  • A268355 (program): Highest power of 8 dividing n.
  • A268357 (program): Highest power of 11 dividing n.
  • A268358 (program): Number of n-digit numbers in base ten having at least five different digits with no leading zeros allowed.
  • 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.
  • A268370 (program): Number of North-East lattice paths from (0,0) to (n,n) that have exactly three east steps below the subdiagonal y = x-1.
  • A268375 (program): Numbers k for which A001222(k) = A267116(k).
  • A268376 (program): Numbers n for which A001222(n) > A267116(n).
  • A268377 (program): Numbers n such that any prime factor of the form 4k+1 has even multiplicity.
  • A268379 (program): Numbers having more prime factors of the form 4*k+1 than of the form 4*k+3, when counted with multiplicity.
  • A268380 (program): Numbers having fewer prime factors of the form 4*k+1 than of the form 4*k+3, when counted with multiplicity.
  • A268381 (program): Numbers having at least the same number of prime factors of the form 4*k+1 than of the form 4*k+3, when counted with multiplicity.
  • 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.
  • A268388 (program): “Fermi-Dirac composites”: numbers k for which A064547(k) > 1.
  • A268389 (program): a(n) = greatest k such that polynomial (X+1)^k divides the polynomial (in polynomial ring GF(2)[X]) that is encoded in the binary expansion of n. (See the comments for details).
  • A268390 (program): Positions of zeros in A268387: numbers n such that when the exponents e_1 .. e_k in their prime factorization n = p_1^e_1 * … * p_k^e_k are bitwise-xored together, the result is zero.
  • A268391 (program): Numbers of the form p^A001317(k) where p is prime and k >= 0.
  • A268395 (program): Partial sums of A268389.
  • A268398 (program): Partial sums of A085731.
  • A268399 (program): Number of North-East lattice paths from (0,0) to (n,n) that have exactly four east steps below the subdiagonal y = x-1.
  • A268407 (program): Number of North-East lattice paths that do not bounce off the diagonal y = x to the right.
  • A268409 (program): a(n) = 4*a(n - 1) + 2*a(n - 2) for n>1, a(0)=3, a(1)=5.
  • A268410 (program): a(n) = a(n - 1) + a(n - 2) + a(n - 3) for n>2, a(0)=5, a(1)=7, a(2)=9.
  • A268411 (program): Parity of number of runs of 1’s in binary representation of n.
  • A268412 (program): Balanced evil numbers: numbers with an even number of runs of 1’s in their binary expansion.
  • A268413 (program): a(n) = Sum_{k = 0..n} (-1)^k*14^k.
  • A268414 (program): a(n) = 5*a(n - 1) - 2*n for n>0, a(0) = 1.
  • A268415 (program): Balanced odious numbers: numbers with an odd number of runs of 1’s in their binary expansion.
  • A268428 (program): a(n) = (3*(n^2+n+99)+cos(Pi*n/2)-sin(Pi*n/2))/2.
  • A268430 (program): Number of North-East paths from (0,0) to (n,n) that have even number of times bounce off y = x to the right.
  • A268431 (program): Number of North-East paths from (0,0) to (n,n) that have odd number of times bounce off y = x to the right.
  • A268433 (program): a(n) = A106184(n) / A001316(n).
  • A268444 (program): a(n) = Product_{i=0..k}(n_i+1) where n = Sum_{i=0..k}n_i*4^i is the base-4 representation of n.
  • A268446 (program): Number of North-East lattice paths from (0,0) to (n,n) that cross the diagonal y = x horizontally exactly three times.
  • A268447 (program): Number of North-East lattice paths from (0,0) to (n,n) that cross the diagonal y = x horizontally exactly four times.
  • 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 - 12*x + 8*x^2))/(1 - 2*x)^4.
  • A268466 (program): Smallest m > 1 such that m^m == 1 (mod n).
  • A268479 (program): For p = prime(n), number of primes (including p) in the trajectory of p under the procedure in A244550, also allowing the Wieferich prime 2, that are not terms of a repeating cycle.
  • A268484 (program): a(n) = (n + 1)*(4*n^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.
  • A268492 (program): Orbit of 2 under the map A268488: n -> least number k of the form k = n*(last digit of k) + (k without its last digit).
  • A268493 (program): Orbit of 3 under the map A268488: n -> least number k of the form k = n*(last digit of k) + (k without its last digit).
  • A268508 (program): Decimal expansion of Pi*sqrt(3)/8.
  • A268514 (program): a(0)=0; thereafter a(2n+1)=3*a(n)+1, a(2n)=2*a(n)+a(n-1)+1.
  • A268519 (program): Odd powers of 2 written between a pair of 1’s.
  • A268524 (program): a(n) = r*a(ceiling(n/2))+s*a(floor(n/2)) with a(1)=1 and (r,s)=(3,1).
  • A268525 (program): a(n) = r*a(ceiling(n/2))+s*a(floor(n/2)) with a(1)=1 and (r,s)=(2,3).
  • A268526 (program): a(n) = r*a(ceiling(n/2))+s*a(floor(n/2)) with a(1)=1 and (r,s)=(3,2).
  • A268527 (program): a(n) = r*a(ceiling(n/2))+s*a(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.
  • A268543 (program): The diagonal of 1/(1 - (y + z + x z + x w + x y w)).
  • A268545 (program): From the diagonal of 1/(1 - (y + z + x w + x z w + x y w)).
  • A268549 (program): Diagonal of (1 - 9 x y)/((1 - 3 y - 2 x + 3 y^2 + 9 x^2 y) * (1 - u - z) * (1 - v - w)).
  • A268552 (program): Diagonal of the rational function 1/((1 - u v - u w - v w - u v w) * (1 - x y - x z - y z)).
  • A268553 (program): Diagonal of the rational function 1/((1 - u v - u w - v w) * (1 - x y - x z - y z)).
  • A268554 (program): Diagonal of the rational function 1/((1 - w - u v) * (1 - x y - x z - y z)).
  • A268555 (program): Diagonal of the rational function of six variables 1/((1 - w - u v - u v w) * (1 - z - x y)).
  • A268577 (program): Numbers m such that 3*m^2-5 is a prime.
  • A268579 (program): Expansion of (1 + 6*x + x^2 + 12*x^3 - 2*x^4)/((1 - x)^4*(1 + x)^3).
  • A268581 (program): a(n) = 2*n^2 + 8*n + 5.
  • A268586 (program): Expansion of (x^3*(3*x - 2))/(2*x - 1)^3.
  • A268587 (program): Expansion of x^4*(5 - 16*x + 13*x^2)/(1 - 2*x)^4.
  • A268598 (program): Expansion of x^5*(4 - 5*x)/(1 - 2*x)^4.
  • A268600 (program): Expansion of 1/(2*f(x)) + 1/(4 - 2*g(x)), where f(x) = sqrt(1 - 4*x) and g(x) = sqrt(1 + 4*x).
  • A268601 (program): Expansion of 1/(2*f(x)) - 1/(4 - 2*g(x)), where f(x) = sqrt(1 - 4*x) and g(x) = sqrt(1 + 4*x).
  • A268604 (program): Decimal expansion of 6/sqrt(sqrt(3)).
  • 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.
  • A268620 (program): Numbers whose digital sum is a multiple of 4.
  • 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) = 4*n^3 - 3*n^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).
  • A268670 (program): a(n) = A006068(A268669(n)).
  • A268671 (program): a(n) = (A268670(n)+1) / 2.
  • A268676 (program): a(n) = A101080(n,A268823(3+n)), where A101080(x,y) gives the Hamming distance between binary expansions of x and y.
  • A268677 (program): Complement of A268678; numbers that do not occur in A268395.
  • A268678 (program): Distinct values in A268395; partial sums of A268679.
  • A268679 (program): a(n) = A268389(A001969(1+n)); A268389 without its zero terms.
  • A268680 (program): Least monotonic left inverse of A268678.
  • 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)*(3*n + 1)*(3*n + 4)/4.
  • A268708 (program): Number of iterations of A268395 needed to reach zero: a(0) = 0, for n >= 1, a(n) = 1 + a(A268395(n)).
  • 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))).
  • A268730 (program): a(n) = Product_{k = 0..n} 2*(8*k + 5).
  • A268732 (program): Sum of the numbers of divisors of gcd(x,y) with x*y <= n.
  • A268733 (program): a(n) = A000203(A251720(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.
  • A268752 (program): Cubefree numbers n such that n^2 + 1 is prime.
  • A268753 (program): Primes congruent to 1 mod 13.
  • A268759 (program): Triangle T(n,k) read by rows: T(n,k) = (1/4)*(1 + k)*(2 + k)*(k - n)*(1 + k - n).
  • 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.
  • A268783 (program): Number of n X 2 binary arrays with some element plus some horizontally, vertically or antidiagonally adjacent neighbor totalling two exactly once.
  • A268810 (program): a(n) = 2*floor(3*n*(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)).
  • A268822 (program): Permutation of nonnegative integers: a(0) = 0, a(n) = A268718(1+A268718(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.
  • A268858 (program): Prime numbers ending in 39.
  • A268859 (program): Prime numbers ending in 21.
  • A268860 (program): Prime numbers ending in 27.
  • A268861 (program): Cubefree numbers n such that n + 1 is a perfect cube.
  • A268866 (program): Records in A268865.
  • A268868 (program): a(n) is the sum of the prime factors (with repetition) of the sum of the preceding terms; a(1)=a(2)=1.
  • A268878 (program): Breadth-first traversal of a binary tree in which the value at the n-th node is equal to ParentNode()*prime(n-1).
  • A268887 (program): Number of 2 X n binary arrays with some element plus some horizontally or antidiagonally adjacent neighbor totalling two exactly once.
  • 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.
  • A268901 (program): Number of n X 5 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.
  • A268922 (program): One of the two successive approximations up to 5^n for the 5-adic integer sqrt(-4). These are the 1 mod 5 numbers, except for n = 0.
  • A268924 (program): One of the two successive approximations up to 3^n for the 3-adic integer sqrt(-2). These are the numbers congruent to 1 mod 3 (except for n = 0).
  • A268933 (program): Permutation of nonnegative integers: a(0) = 0, for n >= 1, a(n) = A268717(1 + A268831(n-1)).
  • A268935 (program): a(1)=2, a(2)=3. For n>2 a(n) is the sum of the prime factors (with repetition) of a(n-1) + a(n-2).
  • A268938 (program): Number of length-n 0..2 arrays with no repeated value unequal to the previous repeated value plus one mod 2+1.
  • A268939 (program): Number of length-n 0..3 arrays with no repeated value unequal to the previous repeated value plus one mod 3+1.
  • A268940 (program): Number of length-n 0..4 arrays with no repeated value unequal to the previous repeated value plus one mod 4+1.
  • A268941 (program): Number of length-n 0..5 arrays with no repeated value unequal to the previous repeated value plus one mod 5+1.
  • A268942 (program): Number of length-n 0..6 arrays with no repeated value unequal to the previous repeated value plus one mod 6+1.
  • A268943 (program): Number of length-n 0..7 arrays with no repeated value unequal to the previous repeated value plus one mod 7+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.
  • A268967 (program): Number of n X 4 0..2 arrays with some element plus some horizontally or antidiagonally adjacent neighbor totalling two not more than once.
  • A268968 (program): Number of n X 5 0..2 arrays with some element plus some horizontally or antidiagonally adjacent neighbor totalling two not more than once.
  • A268972 (program): Number of 2 X n 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.
  • A268996 (program): Number of 2 X n binary arrays with some element plus some horizontally or antidiagonally adjacent neighbor totalling two not more than once.
  • A269004 (program): a(n) is the sum of the prime factors, with repetition, of the sum of all preceding terms, with initial terms a(1)=1 and a(2)=2.
  • A269012 (program): Number of 2 X n binary arrays with some element plus some horizontally, diagonally or antidiagonally adjacent neighbor totalling two exactly 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).
  • A269028 (program): a(n) = 40*a(n - 1) - a(n - 2) for n>1, a(0) = 1, a(1) = 1.
  • 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.
  • A269067 (program): Numerator of the volume of d dimensional symmetric convex cuboid with constraints |x1 + x2 + … xd| <= 1 and |x1|, |x2|, …, |xd| <= 1.
  • A269068 (program): a(n+2) = a(n+1) + L(n+1)*a(n), where L = Lucas number (A000032) and a(0) = a(1) = 1.
  • A269083 (program): Number of n X 2 binary arrays with some element plus some horizontally, vertically or antidiagonally adjacent neighbor totalling two not more than once.
  • A269091 (program): Number of n X 2 0..3 arrays with some element plus some horizontally or vertically adjacent neighbor totalling three exactly once.
  • A269098 (program): Expansion of (1 + 2*x + 3*x^2 + x^3 + x^5)/(1 - x^3)^2.
  • A269100 (program): a(n) = 13*n + 11.
  • A269101 (program): Numbers of circles with the largest possible sum of radii packed inside an ellipse admitting circular solution.
  • 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*(2*n+1)/5).
  • A269137 (program): Number of n X 2 0..3 arrays with some element plus some horizontally, antidiagonally or vertically adjacent neighbor totalling three no more than once.
  • A269146 (program): Number of n X 2 0..3 arrays with some element plus some horizontally, antidiagonally or vertically adjacent neighbor totalling three exactly once.
  • 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).
  • A269164 (program): Numbers not in range of A269160; indices of zeros in A269162 from n >= 1 onward.
  • 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.
  • A269225 (program): Smallest k such that k! > 2^n.
  • A269226 (program): Period 6: repeat [3, 9, 6, 6, 9, 3].
  • A269232 (program): a(n) = (n + 1)*(6*n^2 + 15*n + 4)/2.
  • A269237 (program): a(n) = (n + 1)^2*(5*n^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.
  • A269250 (program): Number of times the digit 0 appears in the decimal expansion of n^3.
  • A269255 (program): a(n) = (2^(2*n+1) - 1)*(3^(n+1) - 1)/2.
  • A269265 (program): a(0) = a(1) = 1; thereafter a(n) = a(n-1) + a(n-2) if n is even, otherwise a(n) = a(n-1)^2.
  • A269266 (program): a(n) = 2^n mod 31.
  • A269268 (program): Kolakoski-(1,5) sequence: a(n) is length of n-th run.
  • A269270 (program): Number of n X 2 0..3 arrays with some element plus some horizontally or antidiagonally adjacent neighbor totalling three exactly once.
  • A269271 (program): Number of n X 3 0..3 arrays with some element plus some horizontally or antidiagonally adjacent neighbor totalling three exactly once.
  • A269284 (program): Number of n X 3 0..3 arrays with some element plus some horizontally or antidiagonally adjacent neighbor totalling three no more than 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).
  • A269341 (program): Records in A269340.
  • A269342 (program): a(n) = (n + 1)*(2*n + 1)*(4*n + 9)/3.
  • A269345 (program): Smaller of two consecutive odd composites.
  • A269348 (program): Kolakoski-(1,6) sequence: a(n) is length of n-th run.
  • A269349 (program): Kolakoski-(1,7) sequence: a(n) is length of n-th run.
  • A269350 (program): Kolakoski-(1,8) sequence: a(n) is length of n-th run.
  • A269352 (program): Kolakoski-(1,10) sequence: a(n) is length of n-th run.
  • A269362 (program): Least monotonic left inverse of A269389.
  • A269364 (program): Difference between the number of occurrences of prime gaps not divisible by 3, versus number of prime gaps that are multiples of 3, up to n-th prime gap: a(n) = A269849(n) - A269850(n).
  • A269371 (program): Least monotonic left inverse of A179016.
  • A269381 (program): Least monotonic left inverse of A233271.
  • A269389 (program): Numbers n for which prime(n+7)-prime(n+6) is not a multiple of three.
  • A269390 (program): Complement of A233271.
  • A269399 (program): Numbers n for which prime(n+7)-prime(n+6) is a multiple of three.
  • A269403 (program): Expansion of x*(2 - x + 2*x^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.
  • A269411 (program): Number of length-5 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).
  • A269428 (program): Alternating sum of heptagonal pyramidal numbers.
  • 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.
  • A269437 (program): Number of length-5 0..n arrays with no repeated value greater than the previous repeated value.
  • A269440 (program): Alternating sum of 9-gonal (or decagonal) pyramidal numbers.
  • A269441 (program): Alternating sum of 10-gonal (or decagonal) pyramidal numbers.
  • 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.
  • A269450 (program): a(n) = (n-1)*a(n-1) - a(n-2) + (n-2)*a(n-3) with a(0)=0, a(1)=a(2)=1.
  • A269454 (program): Safe primes that are not congruent to -1 mod 8.
  • A269457 (program): a(n) = 5*(n + 1)*(n + 4)/2.
  • A269461 (program): Number of length-n 0..2 arrays with no repeated value equal to the previous repeated value.
  • A269462 (program): Number of length-n 0..3 arrays with no repeated value equal to the previous repeated value.
  • A269463 (program): Number of length-n 0..4 arrays with no repeated value equal to the previous repeated value.
  • A269464 (program): Number of length-n 0..5 arrays with no repeated value equal to the previous repeated value.
  • A269465 (program): Number of length-n 0..6 arrays with no repeated value equal to the previous repeated value.
  • A269466 (program): Number of length-n 0..7 arrays with no repeated value equal to the previous repeated value.
  • 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.
  • A269488 (program): Number of length-n 0..2 arrays with no repeated value differing from the previous repeated value by one.
  • 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).
  • A269501 (program): Subsequence immediately following the instances of n in the sequence is n, n-1, …, 1, n+1, n+2, ….
  • A269509 (program): a(n) = (n-1)*a(n-1) - a(n-2) + (n-2)*a(n-3) with a(0)=a(1)=1, a(2)=0.
  • A269511 (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 342”, based on the 5-celled von Neumann neighborhood.
  • A269512 (program): First differences of number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by “Rule 342”, based on the 5-celled von Neumann neighborhood.
  • A269527 (program): a(n) = n^20 + n^15 + n^10 + n^5 + 1.
  • A269528 (program): Parity of number of runs of 1’s in negabinary representation of n.
  • A269529 (program): An analog of the Golay-Rudin-Shapiro sequence (A020985) in base -2 (see comments).
  • A269531 (program): Number of length-n 0..2 arrays with no repeated value differing from the previous repeated value by other than one.
  • 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.
  • A269548 (program): Expansion of (-7*x^2 + 134*x + 1)/(x^3 - 99*x^2 + 99*x - 1).
  • A269549 (program): Expansion of (-x^2 + 298*x - 1)/(x^3 - 99*x^2 + 99*x - 1).
  • A269550 (program): Expansion of (-5*x^2 + 228*x - 7)/(x^3 - 99*x^2 + 99*x - 1).
  • A269551 (program): Expansion of (3*x^2 + 258*x - 5)/(x^3 - 99*x^2 + 99*x - 1).
  • A269552 (program): Expansion of (-3*x^2 + 94*x - 3)/(x^3 - 99*x^2 + 99*x - 1).
  • A269553 (program): Expansion of (-5*x^2 + 138*x + 3)/(x^3 - 99*x^2 + 99*x - 1).
  • A269554 (program): Expansion of (3*x^2 + 244*x + 1)/(x^3 - 99*x^2 + 99*x - 1).
  • A269555 (program): Expansion of (x^2 + 254*x - 7)/(x^3 - 99*x^2 + 99*x - 1).
  • A269556 (program): Expansion of (-7*x^2 + 148*x - 5)/(x^3 - 99*x^2 + 99*x - 1).
  • A269571 (program): Numbers having binary fractility 1.
  • A269576 (program): a(n) = Product_{i=1..n} (4^i - 3^i).
  • A269578 (program): Number of length-n 0..2 arrays with no repeated value differing from the previous repeated value by more than one.
  • 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.
  • A269590 (program): One of the two successive approximations up to 5^n for the 5-adic integer sqrt(-4). These are the 4 mod 5 numbers (except for n=0).
  • A269591 (program): Digits of one of the two 5-adic integers sqrt(-4).
  • A269592 (program): Digits of one of the two 5-adic integers sqrt(-4). Here the ones related to A269590.
  • A269594 (program): a(n) = (A269590(n)^2 + 4)/5^n, n >= 0.
  • 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.
  • A269613 (program): Number of length-n 0..2 arrays with no repeated value differing from the previous repeated value by other than plus two, zero or minus 1.
  • 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.
  • A269659 (program): Number of length-6 0..n arrays with no adjacent pair x,x+1 repeated.
  • A269661 (program): a(n) = Product_{i=1..n} (5^i - 4^i).
  • A269667 (program): a(n) = A270172(10*n).
  • A269673 (program): Number of length-n 0..3 arrays with no repeated value differing from the previous repeated value by other than plus or minus one modulo 3+1.
  • A269674 (program): Number of length-n 0..4 arrays with no repeated value differing from the previous repeated value by other than plus or minus one modulo 4+1.
  • A269675 (program): Number of length-n 0..5 arrays with no repeated value differing from the previous repeated value by other than plus or minus one modulo 5+1.
  • A269676 (program): Number of length-n 0..6 arrays with no repeated value differing from the previous repeated value by other than plus or minus one modulo 6+1.
  • A269677 (program): Number of length-n 0..7 arrays with no repeated value differing from the previous repeated value by other than plus or minus one modulo 7+1.
  • 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.
  • A269685 (program): Number of length-n 0..3 arrays with no repeated value differing from the previous repeated value by plus or minus one modulo 3+1.
  • A269686 (program): Number of length-n 0..4 arrays with no repeated value differing from the previous repeated value by plus or minus one modulo 4+1.
  • A269687 (program): Number of length-n 0..5 arrays with no repeated value differing from the previous repeated value by plus or minus one modulo 5+1.
  • A269688 (program): Number of length-n 0..6 arrays with no repeated value differing from the previous repeated value by plus or minus one modulo 6+1.
  • A269689 (program): Number of length-n 0..7 arrays with no repeated value differing from the previous repeated value by plus or minus one modulo 7+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.
  • A269694 (program): Product of first n nonzero Jacobsthal numbers (A001045).
  • A269695 (program): Number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by “Rule 6”, based on the 5-celled von Neumann neighborhood.
  • 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.
  • A269697 (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 6”, based on the 5-celled von Neumann neighborhood.
  • A269698 (program): First differences of the numbers of active (ON,black) cells in n-th stage of growth of 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
  • A269703 (program): Numbers k such that prime(k) == 1 (mod 7).
  • A269704 (program): Numbers k such that prime(k) == 1 (mod 8).
  • 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.
  • A269708 (program): Number of active (ON,black) cells at stage 2^n-1 of the two-dimensional cellular automaton defined by “Rule 14”, based on the 5-celled von Neumann neighborhood.
  • A269709 (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 14”, based on the 5-celled von Neumann neighborhood.
  • 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.
  • A269716 (program): Number of active (ON,black) cells at stage 2^n-1 of the two-dimensional cellular automaton defined by “Rule 22”, 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.
  • A269725 (program): a(n) = row number of extended Wythoff array (see A035513) which contains the sequence n times the Fibonacci numbers 1,2,3,5,8,13,21,… .
  • A269726 (program): a(n) = row number of extended Wythoff array (see A035513) which contains the sequence n times the Lucas numbers 1,3,4,7,11,18,… (A000204).
  • A269727 (program): Primes avoided by certain exponential sums.
  • A269730 (program): Dimensions of the 2-polytridendriform operad TDendr_2.
  • A269731 (program): Dimensions of the 3-polytridendriform operad TDendr_3.
  • A269732 (program): Dimensions of the 4-polytridendriform operad TDendr_4.
  • A269735 (program): G.f.: Sum_{k >= 0} x^(2^k)*(1-x^(2^k))/(1+x^(2^k)).
  • 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.
  • A269752 (program): Table of inverse permutations of the rows of A131987: Position of numbers inserted in “storage order” into a perfect binary table of 2^k-1 nodes.
  • A269760 (program): Number of n X 1 0..5 arrays with some element plus some horizontally or vertically adjacent neighbor totalling five exactly once.
  • A269761 (program): Number of n X 2 0..5 arrays with some element plus some horizontally or vertically adjacent neighbor totalling five exactly once.
  • A269771 (program): Number of length-n 0..3 arrays with every repeated value unequal to the previous repeated value plus one mod 3+1.
  • A269772 (program): Number of length-n 0..4 arrays with every repeated value unequal to the previous repeated value plus one mod 4+1.
  • A269773 (program): Number of length-n 0..5 arrays with every repeated value unequal to the previous repeated value plus one mod 5+1.
  • A269774 (program): Number of length-n 0..6 arrays with every repeated value unequal to the previous repeated value plus one mod 6+1.
  • A269775 (program): Number of length-n 0..7 arrays with every repeated value unequal to the previous repeated value plus one mod 7+1.
  • A269777 (program): Number of length-5 0..n arrays with every repeated value unequal to the previous repeated value plus one mod n+1.
  • A269778 (program): Number of length-6 0..n arrays with every repeated value unequal to the previous repeated value plus one mod n+1.
  • A269784 (program): Primes p such that 2*p + 11 is a square.
  • A269785 (program): Primes p such that 2*p + 23 is a square.
  • A269786 (program): Primes p such that 2*p + 31 is a square.
  • A269787 (program): Primes p such that 2*p + 43 is a square.
  • A269788 (program): Primes p such that 2*p + 47 is a square.
  • A269789 (program): Primes p such that 2*p + 59 is a square.
  • A269790 (program): Primes p such that 2*p + 79 is a square.
  • A269792 (program): a(n) = 5*n^4.
  • A269796 (program): a(n) = 4^n * A000108(n+1).
  • A269799 (program): Number of vertices of the fractional perfect matching polytope for the complete graph on n vertices.
  • A269801 (program): Total sum of the divisors of the primes p,q such that n=p+q and p>=q.
  • A269803 (program): a(n) = F(n+1)*F(n+2) - F(n), where F = A000045 (Fibonacci numbers).
  • A269815 (program): Number of active (ON,black) cells at stage 2^n-1 of the two-dimensional cellular automaton defined by “Rule 35”, based on the 5-celled von Neumann neighborhood.
  • A269819 (program): Numbers that are congruent to {5, 11, 13, 19} mod 24.
  • A269820 (program): a(n) = 2*(n-1)*a(n-1) - a(n-2) + 2*(n-2)*a(n-3) with a(0)=a(1)=a(2)=1.
  • 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.
  • A269837 (program): Irregular triangle read by rows: even terms of A094728(n+1) divided by 4.
  • A269840 (program): Lesser of twin primes where both are the sum of 3 nonzero squares.
  • 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.
  • A269860 (program): Numbers n such that n and A048673(n) are of the same parity.
  • A269861 (program): Numbers n such that n and A048673(n) are of opposite parity.
  • A269862 (program): Least monotonic left inverse of A269861.
  • A269870 (program): Numbers coprime to the number of their odd divisors.
  • 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.
  • A269880 (program): First differences of number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by “Rule 4”, based on the 5-celled von Neumann neighborhood.
  • A269889 (program): The number of permutations of 1, 2,…, n such that none of 123, 132, 213, 231, 312, 321 appear in the permutation.
  • 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.
  • A269949 (program): Triangle read by rows, T(n,k) = denominator(binomial(-1/2, n-k))*binomial(n-1/2, k-1/2), for n>=0 and 0<=k<=n.
  • A269950 (program): Triangle read by rows, T(n,k) = denominator(binomial(1/2,n-k))*binomial(n+1/2, k+1/2), for n>=0 and 0<=k<=n.
  • A269956 (program): Triangle read by rows, T(n,k) = binomial(3*n,n+k) for n>=0 and 0<=k<=n.
  • A269962 (program): Start with a square; at each stage add a square at each expandable vertex so that the ratio of the side of the squares at stage n+1 and at stage n is the golden ratio phi=0.618…; a(n) is the number of squares at n-th stage.
  • A269963 (program): Start with a square; at each stage add a square at each expandable vertex so that the ratio of the side of the squares at stage n+1 and at stage n is the golden ratio phi=0.618…; a(n) is the number of squares in a portion of the n-th stage (see below).
  • A269964 (program): Start with a square; at each stage add a square at each expandable vertex so that the ratio of the side of the squares at stage n+1 and at stage n is the golden ratio phi=0.618…; a(n) is the number of squares in a portion of the n-th stage (see below).
  • A269965 (program): Start with a square; at each stage add a square at each expandable vertex so that the ratio of the side of the squares at stage n+1 and at stage n is the golden ratio phi=0.618…; a(n) is the number of squares in a portion of the n-th stage (see below)
  • 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.
  • A270009 (program): First differences of 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.
  • A270013 (program): First differences of 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).
  • A270048 (program): a(1) = 0; a(n+1) = a(n) + n * the number of digits of a(n).
  • A270049 (program): Number of 123 avoiding set partitions of [n].
  • A270050 (program): Numbers of the form 2 * (x^2 + xy + y^2).
  • A270052 (program): Number of nX2 0..4 arrays with some element plus some horizontally or vertically adjacent neighbor totalling four exactly once.
  • A270059 (program): Number of distinct digits needed to write n in all bases >= 2.
  • A270060 (program): Number of incomplete rectangles of area n.
  • A270062 (program): Number of tilings of a 2 X n rectangle using monominoes and trominoes of any shape.
  • A270080 (program): Number of active (ON,black) cells at stage 2^n-1 of the two-dimensional cellular automaton defined by “Rule 62”, based on the 5-celled von Neumann neighborhood.
  • A270084 (program): Number of active (ON,black) cells at stage 2^n-1 of the two-dimensional cellular automaton defined by “Rule 65”, based on the 5-celled von Neumann neighborhood.
  • A270088 (program): Number of active (ON,black) cells at stage 2^n-1 of the two-dimensional cellular automaton defined by “Rule 73”, based on the 5-celled von Neumann neighborhood.
  • A270097 (program): Discriminator sequence for the powers of 2: smallest positive integer d such that 2^0, 2^1, …, 2^{n-1} are all incongruent modulo d.
  • A270105 (program): a(n) = Sum_{k=0..n} k*A000009(k).
  • 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.
  • A270107 (program): First differences of 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.
  • A270125 (program): Number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by “Rule 86”, based on the 5-celled von Neumann neighborhood.
  • 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.
  • A270127 (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 86”, based on the 5-celled von Neumann neighborhood.
  • A270128 (program): First differences of number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by “Rule 86”, based on the 5-celled von Neumann neighborhood.
  • A270130 (program): Number of active (ON,black) cells at stage 2^n-1 of the two-dimensional cellular automaton defined by “Rule 89”, based on the 5-celled von Neumann neighborhood.
  • A270189 (program): Numbers n for which (prime(n+1)-prime(n)) is not a multiple of three.
  • A270190 (program): Numbers n for which prime(n+1)-prime(n) is a multiple of three.
  • A270191 (program): Numbers n for which (prime(n+1)-prime(n)) mod 3 = 1.
  • A270192 (program): Numbers n for which (prime(n+1)-prime(n)) mod 3 = 2.
  • A270198 (program): a(n) = A054429(A055938(A054429(n))).
  • 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.
  • A270218 (program): Number of active (ON,black) cells at stage 2^n-1 of the two-dimensional cellular automaton defined by “Rule 129”, based on the 5-celled von Neumann neighborhood.
  • 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.
  • A270225 (program): Lesser of twin primes where both primes are the sum of three squares.
  • A270226 (program): a(n) is the number of terms in the n-th block of consecutive integers of A136119.
  • A270229 (program): Number of matchings (i.e., Hosoya index) in P_{2} X K_{n}.
  • A270230 (program): Decimal expansion of 3/(4*Pi).
  • A270248 (program): Even Löschian numbers.
  • 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.
  • A270287 (program): Number of active (ON,black) cells at stage 2^n-1 of the two-dimensional cellular automaton defined by “Rule 145”, based on the 5-celled von Neumann neighborhood.
  • 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.
  • A270298 (program): Numbers which are representable as a sum of eight but no fewer consecutive nonnegative integers.
  • A270299 (program): Numbers which are representable as a sum of eleven but no fewer consecutive nonnegative integers.
  • A270300 (program): Numbers which are representable as a sum of thirteen but no fewer consecutive nonnegative integers.
  • A270301 (program): Numbers which are representable as a sum of sixteen but no fewer consecutive nonnegative integers.
  • A270302 (program): Numbers which are representable as a sum of seventeen but no fewer consecutive nonnegative integers.
  • A270303 (program): Numbers which are representable as a sum of nineteen but no fewer consecutive nonnegative integers.
  • A270307 (program): Expansion of -(4*x^3+8*x^2+4*x+1)/(2*x^4+4*x^3+2*x^2-x-1).
  • A270312 (program): Numerator of Fibonacci(n)/n.
  • A270313 (program): Denominator of Fibonacci(n)/n.
  • A270342 (program): Positive integers n such that the sum of the Pell numbers A000129(0) + … + A000129(n-1) is divisible by n.
  • A270346 (program): a(n) is the number whose base-11 digits are, in order, the first n terms of the simple periodic sequence: repeat 2,3,5,7.
  • A270359 (program): Positive integer averages of first n Pell numbers; Sum{k=0..n-1} A000129(k) / n where n is in A270342.
  • A270362 (program): Running maxima of Stern’s diatomic sequence.
  • A270363 (program): a(n) = (n+1)*Sum_{k=0..(n-1)/2}((binomial(2*n-3*k-2,n-k-1))/(n-k)).
  • A270369 (program): Expansion of (1-7*x)/(1-9*x).
  • A270370 (program): a(n) = Sum_{k=0..n} (-1)^k*floor(k^(1/3)).
  • A270383 (program): Number of ordered pairs (i,j) with i >= j, |i|, |j| <= n, and |i * j| <= n.
  • A270384 (program): Primes p such that (3/4)(p + 1) - 1 is also prime.
  • A270386 (program): Expansion of (4/(3*x/(1-x))) * sin((1/3)*arcsin(sqrt(27*x/4/(1-x))))^2.
  • A270388 (program): a(n) = A048739(n-2) mod n.
  • A270390 (program): Greatest common divisor of 2^n-1 and 5^n-1.
  • A270417 (program): Number of integer-sided right triangles with semiperimeter n.
  • A270428 (program): Exponentially odious numbers: 1 together with positive integers n such that all exponents in prime factorization of n are odious numbers (A000069).
  • A270438 (program): a(n) is the number of entries == 1 mod 4 in row n of Pascal’s triangle.
  • A270439 (program): Alternating sum of nonsquares (A000037).
  • A270440 (program): Least k such that binomial(k, 2) >= binomial(2*n, n).
  • A270444 (program): Expansion of 2*(1+2*x) / (1-8*x+4*x^2).
  • A270445 (program): Expansion of 2*x*(1+4*x) / (1-12*x+16*x^2).
  • A270447 (program): Binomial transform(2) of Catalan numbers.
  • 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 (1-3*x)/(1-7*x).
  • A270472 (program): Expansion of (1-2*x)/(1-9*x).
  • A270473 (program): Expansion of (1-5*x)/(1-9*x).
  • A270489 (program): Sum_{k=0..n} ((binomial(3*k,k)*binomial(2*n-k,n))/(2*k+1)).
  • A270490 (program): a(n) = Sum_{i=0..(n+1)/2} binomial(2*i+1,i)*binomial(2*n-2*i,n)/(2*i+1).
  • A270494 (program): Sum of the sizes of the second blocks in all set partitions of {1,2,…,n}.
  • A270510 (program): Number of 2X2X2 triangular 0..n arrays with some element plus some adjacent element totalling n+1 exactly once.
  • A270528 (program): Sum of divisors of the products of the smaller and larger parts of the partitions of n into two parts.
  • A270530 (program): a(n) = Sum_{k=0..n}((binomial(2*k,k)/(k+1)*binomial(2*n+2,n-k))).
  • A270531 (program): a(n) = Sum_{i=1..floor(n/2)} (i*(n-i))!.
  • A270541 (program): a(n) = A001359(n) - A001359(n+1) - A001359(n+2) + A001359(n+3).
  • A270544 (program): Number of ordered pairs (i,j) with |i|, |j| <= n, |i * j| <= n, and i odd.
  • A270545 (program): Number of equilateral triangle units forming perimeter of equilateral triangle.
  • A270560 (program): a(n) = Sum_{i=0..n/2}((binomial(2*i+1,i)*binomial(2*n+2,n-2*i))/(2*i+1)).
  • A270561 (program): Binomial transform(2) of Motzkin numbers.
  • A270567 (program): Expansion of (1+4*x)/(1-5*x).
  • A270568 (program): Expansion of (1+4*x)/(1-8*x).
  • A270570 (program): Largest number in the sequence for the Collatz problem (excluding the original number) when started at n.
  • A270572 (program): a(1)=3; thereafter a(n) is the number of occurrences of a(n-1) in {a(1), … , a(n-1)}.
  • A270576 (program): Expansion of (1+2*x)/(1-6*x).
  • A270577 (program): Generalized Catalan numbers C(3,n), where the (m,n)-th Catalan is the number of paths in R^m from the origin to the point (n,…,n,(m-1)n) with m kinds of moves such that the path never rises above the hyperplane x_m = x_1+…+x_{m-1}.
  • A270593 (program): Total number of subtrees of the complete simple undirected graph K_n on n vertices.
  • A270607 (program): Number of 2X2X2 triangular 0..n arrays with some element plus some adjacent element totalling n+1 or n-1 exactly once.
  • A270641 (program): The sequence a of 1’s and 2’s starting with (1,1,1,1) such that a(n) is the length of the (n+1)st run of a.
  • A270642 (program): The sequence a of 1’s and 2’s starting with (1,1,2,2) such that a(n) is the length of the (n+2)nd run of a.
  • A270643 (program): The sequence a of 1’s and 2’s starting with (1,2,2,1) such that a(n) is the length of the (n+3)rd run of a.
  • A270644 (program): The sequence a of 1’s and 2’s starting with (1,2,2,2) such that a(n) is the length of the (n+2)nd run of a.
  • A270645 (program): The sequence a of 1’s and 2’s starting with (2,1,1,1) such that a(n) is the length of the (n+2)nd run of a.
  • A270646 (program): The sequence a of 1’s and 2’s starting with (2,2,1,1) such that a(n) is the length of the (n+2)nd run of a.
  • A270647 (program): The sequence a of 1’s and 2’s starting with (2,2,1,2) such that a(n) is the length of the (n+3)rd run of a.
  • A270648 (program): The sequence a of 1’s and 2’s starting with (2,2,2,2) such that a(n) is the length of the (n+1)st run of a.
  • A270650 (program): Min(i, j), where p(i)*p(j) is the n-th term of A006881.
  • A270652 (program): Max(i,j), where p(i)*p(j) is the n-th term of A006881.
  • A270653 (program): Integers k such that A003266(k) is divisible by k.
  • A270660 (program): Numbers in the range of the sum of abundant divisors function.
  • A270672 (program): Löschian numbers (A003136) that are multiples of 3.
  • 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.
  • A270682 (program): Number of active (ON,black) cells at stage 2^n-1 of the 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.
  • A270693 (program): Alternating sum of centered 25-gonal numbers.
  • A270694 (program): Alternating sum of centered heptagonal pyramidal numbers.
  • A270695 (program): Alternating sum of centered octagonal pyramidal numbers.
  • A270700 (program): Triangular Star of David numbers (the figurate number of triangles framing a hexagram: a(0) = 12; thereafter a(n) = 36*n+6).
  • A270701 (program): Total sum T(n,k) of the sizes of all blocks with maximal element k in all set partitions of {1,2,…,n}; triangle T(n,k), n>=1, 1<=k<=n, read by rows.
  • A270702 (program): Total sum T(n,k) of the sizes of all blocks with minimal element k in all set partitions of {1,2,…,n}; triangle T(n,k), n>=1, 1<=k<=n, read by rows.
  • A270703 (program): Total sum of the sizes of all blocks with maximal element n in all set partitions of {1,2,…,2n-1}.
  • A270704 (program): Even 14-gonal (or tetradecagonal) numbers.
  • A270710 (program): a(n) = 3*n^2 + 2*n - 1.
  • A270714 (program): Decimal expansion of (1/2)^(1/3).
  • A270715 (program): a(n) = ((n+2)/2)*Sum_{k=0..n/2}(Sum_{i=0..n-2*k}(binomial(k+1,n-2*k-i)*binomial(k+i,k))/(k+1).
  • A270737 (program): a(n) = ((n+2)/2)*Sum_{k=0..n/2} (Sum_{i=0..n-2*k} (binomial(k+1,n-2*k-i)*binomial(k+i,k))*F(k+1)/(k+1)), where F(k) is Fibonacci numbers.
  • 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.
  • A270756 (program): Total sum of the sizes of all blocks with maximal element 2 in all set partitions of {1,2,…,n}.
  • A270757 (program): Total sum of the sizes of all blocks with maximal element 3 in all set partitions of {1,2,…,n}.
  • A270758 (program): Total sum of the sizes of all blocks with maximal element 4 in all set partitions of {1,2,…,n}.
  • A270759 (program): Total sum of the sizes of all blocks with maximal element 5 in all set partitions of {1,2,…,n}.
  • A270760 (program): Total sum of the sizes of all blocks with maximal element 6 in all set partitions of {1,2,…,n}.
  • A270761 (program): Total sum of the sizes of all blocks with maximal element 7 in all set partitions of {1,2,…,n}.
  • A270762 (program): Total sum of the sizes of all blocks with maximal element 8 in all set partitions of {1,2,…,n}.
  • A270763 (program): Total sum of the sizes of all blocks with maximal element 9 in all set partitions of {1,2,…,n}.
  • A270764 (program): Total sum of the sizes of all blocks with maximal element 10 in all set partitions of {1,2,…,n}.
  • A270765 (program): Total sum of the sizes of all blocks with minimal element 2 in all set partitions of {1,2,…,n}.
  • A270766 (program): Total sum of the sizes of all blocks with minimal element 3 in all set partitions of {1,2,…,n}.
  • A270767 (program): Total sum of the sizes of all blocks with minimal element 4 in all set partitions of {1,2,…,n}.
  • A270768 (program): Total sum of the sizes of all blocks with minimal element 5 in all set partitions of {1,2,…,n}.
  • A270769 (program): Total sum of the sizes of all blocks with minimal element 6 in all set partitions of {1,2,…,n}.
  • A270770 (program): Total sum of the sizes of all blocks with minimal element 7 in all set partitions of {1,2,…,n}.
  • A270771 (program): Total sum of the sizes of all blocks with minimal element 8 in all set partitions of {1,2,…,n}.
  • A270772 (program): Total sum of the sizes of all blocks with minimal element 9 in all set partitions of {1,2,…,n}.
  • A270773 (program): Total sum of the sizes of all blocks with minimal element 10 in all set partitions of {1,2,…,n}.
  • A270775 (program): a(n) is the number of invertible 2 X 2 upper triangular matrices over Z_p where p = prime(n).
  • A270784 (program): Expansion of (1-sqrt(1-4*x^4/(1-x)^4))/(2*x^4*(1-x)).
  • A270785 (program): Number of Schur rings over Z_{3^n}.
  • A270788 (program): Unique fixed point of the 3-symbol Fibonacci morphism phi-hat_2.
  • A270792 (program): The prime/nonprime compound sequence ABA.
  • A270794 (program): The prime/nonprime compound sequence BAA.
  • A270795 (program): The prime/nonprime compound sequence BAB.
  • 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.
  • A270807 (program): Trajectory of 1 under the map n -> n + n/gpf(n) + 1 (see A269304).
  • A270808 (program): First differences of A270807, divided by 2.
  • A270809 (program): a(n) = n^3/3 - 7*n/3 + 4.
  • A270810 (program): Expansion of (x - x^2 + 2*x^3 + 2*x^4)/(1 - 3*x + 2*x^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).
  • A270822 (program): Expansion of 1/((1-4*x^2)^(3/2)-2*x*(1-4*x^2)).
  • A270823 (program): Period 16: repeat [0,2,3,1,1,3,2,0,1,3,2,0,0,2,3,1].
  • A270824 (program): Period 16: repeat [0, 1, 1, 0, 2, 3, 3, 2, 3, 2, 2, 3, 1, 0, 0, 1].
  • A270826 (program): Maximum number of iterations needed in the Euclid algorithm for gcd(x,y) in [1..n].
  • A270828 (program): a(n) = (Sum_{k=1..2n-1} prime(k)) mod prime(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.
  • A270863 (program): Self-composition of the Fibonacci sequence.
  • A270867 (program): a(n) = n^3 + 2*n^2 + 4*n + 1.
  • A270868 (program): a(n) = n^4 + 3*n^3 + 8*n^2 + 9*n + 2.
  • A270869 (program): a(n) = n^5 + 4*n^4 + 13*n^3 + 23*n^2 + 25*n + 3.
  • A270870 (program): a(n) = n^6 + 5*n^5 + 19*n^4 + 44*n^3 + 72*n^2 + 69*n + 5.
  • A270886 (program): Numbers written in binary balanced system (A270885) that have exactly one zero.
  • A270887 (program): Numbers written in binary balanced system (A270885) that have exactly two zeros.
  • A270888 (program): Numbers written in binary balanced system (A270885) have exactly three zeros.
  • A270889 (program): Integers n such that the circular graph C_n has a square size deficiency.
  • A270913 (program): Coefficient of x^n in Product_{k>=1} (1+x^k)^n.
  • A270919 (program): Coefficient of x^n in Product_{k>=1} ((1 + x^k) / (1 - x^k))^n.
  • A270927 (program): Smallest k such that k*n^m + 1 is prime, case m=4.
  • 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.
  • A270992 (program): Number of distinct prime divisors of prime(n)+1 and prime(n+1)+1.
  • A270993 (program): Values of A076336(n) such that A076336(n) = A076336(n+1) - 14.
  • A270994 (program): a(n) = 9454129 + 11184810*n.
  • A270997 (program): Numbers k such that k | A006190(k-1).
  • A271005 (program): Number of active (ON,black) cells at stage 2^n-1 of the two-dimensional cellular automaton defined by “Rule 245”, based on the 5-celled von Neumann neighborhood.
  • 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.
  • A271025 (program): A(n, k) is the n-th binomial transform of the Catalan sequence (A000108) evaluated at k. Array read by descending antidiagonals for n >= 0 and k >= 0.
  • 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.
  • A271054 (program): Number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by “Rule 259”, based on the 5-celled von Neumann neighborhood.
  • A271055 (program): Number of active (ON,black) cells at stage 2^n-1 of the two-dimensional cellular automaton defined by “Rule 259”, based on the 5-celled von Neumann neighborhood.
  • A271056 (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 259”, based on the 5-celled von Neumann neighborhood.
  • A271057 (program): First differences of number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by “Rule 259”, based on the 5-celled von Neumann neighborhood.
  • 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.
  • A271064 (program): First differences of 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.
  • A271079 (program): Residues (mod 32) of partial sums of Fibonacci numbers starting with F(2).
  • A271091 (program): Number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by “Rule 275”, based on the 5-celled von Neumann neighborhood.
  • A271092 (program): Number of active (ON,black) cells at stage 2^n-1 of the two-dimensional cellular automaton defined by “Rule 275”, based on the 5-celled von Neumann neighborhood.
  • A271093 (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 275”, based on the 5-celled von Neumann neighborhood.
  • A271094 (program): First differences of number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by “Rule 275”, based on the 5-celled von Neumann neighborhood.
  • A271102 (program): a(n) is multiplicative with a(p^e) = -1 if e=2, a(p^e) = 0 if e=1 or e>2.
  • A271114 (program): Expansion of (1+x)*(2+x)/(1-x)^2.
  • A271176 (program): Expansion of -(4*x^3-7*x^2+4*x-1)/(2*x^4-5*x^3+8*x^2-5*x+1).
  • A271183 (program): Löschian numbers (A003136) k such that k + 1 is also Löschian number.
  • A271185 (program): Löschian numbers (A003136) of the form k^3+1.
  • A271186 (program): Odd integers k such that k^k + 1 is the sum of 2 nonzero squares.
  • A271187 (program): Triangle T(n,k) read by rows: T(n,k) is the squarefree part of C(n,k).
  • A271197 (program): Expansion of -(sqrt(x^2-6*x+1)+3*x-1)/((7*x-1)*sqrt(x^2-6*x+1)+x^2-6*x+1)/x.
  • A271208 (program): a(n) = n^5 + n - 1.
  • A271209 (program): a(n) = n^5 + n + 1.
  • A271211 (program): Composite integers sandwiched between primes p, q with q-p = 4.
  • A271212 (program): a(n) = (2n-1)*a(n-1) + 2*(n-2)*a(n-2).
  • A271216 (program): a(n) = 2^n floor(n/2)!
  • A271218 (program): Number of symmetric linked diagrams with n links and no simple link.
  • A271220 (program): Concatenate sum of digits of previous term and product of digits of previous term, starting with 6.
  • A271222 (program): One of the two successive approximations up to 3^n for the 3-adic integer sqrt(-2). These are the numbers congruent to 2 mod 3 (except for the initial 0).
  • A271223 (program): Digits of one of the two 3-adic integers sqrt(-2).
  • A271224 (program): Digits of one of the two 3-adic integers sqrt(-2). Here the sequence with first digit 2.
  • A271225 (program): a(n) = (A268924(n)^2 + 2)/3^n, n >= 0.
  • A271226 (program): a(n) = (A271222(n)^2 + 2)/3^n, n >= 0.
  • A271232 (program): Composite integers sandwiched between primes p, q with q-p = 6.
  • A271233 (program): Composite integers sandwiched between primes p, q with q-p = 8.
  • A271234 (program): 2^(p-1) modulo p^3, where p = prime(n).
  • A271235 (program): G.f. equals the square root of P(4*x), where P(x) is the g.f. of the partition numbers (A000041).
  • A271236 (program): G.f.: Product_{k>=1} 1/(1 - (9*x)^k)^(1/3).
  • A271254 (program): Number of active (ON,black) cells at stage 2^n-1 of the two-dimensional cellular automaton defined by “Rule 323”, based on the 5-celled von Neumann neighborhood.
  • A271266 (program): a(n) = Product_{k=1..n} (k^2 + 21).
  • A271286 (program): Number of active (ON,black) cells at stage 2^n-1 of the two-dimensional cellular automaton defined by “Rule 337”, based on the 5-celled von Neumann neighborhood.
  • A271317 (program): Fibonacci(n) divides the n-th primorial.
  • A271318 (program): Expansion of 1/(-x*sqrt(4*x^2+1)-x^2+1).
  • A271319 (program): Number of distinct prime factors of the n-th n-gonal number (A060354).
  • A271320 (program): Number of prime factors, with multiplicity, of the n-th n-gonal number (A060354).
  • A271321 (program): Smallest prime factor of the n-th n-gonal number (A060354).
  • A271322 (program): Largest prime factor of the n-th n-gonal number (A060354).
  • A271324 (program): a(n) = n + floor(n/4) + (n mod 4).
  • A271329 (program): a(n) is the sum of the divisors of the n-th sphenic number (A007304).
  • A271342 (program): Sum of all even divisors of all positive integers <= n.
  • A271345 (program): Integers n such that (n-1)! is divisible by n^3.
  • A271346 (program): Numbers k such that the final digit of k^k is 6.
  • A271347 (program): Primes p such that p + 38 is also prime.
  • A271350 (program): a(n) = 3^n mod 83.
  • A271351 (program): a(n) = 3^n mod 131.
  • A271352 (program): a(n) = 3^n mod 211.
  • 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) = k*Fibonacci(2*n+1) + (k+1)*Fibonacci(2*n), where k=3.
  • A271358 (program): a(n) = k*Fibonacci(2*n+1) + (k+1)*Fibonacci(2*n), where k=4.
  • A271359 (program): a(n) = k*Fibonacci(2*n+1) + (k+1)*Fibonacci(2*n), where k=5.
  • A271367 (program): Primes congruent to 11, 13, 17 or 19 (mod 30).
  • 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 - 2*k)^(n - 2*k).
  • A271387 (program): Numerator of prime(n)#/n!, where prime(n)# is the prime factorial function.
  • 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) = (2*n + 1)^(2*floor((n-1)/2) + 1).
  • A271391 (program): Expansion of (1 + x + 2*x^2 + 6*x^3 + x^4 + x^5)/(1 - x^2)^3.
  • A271422 (program): Concatenation of prime(n) and its square.
  • 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).
  • A271451 (program): Triangle read by rows of coefficients of polynomials Q_n(x) = 2^(-n)*((x + sqrt(x*(x + 6) - 3) + 1)^n - (x - sqrt(x*(x + 6) - 3) + 1)^n)/sqrt(x*(x + 6) - 3).
  • A271460 (program): Triangle read by rows: T(n,m) = (m/(n-m))*Sum_{k=1..n-m}((-1)^k*binomial(m-1,k-1)*binomial(3*(n-m)-k-1,n-m-k)), T(n,n)=1.
  • A271469 (program): G.f. satisfies: A(x) = 1 + x*(A(x)^3 - A(x)^4 + A(x)^5).
  • A271473 (program): a(1)=0; thereafter a(2k)=k+a(k), a(2k+1)=k+a(6k+4).
  • A271474 (program): Maximal number of flips required to sort a stack of n unburnt pancakes using the big-3 flips.
  • 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)).
  • A271485 (program): Maximal term of TRIP-Stern sequence of level n corresponding to permutation triple (e,13,e).
  • A271490 (program): Size of maximal subset of points of n X n grid such that no two points are at the same distance.
  • A271491 (program): Arises in enumeration of locally convex functions.
  • A271494 (program): Expansion of (1+16*x)/((1+4*x)*(1-8*x)).
  • A271499 (program): Positive numbers n such that the number of 1’s in the binary expansion of n is not a power of 2.
  • 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 = (2*i + 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.
  • A271532 (program): a(n) = (-1)^n*(n + 1)*(5*n^2 + 10*n + 1).
  • A271535 (program): a(n) = ( n*(n + 1)*(2*n + 1)/6 )^2.
  • A271566 (program): a(n) is the length of the n-th run in A137734.
  • 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.
  • A271584 (program): Irregular triangle read by rows: alternate (k-1)*k, k^2, for k = 0 to n.
  • A271622 (program): Expansion of -2/(x*sqrt(4*x+1)+x-2).
  • A271623 (program): a(0)=7; a(n) = 7*a(n-1) + 1 if a(n-1) is odd, a(n) = a(n-1)/2 otherwise.
  • A271624 (program): a(n) = 2n^2 - 4n + 4.
  • A271625 (program): a(n) = 2n^2 + 4n - 3.
  • A271636 (program): a(n) = 4*n*(4*n^2 + 3).
  • A271638 (program): The total sum of the cubes of all parts of all compositions of n.
  • A271647 (program): Irregular triangle read by rows: the natural numbers from right to left.
  • A271649 (program): a(n) = 2*(n^2 - n + 2).
  • A271654 (program): a(n)=Sum_{k|n} binomial(n-1,k-1)
  • A271661 (program): Expansion of phi(-x^6) / f(-x) in powers of x where phi(), f() are Ramanujan theta functions.
  • A271662 (program): Convolution of nonzero pentagonal numbers (A000326) with themselves.
  • A271663 (program): Convolution of nonzero squares (A000290) with nonzero pentagonal numbers (A000326).
  • A271666 (program): Primes p such that 4*p^2+4*p-1 is prime.
  • A271668 (program): Triangle read by rows. The first column is A000217(n+1). From the second row we apply - A002262(n) for the following terms of the row.
  • A271675 (program): Numbers m such that 3*m + 4 is a square.
  • A271703 (program): Triangle read by rows: the unsigned Lah numbers T(n,k) = binomial(n-1, k-1)*n!/k! if n > 0 and k > 0, T(n,0) = 0^n and otherwise 0, for n >= 0 and 0 <= k <= n.
  • A271704 (program): Triangle read by rows, T(n,k) = Sum_{j=0..n} (-1)^(n-j)*C(-j,-n)*L(j,k), L the unsigned Lah numbers A271703, for n>=0 and 0<=k<=n.
  • A271705 (program): Triangle read by rows, T(n,k) = Sum_{j=0..n} (-1)^(n-j)*C(-j-1,-n-1)*L(j,k), L the unsigned Lah numbers A271703, for n>=0 and 0<=k<=n.
  • A271706 (program): Triangle read by rows, T(n,k) = Sum_{j=0..n} C(-j-1,-n-1)*L(j,k), L the unsigned Lah numbers A271703, for n>=0 and 0<=k<=n.
  • A271709 (program): Table T(n,k) = 2^n + 2^k read by antidiagonals.
  • A271710 (program): Table T(n,k) = 2^n XOR 2^k read by antidiagonals, where XOR is the binary exclusive or operator.
  • A271713 (program): Numbers n such that 3*n - 5 is a square.
  • A271723 (program): Numbers k such that 3*k - 8 is a square.
  • A271726 (program): Let f(x) = 1 -x^3+ Sum_{j>=2} (x^(2^j)-x^(1+2^j)). Then a(n) is n times the coefficient of x^n in the expansion of log(f(x)).
  • A271740 (program): a(n) = 3*n^2 - 2*n + 2.
  • A271743 (program): Number of set partitions of [n] such that 4 is the largest element of the last block.
  • A271744 (program): Number of set partitions of [n] such that 5 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].
  • A271752 (program): Number of set partitions of [n+1] such that n is the largest element of the last block.
  • A271753 (program): Number of set partitions of [n+2] such that n is the largest element of the last block.
  • A271771 (program): Maximum total Hamming distance between pairs of consecutive elements in any permutation of all 2^n binary words of length n.
  • A271776 (program): Triangle T(n,m) = Sum_{k=0..m} (-1)^(m-k)*binomial(m,k)*binomial(n-m+k-1,m-1)*binomial(2*n-3*m+k-1,n-m), T(n,n)=1.
  • A271777 (program): a(n) = Sum_{k=1..n} ((-1)^(n-k) * k / ((n+1)^2 + (k-1)*(n+1))) * binomial(n+1, k+1) * binomial(n+k, k)^2.
  • A271779 (program): a(n) = n^3 + 2*n^2 + 5*n + 11.
  • A271783 (program): Numbers that have exactly four zeros when written in binary balanced system (A270885).
  • A271784 (program): Numbers that have exactly five zeros when written in binary balanced system (A270885).
  • A271785 (program): a(n) = Sum_{k=0..(n-1)/2} (n+2-k)*binomial(n-1-k,k).
  • A271786 (program): Expansion of 2*(1-x)*(2*x^2+4*x+1) / (1-x-x^2)^2.
  • A271787 (program): Integers n that are the sum of two nonzero squares while n*(n+1) is not.
  • A271800 (program): Five steps forward, four steps back.
  • A271823 (program): a(n) = binomial(2*n-4,n-1)*(n+3)/n.
  • A271825 (program): Triangle read by rows: T(n,m) = (-1)^(n-m-1)*m*binomial(2*n-3*m-1,n-m-1)/(n-m), T(n,n)=1.
  • A271827 (program): Expansion of (x^5-2*x^4+2*x^3-x+1)/(x^4-2*x^3+3*x^2-3*x+1).
  • A271828 (program): a(n) = 4*n^3 - 18*n^2 + 27*n - 12.
  • A271830 (program): Expansion of (3 - 4*x + 3*x^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].
  • A271833 (program): Expansion of (1 + 2*x + 2*x^2 + 2*x^3 - 5*x^4 + 2*x^5 + 2*x^6 + 2*x^7)/((1 - x)^2*(1 + x + x^2 + x^3 + x^4 + x^5 + x^6 + x^7)).
  • A271834 (program): a(n) = 2^n - Sum_{m=0..n} binomial(n/gcd(n,m), m/gcd(n,m)) = 2^n - A082906.
  • A271836 (program): Decimal expansion of 3^(1/3) / 2^(1/6).
  • A271840 (program): Primes of the form n^3 + 2n^2 + 5n + 11.
  • A271859 (program): Six steps forward, five steps back.
  • A271860 (program): a(n) = -Sum_{i=1..n} (-1)^floor(n/i).
  • A271870 (program): Convolution of nonzero hexagonal numbers (A000384) with themselves.
  • A271875 (program): Triangle T(n,m) = Sum_{k=1..n-m} (k*(-1)^k*binomial(m+k-1,k)*binomial(2*(n-m),n-m-k))/(n-m), with T(n,n)=1.
  • A271893 (program): Expansion of (2*x+1)*(1-x) / ( 1-2*x-4*x^2+6*x^3 ).
  • A271894 (program): Expansion of (1+x-3*x^2) / ( 1-2*x-4*x^2+6*x^3 ).
  • A271895 (program): Expansion of (1-2*x^2) / ( 1-2*x-4*x^2+6*x^3 ).
  • A271896 (program): Expansion of (x-1)^2 / ( 1-4*x+5*x^2-4*x^3 ).
  • A271897 (program): Expansion of ( 1-2*x+3*x^2 ) / ( 1-4*x+5*x^2-4*x^3 ).
  • A271898 (program): Expansion of ( 1+x^2 ) / ( 1-4*x+5*x^2-4*x^3 ).
  • A271900 (program): Expansion of 1/((1-x^3)*(1-x^5)*(1-x^17)).
  • 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.
  • A271909 (program): Numbers k such that k and 3*k+1 have the same number of prime divisors (including multiplicities).
  • A271911 (program): Number of ways to choose three distinct points from a 2 X n grid so that they form an isosceles triangle.
  • A271912 (program): Number of ways to choose three distinct points from a 3 X n grid so that they form an isosceles triangle.
  • A271916 (program): Array read by antidiagonals: T(m,n) (m>=1, n>=1) = f(m,n) if m <= n or f(n,m) if n < n, where f(m,n) = m*(m-1)*(3*n-m-1)/6.
  • A271919 (program): Numerator of Product_{j=1..n-1} ((3*j+1)/(3*j+2)).
  • A271920 (program): Denominator of Product_{j=1..n-1} ((3*j+1)/(3*j+2)).
  • A271921 (program): Numerator of n*Product_{j=1..n-1} ((3*j + 1)/(3*j + 2)).
  • A271922 (program): Denominator of n*Product_{j=1..n-1} ((3*j + 1)/(3*j + 2)).
  • 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.
  • A271941 (program): Number of peaks in all bargraphs having semiperimeter n (n>=2).
  • A271943 (program): The sum of the widths of all bargraphs of semiperimeter n (n>=2).
  • A271944 (program): Expansion of 2*x*(1 + x)/(1 - x - 9*x^2 + x^3).
  • A271945 (program): Expansion of 4*x^2/(1 - x - 9*x^2 + x^3).
  • A271970 (program): Linear recurrence, with both signature and original terms = 1,0,1,0,1
  • A271972 (program): Expansion of (1 + 3*x)/(1 - 4*x + 7*x^2).
  • A271974 (program): Let p = prime(n): if p mod 4 == 1 then a(n) = (1+p)/2 otherwise if p mod 4 == 3 then a(n) = (1-p)/2.
  • A271981 (program): Primes p such that p + 40 is also prime.
  • A271982 (program): Primes p such that p + 42 is also prime.
  • 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.
  • A271999 (program): Halogen sequence: a(n) = A018227(n)-1.
  • 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.
  • A272008 (program): a(n) is the numerator of the fractional part of sigma(n)/n, where sigma(n) is the sum of the divisors of n.
  • 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.
  • A272010 (program): First differences of 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.
  • A272024 (program): Number of partitions of the sum of the divisors of n.
  • A272027 (program): a(n) = 3*sigma(n).
  • A272039 (program): a(n) = 10*n^2 + 4*n + 1.
  • A272042 (program): a(n) = 2*prime(2n) - prime(n).
  • 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.
  • A272068 (program): a(n) = (10^n-1)^5.
  • A272071 (program): Expansion of x*(3 - 2*x + 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.
  • A272078 (program): Numbers k such that k^2 + 1 is product of 3 distinct primes.
  • A272093 (program): a(n) = Product_{k=0..n} binomial(k*n,k).
  • A272094 (program): a(n) = Product_{k=0..n} binomial(k^2,k).
  • A272095 (program): a(n) = Product_{k=0..n} binomial(n^2,k).
  • A272099 (program): Triangle read by rows, T(n,k) = C(n+1,k+1)*F([k-n, k-n-1], [-n-1], -1), where F is the generalized hypergeometric function, for n>=0 and 0<=k<=n.
  • A272100 (program): Integers n that are the sum of three nonzero squares while n*(n+1) is not.
  • A272101 (program): Square root of largest square dividing A069482(n).
  • A272103 (program): Convolution of nonzero heptagonal numbers (A000566) with themselves.
  • A272104 (program): Sum of the even numbers among the larger parts of the partitions of n into two parts.
  • A272122 (program): a(n) is the number of positive divisors of A003266(n).
  • A272123 (program): a(n) = Fibonacci(3n) - Fibonacci(2n).
  • A272124 (program): a(n) = 12*n^4 + 16*n^3 + 10*n^2 + 4*n + 1.
  • A272125 (program): a(n) = n^3*(2*n^2+1)/3.
  • A272126 (program): a(n) = 120*n^3 + 60*n^2 + 2*n + 1.
  • A272129 (program): a(n) = 32*n^2 - 56*n + 25.
  • A272130 (program): a(n) = 16*n^3 + 10*n^2 + 4*n + 1.
  • A272134 (program): a(n) = n*(15*n^2 - 15*n + 4).
  • A272136 (program): a(n+1) = a(n-1) + A001414(a(n)) with a(1)=1, a(2)=2.
  • 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.
  • A272173 (program): Product of the sum of the divisors of n and the sum of the divisors of n-th prime.
  • A272176 (program): Primes p such that p + 44 is also prime.
  • 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.
  • A272190 (program): Either 6th power of a prime, or product of the square of two different primes.
  • A272199 (program): Expansion of 1/(1 - 2*x + 13*x^2).
  • A272209 (program): Number of partitions of the number of divisors of n.
  • 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.
  • A272214 (program): Square array read by antidiagonals upwards in which T(n,k) is the product of the n-th prime and the sum of the divisors of k, n >= 1, k >= 1.
  • A272229 (program): Numbers n such that n and 3n+1 have the same number of distinct prime divisors.
  • A272244 (program): a(n) = Product_{k=0..n} (n^2 + k^2).
  • A272246 (program): a(n) = Product_{k=0..n} (n^3 + k^3).
  • A272247 (program): a(n) = Product_{k=0..n} (n^4 + k^4).
  • A272248 (program): a(n) = Product_{k=0..n} (n^5 + k^5).
  • A272261 (program): Number of one-to-one functions f from [n] to [2n] where f(x) may not be equal to x or to 2n+1-x.
  • A272263 (program): a(n) = numerator of A000032(n) - 1/2^n.
  • A272266 (program): The union of squares (A000290) and 10-gonal numbers (A001107).
  • A272270 (program): Positive integers n where the number of parts function on the set of 4-ary partitions of n is equidistributed mod 4.
  • A272297 (program): a(n) = n^4 + 64.
  • A272298 (program): a(n) = n^4 + 324.
  • A272299 (program): a(n) = n + 2*floor(n/2) + 3*floor(n/3).
  • A272303 (program): Magic sums of 4 X 4 semimagic squares composed of primes.
  • A272306 (program): Lesser of two consecutive semiprimes whose sum is also semiprime.
  • A272309 (program): Lesser of two consecutive semiprimes with a prime difference.
  • 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.
  • A272344 (program): Positive integers n where the number of parts function on the set of 3-ary partitions of n is equidistributed mod 3.
  • A272347 (program): Least number divisible by n and by the number of its own divisors.
  • 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.
  • A272357 (program): a(n) = n*(105*n^3 - 210*n^2 + 147*n - 34).
  • A272361 (program): Numbers n such that (2^n + 1) / gcd(n, 2^n + 1) is not squarefree.
  • A272362 (program): Expansion of (1 + x - x^2 - x^3 - x^4)/((1 - x)*(1 - x - 2*x^2 - 2*x^3 - x^4)).
  • 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*(6*n^2 - 8*n + 3).
  • A272379 (program): a(n) = n*(24*n^3 - 60*n^2 + 54*n - 17).
  • 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.
  • A272441 (program): Primes with a prime number of binary digits.
  • 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.
  • A272475 (program): Numbers n such that 2^n-1 and 3^n-1 are not coprime.
  • A272476 (program): a(n) = n if n is prime, a(n) = 2*n+3 otherwise.
  • A272492 (program): Number of ordered set partitions of [n] with nondecreasing block sizes and maximal block size equal to two.
  • A272514 (program): Number of set partitions of [n] into two blocks with distinct sizes.
  • A272524 (program): Refactorable triangular numbers.
  • 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 + 5*x - 3*x^2 + 7*x^3 + 3*x^4 + 3 *x^5 - x^6 + x^7)/((1 - x)^3*(1 + x + x^2 + x^3)^2).
  • A272569 (program): A variation on Stern’s diatomic sequence.
  • 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)).
  • A272582 (program): The number of strongly connected digraphs with n vertices and n+1 edges.
  • A272586 (program): Number of active (ON,black) cells at stage 2^n-1 of the two-dimensional cellular automaton defined by “Rule 507”, based on the 5-celled von Neumann neighborhood.
  • A272590 (program): a(n) is the smallest number m such that the multiplicative group modulo m is the direct product of n cyclic groups.
  • A272591 (program): The unique positive root of x^5 - 2*x^4 - x^2 - x - 1.
  • A272592 (program): Numbers n such that the multiplicative group modulo n is the direct product of 2 cyclic groups.
  • A272593 (program): Numbers n such that the multiplicative group modulo n is the direct product of 3 cyclic groups.
  • A272594 (program): Numbers n such that the multiplicative group modulo n is the direct product of 4 cyclic groups.
  • A272595 (program): Numbers n such that the multiplicative group modulo n is the direct product of 5 cyclic groups.
  • A272596 (program): Numbers n such that the multiplicative group modulo n is the direct product of 6 cyclic groups.
  • A272597 (program): Numbers n such that the multiplicative group modulo n is the direct product of 7 cyclic groups.
  • A272603 (program): Number of permutations of [n] whose cycle lengths are factorials.
  • A272604 (program): Maximum subrange sum over n written out in binary with -1 for each zero (cf. A276691).
  • A272614 (program): Numbers whose binary digits, except for the first “1”, are given by floor(((k-n)/n) mod 2) with 1<=k<=n.
  • A272630 (program): a(n) = binomial(3*prime(n), prime(n)) - 3*binomial(2*prime(n), prime(n)) + 3.
  • A272631 (program): Sum of three or more consecutive Fibonacci numbers.
  • A272632 (program): Non-Fibonacci numbers that are both a sum and a difference of two Fibonacci numbers.
  • A272635 (program): Numbers that are not a sum or a difference of two Fibonacci numbers.
  • A272636 (program): a(0)=0, a(1)=1; thereafter a(n) = squarefree part of a(n-1)+a(n-2).
  • A272642 (program): Expansion of (x^4+x^3+x^2-x-1)/(x^4+2*x^3+2*x^2+x-1).
  • A272646 (program): a(0)=a(1)=1; thereafter a(n) = (4*n-3)*a(n-1) + 2*a(n-2).
  • A272647 (program): a(n) = A001517(n) mod 7.
  • A272648 (program): a(n) = A002119(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.
  • A272656 (program): Bisection of A003319: a(n) = A003319(2n).
  • A272657 (program): Bisection of A003319: a(n) = A003319(2n+1).
  • A272664 (program): (001)(001)(001)(10)*.
  • A272665 (program): Imaginary parts of b(n) sequence used to define A143056.
  • 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.
  • A272670 (program): Numbers whose binary expansion is not palindromic but which when reversed and leading zeros omitted, does form a palindrome.
  • A272688 (program): The antibracket constants {x_n}^n.
  • A272690 (program): a(n) = 22*Sum_{i=0..n-2} 46^i*2^(n-2-i) + 2^(n-1).
  • A272697 (program): Powers of 2 with exactly one odd decimal digit.
  • 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.
  • A272706 (program): Number of active (ON,black) cells at stage 2^n-1 of the 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.
  • A272721 (program): The circle curvature (rounded down) inscribed in the area related to critical point of Mandelbrot set at C = 1/4.
  • A272729 (program): a(n) is the number of repetitions of 2n-1 in A272727.
  • 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).
  • A272762 (program): Number of active (ON,black) cells at stage 2^n-1 of the two-dimensional cellular automaton defined by “Rule 822”, based on the 5-celled von Neumann neighborhood.
  • A272775 (program): Squares of the form P(n, 5) + n, where P(x,k) is the Pochhammer function and n = square (A000290).
  • A272777 (program): In the interval [prime(n), 2*prime(n)], the greatest k with the maximal number of divisors.
  • A272795 (program): Decimal expansion of 2*sin(1/2).
  • A272799 (program): Numbers k such that 2*k - 1 and 2*k + 1 are squarefree.
  • A272800 (program): Flavius Josephus factor of n.
  • A272815 (program): Prime pairs of the form (p, p+16).
  • A272816 (program): Prime pairs of the form (p, p+20).
  • A272832 (program): Number of active (ON,black) cells at stage 2^n-1 of the two-dimensional cellular automaton defined by “Rule 694”, based on the 5-celled von Neumann neighborhood.
  • A272850 (program): a(n) = (n^2 + (n+1)^2)*(n^2 + (n+1)^2 + 2*n*(n+1)).
  • A272863 (program): Numerator of the ratio of consecutive prime gaps.
  • A272866 (program): Triangle read by rows, T(n,k) = GegenbauerC(m,-n,-3/2) where m = k if k<n else 2*n-k, for n>=0 and 0<=k<=2n.
  • A272867 (program): Triangle read by rows, T(n,k) = GegenbauerC(m,-n,-2) where m = k if k<n else 2*n-k, for n>=0 and 0<=k<=2n.
  • A272868 (program): Triangle read by rows, T(n,k) = 2^k*GegenbauerC(k,-n,-1/4), for n>=0 and 0<=k<=n.
  • A272870 (program): Real part of (n + i)^4.
  • A272871 (program): Imaginary part of (n + i)^4.
  • A272872 (program): Numbers k such that k+1 is divisible by number of divisors of k.
  • A272874 (program): Decimal expansion of the infinite nested radical sqrt(-1 + sqrt(1 + sqrt(-1 + sqrt(1 + …))).
  • A272887 (program): Number of ways to write prime(n) as (4*x + 2)*y + 4*x + 1 where x and y are nonnegative integers.
  • A272890 (program): Numbers n such that the product of n and the sum of the reciprocal of their anti-divisors is an integer.
  • A272896 (program): Difference between the number of odd and even digits in the decimal expansion of 2^n.
  • A272900 (program): Fibonacci-products fractal sequence.
  • A272902 (program): Numbers n such that 6n - 5 is not prime.
  • A272903 (program): Least nonnegative integer x such that n^2+nx-2n-x is prime.
  • 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.
  • A272920 (program): Number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by “Rule 555”, based on the 5-celled von Neumann neighborhood.
  • A272921 (program): Number of active (ON,black) cells at stage 2^n-1 of the two-dimensional cellular automaton defined by “Rule 555”, based on the 5-celled von Neumann neighborhood.
  • A272922 (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 555”, based on the 5-celled von Neumann neighborhood.
  • A272923 (program): First differences of number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by “Rule 555”, based on the 5-celled von Neumann neighborhood.
  • A272928 (program): Partial sums of A147562.
  • A272931 (program): a(n) = 2^(n+1)*cos(n*arctan(sqrt(15))).
  • A272933 (program): Numbers of the form x^2 + 12*y^2.
  • A272952 (program): Number of n X 2 0..1 arrays with exactly n+2-2 having value 1 and no three 1s forming an isosceles right triangle.
  • 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.
  • A272985 (program): Numbers n such that the elements of the Collatz trajectory of n are exactly the same as the divisors of n.
  • A273001 (program): Number of permutations of [n] whose cycle lengths are Fibonacci numbers.
  • A273003 (program): Arrange the base 10 digits of the n-th Fibonacci number in descending order.
  • A273004 (program): Sum of coefficients in the hereditary representation of n in base 2.
  • A273005 (program): Sum of coefficients in the hereditary representation of n in base 10.
  • A273011 (program): Numbers n such that d_i(n) >= d_i(k) for k = 1 to n-1, where d_i(n) is the number of infinitary divisors of n (A037445).
  • A273012 (program): Totient of the n-th semiprime.
  • A273015 (program): Ramanujan’s largely composite numbers having 3 as the greatest prime divisor.
  • A273019 (program): a(n) = hypergeom([-2*n-1, 1/2], [2], 4) + (2*n+1)*hypergeom([-n+1/2, -n], [2], 4).
  • A273020 (program): a(n) = Sum_{k=0..n} C(n,k)*((-1)^n*(C(k,n-k)-C(k,n-k-1))+C(n-k,k+1)).
  • A273040 (program): Least k >= 2 such that the base-k digits of n are nondecreasing.
  • A273045 (program): Fibonacci numbers with digits in nondecreasing order.
  • A273050 (program): Numbers k such that ror(k) XOR rol(k) = k, where ror(x)=A038572(x) is x rotated one binary place to the right, rol(x)=A006257(x) is x rotated one binary place to the left, and XOR is the binary exclusive-or operator.
  • A273052 (program): Numbers n such that 7*n^2 + 8 is a square.
  • A273053 (program): Numbers n such that 15*n^2 + 16 is a square.
  • A273054 (program): Numbers n such that 19*n^2 + 20 is a square.
  • A273055 (program): a(n) = Sum_{k=0..n} binomial(2*k, k) * binomial(2*n+1, 2*k).
  • A273060 (program): a(n) = phi(n!)/phi(n).
  • A273065 (program): Decimal expansion of the negative reciprocal of the real root of x^3 - 2x + 2.
  • A273066 (program): Decimal expansion of the real root of x^3 - 2x + 2, negated.
  • A273067 (program): Decimal expansion of the constant term, which is also a root, of the cubic polynomial below.
  • A273088 (program): a(n) is a multiple of 6 and a(n)-1 or a(n)+1 is an isolated (non-twin) prime number.
  • A273092 (program): a(n) = 2^n - 1 written backwards.
  • A273105 (program): a(n) = A038572(n) + A006257(n), sum of the two numbers obtained by rotating the binary representation of n by one place to the right and to the left.
  • 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.
  • A273144 (program): Number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by “Rule 597”, based on the 5-celled von Neumann neighborhood.
  • A273145 (program): Number of active (ON,black) cells at stage 2^n-1 of the two-dimensional cellular automaton defined by “Rule 597”, based on the 5-celled von Neumann neighborhood.
  • A273146 (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 597”, based on the 5-celled von Neumann neighborhood.
  • A273147 (program): First differences of number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by “Rule 597”, based on the 5-celled von Neumann neighborhood.
  • A273149 (program): a(n) = A053839(n)+1.
  • A273150 (program): Number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by “Rule 598”, based on the 5-celled von Neumann neighborhood.
  • A273151 (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 598”, based on the 5-celled von Neumann neighborhood.
  • A273152 (program): First differences of number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by “Rule 598”, based on the 5-celled von Neumann neighborhood.
  • A273153 (program): a(n) = Numerator of (0 followed by 1’s) - n/2^n.
  • A273156 (program): Product of all parts in Zeckendorf representation of n.
  • A273159 (program): Numbers whose digit sum is divisible by 7.
  • A273160 (program): a(n) = Sum_{k=1..n} C(n, floor((n-k)/k)).
  • A273161 (program): a(n) = Sum_{k=1..n} C(n-k, floor((n-k)/k)).
  • A273167 (program): Numerators of coefficient triangle for expansion of x^(2*n) in terms of Chebyshev polynomials of the first kind T(2*m, x) (A127674).
  • A273179 (program): Numbers k for which 2 has exactly four square roots mod k.
  • A273180 (program): Numbers n such that ror(n) + rol(n) is a power of 2, where ror(n)=A038572(n) is n rotated one binary place to the right, rol(n)=A006257(n) is n rotated one binary place to the left.
  • 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.
  • A273188 (program): Numbers whose digit sum is divisible by 8.
  • 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.
  • A273190 (program): a(n) is the number of nonnegative m < n for which m + n is a perfect square.
  • A273194 (program): a(n) = numerator(R(n,3)), where R(n,d) = (Product_{j prime to d)} Pochhammer(j/d, n)) / n!.
  • A273220 (program): a(n) = 8n^2 - 12n + 1.
  • A273225 (program): Number of bipartitions of n wherein odd parts are distinct (and even parts are unrestricted).
  • A273226 (program): G.f. is the cube of the g.f. of A006950.
  • A273227 (program): Consider all ways of writing the n-th composite number as the product of two divisors d1*d2 = d3*d4 = …; a(n) is the minimum of the sums {d1 + d2, d3 + d4, …}.
  • A273228 (program): G.f. is the fourth power of the g.f. of A006950.
  • A273239 (program): Non-palindromic numbers whose reversal is a palindrome.
  • A273245 (program): Non-palindromic binary numbers whose reversal is a palindrome.
  • A273251 (program): Number of active (ON,black) cells at stage 2^n-1 of the two-dimensional cellular automaton defined by “Rule 619”, based on the 5-celled von Neumann neighborhood.
  • A273264 (program): Volume of unit n-ball, rounded to the nearest integer.
  • A273293 (program): Numbers k such that k and k^2 are the sums of two nonzero squares in exactly two ways.
  • 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.
  • A273319 (program): a(n) = ((2*n+1)^(n+1) + (-1)^n)/(n+1)^2.
  • 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.
  • A273331 (program): Number of active (ON,black) cells at stage 2^n-1 of the two-dimensional cellular automaton defined by “Rule 654”, based on the 5-celled von Neumann neighborhood.
  • 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.
  • A273345 (program): Number of levels in all bargraphs having semiperimeter n (n>=2). A level in a bargraph is a maximal sequence of two or more adjacent horizontal steps; it is preceded and followed by either an up step or a down step.
  • A273348 (program): The sum of the semiperimeters of the bargraphs of area n (n>=1).
  • A273352 (program): a(n) = 2^(2n+2) F(n) where F(n) is Ramanujan’s F(n) = Sum_{k>=1} k^(4n-1)/(e^(Pi*k)-1) - 16^n* Sum_{k>=1} k^(4n-1)/(e^(4*Pi*k)-1).
  • A273365 (program): Numbers k such that 10*k+4 is a perfect square.
  • A273366 (program): a(n) = 10*n^2 + 10*n + 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.
  • A273417 (program): Number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by “Rule 705”, based on the 5-celled von Neumann neighborhood.
  • A273418 (program): Number of active (ON,black) cells at stage 2^n-1 of the two-dimensional cellular automaton defined by “Rule 705”, based on the 5-celled von Neumann neighborhood.
  • A273419 (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 705”, based on the 5-celled von Neumann neighborhood.
  • A273420 (program): First differences of number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by “Rule 705”, 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.
  • A273446 (program): Number of active (ON,black) cells at stage 2^n-1 of the 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.
  • A273459 (program): Even numbers such that the sum of the odd divisors is a prime p and the sum of the even divisors is 2p.
  • 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.
  • A273493 (program): a(n) = A245327(n) + A245328(n).
  • A273494 (program): a(n) = A245325(n) + A245326(n).
  • A273495 (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 20”, based on the 5-celled von Neumann neighborhood.
  • A273496 (program): Triangle read by rows: coefficients in the expansion cos(x)^n = (1/2)^n * Sum_{k=0..n} T(n,k) * cos(k*x).
  • A273499 (program): Number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by “Rule 771”, based on the 5-celled von Neumann neighborhood.
  • A273500 (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 771”, based on the 5-celled von Neumann neighborhood.
  • A273501 (program): First differences of number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by “Rule 771”, based on the 5-celled von Neumann neighborhood.
  • A273512 (program): Expansion of Lemniscate constant or Gauss’s constant in base 2.
  • 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.
  • A273531 (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 20”, based on the 5-celled von Neumann neighborhood.
  • 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.
  • A273546 (program): Integers n such that n^n is the average of a nonzero square and a positive cube.
  • A273561 (program): Number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by “Rule 790”, based on the 5-celled von Neumann neighborhood.
  • A273562 (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 790”, based on the 5-celled von Neumann neighborhood.
  • A273563 (program): First differences of number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by “Rule 790”, based on the 5-celled von Neumann neighborhood.
  • A273565 (program): Number of active (ON,black) cells at stage 2^n-1 of the two-dimensional cellular automaton defined by “Rule 793”, 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.
  • A273577 (program): Number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by “Rule 803”, based on the 5-celled von Neumann neighborhood.
  • A273578 (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 803”, based on the 5-celled von Neumann neighborhood.
  • A273579 (program): First differences of number of active (ON,black) cells in n-th stage of growth of two-dimensional cellular automaton defined by “Rule 803”, based on the 5-celled von Neumann neighborhood.
  • A273596 (program): For n >= 2, a(n) is the number of slim rectangular diagrams of length n.
  • 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.
  • A273619 (program): Table read by antidiagonals (n>1, k>0): A(n,k) = leading digit of k in base n.
  • A273622 (program): a(n) = (1/3)*(Lucas(3*n) - Lucas(n)).
  • A273623 (program): a(n) = Fibonacci(3*n) - (2 + (-1)^n)*Fibonacci(n).
  • A273624 (program): a(n) = (1/11)*(Fibonacci(4*n) + Fibonacci(6*n)).
  • A273625 (program): a(n) = (1/12)*(Fibonacci(2*n) + Fibonacci(4*n) + Fibonacci(6*n)).
  • A273626 (program): A fourth-order divisibility sequence: a(n) = (1/14)*(Pell(4*n) + Pell(2*n)).
  • A273627 (program): A divisibility sequence: (1/8)*(Pell(4*n) - 2*Pell(2*n)).
  • A273628 (program): a(n) = (7*n)!/((5*n)!*n!^2).
  • A273629 (program): a(n) = (9*n)!/((7*n)!*n!^2).
  • A273630 (program): a(n) = Sum_{k = 0..n} (-1)^k*k^3*binomial(n,k)^3.
  • A273631 (program): a(n) = Sum_{k = 0..n} (-1)^k*binomial(k,2)^3*binomial(n,k)^3.
  • 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.
  • A273662 (program): Least monotonic left inverse for A256450: a(1) = 0; for n > 1, a(n) = A257680(n) + a(n-1).
  • A273663 (program): Least monotonic left inverse for A273670: a(1) = 0; for n > 1, a(n) = A257680(A225901(n)) + a(n-1).
  • A273664 (program): a(n) = A249746(A032766(n)).
  • A273669 (program): Decimal representation ends with either 2 or 9.
  • A273670 (program): Numbers with at least one maximal digit in their factorial base representation.
  • 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.
  • A273676 (program): Number of active (ON,black) cells at stage 2^n-1 of the 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.
  • A273692 (program): a(n) is the denominator of 2*O(n+1) - O(n+2) where O(n) = n/2^n, the n-th Oresme number.
  • A273711 (program): The Hadamard product of omega(n) and A007875(n).
  • A273714 (program): Number of doublerises in all bargraphs having semiperimeter n (n>=2). A doublerise in a bargraph is any pair of adjacent up steps.
  • A273716 (program): The number of peaks of width 1 (i.e., UHD configurations, where U = (0,1), H=(1,0), D=(0,-1)) in all bargraphs of semiperimeter n (n>=2).
  • A273720 (program): Number of horizontal steps in the peaks of all bargraphs having semiperimeter n (n>=2).
  • 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.
  • A273767 (program): Number of active (ON,black) cells at stage 2^n-1 of the 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.
  • A273774 (program): Decimal expansion of Jevon’s number.
  • A273777 (program): Consider all ways of writing the n-th composite number as the product of two divisors d1*d2 = d3*d4 = … where each divisor is larger than 1; a(n) is the maximum of the sums {d1 + d2, d3 + d4, …}.
  • 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.
  • A273796 (program): Number of active (ON,black) cells at stage 2^n-1 of the two-dimensional cellular automaton defined by “Rule 942”, 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.
  • A273828 (program): Number of active (ON,black) cells at stage 2^n-1 of the two-dimensional cellular automaton defined by “Rule 950”, based on the 5-celled von Neumann neighborhood.
  • 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.
  • A273845 (program): Expansion of Product_{n>=1} (1 - x^(3*n))/(1 - x^n)^3 in powers of x.
  • 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.
  • A273848 (program): Number of active (ON,black) cells at stage 2^n-1 of the 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.
  • A273860 (program): Number of active (ON,black) cells at stage 2^n-1 of the two-dimensional cellular automaton defined by “Rule 1006”, based on the 5-celled von Neumann neighborhood.
  • A273878 (program): Numerator of (2*(n+1)!/(n+2)).
  • A273889 (program): a(n) = ((4n-3)!! + (4n-2)!!) / (4n-1).
  • A273892 (program): Numbers starting with an even (decimal) digit.
  • A273893 (program): Denominator of n/3^n.
  • A273898 (program): Sum of the abscissae of the first descents of all bargraphs of semiperimeter n (n>=2).
  • A273900 (program): Number of columns of length 1 in all bargraphs of semiperimeter n (n>=2).
  • A273909 (program): Let p = prime(n) and q = prime(n+1), then a(n) = p*q - p^2 - 2*q.
  • A273910 (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 614”, based on the 5-celled von Neumann neighborhood.
  • A273911 (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 614”, based on the 5-celled von Neumann neighborhood.
  • A273912 (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 614”, based on the 5-celled von Neumann neighborhood.
  • 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).
  • A273927 (program): Absolute difference between A000290(n) and the nearest term of A000578.
  • A273929 (program): Numbers that are congruent to {5, 6, 7} mod 8 and are squarefree.
  • A273935 (program): Number of ways to arrange n women and n men around a circular table so that they can be divided into n nonintersecting pairs of 1 woman and 1 man sitting side-by-side.
  • A273938 (program): Sum of the divisors of the n-th odd prime power.
  • A273939 (program): a(0) = 1, a(1) = 2; for k>0, a(2*k) = k*a(2*k-1) + a(2*k-2), a(2*k+1) = a(2*k) + a(2*k-1).
  • A273954 (program): E.g.f. satisfies: A(x) = Sum_{n>=0} x^n/n! * exp(n*x) * A(x)^n.
  • A273960 (program): a(n) = (-1)^n*prime(n).
  • A273972 (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 20”, based on the 5-celled von Neumann neighborhood.
  • A273973 (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 20”, based on the 5-celled von Neumann neighborhood.
  • A273982 (program): Number of little cubes visible around an n X n X n cube with a face on a table.
  • A273983 (program): a(n) = ((4*n)!! - (4*n-1)!!)/(4*n+1).
  • A274004 (program): First differences of A002960.
  • A274006 (program): Largest proper prime power divisor of n, or 1 if n is squarefree.
  • 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.
  • A274017 (program): Number of n-bead binary necklaces (no turning over allowed) that avoid the subsequence 110.
  • A274018 (program): Number of n-bead ternary necklaces (no turning over allowed) that avoid the subsequence 110.
  • A274029 (program): Product of infinitary divisors of n.
  • A274039 (program): Expansion of (x^4 + x^10) / (1 - 2*x + x^2).
  • A274047 (program): Diameter of Generalized Petersen Graph G(n, 2).
  • A274048 (program): a(n) = A116640(A018900(n)) = A116623(A059893(A018900(n))).
  • A274056 (program): Number of unrooted labeled trees on 2n nodes with node degree either one or three.
  • A274060 (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 22”, based on the 5-celled von Neumann neighborhood.
  • 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.
  • A274075 (program): Sum of n-th powers of the roots of x^3 + x^2 - 9*x - 1.
  • A274077 (program): a(n) = n^3 + 4.
  • A274079 (program): Table read by rows: the n-th row is the list of numbers diagonally up and to the right of n in the natural numbers read by antidiagonals.
  • A274081 (program): Number of unrooted labeled trees on 3n+2 nodes with node degree either one or four.
  • 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.
  • A274100 (program): Number of partitions of 2^n into at most four parts.
  • A274104 (program): a(n) = Sum_{k=0..n} (3*k+2)*Catalan(k).
  • A274108 (program): Number of partitions of n into parts with exactly two different sizes, the sizes being relatively prime.
  • A274110 (program): Number of equivalence classes of ballot paths of length n for the string uu.
  • A274112 (program): Number of equivalence classes of ballot paths of length n for the string ddu.
  • A274115 (program): Number of equivalence classes of Dyck paths of semilength n for the string duu.
  • A274119 (program): a(n) = (Product_{i=0..4}(i*n+2) - Product_{i=0..4}(-i*n-1))/(4*n+3).
  • A274129 (program): Sum of all numbers that appear when we interpret an ordered subset of [0,1,…,n] containing n as the digits, possibly larger than nine, of a base ten number, with the smallest element being the least significant.
  • A274136 (program): a(n) = (n+1)*(2*n+2)!/(n+2).
  • 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.
  • A274141 (program): Positive numbers divisible by 3^3 or by the square of some other prime.
  • A274162 (program): Number of real integers in n-th generation of tree T(3i) defined in Comments.
  • A274163 (program): Number of real integers in n-th generation of tree T(4i) defined in Comments.
  • A274179 (program): Expansion of f(x^1, x^6) in powers of x where f() is Ramanujan’s general theta function.
  • A274181 (program): Decimal expansion of Phi(1/2, 2, 2), where Phi is the Lerch transcendent.
  • A274202 (program): Primes congruent to 31 mod 65.
  • A274203 (program): Expansion of x*(1 - x - x^3)/((1 - x)*(1 - 2*x - 3*x^2 - 2*x^3 - x^4)).
  • A274212 (program): The factorization of n contains only lesser of twin primes.
  • A274213 (program): Meta recurrence: a(0) = 1, a(1) = 2, a(2) = 3, a(n) = a(n - a(n-3)) + 3 for n > 2.
  • A274216 (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 22”, based on the 5-celled von Neumann neighborhood.
  • A274220 (program): a(n) = (-cos(Pi/7)/cos(2*Pi/7))^n + (-cos(2*Pi/7)/cos(3*Pi/7))^n + (cos(3*Pi/7)/cos(Pi/7))^n.
  • A274221 (program): List of quadruples: 3*n*(3*n-1), 3*n*(3*n+1), (3*n+1)^2, (3*n+2)^2.
  • A274224 (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 22”, based on the 5-celled von Neumann neighborhood.
  • A274225 (program): Denominator of the ratio of consecutive prime gaps.
  • A274230 (program): Number of holes in a sheet of paper when you fold it n times and cut off the four corners.
  • A274231 (program): Ternary representation with index set {0, 1, 5}.
  • 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.
  • A274243 (program): Numbers n for which the sum of the odd numbers in the Collatz (3x+1) iteration of n is prime.
  • A274246 (program): a(n) = Sum_{k=0..n} binomial(n, k)^3 * 2^(n-k) * k!.
  • 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.
  • A274253 (program): Number of partitions of n^7 into at most three parts.
  • A274254 (program): Number of partitions of n^11 into at most three parts.
  • A274263 (program): Integer part of the ratio of consecutive prime gaps.
  • A274265 (program): a(n) = (3*n - 1)^(n-1).
  • A274266 (program): E.g.f. (1 + x)^3*log(1 + x).
  • A274267 (program): a(n) = (4*n - 1)^(n-1).
  • A274268 (program): E.g.f. (1 + x)^4*log(1 + x).
  • A274269 (program): a(n) = (5*n - 1)^(n-1).
  • A274270 (program): E.g.f. (1 + x)^5*log(1 + x).
  • A274271 (program): Number of partitions of 3^n into at most four parts.
  • A274272 (program): Number of partitions of 5^n into at most four parts.
  • A274273 (program): Number of noncomposite areas of a Venn diagram for n multisets.
  • A274274 (program): Number of ordered ways to write n as x^3 + y^2 + z^2, where x,y,z are nonnegative integers with y <= z.
  • A274278 (program): a(n) = ((n+1)^(n-1) - (n-1)^(n-1))/2 for n>=1.
  • A274294 (program): a(n) = 1+(n+1)^2+n!+Sum_{k=1..n-1} binomial(n,k)*n!/(n-k)!.
  • A274298 (program): A bisection of A002326.
  • A274299 (program): A bisection of A002326.
  • A274300 (program): Arises in study of A000587.
  • A274301 (program): a(n) = 24*A274300(n) + 14.
  • A274304 (program): A bisection of A002866.
  • A274306 (program): a(n) = Product_{k=1..n} (4*k^4+1).
  • A274308 (program): Number of n-tuples of singular vectors of a 3 X 3 X 3 X … X 3 n-dimensional tensor.
  • A274311 (program): a(n) = 15*binomial(n,6)-6*binomial(n-2,4)+binomial(n-4,4).
  • A274319 (program): Numbers whose digit sum is divisible by 6.
  • A274322 (program): Number of partitions of n^2 into at most five parts.
  • 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.
  • A274327 (program): Expansion of Product_{n>=1} (1 - x^(4*n))/(1 - x^n)^4 in powers of x.
  • 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 period 3 sequence of the iterated sum of deficient divisors function (A187793) starting at 15.
  • A274340 (program): The period 4 sequence of the iterated sum of deficient divisors function (A187793) starting at 19.
  • A274378 (program): G.f. satisfies: A(x) = (1 + x*A(x))^2 * (1 + x^2*A(x)^3).
  • A274379 (program): G.f. satisfies: A(x) = (1 + x*A(x))^3 * (1 + x^2*A(x)^3).
  • A274380 (program): The period 4 sequence of the iterated sum of deficient divisors function (A187793) starting at 34.
  • A274382 (program): a(n) = gcd(n, n*(n+1)/2 - sigma(n)).
  • A274384 (program): Numbers n such that 2^n is not the average of three positive cubes.
  • A274397 (program): Positive integers m such that sigma(m) is divisible by 5.
  • A274406 (program): Numbers m such that 9 divides m*(m + 1).
  • A274427 (program): Positions in A274426 of products of distinct Fibonacci numbers > 1.
  • A274428 (program): Positions in A274426 of products of distinct Lucas 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).
  • A274448 (program): Denominators in expansion of W(exp(x)) about x=1, where W is the Lambert function.
  • A274450 (program): Largest number of antipower periods possible for a binary string of length n.
  • A274457 (program): Shortest possible antipower period of a binary string of length n.
  • A274465 (program): Primes which are the sum of cousin prime pairs - 1.
  • A274473 (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 22”, based on the 5-celled von Neumann neighborhood.
  • A274488 (program): Triangle read by rows: T(n,k) is the number of bargraphs of semiperimeter n having least column-height k (n>=2, k>=1).
  • A274489 (program): a(n) = floor(sinh(n) / n^2).
  • A274492 (program): Number of horizontal segments of length 1 in all bargraphs of semiperimeter n (n>=2). By a horizontal segment of length 1 we mean a horizontal step that is not adjacent to any other horizontal step.
  • A274496 (program): Triangle read by rows: T(n,k) is the number of binary words of length n having degree of asymmetry equal to k (n >= 0; 0 <= k <= n/2).
  • A274497 (program): Sum of the degrees of asymmetry of all binary words of length n.
  • A274498 (program): Triangle read by rows: T(n,k) is the number of ternary words of length n having degree of asymmetry equal to k (n>=0; 0<=k<=n/2).
  • A274499 (program): Sum of the degrees of asymmetry of all ternary words of length n.
  • A274501 (program): a(n) = 25*binomial(n-1,6) + binomial(n-1,5).
  • A274502 (program): a(n) = 90*binomial(n-1,7) + 9*binomial(n-1,6).
  • A274515 (program): a(n) is the number of times that the value of ternary n when read as hyperbinary occurs in the set of hyperbinary representations.
  • 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).
  • A274539 (program): E.g.f.: exp(sum(bell(n)*z^n/n, n=1..infinity).
  • A274544 (program): Values of k such that 2*k-1 and 5*k-1 are both perfect squares.
  • A274545 (program): Values of k such that 5*k-1 and 10*k-1 are both perfect squares.
  • A274546 (program): Numbers n such that 5n is squarefree.
  • 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).
  • A274587 (program): Values of n such that 2*n-1 and 4*n-1 are both triangular numbers.
  • A274588 (program): Values of n such that 2*n-1 and 7*n-1 are both triangular numbers.
  • A274593 (program): a(0) = 0; thereafter, a(2*n+1) = a(n)+2*n+1, otherwise a(n) = n.
  • A274595 (program): Numbers n such that n^2 + 2 is the sum of two nonzero squares.
  • A274601 (program): a(n) = 2*3^(s-1) - n, where s is the number of trits of n in balanced ternary form.
  • A274602 (program): Triangle read by rows: T(n,k) = k*(n-k+1)^2 + n - k, 0 <= k <= n.
  • A274603 (program): Numbers n such that 2*n+1 and 3*n+1 are both triangular numbers.
  • A274604 (program): Running sum of Noergaard’s “infinity sequence” A004718.
  • A274610 (program): Values of c such that p^2-c and p^2+c are both positive primes, for the special case when p^2-c = 3, or c = p^2-3, where p is a prime.
  • A274611 (program): a(n) = n/8 if A007814(n) == 3 (mod 4), else a(n) = 2n.
  • A274613 (program): Array T(n,k) = numerator of binomial(k,n)/2^k read by antidiagonals omitting the zeros (upper triangle), a sequence related to Jacobsthal numbers.
  • A274616 (program): Maximal number of non-attacking queens on a right triangular board with n cells on each side.
  • A274621 (program): Coefficients in the expansion Product_{ n>=1 } (1-q^(2n-1))^2/(1-q^(2n))^2.
  • A274626 (program): a(n) = Product_{i=0..2} (2^floor((n+i)/3)-1).
  • A274627 (program): Product_{i=0..3} (2^floor((n+i)/4)-1).
  • A274628 (program): Nathanson’s orphan-counting function h(n).
  • A274629 (program): Partial sums of A274628.
  • A274634 (program): a(n) = n!*A003436(n).
  • A274638 (program): Main diagonal of A274637.
  • A274654 (program): Denominators of coefficients of z^n/n! for the expansion of Fricke’s hypergeometric function F_1(1/2,1/2;z).
  • A274657 (program): Numerators of the coefficients of z^n/n! for the expansion of hypergeometric([1/2,1/2],[1];z).
  • A274658 (program): Irregular triangle which lists in row n the divisors of 2*n+1.
  • A274663 (program): Sum of n-th powers of the roots of x^3 + 4*x^2 - 11*x - 1.
  • A274665 (program): Diagonal of the rational function 1/(1 - x - y - z + x*y + x*z - y*z).
  • A274668 (program): Diagonal of the rational function 1/(1 - x - y - z - x y + x z - y z + x y z).
  • A274671 (program): Diagonal of the rational function 1/(1 - x - y - z - x y + x z + y z - x y z).
  • A274680 (program): Values of n such that 2*n+1 and 4*n+1 are both triangular numbers.
  • 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.
  • A274685 (program): Odd numbers n such that sigma(n) is divisible by 5.
  • A274687 (program): Sequence and first differences (A274688) together list every integer except zero exactly once.
  • A274688 (program): First differences of A274687.
  • A274698 (program): a(n)=prime(n)-(2*last digit of prime(n)).
  • A274701 (program): First differences of A259280.
  • A274707 (program): a(n) = A(n) if n is even else a(n) = A(n)*(n-1)/(n+1) with A(n) = ((n-1)!/ floor((n-1)/2)!^2).
  • A274716 (program): a(2*n+1) = a(2*floor(n/2)+1) + n, a(2*n) = a(n), for n>=1 with a(1)=0.
  • A274719 (program): Expansion of Product_{k >= 1} (1-q^(2*k)).
  • A274734 (program): G.f. satisfies: A(x) = (1 + x*A(x))^2 * (1 + x*A(x)^2).
  • A274735 (program): G.f. satisfies: A(x) = (1 + x*A(x))^3 * (1 + x*A(x)^2).
  • A274742 (program): Triangle read by rows: T(n,k) (n>=3, 0<=k<=n-3) = number of n-sequences of 0’s and 1’s that begin with 1 and have exactly one pair of adjacent 0’s and exactly k pairs of adjacent 1’s.
  • A274743 (program): Repunits with odd indices multiplied by 99, i.e., 99*(1, 111, 11111, 1111111, …).
  • A274745 (program): Number of n X 4 0..2 arrays with no element equal to any value at offset (-1,-2) (0,-1) or (-1,0) and new values introduced in order 0..2.
  • A274750 (program): Number of 3 X n 0..2 arrays with no element equal to any value at offset (-1,-2) (0,-1) or (-1,0) and new values introduced in order 0..2.
  • A274755 (program): Repunits with even indices multiplied by 99, i.e., 99*(11, 1111, 111111, 11111111, …).
  • A274756 (program): Values of n such that 2*n+1 and 6*n+1 are both triangular numbers.
  • A274757 (program): Numbers k such that 6*k+1 is a triangular number (A000217).
  • A274760 (program): The multinomial transform of A001818(n) = ((2*n-1)!!)^2.
  • A274761 (program): a(n) = a(n-1) + a(n-2) + a(n-3), with a(0) = 3, a(1) = 2, a(2) = 5.
  • A274766 (program): Multiplication of pair of contiguous repunits, i.e., (0*1, 1*11, 11*111, 111*1111, 1111*11111, …).
  • A274772 (program): Zero together with the partial sums of A056640.
  • A274773 (program): a(n) = floor(sqrt(2*n-1) + 1/2) - abs(2*(n-1) - (floor(sqrt(2*n-1) + 1/2))^2) + 1.
  • A274776 (program): Irregular triangle read by rows: T(n,k) = number of arrangements of n circles in the affine plane forming k regions, including the regions that do not belong to the circles.
  • A274779 (program): Numbers whose square is the sum of two positive triangular numbers in exactly one way.
  • A274786 (program): Diagonal of the rational function 1/(1-(wxz + wy + wz + xy + xz + y + z)).
  • A274787 (program): Diagonal of the rational function 1/(1-(wxyz + wxy + wxz + wy + xz + y + z)).
  • A274788 (program): Diagonal of the rational function 1/(1-(wxyz + wxz + wy + wz + xy + xz + y + z)).
  • A274789 (program): Diagonal of the rational function 1/(1-(wxyz + wxy + wxz + wy + wz + xy + xz + y + z)).
  • A274798 (program): Number of n X 3 0..2 arrays with no element equal to any value at offset (-1,-2) (-2,-1) (0,-1) or (-1,0) and new values introduced in order 0..2.
  • A274817 (program): a(n) = 2*a(n-1) - a(n-3) + 2*a(n-4) for n>3, a(0)=1, a(1)=-1, a(2)=4, a(3)=8.
  • A274824 (program): Triangle read by rows: T(n,k) = (n-k+1)*sigma(k), n>=1, 1<=k<=n.
  • A274830 (program): Numbers n such that 7*n+1 is a triangular number (A000217).
  • A274832 (program): Values of n such that 2*n+1 and 7*n+1 are both triangular numbers (A000217).
  • A274845 (program): a(0)=1, a(1)=0, a(4n+2) = a(4n+3) = a(4n+5) = (4^(n+1) +(-1)^n)/5, a(4n+4) = (2*4^(n+1) -3*(-1)^n)/5.
  • A274853 (program): Number of n X 3 0..2 arrays with no element equal to any value at offset (-1,0) (0,-1) or (-2,-2) and new values introduced in order 0..2.
  • 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.
  • A274869 (program): Number of set partitions of [n] into exactly five blocks such that all odd elements are in blocks with an odd index and all even elements are in blocks with an even index.
  • A274912 (program): Square array read by antidiagonals upwards in which each new term is the least nonnegative integer distinct from its neighbors.
  • A274913 (program): Square array read by antidiagonals upwards in which each new term is the least positive integer distinct from its neighbors.
  • A274918 (program): Numbers n such that the sum of numbers less than n that do not divide n is odd.
  • A274919 (program): Sum of perimeters of the parts of the symmetric representation of sigma(n).
  • A274922 (program): a(n) = (-1)^n * n if n>0, a(0) = 1.
  • A274923 (program): List of y-coordinates of point moving in counterclockwise square spiral.
  • A274933 (program): Maximal number of non-attacking queens on a quarter chessboard containing n^2 squares.
  • A274946 (program): Boyd’s Pisot-like sequence F(0,5,11).
  • A274949 (program): Complete list of prime powers arising in classification of modular curves of prime-power level and genus 0 with infinitely many rational points.
  • A274951 (program): Pisot sequence E(8,12), a(n) = floor( a(n-1)^2/a(n-2) + 1/2 ).
  • A274954 (program): Number of n X 3 0..2 arrays with no element equal to any value at offset (-1,-1) (-2,0) or (0,-2) and new values introduced in order 0..2.
  • A274968 (program): Even numbers n >= 4 which are not m-gonal number for 3 <= m < n.
  • A274969 (program): Number of walks in the first quadrant starting and ending at (0,0) consisting of 3n steps taken from {E=(1, 0), D=(-1, 1), S=(0, -1)}, no S step occurring before the final E step.
  • A274972 (program): Numbers x such that there exists n in N : (x+1)^3 - x^3 = 61*n^2.
  • A274973 (program): Centered cubohemioctahedral numbers: a(n) = 2*n^3+9*n^2+n+1.
  • A274974 (program): Centered octahemioctahedral numbers: a(n) = (4*n^3+24*n^2+8*n+3)/3.
  • A274975 (program): Sum of n-th powers of the three roots of x^3-2*x^2-x+1.
  • A274977 (program): a(n) = a(n-1) + 3*a(n-2) with n>1, a(0)=1, a(1)=6.
  • 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.
  • A275001 (program): Expansion of 1/(1 - Sum_{k>=1} x^(prime(k)^2)).
  • A275009 (program): Table of F[k]_n(2) with rows k >= 0 and columns 0 <= n <= 2.
  • A275015 (program): Number of neighbors of each new term in an isosceles triangle read by rows.
  • A275016 (program): a(n) = (2^n - (-1+i)^n - (-1-i)^n)/4 - 1 where i is the imaginary unit.
  • A275017 (program): a(1)=1, a(2)=2, a(n) = prime(n-2) - a(n-2) for n > 2.
  • A275019 (program): 2-adic valuation of tetrahedral numbers C(n+2,3) = n(n+1)(n+2)/6 = A000292.
  • A275024 (program): Total weight of the n-th twice-prime-factored multiset partition.
  • A275027 (program): a(n) = Sum_{k=0..n} C(n,k)^2*C(n-k,k), where C(n,k) denotes the binomial coefficient n!/(k!*(n-k)!).
  • A275030 (program): a(1) = 2. a(n) is the smallest prime such that a(n) - a(n-1) is a triangular number.
  • A275047 (program): Diagonal of the rational function 1/(1-(1+w)(xy + xz + yz)) [even-indexed terms only].
  • A275059 (program): Numbers n such that A000010(n) + n^2 is a prime.
  • A275060 (program): Numbers n such that there exists x in N : (x+1)^3 - x^3 = 61*n^2.
  • A275063 (program): Number of permutations p of [n] such that p(i)-i is a multiple of eight for all i in [n].
  • A275070 (program): Number of set partitions of [n] such that i-j is a multiple of three for all i,j belonging to the same block.
  • A275071 (program): Number of set partitions of [n] such that i-j is a multiple of four for all i,j belonging to the same block.
  • A275073 (program): Number of set partitions of [n] such that i-j is a multiple of six for all i,j belonging to the same block.
  • A275075 (program): Number of set partitions of [n] such that i-j is a multiple of eight for all i,j belonging to the same block.
  • A275100 (program): Number of set partitions of [3*n] such that within each block the numbers of elements from all residue classes modulo n are equal for n>0, a(0)=1.
  • A275106 (program): Limiting sequence of the least significant digits of the even-indexed terms of A027878 in reverse order.
  • A275107 (program): Limiting sequence of the least significant digits of the odd-indexed terms of A027878 in reverse order.
  • A275110 (program): Decimal expansion of the sum of the alternating series of reciprocals of composite numbers with distinct prime factors.
  • 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.
  • A275120 (program): List the least common multiples of {1, 2, …, k} for k = 0, 1, …; this sequence gives the length of the n-th block of consecutive equal numbers.
  • A275121 (program): a(n) is the smallest multiple of n that is a practical number.
  • A275124 (program): Multiples of 5 where Pisano periods of Fibonacci numbers A001175 and Lucas numbers A106291 agree.
  • 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.
  • A275139 (program): Number of n X 5 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) = 3*a(n-1) + 2*sqrt(2*a(n-1)*(a(n-1)-7)) - 7 for n > 1.
  • A275155 (program): a(1) = 18; a(n) = 3*a(n - 1) + 2*sqrt(2*a(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.
  • A275173 (program): a(n) = (a(n-3) + a(n-1) * a(n-5)) / a(n-6), a(0) = a(1) = … = a(5) = 1.
  • A275175 (program): a(n) = (2 * a(n-3) + a(n-1) * a(n-5)) / a(n-6), a(0) = a(1) = … = a(5) = 1.
  • A275176 (program): a(n) = (3 * a(n-3) + a(n-1) * a(n-5)) / a(n-6), a(0) = a(1) = … = a(5) = 1.
  • A275184 (program): Number of 4 X n 0..2 arrays with no element equal to any value at offset (-2,-1) (-1,0) or (-1,1) and new values introduced in order 0..2.
  • A275195 (program): Sum of n-th powers of the roots of x^3 - 7*x^2 - 49*x - 49.
  • A275198 (program): Triangle, read by rows, formed by reading Pascal’s triangle (A007318) mod 14.
  • A275202 (program): Subword complexity (number of distinct blocks of length n) of the period doubling sequence A096268.
  • A275205 (program): Partial sums of the Dirichlet inverse of the Euler totient function.
  • A275206 (program): Expansion of (A(x)^2 - A(x^2))/2 where A(x) = A000108(x) - 1.
  • A275222 (program): Number of n X 2 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.
  • 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.
  • A275238 (program): a(n) = n*(10^floor(log_10(n)+1) + 1) + (-1)^n.
  • A275245 (program): Numbers n such that phi(n) divides n^2 while phi(n) does not divide n.
  • A275246 (program): Sequence of pairwise relatively prime numbers of class P_3 (see comment).
  • A275248 (program): Sequence of pairwise relatively prime numbers of class P_4 (see comment in A275246).
  • A275257 (program): Array read by upwards antidiagonals: LegendrePhi phi(x,n), x,n >=1.
  • A275277 (program): a(n) = a(n-1) + 3*a(n-2) + 3*a(n-3) + a(n-4), where a(0) = a(1) = a(2) = a(3) = 1.
  • A275286 (program): a(n) = ((2n+1)!!)^2 * Sum_{k=0..n}(-1)^k/(2k+1)^2.
  • A275289 (program): Number of set partitions of [n] with symmetric block size list of length three.
  • A275293 (program): Number of set partitions of [2n] with symmetric block size list of length four.
  • A275314 (program): Euler’s gradus (“suavitatis gradus”, or degrees of softness) function.
  • A275317 (program): Prime numbers of the form 100*n+57.
  • A275319 (program): Numbers n such that n concatenated with n+1 is not a prime.
  • A275324 (program): Expansion of (x*(1-4*x^2)^(-3/2) + (1-4*x^2)^(-1/2) + x + 1)/2.
  • A275329 (program): a(n) = (2+[n/2])*n!/((1+[n/2])*[n/2]!^2).
  • A275334 (program): Number of simple labeled graphs on n vertices that have at least one vertex of odd degree and at least one vertex of even degree.
  • A275340 (program): Nontrivial centered polygonal numbers: numbers of the form A101321(n,k) where n>=1 and k>=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.
  • A275377 (program): Number of odd prime factors (with multiplicity) of generalized Fermat number 3^(2^n) + 1.
  • 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.
  • A275384 (program): Composite squarefree numbers such that the arithmetic mean of its prime factors is an integer.
  • A275387 (program): Numbers of ordered pairs of divisors d < e of n such that gcd(d, e) > 1.
  • A275388 (program): Convolution of Fibonacci numbers (A000045) and partition numbers (A000041).
  • A275402 (program): Number of 3 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.
  • A275423 (program): Number of set partitions of [n] such that five is a multiple of each block size.
  • A275425 (program): Number of set partitions of [n] such that seven is a multiple of each block size.
  • A275434 (program): Sum of the degrees of asymmetry of all compositions of n.
  • A275436 (program): Sum of the asymmetry degrees of all 00-avoiding binary words of length 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)).
  • A275439 (program): Sum of the asymmetry degrees of all compositions of n with parts in {1,2}.
  • A275441 (program): Sum of the asymmetry degrees of all compositions of n into odd parts.
  • A275443 (program): Sum of the asymmetry degrees of all compositions of n without 2’s.
  • A275445 (program): Sum of the asymmetry degrees of all compositions of n with parts in {1,2,3}.
  • A275448 (program): The number of weakly alternating bargraphs of semiperimeter n. A bargraph is said to be weakly alternating if its ascents and descents alternate. An ascent (descent) is a maximal sequence of consecutive U (D) steps.
  • A275464 (program): a(n) = n - A038802(n).
  • A275465 (program): a(n) = f^(n/f), where f is the smallest prime factor of n.
  • A275486 (program): Decimal expansion of Pi_3, the analog of Pi for generalized trigonometric functions of order p=3.
  • A275490 (program): Square array of 5D pyramidal numbers, read by antidiagonals.
  • A275495 (program): a(n) = Sum_{k=2..n} floor(n/k) - 2*floor(n/(2*k)).
  • A275496 (program): a(n) = n^2*(2*n^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.
  • A275510 (program): Triangle read by rows, T(n,k) = floor(n/k) - 2*floor(n/(2*k)), for n>=2 and 2<=k<=n; additionally T(1,2) = 0.
  • A275514 (program): Triangle read by rows: the coefficient [t^k] of the Ehrhart polynomial of the 2-hypersimplex in dimension n.
  • A275518 (program): Number of simplices in corner-cut triangulation of the n-cube.
  • A275519 (program): Decimal expansion of sum of reciprocals of all prime triples.
  • A275521 (program): Number of (n+floor(n/2))-block bicoverings of an n-set.
  • A275527 (program): Number of distinct classes of permutations of length n under reversal and complement to n+1.
  • A275534 (program): Number of primes of the form x^2 + y^2 less than or equal to 2*n^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.
  • A275537 (program): Let S be a set of n-digit positive numbers; a(n) is the cardinality of S which guarantees there exist two disjoint subsets of S with equal sums of elements.
  • A275539 (program): a(n) = n! + n*(n-1)!!.
  • A275540 (program): a(n) = n! + n!! - n - 1.
  • A275541 (program): (n)! + (n + 1)!!/(n + 1) - 2
  • A275543 (program): A081585 and A069129 interleaved.
  • A275548 (program): Number of compositions of n if only the order of the odd numbers matter.
  • A275549 (program): Number of classes of endofunctions of [n] under reversal.
  • A275552 (program): Number of classes of endofunctions of [n] under vertical translation mod n and complement to n+1.
  • A275561 (program): Number of n X 4 0..2 arrays with no element equal to any value at offset (-2,0) (-1,2) or (0,-2) and new values introduced in order 0..2.
  • 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.
  • A275585 (program): Expansion of Product_{k>=1} 1/(1 - x^k)^(sigma_2(k)).
  • A275591 (program): a(n) = n^2 + 9*n + 1.
  • A275606 (program): Spiral constructed on the nodes of the triangular net such that a(n) = signum(A274920(n)).
  • A275607 (program): a(n) = 2*12^n*Gamma(n+1/2)*(n+1)/(sqrt(Pi)*Gamma(n+3)).
  • A275610 (program): Hexagonal spiral constructed on the nodes of the triangular net in which every 1 of A275606 is replaced with the least positive integer not yet in the sequence.
  • A275615 (program): Decimal expansion of 22/111.
  • A275616 (program): Numbers n such that n and omega(n) are relatively prime, where omega(n) (A001221) is the number of distinct prime divisors of n.
  • A275627 (program): Expansion of (6*x^5+5*x^4+4*x^3+3*x^2+2*x+8)/(1-x-x^6).
  • A275628 (program): Pisot sequence E(31,51), a(n)=[a(n-1)^2/a(n-2)+1/2].
  • A275630 (program): a(n) = product of distinct primes dividing prime(n)^2 - 1.
  • A275634 (program): Expansion of ( 3-2*x-2*x^2 ) / ( 1-5*x+2*x^2+3*x^3 ).
  • 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!.
  • A275637 (program): a(n) = (3^n-1)*(3^n-3)*(3^n+3)*(3^n-4)/5!.
  • A275638 (program): Expansion of (1-q)^k/Product_{j=1..k} (1-q^j) for k=4.
  • A275645 (program): Numbers n such that the n X n queens graph is colorable with n colors.
  • A275651 (program): a(n) = (2*n)!*Sum_{k = 0..n} (-1)^k/(2*k)!.
  • A275652 (program): a(n) = binomial(3*n,3*n/2)*binomial(2*n,n)*binomial(5*n/2,n/2)/binomial(n,n/2).
  • A275653 (program): a(n) = binomial(4*n,2*n)*binomial(3*n,2*n).
  • A275655 (program): a(n) = binomial(6*n,3*n)*binomial(2*n,n).
  • A275664 (program): a(n) is the sum of the LCM and GCD of all previous terms, with a(0) = 2.
  • A275665 (program): Numbers n such that n and sopf(n) are relatively prime, where sopf(n) (A008472) is the sum of the distinct primes dividing n.
  • A275667 (program): Number of ON cells after n generations in a 2-dimensional “Odd-Rule” cellular automaton on triangular tiling.
  • A275669 (program): Numbers k such that 3*k-1 is composite.
  • A275671 (program): Even values produced by the sigma function A000203, in increasing order.
  • A275673 (program): List of numbers that are in a spoke of a hexagonal spiral.
  • A275699 (program): Excess of numbers that are not squarefree.
  • A275700 (program): a(n) = Product_{d|n} prime(d).
  • A275704 (program): Digital root of n + (n+1)^2.
  • A275707 (program): Number of partial functions f:{1,2,…,n}->{1,2,…,n} such that every element in the domain of definition of f is mapped to a fixed point or to an element that is undefined by f.
  • A275709 (program): a(n) = 2*n^3 + 3*n^2.
  • A275715 (program): Permutation of natural numbers: a(n) = A243071(A249823(n)).
  • A275716 (program): Permutation of natural numbers: a(0) = 1, a(1) = 2, a(2n) = A273669(a(n)), a(2n+1) = A273664(a(n)).
  • A275727 (program): a(0) = 0, for n >= 1, a(n) = A275736(n) + 2*a(A257684(n)).
  • A275729 (program): A275735-polynomials evaluated at x=2: a(n) = A048675(A275735(n)).
  • A275732 (program): One-based positions of 1-digits in the factorial base representation of n are converted to primes with those indices, then multiplied together.
  • A275733 (program): a(0) = 1; for n >= 1, a(n) = A275732(n) * A003961(a(A257684(n))).
  • A275735 (program): Prime-factorization representations of “factorial base level polynomials”: a(0) = 1; for n >= 1, a(n) = 2^A257511(n) * A003961(a(A257684(n))).
  • A275736 (program): a(n) has base-2 representation with ones in those digit-positions where n contains ones in its factorial base representation, and zeros in all the other positions.
  • A275740 (program): Sums of n consecutive nonsquare integers.
  • A275766 (program): a(n) = (5^(2*(n + 1)) - 1)/4.
  • A275770 (program): Primes p == 5 (mod 6) that are not Sophie Germain primes.
  • A275778 (program): Tribonacci-like sequence a(n) = a(n-1) + a(n-2) + a(n-3) for n >= 3, with a(0) = 1, a(1) = 2, a(2) = 1.
  • A275779 (program): a(n) = (2^(n^2) - 1)/(1 - 1/2^n).
  • A275786 (program): a(n) = Product_{d|n} T(d) where T(x) = x*(x+1)/2 = A000217(x) = x-th triangular number.
  • A275788 (program): a(0) = 0, a(n+1) = 2*a(n) + (-1)^floor(n/3).
  • A275789 (program): Least k such that sigma(n) divides Fibonacci(k) (k > 0).
  • 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.
  • A275806 (program): a(n) = number of distinct nonzero digits in factorial base representation of n.
  • A275812 (program): Sum of exponents larger than one in the prime factorization of n: A001222(n) - A056169(n).
  • A275822 (program): Alternating sums of the cubes of the central binomial coefficients.
  • A275825 (program): Third-order sequence with non-constant coefficients: a(n) = (n-3)*a(n-1) + (n-1)*a(n-3); a(0) = a(1) = a(2) = 1.
  • A275827 (program): a(n) = Sum_{k=0..n} binomial(n+k+2,k)*binomial(2*n+1,n-k).
  • A275828 (program): Decimal expansion of the nested surd sqrt(phi + sqrt(phi + sqrt(phi + sqrt(phi + … )))) where phi is golden ratio = (1 + sqrt(5))/2; see A001622.
  • A275830 (program): a(n) = (2*sqrt(7)*sin(Pi/7))^n + (-2*sqrt(7)*sin(2*Pi/7))^n + (-2*sqrt(7)*sin(4*Pi/7))^n.
  • A275831 (program): a(n) = (sqrt(7)*csc(Pi/7)/2)^n + (-sqrt(7)*csc(2*Pi/7)/2)^n + (-sqrt(7)*csc(4*Pi/7)/2)^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.
  • A275856 (program): a(n) = floor(c*s*a(n-1)) + floor(d*r*a(n-2)), where r = (1+sqrt(5))/2, s = r/(r-1), c = 1, d = 1, a(0) = 1, a(1) = 1.
  • A275857 (program): a(n) = floor(c*s*a(n-1)) + floor(d*r*a(n-2)), where r = (1+sqrt(5))/2, s = r/(r-1), c = 1, d = 1, a(0) = 1, a(1) = 2.
  • A275858 (program): a(n) = floor(c*r*a(n-1)) - floor(d*s*a(n-2)), where r = (1+sqrt(5))/2, s = r/(r-1), c = 1, d = 1, a(0) = 1, a(1) = 1.
  • A275859 (program): a(n) = floor(c*s*a(n-1)) + floor(d*r*a(n-2)), where r = 1 + sqrt(2), s = r/(r-1), c = 2, d = 1, a(0) = 1, a(1) = 1.
  • A275862 (program): floor(r*a(n-1)) + floor(r*a(n-2)), where r = 3/2, a(0) = 1, a(1) = 1.
  • A275863 (program): Floor(r*a(n-1)) + floor(r*a(n-2)), where r = 5/2, a(0) = 1, a(1) = 1.
  • A275864 (program): Floor(r*a(n-1)) + floor(r*a(n-2)), where r = 5/3, a(0) = 1, a(1) = 1.
  • A275865 (program): Floor(r*a(n-1)) - floor(r*a(n-2)), where r = 3/2, a(0) = 1, a(1) = 1.
  • 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.
  • A275871 (program): Row sums and second diagonal of A046934.
  • A275872 (program): A binomial convolution recurrence sequence.
  • A275873 (program): a(n) = floor(r*a(n-1)) + floor(r*a(n-2)) + floor(r*a(n-3)), where r = 3/2, a(0) = a(1) = a(2) = 1.
  • A275874 (program): a(n) = (n-4)*(n+1)*(n+3)/6.
  • A275875 (program): Subadditive triangle read by rows associated with the Grundy function A025480.
  • A275876 (program): a(n) = 4*n*(n^2 - 3*n - 1)/3.
  • A275878 (program): Standard Jacobi primes.
  • A275903 (program): Expansion of (1+4*x^2) / (1-5*x+4*x^2-4*x^3).
  • A275905 (program): Expansion of (1-x-2*x^2) / (1-6*x+3*x^2-2*x^3).
  • A275906 (program): Expansion of (1+x+x^2) / (1-4*x-4*x^2-x^3).
  • A275907 (program): Expansion of (1+x-x^3) / (1-4*x-x^4-x^5).
  • A275910 (program): Numbers not congruent to 0, 1 or 8 mod 9.
  • A275925 (program): Trajectory of 3 under repeated application of the morphism sigma: 3 -> 3656, 5 -> 365656, 6 -> 3656656.
  • A275929 (program): a(n) = 2*(n-1)! + n + 1.
  • A275930 (program): a(n) = F(n+5)*F(n+2)^5, where F = Fibonacci (A000045).
  • A275931 (program): a(n) = F(2*n+3)*F(2*n+1)^3, where F = Fibonacci (A000045).
  • A275932 (program): a(n) = F(2*n+6)*F(2*n+2)^3, where F = Fibonacci (A000045).
  • A275934 (program): Shifts 4 places left under binomial transform.
  • A275935 (program): Shifts 5 places left under binomial transform.
  • 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.
  • A275944 (program): Gaussian binomial coefficient [n,3] for q = 10.
  • A275948 (program): Number of nonzero digits that occur only once in factorial base representation of n: a(n) = A056169(A275735(n)).
  • A275949 (program): Number of distinct nonzero digits that occur multiple times in factorial base representation of n: a(n) = A056170(A275735(n)).
  • A275950 (program): Square array A(1,k) = A265905(k), A(n>1,k) = A(n-1, k+1) - A(n-1, k); successive differences of A265905 read by descending antidiagonals as A(1,1), A(1,2), A(2,1), A(1,3), A(2,2), A(3,1), …
  • A275951 (program): Transpose of array A275950.
  • A275953 (program): First differences of A265906; second differences of A265905.
  • A275955 (program): Leftmost column of array A275950.
  • A275959 (program): Sum of distinct terms of A002674: a(0) = 0, a(2n) = A255411(A153880(a(n))), a(2n+1) = 1+A255411(A153880(a(n))).
  • A275964 (program): Total number of nonzero digits with multiple occurrences in factorial base representation of n (counted with multiplicity): a(n) = A275812(A275735(n)).
  • A275966 (program): a(n) is the real part of -I*Sum_{d|n}(mobius(d)*I^(n/d)), I=sqrt(-1), mobius(n) is A008683.
  • 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.
  • A275975 (program): Decimal expansion of Sum_{k>=0}((-1)^k/2^(2^k)).
  • A275988 (program): a(n) = prime(3n) - prime(n).
  • A275989 (program): a(n) = prime(prime(n)+1) - prime(n).
  • A275990 (program): a(n) = prime(prime(n)-1) - prime(n).
  • A275991 (program): a(n) = prime(composite(n)) - prime(n).
  • A275994 (program): Numerators of coefficients in the asymptotic expansion of the logarithm of the central binomial coefficient
  • A275995 (program): Denominators of coefficients in the asymptotic expansion of the logarithm of the central binomial coefficient.
  • A276000 (program): Least k such that n! divides phi(k!) (k > 0).
  • A276008 (program): Substitute ones for all nonzero digits in factorial base representation of n: a(n) = A059590(A275727(n)).
  • A276009 (program): Decrement each nonzero digit by one in factorial base representation of n: a(n) = n - A276008(n).
  • A276014 (program): Diagonal of (1 - 9 x y) / ((1 - 3 y - 2 x + 3 y^2 + 9 x^2 y) * (1 - u - v - z - w)).
  • A276016 (program): Diagonal of (1 - 9 x y)/((1 - 3 y - 2 x + 3 y^2 + 9 x^2 y) * (1 - u - v - w)).
  • A276018 (program): n^2 * a(n) = 3*(3*n-2)^2 * a(n-1), with a(0) = 1.
  • A276023 (program): Decimal expansion of 32*Pi^4/945.
  • A276026 (program): a(n) = Sum_{k=0..7} (n + k)^2.
  • A276031 (program): Number of edges in the graded poset of the partitions of n taken modulo 3, where a partition into k parts is joined to a partition into k+1 parts if the latter is a refinement of the former.
  • A276032 (program): Number of refinements of the partition n^1 with all numbers taken modulo 2.
  • A276033 (program): Number of generalizations of the partition 1^n with all elements taken modulo 2.
  • A276037 (program): Numbers using only digits 1 and 5.
  • A276038 (program): Numbers n such that product of digits of n is a power of 6.
  • A276039 (program): Numbers using only digits 1 and 7.
  • A276040 (program): Least k such that n^n divides phi(k^k) (k > 0).
  • A276041 (program): Exponential convolution of odd numbers (A005408) with themselves.
  • A276042 (program): Exponential convolution of central polygonal numbers (A000124) with themselves.
  • A276045 (program): Primes p such that d(p*(2p+1)) = 8 where d(n) is the number of divisors of n (A000005).
  • A276048 (program): Sequence associated with the functional equation of the Riemann zeta zero spectrum (see formulas).
  • A276055 (program): Number of palindromic compositions of n with parts in {1,2,4,6,8,10,…}.
  • A276057 (program): Sum of the asymmetry degrees of all compositions of n with parts in {1,3}.
  • A276063 (program): Sum of the asymmetry degrees of all compositions of n with parts in {1,4}.
  • A276065 (program): Sum of the asymmetry degrees of all compositions of n with parts in {1,5}.
  • A276068 (program): Sum of the lengths of the first descents in all bargraphs having semiperimeter n (n>=2). A descent is a maximal sequence of consecutive down steps.
  • A276071 (program): n^3 followed by n^2 followed by n^4 followed by n.
  • A276073 (program): A276076-polynomials evaluated at x=2: a(n) = A048675(A276076(n)).
  • A276074 (program): A276076-polynomials evaluated at X=2 over the field GF(2): a(n) = A248663(A276076(n)).
  • A276075 (program): a(1) = 0, a(n) = (e1*i1! + e2*i2! + … + ez*iz!) for n = prime(i1)^e1 * prime(i2)^e2 * … * prime(iz)^ez, where prime(k) is the k-th prime, A000040(k).
  • A276076 (program): Factorial base exp-function: digits in factorial base representation of n become the exponents of successive prime factors whose product a(n) is.
  • A276077 (program): Number of distinct prime factors p of n such that p^(1+A000720(p)) is a divisor of n, where A000720(p) gives the index of prime p, 1 for 2, 2 for 3, 3 for 5, and so on.
  • A276078 (program): Numbers n in whose prime factorization no exponent of any prime(k) exceeds k.
  • A276079 (program): Numbers n such that prime(k)^(k+1) divides n for some k.
  • A276080 (program): a(n) = A276075(A206296(n)).
  • A276082 (program): a(0) = 0, a(2n) = A153880(a(n)), a(2n+1) = 1+A255411(a(n)).
  • A276083 (program): a(0) = 0, a(2n) = A255411(a(n)), a(2n+1) = 1+A153880(a(n)).
  • A276084 (program): a(n) = Number of trailing zeros in primorial base representation of n (A049345); largest k such that A002110(k) divides n.
  • A276085 (program): Primorial base log-function: a(1) = 0, a(n) = (e1*A002110(i1-1) + … + ez*A002110(iz-1)) for n = prime(i1)^e1 * … * prime(iz)^ez, where prime(k) is the k-th prime, A000040(k) and A002110(k) (the k-th primorial) is the product of first k primes.
  • A276086 (program): Primorial base exp-function: 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)).
  • A276088 (program): The least significant nonzero digit in primorial base representation of n: a(n) = A276094(n) / A002110(A276084(n)) (with a(0) = 0).
  • A276090 (program): Left inverse of A276089: For n = sum_{i=1..} d(i)*i! (with each d(i) <= i), a(n) = sum_{j=1..} d(2j-1)*j!.
  • A276091 (program): Numbers obtained by reinterpreting base-2 representation of n in A001563-base (A276326): a(n) = Sum_{k>=0} A030308(n,k)*A001563(k+1).
  • A276092 (program): a(n) = Product_{i=1..n} prime(i)^(prime(i)-1), a(0)=1.
  • A276093 (program): The least significant nonzero digit in primorial base is replaced with zero: a(n) = n - A276094(n), a(0) = 0.
  • A276094 (program): a(n) = n modulo A002110(A257993(n)), a(0) = 0.
  • A276095 (program): A nonlinear recurrence of order 4: a(1)=a(2)=a(3)=a(4)=1; a(n)=(a(n-1)+a(n-2)+a(n-3))^2/a(n-4).
  • A276098 (program): a(n) = (7*n)!*(3/2*n)!/((7*n/2)!*(3*n)!*(2*n)!).
  • A276099 (program): a(n) = (9*n)!*(5/2*n)!/((9*n/2)!*(5*n)!*(2*n)!).
  • A276106 (program): Number of compositions of n into parts 1, 7, and 8.
  • A276112 (program): Numbers with precipice 1: descending by the main diagonal of the pyramid described in A245092, the height difference between the level a(n) (starting from the top) and the level of the next terrace is equal to 1.
  • A276122 (program): a(0) = a(1) = a(2) = 1; for n > 2, a(n) = (a(n-1)^2+a(n-2)^2+a(n-1)+a(n-2))/a(n-3).
  • A276123 (program): a(0) = a(1) = a(2) = 1; for n > 2, a(n) = (a(n-1) + 1)*(a(n-2) + 1) / a(n-3).
  • A276129 (program): a(n) is the number of ordered ways to tile a strip of length n+2 with white tiles of odd lengths summing to length n and two red squares.
  • A276133 (program): Exponent of highest power of 2 dividing the product of the composite numbers between the n-th prime and the (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.
  • A276137 (program): Numbers without the decimal digits 2, 4, 6 and 8.
  • A276138 (program): Numbers without the decimal digits 1, 3, 5 and 7.
  • A276139 (program): Series expansion of (1 + 2x + 4x^2)/(1 - 3x - 5x^2).
  • A276146 (program): a(n) = A034968(A225901(n)).
  • A276149 (program): a(0) = 0; for n >= 1, a(n) = A048764(n) * (1+(A084558(n)-A099563(n))).
  • 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).
  • A276154 (program): a(n) = Shift primorial base representation (A049345) of n left by one digit (append one zero to the right, then convert back to decimal).
  • A276155 (program): Complement of A276154; numbers that cannot be obtained by shifting left the primorial base representation (A049345) of some number.
  • A276156 (program): Numbers obtained by reinterpreting base-2 representation of n in primorial base: a(0) = 0, a(2n) = A276154(a(n)), a(2n+1) = 1 + A276154(a(n)).
  • A276158 (program): Triangle read by rows: T(n,k) = 6*k*(n + 1 - k) for 0 < k <= n; for k = 0, T(n,0) = n + 1.
  • A276159 (program): Convolution of nonzero octagonal numbers (A000567) with themselves.
  • A276160 (program): A recurrence of order 3 : a(0)=a(1)=a(2)=1 ; a(n) = (a(n-1)^2 + a(n-2)^2 + a(n-1) + a(n-2) + 1)/a(n-3).
  • A276162 (program): Square array read by antidiagonals: T(n,k) = Product_{i = 1..k} gcd(n, i).
  • 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.
  • A276164 (program): a(n) is the maximum first-player score of a “Coins in a Row” game over all permutations of coins 1..n with both players using a minimax strategy.
  • A276168 (program): a(n) is the minimum 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.
  • A276194 (program): Odd numbers whose binary representation contains an even number of 1’s and at least one 0.
  • A276208 (program): Position of n! in the joint ranking of {2^h} and {k!}, where h >= 0, k >= 0.
  • A276225 (program): a(n+3) = 2*a(n+2) + a(n+1) + a(n) with a(0)=3, a(1)=2, a(2)=6.
  • A276226 (program): a(n+3) = 2*a(n+2) + a(n+1) + a(n) with a(0)=0, a(1)=6, a(2)=8.
  • A276228 (program): a(n+3) = -a(n+2) - 2*a(n+1) + a(n) with a(0)=3, a(1)=-1, a(2)=-3.
  • A276229 (program): a(n+3) = -a(n+2) - 2*a(n+1) + a(n) with a(0)=0, a(1)=0, a(2)=1.
  • A276231 (program): E.g.f. A(x) satisfies: A(x)^A(x) = LambertW(-x)/(-x).
  • A276233 (program): a(n) = (n+256)/gcd(n,256).
  • A276234 (program): a(n) = n/gcd(n, 256).
  • A276239 (program): a(n) = numerator of rational fraction of function (Gamma[5/4]^2 Gamma[n + 3/4]^2)/(Gamma[3/4]^2 Gamma[n + 5/4]^2).
  • A276240 (program): a(n) = denominator of rational fraction of function Gamma[5/4]^2 Gamma[n + 3/4]^2/(Gamma[3/4]^2 Gamma[n + 5/4]^2).
  • 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.
  • A276256 (program): A nonlinear recurrence of order 3: a(1)=a(2)=a(3)=1; a(n)=(a(n-1)+a(n-2)+1)^2/a(n-3).
  • A276257 (program): a(1) = a(2) = a(3) = a(4) = 1; for n>4, a(n) = ( a(n-1)+a(n-2)+a(n-3)+1 )^2 / a(n-4).
  • A276258 (program): a(n) = 4*a(n-1)*a(n-2) - a(n-3), with a(1) = a(2) = a(3) = 1.
  • A276259 (program): a(n) = 5*a(n-1)*a(n-2)*a(n-3) - a(n-4) with n>4, a(1) = a(2) = a(3) = a(4) = 1.
  • A276261 (program): Centered 21-gonal primes.
  • A276262 (program): Centered 22-gonal primes.
  • A276263 (program): Centered 23-gonal primes.
  • A276264 (program): Centered 25-gonal primes.
  • A276265 (program): Expansion of (1 + 2*x)/(1 - 6*x + 6*x^2).
  • A276267 (program): a(n) = ( a(n-1)^2*a(n-2)^2*a(n-3)^2 + 1 ) / a(n-4), with a(0)=a(1)=a(2)=a(3)=1.
  • A276268 (program): a(0) = a(1) = a(2) = a(3) = 1; for n>3, a(n) = ( a(n-1)*a(n-2)*a(n-3) + 1 )^2 / a(n-4).
  • 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”).
  • A276275 (program): Padovan like sequence: a(n) = a(n-2) + a(n-3) for n>3, a(1)=2, a(2)=2, a(3)=0.
  • A276276 (program): a(n) = a(n-2)+a(n-3) with a(1)=2 a(2)=1 a(3)=0.
  • A276278 (program): Complement of A026474.
  • A276283 (program): Expansion of (1 + x + 3*x^2 + x^3)/((1 - x)^2*(1 + x^2)).
  • A276285 (program): Number of ways of writing n as a sum of 13 squares.
  • A276286 (program): Number of ways of writing n as a sum of 14 squares.
  • A276287 (program): Number of ways of writing n as a sum of 15 squares.
  • A276288 (program): a(n) = a(n-1) + 3*a(n-2) if n is even, otherwise a(n) = 3*a(n-1) + a(n-2), a(0)=0, a(1)=1.
  • A276289 (program): Expansion of x*(1 + x)/(1 - 2*x)^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.
  • A276307 (program): Primes p such that d(p*(2p+1)) = 16 where d(n) is the number of divisors of n (A000005).
  • A276308 (program): a(n) = (a(n-1)+1)*(a(n-3)+1)/a(n-4) for n > 3, a(0) = a(1) = a(2) = a(3) = 1.
  • A276309 (program): Integer part of the ratio of alternate consecutive prime gaps.
  • A276310 (program): G.f. A(x) satisfies: x = A(x)-2*A(x)^2-2*A(x)^3.
  • A276314 (program): G.f. A(x) satisfies: x = A(x)-A(x)^2-3*A(x)^3.
  • A276315 (program): G.f. A(x) satisfies: x = A(x)-3*A(x)^2-2*A(x)^3.
  • A276316 (program): G.f. A(x) satisfies: x = A(x)-4*A(x)^2+A(x)^3.
  • A276328 (program): Digit sum when n is expressed in greedy A001563-base (A276326).
  • A276333 (program): The most significant digit in greedy A001563-base (A276326): a(n) = floor(n/A258199(n)), a(0) = 0.
  • A276334 (program): a(n) = A258199(n) * A276333(n).
  • A276335 (program): Discard the most significant digit when n is expressed in greedy A001563-base (A276326), then convert back to decimal: a(n) = n - A276334(n).
  • A276337 (program): Number of nonzero digits in greedy A001563-base representation of n (A276326).
  • 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.
  • A276355 (program): Sum of primes between 100*n and 100*n + 99.
  • A276356 (program): Number of Hamiltonian cycles in the Cartesian product graph K_2 times K_n.
  • A276368 (program): G.f. A(x) satisfies: A(x - 3*x^3) = 1/(1 - 3*x).
  • A276371 (program): E.g.f.: exp(x/2)/(2 - exp(2*x))^(1/4).
  • A276376 (program): Exponent of highest power of 3 dividing product of composite numbers between n-th prime and (n+1)-st prime.
  • A276378 (program): Numbers n such that 6*n is squarefree.
  • A276379 (program): Write a “1” for each distinct prime divisor p of n in the (pi(p) - 1)-th place, ignoring multiplicity.
  • 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).
  • A276397 (program): Trajectory of 0 under the morphism 0 -> 001, 1 -> 0010.
  • A276398 (program): Limit S_oo where S_0 = 0, S_i = S_{i-1} 1^(4^i) S_{i-1} for i >0.
  • A276399 (program): Numerator of n!/(n^n-n).
  • A276400 (program): Denominator of n!/(n^n-n).
  • A276403 (program): a(n) = if n mod 6 = 0 then 4*3^((n-6)/3) elif n mod 6 = 1 then 2^4*3^((n-10)/3) elif n mod 6 = 2 then 2^3*3^((n-8)/3) elif n mod 6 = 3 then 2^2*3^((n-6)/3) elif n mod 6 = 4 then 2*3^((n-4)/3) otherwise 3^((n-2)/3).
  • A276410 (program): Largest determinant of a (real) {0,1}-matrix of order n subject to the restriction that the corresponding 0,1 simplex is acute.
  • A276416 (program): a(n) = a(n-1)*(1 + a(n-1)/a(n-4)), with a(0) = a(1) = a(2) = a(3) = 1.
  • A276418 (program): Starting a random walk on Z at 0 triangle T(j,k) gives the number of paths of length 2*j returning to 0 exactly k times.
  • A276419 (program): Non-Fibonacci numbers n such that A129761(n) = 1.
  • A276431 (program): Number of partitions of n containing no parts that are powers of 2 with positive exponent.
  • A276449 (program): Number of 1-orbits of the cyclic group C_4 for a bi-colored square n X n grid with n squares of one color.
  • A276453 (program): a(n) = (a(n-1)+1)*(a(n-2)+1)*(a(n-3)+1)/a(n-4) with a(0) = a(1) = 1, a(2) = 2, a(3) = 6.
  • A276477 (program): a(n) = a(n-2) + a(n-3) for n >= 3, with a(0) = a(1) = 2, a(2) = 1.
  • A276482 (program): a(n) = 5^n*Gamma(n+1/5)*Gamma(n+1)/Gamma(1/5).
  • A276485 (program): Numerator of Sum_{k=1..n} 1/k^n.
  • A276487 (program): Denominator of Sum_{k=1..n} 1/k^n.
  • A276489 (program): a(n) = 25^(n+1)*Gamma(n+8/5)/Gamma(3/5).
  • A276501 (program): Smallest number k such that k! has at least n terms in its Zeckendorf representation.
  • A276502 (program): Least k > 0 such that A045876(n) divides A045876(n*10^k).
  • A276506 (program): E.g.f.: exp(9*(exp(x)-1)).
  • A276507 (program): E.g.f.: exp(10*(exp(x)-1)).
  • A276508 (program): a(n) = (2*5^n + 3*(-1)^(floor((n-1)/3)) + (-1)^n)/6.
  • A276509 (program): Numbers n in base 10 such that the digits of 2 + n are the digits of 2n written in reverse order.
  • A276516 (program): Expansion of Product_{k>=1} (1-x^(k^2)).
  • A276528 (program): Least number with same prime signature as sigma(n), the sum of the divisors of n: a(n) = A046523(A000203(n)).
  • A276529 (program): a(n) = (a(n-1) * a(n-5) + 1) / a(n-6), a(0) = a(1) = … = a(5) = 1.
  • A276530 (program): a(n) = (a(n-1) * a(n-5) + a(n-3)^3) / a(n-6), a(0) = a(1) = … = a(5) = 1.
  • A276531 (program): a(n) = (a(n-1) * a(n-5) + a(n-2) * a(n-3) * a(n-4)) / a(n-6), with a(0) = a(1) = a(2) = a(3) = a(4) = a(5) = 1.
  • A276532 (program): a(n) = (a(n-1) * a(n-6) + a(n-2) * a(n-3) * a(n-4) * a(n-5)) / a(n-7), with a(0) = a(1) = a(2) = a(3) = a(4) = a(5) = a(6) = 1.
  • A276534 (program): a(n) = a(n-1) * a(n-4) * (a(n-2) * a(n-3) + 1) / a(n-5), with a(0) = a(1) = a(2) = a(3) = a(4) = 1.
  • A276536 (program): Binomial sums of the cubes of the central binomial coefficients.
  • A276537 (program): Alternating binomial sums of the cubes of the central binomial coefficients.
  • A276551 (program): Convolution square of A073592.
  • A276552 (program): Expansion of Product_{k>0} (1 - x^k)^(k*3).
  • A276553 (program): Numbers n such that n^2 and (n + 1)^2 have the same number of divisors.
  • A276555 (program): Number of steps to reach 1 when starting from n and iterating the map x -> x - A061395(x).
  • A276559 (program): Expansion of Sum_{k>=1} k^2*x^k^2/(1 - x^k^2) * Product_{k>=1} 1/(1 - x^k^2).
  • A276560 (program): Expansion of Sum_{k>=1} prime(k)*x^prime(k)/(1 - x^prime(k)) * Product_{k>=1} 1/(1 - x^prime(k)).
  • 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.
  • A276577 (program): Row 5 of A276580: a(n) = A255415(n) modulo 11.
  • A276578 (program): Transpose of square array A255483.
  • A276581 (program): After a(0)=0, each n occurs A261224(n) times.
  • A276586 (program): Square array A(row,col) = Sum_{k=0..row} binomial(row,k)*A002110(col+k), read by descending antidiagonals as A(0,0), A(0,1), A(1,0), A(0,2), A(1,1), A(2,0), …
  • A276587 (program): Transpose of square array A276586.
  • A276588 (program): Square array A(row,col) = Sum_{k=0..row} binomial(row,k)*(1+col+k)!, read by descending antidiagonals as A(0,0), A(0,1), A(1,0), A(0,2), A(1,1), A(2,0), …
  • A276589 (program): Transpose of A276588.
  • A276592 (program): Numerator of the rational part of the sum of reciprocals of even powers of odd numbers, i.e., Sum_{k>=1} 1/(2*k-1)^(2*n).
  • A276593 (program): Denominator of the rational part of the sum of reciprocals of even powers of odd numbers, i.e., Sum_{k>=1} 1/(2*k-1)^(2*n).
  • A276594 (program): Numerator of the rational part of the sum of reciprocals of even powers of even numbers, i.e., Sum_{k>=1} 1/(2*k)^(2*n).
  • A276595 (program): Denominator of the rational part of the sum of reciprocals of even powers of even numbers, i.e., Sum_{k>=1} 1/(2*k)^(2*n).
  • A276598 (program): Values of m such that m^2 + 3 is a triangular number (A000217).
  • A276599 (program): Values of n such that n^2 + 5 is a triangular number (A000217).
  • A276601 (program): Values of k such that k^2 + 9 is a triangular number (A000217).
  • A276602 (program): Values of k such that k^2 + 10 is a triangular number (A000217).
  • A276618 (program): Transpose of table A099884.
  • A276626 (program): Semiprimes n such that (n-1)/3 is prime.
  • A276634 (program): Sum of cubes of proper divisors of n.
  • A276644 (program): Self-composition of the repunits; g.f.: A(x) = G(G(x)), where G(x) = g.f. of A002275.
  • A276647 (program): Number of squares after the n-th generation in a symmetric (with 45-degree angles) non-overlapping Pythagoras tree.
  • A276658 (program): Tribonacci-like sequence a(n) = a(n-1) + a(n-2) + a(n-3) for n >= 3, with a(0) = 1, a(1) = 2, a(2) = 0.
  • A276659 (program): Accumulation of the upper left triangle used in binomial transform of nonnegative integers.
  • A276660 (program): Primes of the form p*2^k - 1 where p is an odd prime and k >= 0.
  • A276661 (program): Least k such that there is a set S in {1, 2, …, k} with n elements and the property that each of its subsets has a distinct sum.
  • 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.
  • A276693 (program): a(n) = a(n-2)*a(n-3) - a(n-1); a(0) = 3, a(1) = 5, a(2) = 7.
  • A276696 (program): Triangle read by rows, T(n,k) = T(n-1, k-1) + T(n-2, k) if k is odd, T(n-1, k-1) + T(n-1, k) if k is even, for k<=0<=n and n>=2 with T(0,0)=T(1,0)=T(1,1)=0 and T(n,k)=0 when k>n, k<0, or n<0.
  • A276704 (program): Records in A249859.
  • A276706 (program): Indices of records in A249860.
  • A276712 (program): Decimal expansion of zeta(3)/8.
  • A276729 (program): Number of nonprime digits in the decimal expansion of n.
  • A276732 (program): Primes p such that (p + 1)/10 is also prime.
  • A276736 (program): a(n) = numerator of Sum_{d|n} tau(d)/d.
  • A276737 (program): a(n) = denominator of Sum_{d|n} tau(d)/d.
  • A276755 (program): a(n) = A275706(n)^2 + A276688(n)^2 = [n]_{1+i}! * [n]_{1-i}!, where [n]_q! is the q-factorial, i = sqrt(-1).
  • A276757 (program): Infinite Fibonacci word on the alphabet {1,2,3,4,5}.
  • A276764 (program): 1^2 + 3^2, 2^2 + 4^2, 5^2 + 7^2, 6^2 + 8^2, …
  • A276770 (program): a(n) is the number of runs of an algorithm. Set b_0 = n, if prime, stop; else, set c_0 = largest divisor of n (!=n); set b_1 = c_0 + b_0/c_0. Run with b_1.
  • A276771 (program): a(n) is the number of runs of an algorithm. Set b_0 = n, if prime or 1 or 0, stop; else, set c_0 = largest divisor of n (!=n); set b_1 = c_0 - b_0/c_0. Run with b_1.
  • 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.
  • A276785 (program): Number of binary strings of length n containing the substring 11011.
  • A276788 (program): First differences of A003144.
  • A276789 (program): First differences of A003145.
  • A276790 (program): Trajectory of 0 under repeated applications of the map psi: 0 -> 0121, 1 -> 0121121, 2 -> 012121.
  • A276791 (program): Indicator function of (A003146 prefixed with 0).
  • A276792 (program): First differences of A003146.
  • A276793 (program): Indicator function for A003144.
  • A276794 (program): Indicator function for A003145.
  • A276795 (program): Folding numbers with an odd number of bits (see A277238 for definition).
  • A276796 (program): Partial sums of A276793.
  • A276797 (program): Partial sums of A276794.
  • A276798 (program): Partial sums of A276791.
  • A276800 (program): Decimal expansion of t^2, where t is the tribonacci constant A058265.
  • A276801 (program): Decimal expansion of t^3, where t is the tribonacci constant A058265.
  • A276804 (program): Second column T[.,2] of array T = A255483: T[0,j] = prime(j), T[i+1,j] = T[i,j]*T[i,j+1]/gcd(T[i,j],T[i,j+1])^2, i >= 0, j >= 1.
  • A276805 (program): a(n) = numerator((n^2 + 3*n + 2)/n^3).
  • A276806 (program): Height of the shortest binary factorization tree of n.
  • A276812 (program): Prime gap residues mod previous prime gap.
  • A276819 (program): a(n) = a(n-1) + 9*n - 5 with a(0) = 1.
  • A276825 (program): Number of ways to write n as x^3 + P_2, where x and P_2 are positive integers with P_2 a product of at most two primes.
  • 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).
  • A276853 (program): Beatty sequence for 2*e.
  • 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.
  • A276861 (program): First differences of the Beatty sequence A038130 for 2*Pi.
  • A276862 (program): First differences of the Beatty sequence A003151 for 1 + sqrt(2).
  • A276863 (program): First differences of the Beatty sequence A276854 for 1 + sqrt(5).
  • 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).
  • A276866 (program): First differences of the Beatty sequence A004976 for 2 + sqrt(5).
  • 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).
  • A276870 (program): First differences of the Beatty sequence A110117 for sqrt(2) + sqrt(3).
  • 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.
  • A276917 (program): Numbers obtained by alternatively adding centered pentagonal layers of 5*(2^n-1) and 5*(3^n-1) elements.
  • A276918 (program): a(2n) = A060867(n+1), a(2n+1) = A092440(n+1).
  • A276924 (program): Number of ordered set partitions of [n] with at most four elements per block.
  • A276939 (program): Row 2 of A276945: a(n) = A002110(n) + A002110(n+1).
  • A276940 (program): a(1) = 2; for n > 1, a(n) = (n-2)! * n^3.
  • A276947 (program): First differences of A256450: a(n) = A256450(n) - A256450(n-1).
  • A276948 (program): First differences of A273670: a(n) = A273670(n) - A273670(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.
  • A276959 (program): Sum of squares of digits in all divisors of n.
  • A276960 (program): a(n) = A000262(n)^2.
  • A276961 (program): Number of set partitions of [2n] with largest set of size n.
  • A276963 (program): a(n) = prime(n+1)^4 - prime(n)^4.
  • A276964 (program): a(n) = A000262(n)*A000262(n+1).
  • A276965 (program): Square row sums of the triangle of Lah numbers (A105278).
  • A276967 (program): Odd integers n such that 2^n == 2^3 (mod n).
  • A276978 (program): a(n) = (ceiling(n/2))^n.
  • A276979 (program): a(n) = (floor(n/2)+1)^n.
  • A276983 (program): Semiprimes n such that n-1 or n+1 is prime.
  • A276984 (program): Sum of squares of numbers less than n that do not divide n.
  • A276985 (program): Triangle read by rows: T(n,k) = number of k-dimensional elements in an n-dimensional cross-polytope, n>=1, 0<=k<n.
  • A276986 (program): Numbers n for which there is a permutation p of (1,2,3,…,n) such that k+p(k) is a Catalan number for 1<=k<=n.
  • A276988 (program): a(n) is the least k such that 10*k+prime(n) is composite.
  • A276989 (program): Reversion of x - x^2 - x^6.
  • A276995 (program): Triangle read by rows, T(n,k) = k^(n-k)*(n-k)!*Sum_{j=0..n-k}(-1)^j/j! for 0<=k<=n.
  • A277001 (program): Denominators of an asymptotic series for the Gamma function (even power series).
  • A277002 (program): Numerators of an asymptotic series for the Gamma function (odd power series).
  • A277004 (program): Triangle read by rows, T(n,k) = k^k*(n-k)!*Sum_{j=0..n-k}(-1)^j/j! for 0<=k<=n.
  • A277006 (program): a(n) = A005940(1+A003714(n)); permutation of squarefree numbers.
  • A277010 (program): a(n) = A156552(A005117(n)); permutation of Fibbinary numbers.
  • A277011 (program): Left inverse of A277012.
  • A277012 (program): Factorial base representation of n is rewritten as a base-2 number with each nonzero digit k replaced by a run of k 1’s (followed by one extra zero if not the rightmost run of 1’s) and with each 0 kept as 0.
  • A277021 (program): Left inverse of A277022.
  • A277046 (program): Triangle read by rows: T(n,k) = 2^n - n + k - 1 for n >= 1, with 1 <= k <= 2n-1.
  • A277050 (program): a(n) = floor(2*n/sqrt(Pi)).
  • A277051 (program): a(n) = floor(n/(1-3/Pi)).
  • A277060 (program): a(n) = 1/2 * Sum_{k=0..n} (binomial(n,k) * binomial(n+k,k+1))^2 for n >= 0.
  • A277061 (program): Numbers with multiplicative digital root > 0.
  • A277065 (program): Sum of cubes of the digits of all divisors of n.
  • A277070 (program): Row length of A276380(n).
  • A277078 (program): Triangular array similar to A255935 but with 0’s and 2’s swapped in the trailing diagonal. The columns alternate in signs.
  • A277082 (program): Generalized 15-gonal (or pentadecagonal) numbers: n*(13*n - 11)/2, n = 0,+1,-1,+2,-2,+3,-3, …
  • A277084 (program): Pisot sequence L(4,14).
  • A277087 (program): a(0) = 1, a(n) = (denominator of the Bernoulli number B_{2n})/3, for n>=1.
  • A277088 (program): Pisot sequences L(5,12), S(5,12).
  • A277089 (program): Pisot sequences L(6,15), S(6,15).
  • A277090 (program): Expansion of Product_{k>=0} 1/(1 - x^(8*k+1)).
  • 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.
  • A277095 (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).
  • A277129 (program): Largest m < n such that 2^m == 2^n (mod n).
  • A277131 (program): Magic numbers of anti-Mackay icosahedra.
  • A277132 (program): The first subdiagonal of triangle A196842.
  • A277137 (program): Numbers k such that cos(k) > 0 and cos(k+2) < 0.
  • A277138 (program): Numbers k such that cos(k) < 0 and cos(k+2) > 0.
  • A277149 (program): Lexicographically least sequence of nonnegative integers that avoids 9/5-powers.
  • A277166 (program): Numbers m such that m divides the number of divisors of m!!.
  • A277168 (program): Coefficients in the series reversion of x*exp(-x^2).
  • A277169 (program): Product of squares of proper divisors of n.
  • A277174 (program): a(n) = Product_{i=1..n} i*rad(i) where rad(n) = A007947(n).
  • A277175 (program): Convolution of Catalan numbers and factorial numbers.
  • A277176 (program): Exponential convolution of Catalan numbers and factorial numbers.
  • A277178 (program): a(n) = Sum_{k=0..n} k*binomial(2*k,k)/2.
  • A277184 (program): E.g.f.: A(x) = x*exp(A(x) - A(x)^2) + A(x)^2.
  • A277188 (program): The binomial sum a(n) = Sum_{k=0..n}(binomial(n,k)*binomial(n+1,k+1)*binomial(n+2,k+2)).
  • A277195 (program): Permutation of nonnegative integers: a(n) = A022290(A277010(n)).
  • A277196 (program): Permutation of natural numbers: a(n) = A107079(A277006(n)).
  • A277209 (program): Partial sums of repdigit numbers (A010785).
  • A277210 (program): Expansion of Product_{k>=1} 1/(1 - x^(3*k+1)).
  • A277212 (program): Expansion of Product_{n>=1} (1 - x^(5*n))/(1 - x^n)^5 in powers of x.
  • A277216 (program): Product of decimal digits of sum of divisors of n.
  • A277219 (program): Triangle read by rows: T(n,k) is the number of independent sets of size k over all simple labeled graphs on n nodes, n>=0, 0<=k<=n.
  • A277220 (program): Exponential convolution of Fibonacci (A000045) and Catalan (A000108) numbers.
  • A277221 (program): Number of permutations of length n which avoid the patterns 4123, 1324, and 3124.
  • A277226 (program): Number of inequivalent (modulo C_4 rotations) square n X n grids with squares coming in two colors and four squares have one of the colors.
  • A277227 (program): Triangular array T read by rows: T(n,k) gives the additive orders k modulo n, for k = 0,1, …, n-1.
  • 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).
  • A277232 (program): Numerators of the partial sums of the cubes of the expansion coefficients of 1/sqrt(1-x).
  • A277233 (program): Numerators of the partial sums of the squares of the expansion coefficients of 1/sqrt(1-x). Also the numerators of the Landau constants.
  • 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.
  • A277247 (program): a(n) = Sum_{k=0..floor(n/2)} binomial(n, k)^2.
  • A277252 (program): a(n) = a(n-2) + a(n-3) + a(n-4) with a(0) = 0, a(1) = a(2) = 1, a(3) = 0.
  • A277253 (program): a(n) = a(n-2) + a(n-3) + a(n-4) for n>3, a(0)=1, a(1)=a(2)=0, a(3)=2.
  • A277264 (program): Expansion of Product_{k>=1} 1/(1 - x^(5*k+1)).
  • A277267 (program): Minimum number of single-direction edges in leveled binary trees with n nodes.
  • A277279 (program): Somos-4 sequence variant: a(n) = (a(n-1) * a(n-3) - a(n-2)^2) / a(n-4), a(0) = 1, a(1) = 1, a(2) = 2, a(3) = -1.
  • A277280 (program): Maximal coefficient in Hermite polynomial of order n.
  • A277281 (program): Maximal coefficient (ignoring signs) in Hermite polynomial of order n.
  • A277282 (program): Max coefficient in n-th Lucas polynomial.
  • A277287 (program): a(n) = binomial(2*n,n) + Sum_{k=1..n} binomial(2*n-k,n-k)*Fibonacci(k).
  • A277297 (program): Diagonal of triangle A277295; a(n) = A277295(n+2,n).
  • 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.
  • A277331 (program): a(n) = A253563(A003714(n)).
  • A277332 (program): a(n) = A253565(A003714(n)).
  • A277335 (program): Fibbinary numbers multiplied by three: a(n) = 3*A003714(n); Numbers where all 1-bits occur in runs of even length.
  • A277337 (program): Number of pairs of functions (f,g) from a set of n elements into itself that are generalized reflexive inverses of each other.
  • A277338 (program): Reverse and Add! sequence starting with 295.
  • A277342 (program): Base-100 digital root of n (equivalent to repeatedly adding pairs of decimal digits starting from the least significant pair).
  • A277345 (program): a(n) = Gamma(n+1, phi)*exp(phi) + Gamma(n+1, 1-phi)*exp(1-phi), where phi=(1+sqrt(5))/2.
  • A277347 (program): a(n) = Product_{k=1..n} (2*k*(k-1)+1).
  • A277349 (program): Expansion of Product_{k>=1} 1/(1 - x^(6*k+1)).
  • A277351 (program): Value of (n+1,n) concatenated in binary representation.
  • A277352 (program): a(n) = Product_{k=1..n} (2*k^2+1).
  • A277353 (program): a(n) = Product_{k=1..n} (3*k^2+1).
  • A277354 (program): a(n) = Product_{k=1..n} (4*k^2+1).
  • A277355 (program): a(n) = Product_{k=1..n} (2^k + k).
  • A277357 (program): a(1) = 1; for n > 1, a(n) = (2^n-1)*a(n-1) + 1.
  • A277358 (program): Number of self-avoiding planar walks starting at (0,0), ending at (n,0), remaining in the first quadrant and using steps (0,1), (1,0), (1,1), (-1,1), and (1,-1).
  • A277359 (program): Number of self-avoiding planar walks starting at (0,0), ending at (n,n), remaining in the first quadrant and using steps (0,1) and (1,0) on or below the diagonal and using steps (1,1), (-1,1), and (1,-1) on or above the diagonal.
  • A277360 (program): Number of self-avoiding planar walks starting at (0,0), ending at (n,n), remaining in the first quadrant and using steps (0,1), (1,0), (1,1), (-1,1), and (1,-1).
  • A277361 (program): a(n) = Sum_{k=0..n} k^3 * binomial(n-k, k).
  • A277367 (program): a(n) = gcd(A006666(n), A006667(n)) where A006666 and A006667 are respectively the number of halving and tripling steps in the ‘3x+1’ problem.
  • A277368 (program): Numbers such that the number of their divisors divide the sum of their aliquot parts.
  • A277369 (program): a(0) = 5, a(1) = 8; for n>1, a(n) = 2*a(n-1) + a(n-2).
  • A277372 (program): a(n) = Sum_{k=1..n} binomial(n,n-k)*n^(n-k)*n!/(n-k)!.
  • A277373 (program): a(n) = Sum_{k=0..n} binomial(n,n-k)*n^(n-k)*n!/(n-k)!.
  • A277377 (program): Each odd integer k is followed by k even integers.
  • A277378 (program): Expansion of e.g.f. exp(2*x/(1-x))/sqrt(1-x^2).
  • A277379 (program): E.g.f.: exp(x/(1-x^2))/sqrt(1-x^2).
  • A277382 (program): a(n) = n!*LaguerreL(n, -3).
  • A277383 (program): Each even integer k is followed by k odd integers.
  • A277384 (program): Least common multiple of n + 4 and n - 4.
  • A277385 (program): Records in A277384.
  • A277386 (program): a(n) = Sum_{k=0..n} binomial(n, k)^3 * 3^(n-k) * k!.
  • A277387 (program): Number of nonnegative solutions of a certain system of linear Diophantine equations depending on an even parameter.
  • A277388 (program): Number of nonnegative solutions of a certain system of linear Diophantine equations depending on an odd parameter.
  • A277390 (program): Decimal expansion of 5-2*sqrt(5)+sqrt(25-10*sqrt(5))-sqrt(5-2*sqrt(5)).
  • A277391 (program): a(n) = n!*LaguerreL(n, -2*n).
  • A277392 (program): a(n) = n!*LaguerreL(n, -3*n).
  • A277393 (program): a(n) = Integral_{x=0..infinity} H_n(x) * exp(-x), where H_n(x) is n-th Hermite polynomial.
  • A277395 (program): a(n) = Sum_{k=0..n} binomial(n+1,k+1)*A001003(k).
  • A277411 (program): Column 1 of triangle A277410.
  • A277418 (program): a(n) = n!*LaguerreL(n, -4*n).
  • A277419 (program): a(n) = n!*LaguerreL(n, -5*n).
  • A277420 (program): a(n) = n!*LaguerreL(n, -6*n).
  • A277421 (program): a(n) = n!*LaguerreL(n, -7*n).
  • A277422 (program): a(n) = n!*LaguerreL(n, -8*n).
  • A277423 (program): a(n) = n!*LaguerreL(n, n).
  • A277425 (program): a(n) = sqrt(16*t^2 - 32*t + k^2 + 8*k - 8*k*t + 16), where t = ceiling(sqrt(n)) and k = t^2 - n.
  • A277426 (program): a(n) = 2^(6n+5).
  • A277431 (program): Expansion of e.g.f.: cosh(sqrt(2)*x)/(1-x).
  • A277432 (program): E.g.f.: sinh(sqrt(2)*x)/(sqrt(2)*(1-x)).
  • A277433 (program): Martin Gardner’s minimal no-3-in-a-line problem, all slopes version.
  • A277436 (program): a(n) = |Gamma(n, i)|^2, where i = sqrt(-1).
  • 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!.
  • A277454 (program): a(n) = 1 + Sum_{k=1..n} binomial(n,k) * 2^k * k^k.
  • A277456 (program): a(n) = 1 + Sum_{k=1..n} binomial(n,k) * 3^k * k^k.
  • A277457 (program): E.g.f.: exp(2*x)/(1+LambertW(-x)).
  • A277458 (program): E.g.f.: -1/(1-LambertW(-x)).
  • A277461 (program): E.g.f.: sin(x)/(1+LambertW(-x)).
  • A277462 (program): E.g.f.: cos(x)/(1 + LambertW(-x)).
  • A277463 (program): E.g.f.: sinh(x)/(1+LambertW(-x)).
  • A277464 (program): E.g.f.: cosh(x)/(1 + LambertW(-x)).
  • A277465 (program): E.g.f.: log(1+x)/(1 + LambertW(-x)).
  • A277466 (program): E.g.f.: -log(1-x)/(1+LambertW(-x)).
  • A277472 (program): a(n) = (-i)^n * Integral_{x>=0} H_n(i*x) * exp(-x), where H_n(x) is n-th Hermite polynomial, i=sqrt(-1).
  • A277473 (program): E.g.f.: -exp(x)*LambertW(-x).
  • A277474 (program): E.g.f.: -exp(-x)*LambertW(-x).
  • A277475 (program): E.g.f.: -sin(x)*LambertW(-x).
  • A277476 (program): E.g.f.: -sinh(x)*LambertW(-x).
  • A277477 (program): E.g.f.: -cos(x)*LambertW(-x).
  • A277478 (program): E.g.f.: -cosh(x)*LambertW(-x).
  • A277481 (program): E.g.f.: -log(1+x)*LambertW(-x).
  • A277482 (program): E.g.f.: log(1-x)*LambertW(-x).
  • A277485 (program): E.g.f.: -exp(2*x)*LambertW(-x).
  • A277491 (program): Number of triangles in the standard triangulation of the n-th approximation of the Koch snowflake fractal.
  • A277499 (program): E.g.f.: -sin(LambertW(-x)).
  • A277505 (program): E.g.f.: -LambertW(-x)/(1-x).
  • A277506 (program): E.g.f.: 1/((1+LambertW(-x))*(1-x)).
  • A277507 (program): E.g.f.: -1/((1-LambertW(-x))*(1-x)).
  • A277508 (program): E.g.f.: -1/((1-LambertW(-x))*(1+x)).
  • A277509 (program): E.g.f.: 1/((1+LambertW(-x))*(1+x)).
  • A277510 (program): E.g.f.: -1/(1-LambertW(-x))^2.
  • A277511 (program): E.g.f.: -LambertW(-x)/(1+x).
  • A277513 (program): Irregular triangle read by rows: T(n,k) is the number of integers greater than 4 such that they have n trits and 2k+1 (k>=1) nonzero trits in their balanced ternary representation, with n>=3 and 1<=k<=(j-1)/2.
  • 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.
  • A277548 (program): Numbers k such that k/5^m == 4 (mod 5), where 5^m is the greatest power of 5 that divides k.
  • A277549 (program): Numbers k such that k/4^m == 1 (mod 4), where 4^m is the greatest power of 4 that divides k.
  • A277550 (program): Numbers k such that k/5^m == 1 (mod 5), where 5^m is the greatest power of 5 that divides k.
  • A277551 (program): Numbers k such that k/5^m == 2 (mod 5), where 5^m is the greatest power of 5 that divides k.
  • A277555 (program): Numbers k such that k/5^m == 3 (mod 5), where 5^m is the greatest power of 5 that divides k.
  • 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).
  • A277563 (program): Fifth column of Euler’s difference table in A068106.
  • A277567 (program): Numbers k such that k/6^m == 1 (mod 6), where 6^m is the greatest power of 6 that divides k.
  • A277568 (program): Numbers k such that k/6^m == 2 (mod 6), where 6^m is the greatest power of 6 that divides k.
  • A277569 (program): Numbers n such that n/6^m == 3 (mod 6), where 6^m is the greatest power of 6 that divides n.
  • A277570 (program): Numbers k such that k/6^m == 4 (mod 6), where 6^m is the greatest power of 6 that divides k.
  • A277571 (program): Numbers k such that k/6^m == 5 (mod 6), where 6^m is the greatest power of 6 that divides k.
  • A277572 (program): (1/2)*A277568.
  • A277573 (program): a(n) = (1/3)*A277569(n).
  • A277574 (program): (1/2)*A277570.
  • A277576 (program): a(1)=1; thereafter a(n) = A007916(a(n-1)).
  • A277584 (program): a(n) = binomial(3n-1, n-1)^2.
  • A277585 (program): Denominator of Sum_{k=0..n} (2^k * (k!)^2)/(2k + 1)!.
  • A277586 (program): Numerator of Sum_{k=0..n} (2^k * (k!)^2)/(2k + 1)!.
  • A277588 (program): Numbers k such that k/10^m == 1 mod 10, where 10^m is the greatest power of 10 that divides n.
  • A277589 (program): Numbers k such that k/10^m == 2 mod 10, where 10^m is the greatest power of 10 that divides n.
  • A277590 (program): Numbers k such that k/10^m == 3 mod 10, where 10^m is the greatest power of 10 that divides n.
  • A277591 (program): Numbers k such that k/10^m == 4 mod 10, where 10^m is the greatest power of 10 that divides n.
  • A277592 (program): Numbers k such that k/10^m == 5 mod 10, where 10^m is the greatest power of 10 that divides n.
  • A277593 (program): Numbers k such that k/10^m == 6 mod 10, where 10^m is the greatest power of 10 that divides n.
  • A277594 (program): Numbers k such that k/10^m == 7 mod 10, where 10^m is the greatest power of 10 that divides n.
  • A277595 (program): Numbers k such that k/10^m == 8 mod 10, where 10^m is the greatest power of 10 that divides k.
  • A277596 (program): Numbers k such that k/10^m == 9 mod 10, where 10^m is the greatest power of 10 that divides n.
  • A277597 (program): a(n) = (1/2)*A277589(n).
  • A277598 (program): (1/2)*A277591.
  • A277599 (program): (1/5)*A277592.
  • A277600 (program): (1/2)*A277593.
  • A277601 (program): (1/2)*A277595.
  • A277604 (program): Array of coefficients T(k,n) of the formal power series A(k,x) read by upwards antidiagonals, where A(k,x) = sqrt(1 + 2*x*A(k,x) + (4*k+1)*x^2*(A(k,x))^2), k >= 0.
  • A277609 (program): Fourth column of Euler’s difference table in A068106. It is 6 times the sequence A000261.
  • A277610 (program): G.f.: 1 / (1 - Sum_{k>=1} k^k * x^k ).
  • A277611 (program): Expansion of 1 / (1 - Sum_{k>=1} k^(k-2) * x^k ).
  • A277614 (program): a(n) is the coefficient of x^n/n! in exp(x + n*x^2/2).
  • 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.
  • A277620 (program): Positive integers that are composed of prime factors 2,3,5 and 11.
  • A277627 (program): Square array read by antidiagonals downwards: T(n,k), n>=0, k>=0, in which column 0 is equal to A057427: 0, 1, 1, 1, …, and for k > 0 column k lists two zeros followed by the partial sums of column k-1.
  • A277636 (program): Number of 3 X 3 matrices having all elements in {0,…,n} with determinant = permanent.
  • A277637 (program): Partial sums of A007004.
  • A277638 (program): Binomial partial sums of sequence A007004.
  • A277639 (program): Double binomial partial sums of A007004.
  • A277643 (program): Partial sums of number of overpartitions (A015128).
  • A277644 (program): Beatty sequence for sqrt(6)/2.
  • A277645 (program): Beatty sequence for 3+sqrt(6).
  • A277646 (program): Triangle T(n,k) = floor(n^2/k) for 1 <= k <= n^2, read by rows.
  • A277647 (program): Triangle T(n,k) = floor(n/sqrt(k)) for 1 <= k <= n^2, read by rows.
  • A277650 (program): Numbers with primitive English number names.
  • A277651 (program): Decimal expansion of the first derivative of the infinite power tower function x^x^x… at x = 1/4.
  • A277652 (program): Numerators on factorial moments of order 2 for the number of parts in dissections of rooted and convex polygons.
  • A277653 (program): Number of n X 2 0..2 arrays with every element equal to some element at offset (-1,0) (-1,1) (0,-1) (0,1) or (1,0) both plus 1 mod 3 and minus 1 mod 3, with new values introduced in order 0..2.
  • A277660 (program): 2nd-order coefficients of the 1/N-expansion of traces of negative powers of complex Wishart matrices with parameter c=2.
  • A277661 (program): 1st-order coefficients of the 1/N-expansion of traces of negative powers of real Wishart matrices with parameter c=2.
  • A277667 (program): Number of n-length words over a quaternary alphabet {a_1,a_2,…,a_4} avoiding consecutive letters a_i, a_{i+1}.
  • A277668 (program): Number of n-length words over a 5-ary alphabet {a_1,a_2,…,a_5} avoiding consecutive letters a_i, a_{i+1}.
  • A277669 (program): Number of n-length words over a 6-ary alphabet {a_1,a_2,…,a_6} avoiding consecutive letters a_i, a_{i+1}.
  • A277673 (program): Number of n-length words over an n-ary alphabet {a_1,a_2,…,a_n} avoiding consecutive letters a_i, a_{i+1}.
  • A277674 (program): a(n) = d(n+1) - d(n), where d(k) is the number of digits in the base-k representation of k!.
  • A277676 (program): Numbers k such that d(k+2) > d(k+1), where d(m) is the number of digits in the base-m representation of m!.
  • 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.
  • A277697 (program): a(n) = Index of the least unitary prime divisor of n or 0 if no such prime-divisor exists.
  • A277698 (program): a(n) = Least unitary prime divisor of n or 1 if no such prime-divisor exists.
  • A277707 (program): a(n) = index of the least prime divisor of n which has an odd exponent, or 0 if n is a perfect square.
  • 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).
  • A277733 (program): Positions of 1’s in A277731.
  • A277734 (program): Positions of 2’s in A277731.
  • A277735 (program): Unique fixed point of the morphism 0 -> 01, 1 -> 20, 2 -> 0.
  • A277736 (program): Positions of 0’s in A277735.
  • A277737 (program): Positions of 1’s in A277735.
  • A277738 (program): Positions of 2’s in A277735.
  • A277745 (program): Trajectory of 1 under repeated application of the morphism 1 -> 1232, 2 -> 1232232, 3 -> 123232.
  • A277752 (program): a(n) = Sum_{k=0..n} (-1)^k*floor(phi^k), where phi is the golden ratio (A001622).
  • A277755 (program): Decimal expansion of Sum(n>=1} |sin((n*Pi)/3)|^n.
  • A277757 (program): a(n) = 2^(6n+1).
  • A277761 (program): Number of n X 2 0..2 arrays with every element equal to some element at offset (-1,-1) (-1,0) (-1,1) (0,-1) (0,1) or (1,0) both plus 1 mod 3 and minus 1 mod 3, with new values introduced in order 0..2.
  • A277780 (program): a(n) is the least k > n such that n*k^2 is a cube.
  • A277782 (program): Number of n X 2 0..2 arrays with every element equal to some element at offset (-1,-1) (-1,0) (-1,1) (0,-1) (0,1) (1,-1) or (1,0) both plus 1 mod 3 and minus 1 mod 3, with new values introduced in order 0..2.
  • A277789 (program): a(n) = Sum_{k=0..n} (-1)^k*floor((1 + sqrt(2))^k).
  • A277790 (program): Numerator of sum of reciprocals of proper divisors of n.
  • A277791 (program): Denominator of sum of reciprocals of proper divisors of n.
  • A277792 (program): Squares that are also pentagonal pyramidal numbers.
  • A277797 (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 1”, based on the 5-celled von Neumann neighborhood.
  • A277798 (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 1”, based on the 5-celled von Neumann neighborhood.
  • 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.
  • A277811 (program): Column 1 of A277810: a(n) = A019565(A065621(n)).
  • 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.
  • A277818 (program): Index of the column where n is located in array A277820: a(n) = 1 + A268389(n).
  • A277822 (program): a(n) = index of the column where n is located in array A277880.
  • A277823 (program): a(n) = A048724(A065621(n)).
  • A277825 (program): a(n) = A048725(A065621(n)) = A048720(A065621(n),5).
  • 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.
  • A277865 (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 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.
  • A277871 (program): a(n) = Sum_{i=0..n+1} binomial(2*n-i,n-i+1)*Catalan(i).
  • A277872 (program): Number of ways of writing n as a sum of powers of 4, each power being used at most four times.
  • A277876 (program): a(n) = n!/(m*(n-m)) with m = floor(n/2).
  • A277877 (program): Number of A’Campo forests of degree n>1 and co-dimension 2.
  • A277885 (program): a(n) = index of the least non-unitary prime divisor of n or 0 if no such prime-divisor exists.
  • A277892 (program): a(n) = A001222(A048675(n)).
  • A277903 (program): a(n) = the least k such that A000123(k) >= n.
  • A277904 (program): Irregular table: row n (n >= 0) is obtained by listing numbers 0 .. A018819(n)-1.
  • A277906 (program): Least number with same prime signature as phi(n): a(n) = A046523(A000010(n)).
  • A277916 (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 4”, based on the 5-celled von Neumann neighborhood.
  • A277917 (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 4”, based on the 5-celled von Neumann neighborhood.
  • A277918 (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 4”, based on the 5-celled von Neumann neighborhood.
  • A277919 (program): Triangle read by rows: CL(n,k) is the number of labeled subgraphs with k edges of the n-cycle C_n.
  • A277924 (program): a(n) = Sum_{i=0..n+1} binomial(2*n,n-i+1).
  • A277926 (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 5”, based on the 5-celled von Neumann neighborhood.
  • A277927 (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 5”, based on the 5-celled von Neumann neighborhood.
  • 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.
  • A277931 (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 6”, based on the 5-celled von Neumann neighborhood.
  • A277932 (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 6”, based on the 5-celled von Neumann neighborhood.
  • A277933 (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 6”, based on the 5-celled von Neumann neighborhood.
  • A277934 (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 6”, 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.
  • A277937 (program): Number of runs of 1’s of length 1 in the binary expansion of n.
  • A277939 (program): Number of n X 2 0..2 arrays with every element plus 1 mod 3 equal to some element at offset (-1,0) (-1,1) (0,-1) (0,1) or (1,0), with upper left element zero.
  • A277948 (program): Squares whose largest decimal digit is 4.
  • A277952 (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 14”, 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.
  • A277956 (program): a(n) = (n+2)*Sum_{i=0..n}(binomial(3*n-2*i+1, n-i)/(2*n-i+2)).
  • A277957 (program): a(n) = (n+3)*Sum_{i=0..n} binomial(3*n-2*i+2,n-i)/(2*n-i+3).
  • A277961 (program): Numbers n such that 4 is the largest decimal digit of n^2.
  • A277963 (program): G.f.: 1/(1+x) * Product_{k>=1} 1/(1-x^k)^k.
  • A277964 (program): Numbers whose largest decimal digit is 2.
  • A277965 (program): Numbers whose largest decimal digit is 3.
  • A277966 (program): Numbers whose largest decimal digit is 4.
  • A277968 (program): Expansion of ((Product_{n>=1} (1 - x^(3*n))/(1 - x^n)^3) - 1)/3 in powers of x.
  • A277969 (program): a(n) = Sum_{k=0..n} binomial(n-3,n-k)*Catalan(k).
  • A277974 (program): Expansion of ((Product_{n>=1} (1 - x^(5*n))/(1 - x^n)^5) - 1)/5 in powers of x.
  • A277975 (program): a(n) = n*x^n + (n-1)*x^(n-1) + . . . + x + 1 for x=5.
  • A277976 (program): a(n) = n*(3*n + 23).
  • A277977 (program): a(n) = n*(1-3n+2*n^2+2*n^3)/2.
  • A277978 (program): a(n) = 3*n*(n+3).
  • A277979 (program): a(n) = 4*n^2 + 18*n.
  • A277980 (program): a(n) = 12*n^2 + 18*n.
  • A277981 (program): a(n) = 4*n^2 + 18*n - 20.
  • A277982 (program): a(n) = 12*n^2 + 10*n - 30.
  • A277983 (program): a(n) = 54*n^2 - 78*n + 36.
  • A277984 (program): a(n) = 6*n*(9*n-5).
  • A277985 (program): a(n) = 3*(9*n - 1)*(3*n - 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) = 54*n^2 + 6*n.
  • A277991 (program): a(n) = 81*n^2 - 9*n.
  • 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.
  • A278008 (program): Number of n X 2 0..2 arrays with every element plus 1 mod 3 equal to some element at offset (-1,-1) (-1,0) (-1,1) (0,-1) (0,1) or (1,0), with upper left element zero.
  • A278023 (program): G.f.: 2*x*(1-x*sqrt(1-4*x))/((1+2*x^2+sqrt(1-4*x))*sqrt(1-4*x)).
  • A278026 (program): Number of 1324-avoiding permutations of length n with a non-intersecting boundary of type (t, 2), for some integer t >= 1,
  • A278029 (program): a(1)=0; for n>1, a(n) = k if n is a non-prime-power, A007916(k), say; or 0 if n is a prime power.
  • A278038 (program): Binary vectors not containing three consecutive 1’s; or, representation of n in the tribonacci base.
  • A278039 (program): The tribonacci representation of a(n) is obtained by appending a 0 to the tribonacci representation of n (cf. A278038).
  • A278040 (program): The tribonacci representation of a(n) is obtained by appending 0,1 to the tribonacci representation of n (cf. A278038).
  • A278041 (program): The tribonacci representation of a(n) is obtained by appending 0,1,1 to the tribonacci representation of n (cf. A278038).
  • A278042 (program): Number of 0’s in tribonacci representation of n (cf. A278038).
  • A278043 (program): Number of 1’s in tribonacci representation of n (cf. A278038).
  • A278044 (program): Length of tribonacci representation of n (cf. A278038).
  • A278045 (program): Number of trailing 0’s in tribonacci representation of n (cf. A278038).
  • A278049 (program): a(n) = 3*(Sum_{k=1..n} phi(k)) - 1, where phi = A000010.
  • A278069 (program): a(n) = hypergeometric([n, -n], [], 1).
  • A278070 (program): a(n) = hypergeometric([n, -n], [], -1).
  • A278072 (program): Riordan array(1/(1+x), (1-sqrt(1-4*x))/(2*x)).
  • A278075 (program): Coefficients of the signed Fubini polynomials in ascending order, F_n(x) = Sum_{k=0..n} (-1)^n*Stirling2(n,k)*k!*(-x)^k.
  • A278078 (program): a(n) is the number of composite numbers prime(n) dominates.
  • A278079 (program): E.g.f. 1/3!*sin^3(x)/cos(x) (coefficients of odd powers only).
  • A278083 (program): a(n) is 1/6 of the number of primitive integral quadruples with sum = 2*m and sum of squares = 2*m^2, where m = 2*n-1.
  • A278088 (program): Number of n X 2 0..1 arrays with every element both equal and not equal to some elements at offset (-1,0) (-1,1) (0,-1) (0,1) or (1,0), with upper left element zero.
  • A278100 (program): Number of squarefree positive integers less than n^2.
  • A278105 (program): a(n) = floor(3/n).
  • A278110 (program): a(n) = Product_{k=1..A056811(n)} A000040(k)^A278109(n,k).
  • A278111 (program): Triangle T(n,k) = floor(2n^2/k) for 1 <= k <= 2n^2, read by rows.
  • A278112 (program): Triangle T(n,k) = floor(n sqrt(2/k)) for 1 <= k <= 2n^2, read by rows.
  • A278114 (program): Number of primes <= 2n^2.
  • 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.
  • A278137 (program): Maximum number of disjoint subgraphs of the Fibonacci cube Gamma(n) that are isomorphic to the hypercube of dimension k, summed over all k.
  • 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).
  • A278147 (program): Triangle read by rows of Cantor pairing function value determining primitive Pythagorean triangles or 0 if there is no such triangle.
  • A278151 (program): Number of n X 2 0..1 arrays with every element both equal and not equal to some elements at offset (-1,-1) (-1,0) (-1,1) (0,-1) (0,1) (1,-1) or (1,0), with upper left element zero.
  • A278159 (program): Run length transform of primorials, A002110.
  • A278160 (program): Least number with the prime signature of ((n+1)^2 - 1).
  • A278161 (program): Run length transform of A008619 (floor(n/2)+1).
  • A278162 (program): Least number with the prime signature of n^2 + 1.
  • A278163 (program): a(n) = the least k such that A131205(1+k) >= n; each n occurs A000123(n) times.
  • A278164 (program): Irregular triangle read by rows: row n (n >= 0) is obtained by listing numbers 0 .. A000123(n)-1.
  • A278169 (program): Characteristic function for A000960.
  • A278171 (program): Number of n X 2 0..1 arrays with every element both equal and not equal to some elements at offset (-1,0) (-1,1) (0,-1) (0,1) (1,-1) or (1,0), with upper left element zero.
  • A278182 (program): Number of dots in Maya numeral representation of n.
  • A278217 (program): Filter-sequence related to base-2 run-length encoding: a(n) = A046523(A075159(1+n)) = A046523(1+A075157(n)).
  • A278218 (program): Triangle read by rows: T(n,k) = Least number with the prime signature of binomial(n,k).
  • A278219 (program): Filter-sequence related to base-2 run-length encoding: a(n) = A046523(A243353(n)).
  • A278220 (program): Filtering sequence (related to prime factorization): a(n) = A046523(A241909(n)).
  • A278221 (program): Filtering sequence (related to prime factorization): a(n) = A046523(A122111(n)).
  • A278222 (program): The least number with the same prime signature as A005940(n+1).
  • A278223 (program): Least number with the same prime signature as the n-th odd number: a(n) = A046523(2n-1).
  • A278224 (program): a(n) = A046523(A048673(n)).
  • A278226 (program): Filter-sequence for primorial base: least number with the same prime signature as A276086(n).
  • A278227 (program): Least number with the prime signature of prime(n)-1.
  • A278228 (program): Least number with the prime signature of prime(n)+1.
  • A278229 (program): Least number with the prime signature of 2*prime(n) - 1.
  • A278230 (program): Least number with the prime signature of 2*prime(n) + 1.
  • A278231 (program): Least number with the same prime signature as the n-th number in Blue-code: a(n) = A046523(A193231(n)).
  • A278235 (program): Filter-sequence for factorial base (digit levels): Least number with the same prime signature as A275735(n).
  • A278236 (program): Filter-sequence for factorial base (digit values): least number with the same prime signature as A276076(n).
  • A278244 (program): Least number with the prime signature of the n-th centered square number (A001844(n)).
  • A278246 (program): a(n) = least number with the same prime signature as n*(n+3)/2.
  • A278247 (program): a(n) = least number with the same prime signature as n + (n+1)^2.
  • A278249 (program): Least number with the prime signature of A000123(n), the number of partitions of 2n into powers of 2.
  • A278251 (program): Least number with the prime signature of the n-th central polygonal number.
  • A278252 (program): Least number with the prime signature of the n-th tetrahedral number, binomial(n+2,3).
  • A278253 (program): Least number with the prime signature of the n-th triangular number.
  • A278254 (program): Least number with the prime signature of n^2; square of the least number with the prime signature of n.
  • A278255 (program): Least number with the prime signature of the n-th pentagonal number.
  • A278256 (program): Least number with the same prime signature as the n-th oblong number (A002378).
  • A278257 (program): Least number with the prime signature of A005187(n).
  • A278260 (program): Least number with the same prime signature as {the n-th quarter-square}+1.
  • A278274 (program): Number of n X 2 0..1 arrays with every element both equal and not equal to some elements at offset (-1,-1) (-1,0) (-1,1) (0,-1) (0,1) or (1,0), with upper left element zero.
  • A278281 (program): Number of 2 X n 0..1 arrays with every element both equal and not equal to some elements at offset (-1,-1) (-1,0) (-1,1) (0,-1) (0,1) or (1,0), with upper left element zero.
  • A278290 (program): Number of neighbors of each new term in a square array read by antidiagonals.
  • A278291 (program): Numbers n such that n-1 has the same number of prime factors as n (with multiplicity).
  • A278293 (program): a(n) is the number of prime factors of A278291(n) (with multiplicity).
  • 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.
  • A278301 (program): Number of permutations of length n in the class of juxtapositions of 321-avoiders with 21-avoiders.
  • 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.
  • A278317 (program): Number of neighbors of each new term in a right triangle read by rows.
  • A278327 (program): Decimal expansion of 1/e - 1/e^2.
  • A278348 (program): Number of 2 X 2 singular integer matrices with elements from {0,…,n} with no elements repeated.
  • A278355 (program): a(n) = sum of the perimeters of the Ferrers boards of the partitions of n. Also, sum of the perimeters of the diagrams of the regions of the set of partitions of n.
  • A278357 (program): Number of n X 2 0..1 arrays with rows and columns in lexicographic nondecreasing order but with exactly one mistake.
  • A278364 (program): A sequence showing denominators in ratios tending to the constant Pi/4 = 0.785398163397448… .
  • A278365 (program): Number of n X 1 0..2 arrays with rows and columns in lexicographic nondecreasing order but with exactly three mistakes.
  • A278375 (program): Edge-distinguishing chromatic number of ladder graph with 2n vertices.
  • A278394 (program): Number of positive meanders (walks starting at the origin and ending at any altitude > 0 that never touch or go below the x-axis in between) with n steps from {-2,-1,1,2}.
  • A278403 (program): a(n) = Sum_{d|n} d^2 * (d+1)/2.
  • A278405 (program): a(n) = Sum_{k=0..n} binomial(n,2k)^2*binomial(n-k,k).
  • A278406 (program): G.f.: x^2 * f’‘(x), where f(x) = Product_{k>=1} 1 / (1 - x^k).
  • A278407 (program): G.f.: x^2 * f’‘(x), where f(x) = Product_{k>=1} (1 + x^k).
  • A278415 (program): a(n) = Sum_{k=0..n} binomial(n, 2k)*binomial(n-k, k)*(-1)^k.
  • A278417 (program): a(n) = n*((2+sqrt(3))^n + (2-sqrt(3))^n)/2.
  • A278429 (program): a(n) = Sum_{k=0..n} binomial(k+n-2,k)*binomial(2*n+1,k+n+1).
  • A278438 (program): Numbers m such that T(m) + 2*T(m+1) is a square, where T = A000217.
  • A278472 (program): a(n) = Sum_{i=0..n} Fibonacci(i+1)*binomial(2*n-i+2, n+2).
  • 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.
  • A278478 (program): a(n) is the 2-adic valuation of A000041(n).
  • A278480 (program): Number of neighbors of the n-th term in a full right triangle read by rows.
  • A278481 (program): Number of neighbors of the n-th term in a full isosceles triangle read by rows.
  • A278484 (program): Main diagonal of A278482.
  • A278491 (program): After a(0)=0, numbers n such that (A002828(1+n) = 1) and (A002828(4+n) = 4).
  • A278509 (program): a(n) = 3^{number of primes congruent to 3 modulo 4 dividing n (with multiplicity)}.
  • A278520 (program): a(n) = A243503(n) - A056239(n).
  • A278525 (program): Filtering sequence (related to prime factorization): a(n) = A046523(A241916(n)).
  • A278528 (program): a(n) = number of the round in which n is removed in the Flavius sieve, 0 if it is never removed (when n is one of the terms of A000960).
  • A278529 (program): a(n) = one-based position in the round in which n is removed in the Flavius sieve, 0 if n is never removed (when n is one of the terms of A000960).
  • A278530 (program): a(n) = A056239(A260443(n)).
  • A278531 (program): a(n) = A046523(A163511(n)).
  • A278533 (program): a(n) = A046523(A253563(n)).
  • A278535 (program): a(n) = A046523(A253565(n)).
  • A278536 (program): First differences of A273324.
  • A278537 (program): a(n) = index of the column where n is located in array A278511, a(1) = 0.
  • A278538 (program): a(n) = index of the row where n is located in array A278505.
  • A278539 (program): a(n) = index of the column where n is located in array A278505.
  • A278541 (program): a(n) = A046523(A209636(n)).
  • A278542 (program): a(n) = A046523(A209637(n)).
  • A278545 (program): Number of neighbors of the n-th term in a full square array read by antidiagonals.
  • A278547 (program): Number of n X 1 0..3 arrays with rows and columns in lexicographic nondecreasing order but with exactly two mistakes.
  • A278554 (program): Number of distinct blocks of length n (a.k.a. subword complexity) of the characteristic sequence of the squarefree numbers A008966.
  • A278565 (program): a(n) = Sum_{t=1..n} binomial(n,t)*t^(1+(n-t)^2).
  • A278568 (program): Twice odd prime powers.
  • A278569 (program): Numbers of the form p^i*q^j*r^k where p,q,r are distinct odd primes and i,j,k >= 1.
  • A278586 (program): Start with X = n^2. Repeatedly replace X with X - ceiling(X/n); a(n) is the number of steps to reach 0.
  • A278587 (program): Value of the Catch-Up game [1,…n] for first player (1 = win, -1 = loss, 0 = draw).
  • A278596 (program): a(n) = Sum_{k=0..n} binomial(k+n+3,k)*binomial(2*n+1,n-k).
  • A278597 (program): One half of A278481.
  • A278602 (program): Sum of the perimeters of all regions of the n-th section of a modular table of partitions.
  • A278603 (program): A prime mountain: peaks and valleys beyond the origin correspond to prime abscissa (see Comments for precise definition).
  • A278604 (program): Number of nX1 0..3 arrays with rows and columns in lexicographic nondecreasing order but with exactly three mistakes.
  • A278612 (program): Sum of terms in level n of TRIP - Stern sequence associated with permutation triple (e, e, e).
  • A278613 (program): Sum of terms in level n of TRIP - Stern sequence associated with permutation triple (e,e,132).
  • A278614 (program): Sum of terms in level n of TRIP - Stern sequence associated with permutation triple (e,12,12).
  • A278615 (program): Sum of terms in level n of TRIP - Stern sequence associated with permutation triple (e,13,23).
  • A278616 (program): Sum of terms in level n of TRIP - Stern sequence associated with permutation triple (e,13,132).
  • 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.
  • A278618 (program): a(n) = Sum_{j=0..n/2} binomial(n-j-1,n-2*j)*binomial(2*n+1,j).
  • A278620 (program): Expansion of x/(1 - 99*x + 99*x^2 - x^3).
  • A278646 (program): a(n) = ((2*n+1)/(n+1))*Sum_{j=0..n/2} binomial(n+1, j)*binomial(n-j-1, n-2*j).
  • A278647 (program): First differences of Hypotenuse numbers A009003.
  • A278648 (program): Consider the set S of integers 1 through n. a(n) is the number of unordered ways in which three distinct elements {a, b, c} of S satisfy a*b = c*n.
  • A278670 (program): Number of n X 2 0..1 arrays with rows in nondecreasing lexicographic order and columns in nonincreasing lexicographic order, but with exactly one mistake.
  • A278677 (program): Popularity of left children in treeshelves avoiding pattern T231.
  • A278678 (program): Popularity of left children in treeshelves avoiding pattern T321.
  • A278679 (program): Popularity of left children in treeshelves avoiding pattern T213.
  • A278681 (program): Pisot sequence T(3,16).
  • A278689 (program): a(n) = Sum_{k=0..n} binomial(n+k,n)*binomial(2*n-3,n-k-1) for n>1, a(n) = n for n<=1.
  • A278690 (program): Expansion of Product_{n>=1} (1 - x^(3*n))/(1 - x^n)^2 in powers of x.
  • A278692 (program): Pisot sequence T(4,14).
  • A278704 (program): Number of triangles in all simple labeled graphs on n nodes.
  • A278705 (program): Number of length-4 cycles in all simple labeled graphs on n nodes.
  • A278706 (program): a(n) = a(n-1) + a(n-3) + a(n-5) - a(n-6), a(0) = a(1) = a(2) = 1, a(3) = 2, a(4) = 3, a(5) = 5.
  • A278708 (program): Fibonacci sequence starting 154, 144.
  • A278710 (program): Convolution square of A255528.
  • A278711 (program): Triangle T read by rows: T(n, m), for n >= 2, and m=1, 2, …, n-1, equals the positive integer solution x of y^2 = x^3 - A(n, m)^2*x with the area A(n, m) = A249869(n, m) of the primitive Pythagorean triangle characterized by (n, m) or 0 if no such triangle exists.
  • A278712 (program): Triangle T read by rows: T(n, m), for n >= 2, and m = 1, 2, …, n-1, equals the square root of the positive integer solution y of y^2 = x^3 - A(n, m)^2*x with the area A(n, m) = A249869(n, m) of the primitive Pythagorean triangle characterized by (n, m) or 0 if no such triangle exists.
  • A278713 (program): Numerators of (n-1)*(n-3)/(6*(2*n-1)); equivalently, numerators of Dedekind sum s(2,2*n-1).
  • A278714 (program): Denominators of (n-1)*(n-3)/(6*(2*n-1)), for n >= 1. Denominators of Dedekind sum s(2, 2*n-1).
  • A278717 (program): Triangle read by rows: T(n, m) gives the difference between the even and odd leg of the primitive Pythagorean triangle determined by (n, m) with n > m >= 1, gcd(n, m) = 1 and n+m odd, or 0 for other (n, m).
  • A278718 (program): Numerators of A189733: periodic sequence repeating [0, 1, 1, 1, 0, -1].
  • A278736 (program): Number of size-4 cliques in all simple labeled graphs on n nodes.
  • A278741 (program): Odd numbers n such that tau(n-1) is a prime.
  • A278753 (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 65”, based on the 5-celled von Neumann neighborhood.
  • A278754 (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 65”, based on the 5-celled von Neumann neighborhood.
  • A278755 (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 65”, based on the 5-celled von Neumann neighborhood.
  • 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.
  • A278757 (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 73”, based on the 5-celled von Neumann neighborhood.
  • A278758 (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 73”, based on the 5-celled von Neumann neighborhood.
  • A278759 (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 73”, based on the 5-celled von Neumann neighborhood.
  • A278760 (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 73”, based on the 5-celled von Neumann neighborhood.
  • A278764 (program): Pisot sequence T(5,13).
  • 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.
  • A278879 (program): a(n) = Sum_{k=0..n-1} (k+1)*binomial(n,k) * a(k) for n > 0 with a(0) = 1.
  • A278881 (program): Triangle where g.f. C = C(x,m) and related series S = S(x,m) and D = D(x,m) satisfy S = x*C*D, C = 1 + x*S*D, and D = 1 + m*x*S*C, as read by rows of coefficients T(n,k) of x^(2*n)*m^k in C(x,m) for n>=0, k=0..n.
  • A278882 (program): Triangle where g.f. D = D(x,m) and related series S = S(x,m) and C = C(x,m) satisfy S = x*C*D, C = 1 + x*S*D, and D = 1 + m*x*S*C, as read by rows of coefficients T(n,k) of x^(2*n)*m^k in C(x,m) for n>=1, k=0..n.
  • A278883 (program): a(n) = (4*n+1) * ( binomial(3*n,n)/(2*n+1) )^2.
  • A278884 (program): a(n) = binomial(3*n-1,n) * binomial(3*n,n)/(2*n+1).
  • A278907 (program): a(n) = floor((n*2^(n+1)+2)/(2*n-(-1)^n+3)) - floor((n*2^(n+1)-2)/(2*n-(-1)^n+3)).
  • A278908 (program): Multiplicative with a(p^e) = 2^omega(e), where omega = A001221.
  • A278910 (program): Triangle of order m: C(n,k) = k*(n-k+1)^(k+m)+n-k, 0 <= k <= n, m = 0, read by rows.
  • A278911 (program): Odd numbers with prime sum of divisors.
  • A278928 (program): Decimal expansion of sqrt(sqrt(2) + 1).
  • A278933 (program): Number of 2 X 2 matrices with entries in {0,1,…,n} and permanent = trace with no entry repeated.
  • A278934 (program): a(n) = Sum_{k=0..n} (-1)^(n-k)*binomial(n,k)*binomial(2*k,k)^2.
  • A278945 (program): Expansion of Sum_{k>=1} k*(2*k - 1)*x^k/(1 - x^k).
  • A278947 (program): Expansion of Sum_{k>=1} (k*(5*k - 3)/2)*x^k/(1 - x^k).
  • A278972 (program): Twice the twin primes.
  • A278990 (program): Number of loopless linear chord diagrams with n chords.
  • A278991 (program): a(n) is the number of simple linear diagrams with n+1 chords.
  • A278992 (program): Number of simple chord-labeled chord diagrams with n chords.
  • A278996 (program): Numbers of the form (3h+1)*3^(2k)-1 or (3h+2)*3^(2k+1)-1 for h,k in N.
  • A278997 (program): Numbers of the form (3h+2)*3^(2k)-1 or (3h+1)*3^(2k+1)-1 for h,k in N.
  • A278998 (program): Numbers of the form (5h+1)*5^k-1 or (5h+4)*5^k-1 for h,k in N.
  • A278999 (program): Numbers of the form (5h+2)*5^k-1 or (5h+3)*5^k-1 for h,k in N.
  • A279004 (program): Irregular triangle read by rows: generalized Catalan triangle C_3(n,k).
  • A279006 (program): Alternating Jacobsthal triangle read by rows (second version).
  • A279008 (program): Triangle read by rows: 2-analog of triangle A112468.
  • A279009 (program): Alternating Jacobsthal triangle A_{-2}(n,k) read by rows.
  • A279010 (program): Alternating Jacobsthal triangle A_3(n,k) read by rows.
  • A279013 (program): a(n) = Sum_{k=0..n} binomial(2*k,k)/(k+1)*binomial(2*n-1,n-k).
  • A279014 (program): a(n) = Sum_{k=0..n} fibonacci(k+1)*binomial(2*n-1,n-k).
  • A279017 (program): a(n) = unreduced numerator in Sum_{k=1..n}(1/k^k).
  • A279019 (program): Least possible number of diagonals of simple convex polyhedron with n faces.
  • A279020 (program): a(n) = unreduced numerator in Sum_{k=1..n} (-1)^(k-1)/k^k.
  • 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.
  • A279029 (program): Numbers k with the property that the smallest and the largest Dyck path of the symmetric representation of sigma(k) do not share line segments.
  • 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.
  • A279031 (program): Expansion of Product_{k>0} 1/(1 + x^k)^(k*3).
  • A279035 (program): Left-concatenate zeros to 2^(n-1) such that it has n digits. In the regular array formed by listing the found powers, a(n) is the sum of (nonzero) digits in column n.
  • A279042 (program): Numbers k such that 2*k+1 and 10*k+1 are both triangular numbers (A000217).
  • A279043 (program): Numbers k such that 3*k+1 and 4*k+1 are both triangular numbers (A000217).
  • A279046 (program): a(n) = A000178(n) * Sum_{k=0..n} (-1)^k/k!.
  • A279048 (program): a(n) = 0 whenever n is a practical number (A005153) otherwise least powers of 2 that when multiplied by n becomes practical.
  • A279051 (program): Sum of odd nonprime divisors of n.
  • 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).
  • A279055 (program): Convolution of squares of factorial numbers (A000142).
  • A279060 (program): Number of divisors of n of the form 6*k + 1.
  • A279061 (program): Number of divisors of n of the form 7*k + 1.
  • A279064 (program): Numbers n such that the sum of numbers less than n that do not divide n is even.
  • A279071 (program): Numbers k such that Fibonacci(k) == +-1 (mod k).
  • 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.
  • A279083 (program): Numbers k such that there exists at least one tetrahedral number with exactly k divisors.
  • 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).
  • A279102 (program): Numbers n having three parts in the symmetric representation of sigma(n).
  • A279105 (program): a(n), n>1, is the smallest number k whose symmetric representation of sigma(k) has two parts and has a larger number of legs in its two parts than a(n-1); a(1)=3.
  • A279106 (program): a(n) = number of legs in each part of the symmetric representation of sigma(A279105(n)).
  • A279107 (program): Denominators of coefficients in expansion of 1/(1 - sin x).
  • A279109 (program): Denominators of coefficients in expansion of 1/(1 + cos(sqrt(x))).
  • A279110 (program): Denominators of coefficients in expansion of 2/(1 + cos(sqrt(x))).
  • A279111 (program): Number of non-equivalent ways to place 2 non-attacking kings on an n X n board.
  • 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.
  • A279120 (program): Numerators of coefficients in expansion of 1/(1 + 2 cos(sqrt(x))).
  • A279121 (program): Denominators of coefficients in expansion of 1/(1 + 2 cos(sqrt(x))).
  • A279122 (program): Denominators of coefficients in expansion of 3/(1 + 2 cos(sqrt(x))).
  • 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.
  • A279127 (program): a(n) = Sum_{0<=m<n} Product_{-m<=j<=m} (n-j).
  • A279136 (program): a(n) = n*Sum_{i=0..n-1} binomial(n,i)*binomial(i-1,n-i-1)/(n-i).
  • A279159 (program): a(n) = Sum_{k=0..n} (k+1)*binomial(3*n-4*k+1,n-k)/(n-k+1).
  • A279169 (program): a(n) = floor( 4*n^2/5 ).
  • A279181 (program): Numerators of coefficients in expansion of 1/(-1 + 2 cos(sqrt(x))).
  • A279182 (program): Denominators of coefficients in expansion of 1/(-1 + 2 cos(sqrt(x))).
  • A279186 (program): Maximal entry in n-th row of A279185.
  • A279187 (program): Maximal entry in row c of A279185, where c = n-th composite number A002808(n).
  • A279188 (program): Maximal entry in row c of triangle in A279185, where c = prime(n)^2 = A001248(n).
  • A279193 (program): Least positive integer whose decimal digits divide the plane into n regions (version for people who write 2 with a curlicue).
  • A279204 (program): Numbers whose decimal expansion is a concatenation of 4 consecutive increasing nonnegative numbers.
  • A279206 (program): Length of first run of 0’s in binary representation of Catalan(n).
  • A279209 (program): Length of first run of 0’s in binary expansion of n.
  • A279210 (program): Length of second run of 1’s in binary expansion of n.
  • 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.
  • A279213 (program): Primes formed by concatenating n with n-3.
  • A279225 (program): Expansion of Product_{k>=1} 1/(1 - x^(k^2))^2.
  • A279226 (program): Expansion of Product_{k>=1} (1 + x^(k^2))^2.
  • A279228 (program): Number of unit steps that are shared by the smallest and largest Dyck path of the symmetric representation of sigma(n).
  • A279230 (program): Expansion of 1/((1-x)^2*(1-2*x+2*x^2)).
  • A279231 (program): Expansion of 1/((1-x)^2*(1-3*x+3*x^2)).
  • A279236 (program): Denominators of coefficients in expansion of 1/(2 - cos(sqrt(x))).
  • A279237 (program): Let k_i be the multiplicity of prime(i) in the prime factorization of the n-th composite number C_n, and let k_i=0 if prime(i) is not a factor of C_n. Then a(n)=1*k_1+10*k_2+100*k_3+…+10^N*k_N, where N is the index of the largest prime factor in C_n.
  • A279241 (program): Let f(n) = 4*n^2 + 2*n + 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.
  • A279244 (program): Numbers k with the property that both the smallest and the largest Dyck path of the symmetric representation of sigma(k) share some line segments.
  • A279245 (program): Number of subsets of {1, 2, 3, …, n} that include no consecutive odd integers.
  • A279257 (program): Numerators of coefficients in expansion of 1/(cos x - sin x).
  • A279258 (program): Denominators of coefficients in expansion of 1/(cos x - sin x).
  • A279260 (program): Numbers which are cyclops palindromic in their binary reflected Gray code representation.
  • A279262 (program): Number of n X 2 0..1 arrays with no element equal to a strict majority of its horizontal and vertical neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.
  • A279269 (program): a(n) = floor( (4 + sqrt(11))^n ).
  • A279275 (program): Numbers k such that 2*k+1 and 5*k+1 are both pentagonal numbers (A000326).
  • A279277 (program): Composition of Lucas numbers A000032 with Fibonacci numbers A000045.
  • A279283 (program): Self-composition of the tetrahedral (or triangular pyramidal) numbers; g.f.: A(x) = G(G(x)), where G(x) = g.f. of A000292.
  • A279285 (program): Self-composition of the Pell numbers; g.f.: A(x) = G(G(x)), where G(x) = g.f. of A000129.
  • A279287 (program): a(n) = numerator of (phi(n)/tau(n)).
  • A279288 (program): a(n) = denominator of (phi(n)/tau(n)).
  • A279289 (program): Numbers n such that phi(n) > tau(n).
  • A279290 (program): Sum of cubes of nonprime divisors of n.
  • A279312 (program): Number of subsets of {1, 2, 3, …, n} that include no consecutive even integers.
  • 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].
  • A279318 (program): Permutation of the nonnegative integers [6k+3, 6k+2, 6k+1, 6k, 6k+5, 6k+4].
  • 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].
  • A279322 (program): Number of n X 1 0..2 arrays with no element equal to a strict majority of its king-move neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.
  • A279329 (program): Number of partitions of n into distinct cubes.
  • A279334 (program): Numerators of coefficients in expansion of exp(x)/(1 - x - x^2).
  • A279335 (program): Denominators of coefficients in expansion of exp(x)/(1 - x - x^2).
  • A279340 (program): First differences of A055938.
  • A279345 (program): a(n) = A000120(A279341(n)).
  • A279357 (program): a(n) = A005187(n) XOR A005187(n+1).
  • A279358 (program): Exponential transform of the cubes A000578.
  • A279361 (program): Exponential transform of the triangular numbers.
  • A279363 (program): Sum of 4th powers of proper divisors of n.
  • A279364 (program): Sum of 5th powers of proper divisors of n.
  • A279370 (program): Numerators of coefficients in expansion of (cos(sqrt(x)))/(1 + cos(sqrt(x))).
  • A279372 (program): Expansion of (Sum_{k>=1} x^(prime(k)^2))^2.
  • A279378 (program): Number of n X 2 0..1 arrays with no element equal to a strict majority of its horizontal, vertical and antidiagonal neighbors, with new values introduced in order 0 sequentially upwards.
  • A279395 (program): a(n) = Sum_{ d >= 1, d divides n} (-1)^(n-d)*d^4.
  • A279400 (program): Row lengths of the irregular triangle A279399.
  • A279402 (program): Domination number for queens’ graph on an n X n toroidal board.
  • A279411 (program): Expansion of Product_{k>0} 1/(1 + x^k)^(k*4).
  • A279412 (program): Expansion of Sum_{k>=1} prime(k)*x^prime(k)/(1 + x^prime(k)) * Product_{k>=1} (1 + x^prime(k)).
  • 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.
  • A279416 (program): Triangle read by rows: T(n,k), n >= k >= 1, is the number of grid points below the diagonal of an n X k grid.
  • A279417 (program): Triangle read by rows: T(n,k), n >= k >= 1, is the number of grid points on or below the diagonal of an n X k grid.
  • A279431 (program): Numbers k such that k^2 has an odd number of digits in base 2 and the middle digit is 1.
  • A279432 (program): Triangle read by rows: T(n,k), n>=k>=1, is the number of triangles with integer coordinates that have a bounding box of size n X k.
  • A279434 (program): Numerators of coefficients in expansion of 1/(1 + e^x - e^(2x)).
  • A279435 (program): Denominators of coefficients in expansion of 1/(1 + e^x - e^(2x)).
  • A279436 (program): Number of nonprimes less than or equal to n that do not divide n.
  • 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.
  • A279456 (program): Numbers n such that number of distinct primes dividing n is odd and number of prime divisors (counted with multiplicity) of n is even.
  • A279457 (program): Numbers n such that number of distinct primes dividing n is odd and number of prime divisors (counted with multiplicity) of n is odd.
  • A279458 (program): Numbers n such that number of distinct primes dividing n is even and number of prime divisors (counted with multiplicity) of n is even.
  • A279482 (program): Sum of the first n Lucas numbers whose indices are prime.
  • A279483 (program): Number of 2 X 2 matrices with entries in {0,1,…,n} and odd determinant with no entry repeated.
  • A279484 (program): Expansion of Product_{k>=1} (1-x^(k^3)).
  • A279495 (program): Number of tetrahedral numbers dividing n.
  • A279496 (program): Number of square pyramidal numbers dividing n.
  • A279497 (program): Number of pentagonal numbers dividing n.
  • A279506 (program): Total number of 1’s in the binary expansion of A003418.
  • A279507 (program): a(n) = floor(phi(n)/tau(n)).
  • A279511 (program): Sierpinski square-based pyramid numbers: a(n) = 5*a(n-1) - (2^(n+1)+7).
  • A279512 (program): Sierpinski octahedron numbers a(n) = 2*6^n + 3*2^n + 1.
  • A279513 (program): Multiplicative with a(p^k) = p*a(k) for any prime p and k>0.
  • A279515 (program): Number of 0’s in the binary expansion of the least common multiple of the first n integers.
  • A279519 (program): a(n) = A049502(A003418(n)).
  • 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.
  • A279543 (program): a(n) = a(n-1) + 3^n * a(n-2) with a(0) = 1 and a(1) = 1.
  • A279553 (program): Number of length n inversion sequences avoiding the patterns 110, 210, 120, 201, and 010.
  • A279557 (program): Number of length n inversion sequences avoiding the patterns 110, 120, and 021.
  • A279560 (program): Number of length n inversion sequences avoiding the patterns 100, 210, 201, and 102.
  • A279561 (program): Number of length n inversion sequences avoiding the patterns 101, 102, 201, and 210.
  • A279563 (program): Number of length n inversion sequences avoiding the patterns 102, 201, and 210.
  • A279565 (program): Number of length n inversion sequences avoiding the patterns 100, 110, 120, 201, and 210.
  • A279574 (program): Number of n X 2 0..2 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.
  • A279587 (program): Coefficients in the expansion of 1/([r] + [2r]x + [3r]x^2 + …); [ ] = floor, r = sqrt(2).
  • A279588 (program): Coefficients in the expansion of 1/([r] + [2r]x + [3r]x^2 + …); [ ] = floor, r = sqrt(3).
  • A279589 (program): Coefficients in the expansion of 1/([r] + [2r]x + [3r]x^2 + …); [ ] = floor, r = -1 + sqrt(5).
  • A279590 (program): Coefficients in the expansion of 1/([r] + [2r]x + [3r]x^2 + …); [ ] = floor, r = e - 1.
  • A279591 (program): Coefficients in the expansion of 1/([r] + [2r]x + [3r]x^2 + …); [ ] = floor, r = e/2.
  • A279594 (program): Coefficients in the expansion of 1/([r] + [2r]x + [3r]x^2 + …); [ ] = floor, r = sqrt(6)/2.
  • A279595 (program): Coefficients in the expansion of 1/([r] + [2r]x + [3r]x^2 + …); [ ] = floor, r = sqrt(e).
  • A279607 (program): Beatty sequence for e/2; i.e., a(n) = floor(n*e/2).
  • A279608 (program): Beatty sequence for e/(e - 2); i.e., a(n) = floor(n*e/(e - 2)).
  • A279610 (program): a(n) = concatenate n consecutive integers, starting with the last number of the previous batch.
  • 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.
  • A279622 (program): Numbers with a prime factor greater than 5.
  • A279634 (program): Coefficients in the expansion of 1/([r] + [2r]x + [3r]x^2 + …); [ ] = floor, r = 3/2.
  • A279635 (program): Denominator of (0 followed by A005126(n)= 2, 4, 7, …)/2^n, a sequence corresponding to A271573.
  • A279637 (program): Exponential transform of the fourth powers A000583.
  • A279638 (program): Exponential transform of the fifth powers A000584.
  • A279639 (program): Exponential transform of the sixth powers A001014.
  • A279640 (program): Exponential transform of the seventh powers A001015.
  • A279641 (program): Exponential transform of the eighth powers A001016.
  • A279642 (program): Exponential transform of the ninth powers A001017.
  • A279643 (program): Exponential transform of the tenth powers A008454.
  • A279645 (program): a(n) = not (n XOR (n shift 1)).
  • A279650 (program): An idempotent self-orthogonal Latin square of order 11, read by rows.
  • A279662 (program): a(n) = (2/3)^n*Gamma(n+3/4)*Gamma(n+1)*Gamma(n+2)/Gamma(3/4).
  • A279663 (program): a(n) = (5/6)^n*Gamma(n+3/5)*Gamma(n+1)*Gamma(n+2)/Gamma(3/5).
  • A279673 (program): The maximum number of coins that can be processed in n weighings where all coins are real except for one LHR-coin starting in the light state.
  • A279674 (program): The maximum number of coins that can be processed in n weighings that all are real except for one LHR-coin starting in the heavy state.
  • A279675 (program): Coefficients in the expansion of 1/([r] + [2r]x + [3r]x^2 + …); [ ] = floor, r = 4/3.
  • A279676 (program): Coefficients in the expansion of 1/([r] + [2r]x + [3r]x^2 + …); [ ] = floor, r = 5/3.
  • A279677 (program): Coefficients in the expansion of 1/([r] + [2r]x + [3r]x^2 + …); [ ] = floor, r = 5/4.
  • A279678 (program): Coefficients in the expansion of 1/([r] + [2r]x + [3r]x^2 + …); [ ] = floor, r = 7/4.
  • A279683 (program): Number of move operations required to sort all permutations of [n] by MTF sort.
  • 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.
  • A279724 (program): Transpose of array A257943.
  • A279726 (program): Partial sums of A187619.
  • A279733 (program): Triangle read by rows which is constructed with the diagram of the triangle of A237048 and filling the empty cells with zeros.
  • 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.
  • A279742 (program): Number of 2 X n 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.
  • A279756 (program): Smallest prime p >= prime(n) such that p == 2 (mod prime(n)).
  • A279758 (program): Expansion of Product_{k>=1} 1/(1 - x^(k*(5*k^2-5*k+2)/2)).
  • A279766 (program): Number of odd digits in the decimal expansions of integers 1 to n.
  • A279768 (program): Numbers n such that the sum of digits of 8n equals 16.
  • A279769 (program): Numbers n such that the sum of digits of 9n is 18.
  • A279770 (program): Numbers n such that the sum of digits of 7n equals 14.
  • A279771 (program): Numbers n such that the sum of digits of 11n equals 11.
  • A279772 (program): Numbers n such that the sum of digits of 2n equals 4.
  • A279773 (program): Numbers n such that the sum of digits of 3n equals 6.
  • A279774 (program): Numbers n such that the sum of digits of 4n equals 8.
  • A279775 (program): Numbers k such that the sum of digits of 5k equals 10.
  • A279776 (program): Numbers n such that the sum of digits of 6n equals 12.
  • A279777 (program): Numbers k such that the sum of digits of 9k is 27.
  • A279780 (program): Coefficients in the expansion of 1/([r] + [2r]x + [3r]x^2 + …); [ ] = floor, r = 8/5.
  • A279792 (program): Number of Goldbach partitions (p,q) of 2n such that 0 < |p-q| < n.
  • A279816 (program): Digital roots of tetrahedral numbers (A000292).
  • A279847 (program): a(n) = Sum_{k=1..n} k^2*(floor(n/k) - 1).
  • A279851 (program): Number of n X 2 0..2 arrays with no element unequal to a strict majority of its horizontal and vertical neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.
  • A279865 (program): Number of n X 1 0..2 arrays with no element unequal to a strict majority of its horizontal and vertical neighbors, with the exception of exactly two elements, and with new values introduced in order 0 sequentially upwards.
  • 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.
  • A279877 (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 213”, based on the 5-celled von Neumann neighborhood.
  • A279878 (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 213”, based on the 5-celled von Neumann neighborhood.
  • A279879 (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 213”, based on the 5-celled von Neumann neighborhood.
  • A279880 (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 213”, based on the 5-celled von Neumann neighborhood.
  • A279882 (program): a(n) = 2^(prime(n) + 1) - 1.
  • A279884 (program): a(n) = (prime(n)-1)^(prime(n)+1) + 1.
  • A279886 (program): a(n) = A057863(n+1) * Sum_{k=0..n}(k! / (2*k+1)!!).
  • A279890 (program): Expansion of x*(1 - x + 2*x^3 - x^4)/((1 - x)*(1 + x)*(1 - x + x^2)*(1 - x - x^2)).
  • A279891 (program): Triangle read by rows, T(n,k) = 2*n, with n>=k>=0.
  • A279895 (program): a(n) = n*(5*n + 11)/2.
  • A279905 (program): Number of 2 X 2 matrices with entries in {0,1,…,n} and odd trace with no elements repeated.
  • A279906 (program): Decimal expansion of the number whose continued fraction expansion consists of the even numbers.
  • A279910 (program): a(n) = Sum_{k=1..n} prime(k+1)*floor(n/prime(k+1)).
  • A279911 (program): a(n) = Sum_{i=1..n} denominator(n^i/i).
  • A279912 (program): a(n) = Sum_{i=1..n} denominator(i^n/n).
  • A279913 (program): Largest n-digit number ending in n.
  • A279914 (program): a(n) = sigma(n) + phi(n) - mu(n).
  • A279927 (program): Expansion of e.g.f. arctan(x)*exp(x).
  • A279929 (program): Expansion of c(q)*c(q^2)/9 - c(q^3)*c(q^6)/3 in powers of q where c() is a cubic AGM theta function.
  • A279932 (program): Expansion of Product_{k>0} 1/(1 + x^k)^(k*5).
  • A279933 (program): Positive integers k such that {(k-1)*r} < 1/2, where r = golden ratio = (1 + sqrt(5))/2 and { } = fractional part.
  • A279934 (program): Positive integers k such that {(k-1)*r} > 1/2, where r = golden ratio = (1 + sqrt(5))/2 and { } = fractional part.
  • A279947 (program): Expansion of f(x^2, x^2) * f(-x, -x^5) in powers of x where f(, ) is Ramanujan’s general theta function.
  • A279952 (program): Number of primes with prime subscripts dividing n.
  • A279959 (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 221”, based on the 5-celled von Neumann neighborhood.
  • A279961 (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 221”, based on the 5-celled von Neumann neighborhood.
  • A279971 (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 two elements, and with new values introduced in order 0 sequentially upwards.
  • A280008 (program): First differences of A002375.
  • A280014 (program): Numbers m == +- 2 (mod 10) but not m == 2 (mod 6).
  • A280021 (program): Expansion of phi_{11, 2}(x) where phi_{r, s}(x) = Sum_{n, m>0} m^r * n^s * x^{m*n}.
  • 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.
  • A280042 (program): a(1) = 1, a(n+1) is the numerator of n-th partial fraction of the continued fraction [1; 10, 100, 1000, …, 10^n].
  • A280048 (program): The Tower of Hanoi word, with a,b,c,a-bar,b-bar,c-bar encoded as 1,2,3,-1,-2,-3 respectively.
  • A280049 (program): Canonical representation of n as a sum of distinct Jacobsthal numbers J(n) (A001045) (see Comments for details); also binary numbers that end in an even number of zeros..
  • A280050 (program): a(n) = Sum_{k=2..n} k/lpf(k), where lpf(k) is the least prime dividing k (A020639).
  • A280053 (program): “Nachos” sequence based on squares.
  • 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.
  • A280057 (program): a(n) = (-1)^n * 4*n/3 if n = 3*k and n!=0, otherwise a(n) = (-1)^n * n except a(0) = 1.
  • 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).
  • A280072 (program): Indices of centered 11-gonal numbers (A060544) that are also 11-gonal numbers (A051682).
  • A280075 (program): Partial products of A211776 (Product_{d|n} tau(d)).
  • A280076 (program): Numbers n such that Sum_{d|n} tau(d) = Product_{d|n} tau(d).
  • A280077 (program): Partial sums of A007429 (Sum_{d|n} sigma(d)).
  • A280078 (program): Partial products of A007429 (Sum_{d|n} sigma(d)).
  • A280084 (program): 1 together with the Pythagorean primes.
  • A280085 (program): Partial sums of A206032 (Product_{d|n} sigma(d)).
  • A280086 (program): Partial products of A206032 (Product_{d|n} sigma(d)).
  • 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.
  • A280100 (program): a(n) = 4^(2*n) * (n!)^3 * (n+1)!.
  • A280107 (program): Numbers n with the property that the symmetric representation of sigma(n) has four parts.
  • 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).
  • A280114 (program): Partial sums of A175317 (Sum_{d|n} pod(d)).
  • A280115 (program): Partial products of A175317 (Sum_{d|n} pod(d)).
  • A280116 (program): Partial sums of A266265 (Product_{d|n} pod(d)).
  • A280117 (program): Partial products of A266265 (Product_{d|n} pod(d)), where pod(n) is the product of the divisors of n (A007955).
  • A280127 (program): Expansion of Product_{k>=2} 1/(1 - mu(k)^2*x^k), where mu(k) is the Moebius function (A008683).
  • A280130 (program): Expansion of Product_{k>=2} (1 + x^(k^3)).
  • A280131 (program): Partial sums of A029940 (Product_{d|n} phi(d)).
  • A280132 (program): Partial products of A029940 (Product_{d|n} phi(d)).
  • A280133 (program): Partial products of A057661 (Sum_{d|n} psi(d)).
  • A280136 (program): Negative continued fraction of e (or negative continued fraction expansion of e).
  • A280151 (program): Expansion of Product_{k>=1} 1/(1 - floor(1/omega(2*k+1))*x^(2*k+1)), where omega() is the number of distinct prime factors (A001221).
  • A280152 (program): Expansion of Product_{k>=1} (1 + floor(1/omega(2*k+1))*x^(2*k+1)), where omega() is the number of distinct prime factors (A001221).
  • A280154 (program): a(n) = 5*Lucas(n).
  • A280166 (program): a(2*n) = 4*n if n>0, a(2*n + 1) = -(2*n + 1), a(0) = 1.
  • A280167 (program): a(2*n) = 3*n if n>0, a(2*n + 1) = -(2*n + 1), a(0) = 1.
  • A280169 (program): Expansion of Product_{k>=2} 1/(1 - mu(2*k-1)^2*x^(2*k-1)), where mu() is the Moebius function (A008683).
  • A280172 (program): Lexicographically earliest table of positive integers read by antidiagonals such that no row or column contains a repeated term.
  • 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).
  • A280184 (program): Number of cyclic subgroups of the group C_n x C_n x C_n x C_n, where C_n is the cyclic group of order n.
  • 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(2*n) = 2, a(2*n + 1) = -1, a(0) = 1.
  • A280194 (program): Expansion of 1/(1 - Sum_{k>=1} mu(k)^2*x^k), where mu(k) is the Moebius function (A008683).
  • A280195 (program): Expansion of 1/(1 - Sum_{k>=2} floor(1/omega(k))*x^k), where omega(k) is the number of distinct prime factors (A001221).
  • A280196 (program): Numbers n such that a^(n-1) == 1 (mod n^2) has no solutions with 1 < a < n^2-1.
  • A280197 (program): Expansion of 1/(1 - Sum_{k>=2} mu(k)^2*x^k), where mu(k) is the Moebius function (A008683).
  • A280198 (program): Expansion of 1/(1 - Sum_{k>=1} mu(2*k-1)^2*x^(2*k-1)), where mu() is the Moebius function (A008683).
  • A280199 (program): Numbers n such that a^(n-1) == 1 (mod n^2) has solutions with 1 < a < n^2-1.
  • A280200 (program): Expansion of 1/(1 - Sum_{k>=2} floor(1/omega(2*k-1))*x^(2*k-1)), where omega() is the number of distinct prime factors (A001221).
  • A280211 (program): a(n) = n*(2^(n^2)).
  • A280218 (program): Number of binary necklaces of length n with no subsequence 0000.
  • A280219 (program): a(1) = 1, a(n+1) is the numerator of n-th partial fraction of the continued fraction [1; 3, 9, 27, …, 3^n].
  • A280220 (program): a(1) = 1, a(n+1) is the numerator of n-th partial fraction of the continued fraction [1; 4, 16, 64, …, 4^n].
  • A280221 (program): a(n) = (-2)^(n-1)*a(n-1) + a(n-2) with a(0) = 0 and a(1) = 1.
  • A280222 (program): a(n) = (-3)^(n-1)*a(n-1) + a(n-2).
  • A280223 (program): Precipice of n: descending by the main diagonal of the pyramid described in A245092, a(n) is the height difference between the n-th level (starting from the top) and the level of the next terrace.
  • A280226 (program): Number of partitions of 2n into two squarefree parts.
  • A280227 (program): Number of n X 2 0..1 arrays with no element unequal to a strict majority of its king-move neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.
  • A280237 (program): Period length 8 sequence [0, 1, 0, 1, -1, 1, 0, 1, …].
  • A280238 (program): Expansion of 1/(1 - Sum_{k>=2} floor(bigomega(k)/2)*floor(2/bigomega(k))*x^k), where bigomega(k) is the number of prime divisors of k counted with multiplicity (A001222).
  • A280240 (program): Expansion of 1/(1 - Sum_{k>=1} x^(k+floor(1/2+sqrt(k)))).
  • A280242 (program): Expansion of (Sum_{k>=2} floor(1/omega(k))*x^k)^2, where omega(k) is the number of distinct prime factors (A001221).
  • A280246 (program): a(n) = Product_{d|n} psi(d), where psi(m) is the sum of totatives of m (A023896).
  • A280247 (program): Partial sums of A280246 (Product_{d|n} psi(d)).
  • A280248 (program): Partial products of A280246 (Product_{d|n} psi(d)).
  • A280250 (program): Sum of the smaller parts of the partitions of 2n into 2 squarefree parts.
  • A280251 (program): Sum of the larger parts of the partitions of 2n into two squarefree parts.
  • A280252 (program): Sum of the parts in the partitions of 2n into two squarefree parts.
  • A280257 (program): Numbers n such that tau(n^(n-1)) is a prime.
  • A280258 (program): a(n) = Sum_{d|n} pxi(d), where pxi(m) is the product of totatives of m (A001783).
  • A280259 (program): Partial sums of A280258.
  • A280260 (program): Partial products of A280258.
  • 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].
  • A280294 (program): a(n) = a(n-1) + 2^n * a(n-2) with a(0) = 1 and a(1) = 1.
  • A280303 (program): Number of binary necklaces of length n with no subsequence 00000.
  • A280304 (program): a(n) = 3*n*(n^2 + 3*n + 4).
  • A280305 (program): a(n) = (n^(2n) - (n-1)^(2n))/(2n-1).
  • A280306 (program): a(n) = A049501(A003418(n)).
  • A280308 (program): Tribonacci numbers: a(n) = a(n-1) + a(n-2) + a(n-3) with a(0)=3, a(1)=4, a(2)=5.
  • A280309 (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 two elements, and with new values introduced in order 0 sequentially upwards.
  • A280321 (program): Number of 2 X 2 matrices with all elements in {0,..,n} having determinant = n*permanent.
  • A280340 (program): a(n) = a(n-1) + 10^n * a(n-2) with a(0) = 1 and a(1) = 1.
  • A280342 (program): Sum of digits of A003418(n).
  • 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].
  • A280351 (program): Expansion of Sum_{k>=1} (x/(1 - x))^(k^3).
  • A280352 (program): Expansion of Sum_{k>=1} (x/(1 - x))^(k*(k+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.
  • A280367 (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 259”, based on the 5-celled von Neumann neighborhood.
  • A280368 (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 259”, based on the 5-celled von Neumann neighborhood.
  • A280369 (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 259”, based on the 5-celled von Neumann neighborhood.
  • A280370 (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 259”, based on the 5-celled von Neumann neighborhood.
  • A280375 (program): Expansion of Sum_{k>=1} k^3*x^(k^2)/(1 - x^k).
  • A280376 (program): Primes formed from the concatenation of n and nextprime(n).
  • A280377 (program): Partial sums of A119619.
  • A280378 (program): Partial products of A119619.
  • A280385 (program): a(n) = Sum_{k=1..n} prime(k)^2*floor(n/prime(k)) .
  • 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.
  • A280400 (program): Number of 2Xn 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.
  • A280405 (program): Odd semiprimes that cannot be represented as 2p+3q, where p and q are primes.
  • 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.
  • A280411 (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 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.
  • A280425 (program): Sixth column of Euler’s difference table in A068106.
  • A280426 (program): Digital roots of tetranacci numbers A000078.
  • A280428 (program): a(n) = 1729*n^3.
  • A280429 (program): Longest word T from a string S using no breakpoint-reuse.
  • A280430 (program): Longest word T from 2 equal length strings S using no breakpoint reuse.
  • A280435 (program): Number of nX3 0..1 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.
  • A280456 (program): Expansion of Product_{k>=0} (1 + x^(6*k+1)).
  • A280458 (program): Partial products of A023896.
  • A280470 (program): Triangle A106534 with reversed rows.
  • A280474 (program): Number of n X 2 0..2 arrays with no element unequal to a strict majority of its horizontal and antidiagonal neighbors, with the exception of exactly two elements, and with new values introduced in order 0 sequentially upwards.
  • A280488 (program): a(n) = n / A280489(n) = n / gcd(n,A241909(n)).
  • A280489 (program): a(n) = gcd(n,A241909(n)).
  • A280490 (program): a(n) = n / A280491(n) = n / gcd(n,A122111(n)).
  • A280491 (program): a(n) = gcd(n,A122111(n)).
  • A280507 (program): a(n) = n XOR A193231(n).
  • 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.
  • A280521 (program): From the “Fibonachos” game: Number of phases of the following routine: during each phase, the player removes objects from a pile of n objects as the Fibonacci sequence until the pile contains fewer objects than the next Fibonacci number. The phases continue until the pile is empty.
  • A280522 (program): The number of restarts for the routine described by A280521.
  • A280523 (program): a(n) = Fibonacci(2n + 1) - n.
  • A280531 (program): a(n) = A049501(A000142(n)).
  • A280533 (program): Decimal expansion of 14*sin(Pi/14).
  • A280542 (program): Expansion of 1/(1 - Sum_{k>=2} x^(k^2)).
  • A280543 (program): Expansion of 1/(1 - x - Sum_{k>=2} floor(1/omega(k))*x^k), where omega(k) is the number of distinct prime factors (A001221).
  • A280544 (program): Expansion of 1/(1 - Sum_{k>=2} (1 - floor(2/d(k)))*x^k), where d(k) is the number of divisors (A000005).
  • 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.
  • A280569 (program): a(n) = (-1)^n * 2 if n = 5*k and n!=0, otherwise a(n) = (-1)^n.
  • A280577 (program): a(n) = eulerphi(n) + floor(n/2).
  • A280580 (program): Triangle read by rows: T(n,k) = binomial(2*n,2*k)*binomial(2*n-2*k,n-k)/(n+1-k) for 0<=k<=n.
  • A280581 (program): a(n) = the product of divisors of sum of divisors of n.
  • A280582 (program): a(n) = the product of divisors of product of divisors of n.
  • A280583 (program): a(n) = product of divisors of the number of divisors of n.
  • A280585 (program): Decimal expansion of 8*sin(Pi/8).
  • A280586 (program): Expansion of Product_{p prime, k>=2} 1/(1 - x^(p^k)).
  • A280598 (program): Number of nX2 0..1 arrays with no element equal to more than two of its horizontal, vertical and antidiagonal neighbors and with new values introduced in order 0 sequentially upwards.
  • A280605 (program): Expansion of 1/(1 - Sum_{p prime, k>=2} x^(p^k)).
  • A280606 (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 294”, based on the 5-celled von Neumann neighborhood.
  • A280607 (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 294”, based on the 5-celled von Neumann neighborhood.
  • A280608 (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 294”, based on the 5-celled von Neumann neighborhood.
  • A280610 (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 294”, based on the 5-celled von Neumann neighborhood.
  • A280618 (program): Expansion of (Sum_{k>=1} x^(k^3))^2.
  • A280619 (program): Integers m such that sigma(m) - eulerphi(m) <= 4*sqrt(m).
  • A280633 (program): Decimal expansion of 18*sin(Pi/18).
  • A280634 (program): Number of partitions of 2n into two refactorable parts.
  • A280637 (program): Sum of the digits of n^2+1.
  • A280651 (program): Numbers k such that k^3 has an odd number of digits in base 2 and the middle digit is 1.
  • A280656 (program): Denominator of Sum_{k=0..n^2-1}((-1)^k*sqrt(Pi)/(Gamma(1/2-k)*Gamma(1+k)))-n).
  • A280658 (program): Numbers ending with their digital root in decimal representation.
  • A280668 (program): Number of n X 3 0..2 arrays with no element equal to more than one of its horizontal and antidiagonal neighbors and with new values introduced in order 0 sequentially upwards.
  • A280682 (program): Integers m such that floor(sqrt(m)) is even.
  • A280684 (program): a(n) = number of divisors of the product of the divisors of n.
  • A280685 (program): a(n) = sum of the divisors of the product of the divisors of n.
  • A280686 (program): Largest Fibonacci proper divisor of n, a(1) = 1.
  • A280687 (program): a(n) = n / A280686(n); n divided by its largest Fibonacci proper divisor, a(1) = 1.
  • A280689 (program): a(n) = A000045(A032742(n)) / A000045(A054576(n)), where A000045(n) gives the n-th Fibonacci number, A032742(n) = the largest proper divisor of n, and A054576(n) = A032742(A032742(n)).
  • A280690 (program): a(n) = A000045(n) / A105800(n); the n-th Fibonacci number divided by its largest Fibonacci proper divisor.
  • A280694 (program): Largest Lucas number (A000032) dividing n.
  • A280695 (program): a(n) = n / A280694(n); n divided by the largest Lucas number (A000032) dividing n.
  • A280696 (program): Largest Lucas proper divisor of n, a(1) = a(2) = 1.
  • A280697 (program): a(n) = n / A280696(n); n divided by its largest Lucas proper divisor, a(1) = 1.
  • A280699 (program): Greatest Lucas number that is a divisor of the n-th Fibonacci number, a(1) = a(2) = 1.
  • A280700 (program): Binary weight of terms of A005187: a(n) = A000120(A005187(n)).
  • A280705 (program): a(n) = A002110(A280700(n)) = A046523(A283475(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.
  • A280714 (program): Partial products of A055067.
  • A280724 (program): Expansion of 1/(1 - x) + (1/(1 - x)^2)*Sum_{k>=0} x^(3^k).
  • A280726 (program): a(n) = A049501(phi(n)).
  • A280729 (program): (p-1)/2 + phi(p-1) as p runs through the odd primes.
  • A280737 (program): a(n) = A007302(n)-1.
  • A280756 (program): Expansion of (1 + 2*x)/(1 - x - 4*x^2 + x^4).
  • A280757 (program): Expansion of x*(2 + x)/(1 - 4*x^2 - x^3 + x^4).
  • A280758 (program): Expansion of (1 + x + x^2)/(1 - x - 3*x^2 - x^3 + x^4).
  • A280761 (program): Solutions y_n to the negative Pell equation y^2 = 72*x^2 - 8.
  • A280762 (program): a(n) = ceiling( log_2( Catalan(n) ) ).
  • A280797 (program): a(n) = (n^n - 1)(n^n + 1)/(n + 1).
  • A280799 (program): a(n) = A049502(phi(n)).
  • A280800 (program): a(n) = A049501(cototient(n)).
  • A280814 (program): The maximum number of squares among the partial sums of any permutation of the integers [1..n].
  • A280817 (program): a(n) = A049501(sigma(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).
  • A280819 (program): Decimal expansion of 12*sin(Pi/12).
  • A280820 (program): Partial sums of A001783.
  • A280821 (program): Partial products of A001783.
  • A280827 (program): a(n) = A076649(n) - A055642(n).
  • A280843 (program): a(n) = A049502(sigma(n)).
  • A280845 (program): a(n) = 16^n * n * (n!)^4.
  • A280863 (program): Expansion of 1/(1 - Sum_{k>=0} x^((2*k+1)^2)).
  • A280873 (program): Numbers whose binary expansion does not begin 10 and do not contain 2 adjacent 0’s; Ahnentafel numbers of X-chromosome inheritance of a male.
  • A280874 (program): Expansion of Product_{k>=1} (1 - x^(6*k)) * (1 + x^k) / (1 - x^k).
  • A280891 (program): Number of certain noncrossing set partitions.
  • A280892 (program): Squareful numbers with both neighbors squarefree.
  • A280896 (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 two elements, and with new values introduced in order 0 sequentially upwards.
  • A280913 (program): Number of dots in International Morse numeral representation of n.
  • A280917 (program): Expansion of 1/(1 - x - Sum_{k>=1} x^prime(k)).
  • A280919 (program): Precipices from the successive terraces, descending by the main diagonal of the pyramid described in A245092. Also first differences of A071562.
  • A280920 (program): Seventh column of Euler’s difference table in A068106.
  • A280931 (program): a(n) = 2*F(n-1) + 9*F(n-4) + 9*F(n-7) where n >= 7 and F = A000045.
  • A280932 (program): a(n) = 2*F(n-1) + 2*F(n-3) + 10*F(n-5) + 9*F(n-8) where n >= 8 and F = A000045.
  • A280939 (program): Expansion of e.g.f.: 2*sinh(x/2) / sqrt(2 - exp(x)).
  • 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.
  • A280946 (program): Numbers n such that n and number of proper divisors (A032741) of n are relatively prime and n is a nonprime (A018252).
  • A280950 (program): Expansion of Product_{k>=0} 1/(1 - x^(3*k*(k+1)/2+1)).
  • A280955 (program): Number of n X 2 0..2 arrays with no element equal to more than one of its horizontal, vertical and antidiagonal neighbors and with new values introduced in order 0 sequentially upwards.
  • A280968 (program): a(n) = A001097(n) + A001097(n+1).
  • A280981 (program): Partial products of A049820; a(1) = a(2) = 1.
  • A280982 (program): Partial products of A024816; a(1) = a(2) = 1.
  • A280987 (program): {Concatenation n, n-1, n-2, …3,2,1} mod sigma(n).
  • A280989 (program): Rounded percent probability that a positive test result for some condition is a true positive when n% of the tested population has that condition and the test is 95% accurate.
  • 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.
  • A280998 (program): Numbers with a prime number of 1’s in their binary reflected Gray code representation.
  • A281000 (program): Triangle read by rows: T(n,k) = binomial(2*n+1, 2*k+1)*binomial(2*n-2*k, n-k)/(n+1-k) for 0 <= k <= n.
  • A281005 (program): Numbers n having at least one odd divisor greater than sqrt(2*n).
  • A281006 (program): a(n) = A000203(n) - A052928(n-1).
  • A281007 (program): Number of middle divisors of the n-th number that has middle divisors.
  • A281009 (program): Number of odd divisors of n minus the number of middle divisors of n.
  • A281015 (program): Numbers with a prime number of dots in their International Morse numeral representation.
  • A281019 (program): Partial products of A051953; a(1) = 1.
  • A281022 (program): Single (or isolated or non-twin) primes that are also safe primes.
  • A281023 (program): Partial sums of A067392.
  • A281024 (program): Partial products of A067392; a(1) = 1.
  • A281025 (program): Partial sums of A066570.
  • A281026 (program): a(n) = floor(3*n*(n+1)/4).
  • A281027 (program): Partial products of A066570.
  • A281048 (program): Expansion of x*(1 - x)*Product_{k>=0} (1 + x^(2^k) - x^(2^(k+1))).
  • A281050 (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 two elements, and with new values introduced in order 0 sequentially upwards.
  • A281064 (program): Values of x such that x^2 = 5*y^2 + 11, where x and y are positive integers.
  • A281066 (program): Concatenation R(n)R(n-1)R(n-2)…R(2)R(1) read mod n, where R(x) is the digit-reversal of x (with leading zeros not omitted).
  • A281071 (program): Largest number k such that b - r is even or r = 0 for all b = 1..k where r = n mod b.
  • A281098 (program): a(n) is the GCD of the sequence d(n) = A261327(k+n) - A261327(k) for all k.
  • A281114 (program): Parity of the n-th squarefree triangular number.
  • 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.
  • A281146 (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 515”, based on the 5-celled von Neumann neighborhood.
  • A281149 (program): Elias gamma code (EGC) for n.
  • A281151 (program): a(n) = floor(4*n*(n+1)/5).
  • A281154 (program): Expansion of (Sum_{k>=2} x^(k^2))^2.
  • A281166 (program): a(n) = 3*a(n-1) - 3*a(n-2) + 2*a(n-3) for n>2, a(0)=a(1)=1, a(2)=3.
  • A281188 (program): Number of refactorable numbers m such that tau(m) = n, or 0 if there are infinitely many such numbers.
  • A281190 (program): Concatenation of the reversed digits of numbers from 1 to n, mod n.
  • 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.
  • A281206 (program): Number of 2 X n 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.
  • A281214 (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 342”, based on the 5-celled von Neumann neighborhood.
  • A281215 (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 342”, based on the 5-celled von Neumann neighborhood.
  • A281216 (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 342”, based on the 5-celled von Neumann neighborhood.
  • A281217 (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 342”, based on the 5-celled von Neumann neighborhood.
  • A281228 (program): Expansion of (Sum_{k>=0} x^(3^k))^2 [even terms only].
  • A281230 (program): Period of the discrete Arnold cat map on an n X n array.
  • 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.
  • A281244 (program): Expansion of Product_{k>=1} (1 + x^(6*k-1)).
  • A281258 (program): Digital root of n*(n+1)*(n+2)/2.
  • A281260 (program): Triangular array of generalized Narayana numbers T(n,k) = 2*binomial(n+1,k)* binomial(n-2,k-1)/(n+1) for n >= 1 and 0 <= k <= n-1, read by rows.
  • A281262 (program): Number of permutations of [2n] with exactly n fixed points.
  • A281264 (program): Base-2 logarithm of denominator of Sum_{k=0..n^2-1}((-1)^k*sqrt(Pi)/(Gamma(1/2-k)*Gamma(1+k)))-n).
  • A281293 (program): Triangular array of generalized Narayana Numbers T(n,k) = 3*binomial(n+1,k)* binomial(n-3,k-1)/(n+1) for n >= 2 and 0 <= k <= n-2, read by rows.
  • A281297 (program): Triangular array of generalized Narayana numbers T(n,k) = 4*binomial(n+1,k)* binomial(n-4,k-1)/(n+1) for n >= 3 and 0 <= k <= n-3, read by rows.
  • A281298 (program): a(n) is the n-th decimal digit from the right in n^n.
  • A281316 (program): Prime number p such that the decimal representation of its binary reflected Gray code is also a prime.
  • 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).
  • A281334 (program): Triangle read by rows: T(n, k) = (n - k)*(k + 1)^3 + k, 0 <= k <= n.
  • A281356 (program): G.f.: 1 + Sum_{n>=1} x^(3*n-2) / Product_{k=1..n} (1-x^k).
  • A281357 (program): G.f.: (Product_{j>=1} 1/(1-q^j)^2 + Product_{j>=1} 1/(1-q^(2*j)))/2.
  • A281362 (program): a(0) = 1, a(1) = 2; for n>1, a(n) = a(n-1) + a(n-2) + floor(n/2).
  • A281363 (program): Smallest m>0 such that (2*n)^2 - 1 divides (2^m)^(2*n) - 1.
  • 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.
  • A281385 (program): Triangular array T(n, k) = n^2 + n*k - k^2.
  • 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.
  • A281388 (program): Write n in binary reflected Gray code and sum the positions where there is a ‘1’ followed immediately to the right by a ‘0’, counting the leftmost digit as position 1.
  • A281392 (program): Number of occurrences of “01” as a subsequence in the binary expansion of n.
  • A281422 (program): Expansion of 1/(1 - Sum_{k>=1} x^prime(prime(k))).
  • A281425 (program): a(n) = [q^n] (1 - q)^n / Product_{j=1..n} (1 - q^j).
  • A281433 (program): Number of maximal matchings in the 2 X n rook graph.
  • A281445 (program): Nonnegative k for which (2*k^2 + 1)/11 is an integer.
  • A281451 (program): Expansion of x * f(x, x) * f(x, x^17) in powers of x where f(, ) is Ramanujan’s general theta function.
  • A281452 (program): Expansion of f(x, x) * f(x^5, x^13) in powers of x where f(, ) is Ramanujan’s general theta function.
  • A281453 (program): Expansion of f(x, x) * f(x^7, x^11) in powers of x where f(, ) is Ramanujan’s general theta function.
  • A281481 (program): a(n) = 2^(n - 1) * (2^n + 1) + 1.
  • A281482 (program): a(n) = 2^(n + 1) * (2^n + 1) - 1.
  • A281485 (program): Triangular array T(n,k) = k Sum_{j=0..k-1} (-1)^j binomial(k-1,j) (n-1-j)^(n-1), 1<=k<=n, read by rows.
  • A281487 (program): a(n+1) = -Sum_{d|n} a(d), a(1) = 1.
  • A281488 (program): a(n) = -Sum_{d divides (n-2), 1 <= d < n} a(d).
  • A281490 (program): Expansion of f(x, x^3) * f(x, x^8) in powers of x where f(, ) is Ramanujan’s general theta function.
  • A281491 (program): Expansion of f(x, x^3) * f(x^2, x^7) in powers of x where f(, ) is Ramanujan’s general theta function.
  • A281492 (program): Expansion of f(x, x^3) * f(x^4, x^5) in powers of x where f(, ) is Ramanujan’s general theta function.
  • A281497 (program): Write n in binary reflected Gray code and sum the positions where there is a ‘1’ followed immediately to the left by a ‘0’, counting the rightmost digit as position 1.
  • A281499 (program): Write n in binary reflected Gray code, interchange the 1’s and 0’s, reverse the code and convert it back to decimal.
  • A281500 (program): Reduced denominators of f(n) = (n+1)/(2^(2+n)-2) with A026741(n+1) as numerators.
  • A281503 (program): Solutions x to the negative Pell equation y^2 = 33*x^2 - 8 with x,y >= 0.
  • A281504 (program): Solutions y to the negative Pell equation y^2 = 33*x^2 - 8 with x,y >= 0.
  • A281546 (program): a(n) = 27*n + 2.
  • A281548 (program): Number of distinct monomials in the expansion of Product_{i=1..n} (y_1+…+y_i+x_i+x_{i+1}).
  • A281552 (program): Write n in the Elias gamma code and sum the positions where there is a ‘1’ followed immediately to the right by a ‘0’, counting the leftmost digit as position 1.
  • 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).
  • A281581 (program): a(n) = (15*2^(2*n+2) + 15*2^(n+2) + 5*2^(n+3)*3^(n+1) - 24*5^(n+1))/120.
  • 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.
  • A281584 (program): Solutions x to the negative Pell equation x^2 - 15*y^2 = -11 with x, y > 0.
  • A281589 (program): Triangular array T(n,k), n > 0 and k = 1..2^(n-1), read by rows, in which row n corresponds to the permutation of [1..2^(n-1)] resulting from folding a horizontal strip of paper, with 2^(n-1) square cells numbered from 1 to 2^(n-1), n-1 times.
  • 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).
  • A281595 (program): a(n) = (n^n - 3*(n-1)^n + 3*(n-2)^n - (n-3)^n)/6.
  • A281596 (program): a(n) = ((n-2)^n - 2*(n-1)^n + n^n)/2.
  • A281620 (program): Triangle read by rows: Poincaré polynomials of orbifold of Fermat hypersurfaces.
  • A281623 (program): Numbers of the form 2^phi(m) + 1, where phi = A000010 = Euler totient function.
  • A281624 (program): Numbers n such that 2^phi(n) + 1 is prime (Fermat prime).
  • A281626 (program): a(n) = (sum of trivial divisors of n) - (sum of nontrivial divisors of n).
  • A281640 (program): Expansion of x * f(x, x) * f(x^5, x^25) in powers of x where f(, ) is Ramanujan’s general theta function.
  • A281647 (program): Solutions x to the negative Pell equation x^2 - 10*y^2 = -6 with x > y > 0.
  • 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.
  • A281662 (program): (Denominator of Bernoulli(2*n)) read mod n.
  • 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).
  • A281681 (program): a(n) = A055396(A071904(n))-1.
  • A281683 (program): Expansion of Product_{k>=1} (1 - x^(2*k-1))^(2*k-1)/(1 - x^(2*k))^(2*k).
  • A281698 (program): a(n) = 5*2^(n-1) + 2^(2*n-1) + 6^n + 1.
  • A281699 (program): Sierpinski stellated octahedron numbers: a(n) = 2*(-3*2^(n+1) + 2^(2n+3) + 5).
  • A281702 (program): Numbers k such that A001221(k) = A001221(A000326(k)).
  • A281703 (program): Numbers k such that A000005(k) = A000005(A000326(k)).
  • A281710 (program): Number of n X 3 0..1 arrays with no element unequal to a strict majority of its horizontal, diagonal and antidiagonal neighbors and with new values introduced in order 0 sequentially upwards.
  • A281716 (program): Number of 2 X n 0..1 arrays with no element unequal to a strict majority of its horizontal, diagonal and antidiagonal neighbors and with new values introduced in order 0 sequentially upwards.
  • A281722 (program): Expansion of r(q) * s(q) in powers of q where r(), s() are cubic AGM functions.
  • A281725 (program): Triangular array T(n,k) is the sum 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.
  • 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.
  • A281733 (program): Positive integers T_i such that Sum_{k >= 0} (S_k * x^(2*k+1)) + 1/24 - Sum_{k >= 1} (T_k * x^(2*k)) = (cos((2/3) * arccos(6 * sqrt(3) * x)))/12 for all real x with |x| <= 1/(6 * sqrt(3)), where S_k = A176898(k).
  • 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.
  • A281774 (program): Number of distinct topologies on an n-set with exactly 6 open sets.
  • A281781 (program): Expansion of Product_{k>=1} (1 - x^(2*k))^(2*k)/(1 - x^(2*k-1))^(2*k-1).
  • A281785 (program): a(n) is multiplicative with a(2^e) = 1, a(3^e) = -8 if e>0, a(p^e) = (p^(e+1) - 1) / (p - 1) if p>3.
  • A281786 (program): Expansion of a(q) * b(q^2) + a(q^2) * b(q) in powers of q where a(), b() are cubic AGM functions.
  • A281787 (program): a(n) = sum of all numbers between 1 and 10^n that are divisible by 3 or 5.
  • A281793 (program): The largest prime factor of (1+n)*(1+n^2).
  • A281794 (program): The largest prime factor of (1+n^2)*(1+n^3).
  • A281795 (program): Number of unit squares (partially) covered by a disk of radius n centered at the origin.
  • 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.
  • A281815 (program): Expansion of f(x, x^10) in powers of x where f(, ) is Ramanujan’s general theta function.
  • A281819 (program): Even numbers k such that half the sum of the even divisors equals the sum of the odd divisors and both are (the same) square.
  • A281824 (program): Numbers that are the sum of 6 consecutive semiprimes.
  • A281831 (program): Number of nX2 0..1 arrays with no element equal to more than four of its king-move neighbors and with new values introduced in order 0 sequentially upwards.
  • A281840 (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 401”, based on the 5-celled von Neumann neighborhood.
  • A281841 (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 401”, based on the 5-celled von Neumann neighborhood.
  • A281842 (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 401”, based on the 5-celled von Neumann neighborhood.
  • A281843 (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 401”, based on the 5-celled von Neumann neighborhood.
  • A281856 (program): One fourth of the order of the abelian non-cyclic groups (Z/A033949(n)*Z)^x.
  • A281857 (program): Numbers occurring in a curious cubic identity.
  • A281858 (program): Curious cubic identities based on the Armstrong number 370.
  • A281859 (program): Curious identities based on the Armstrong number 407 = A005188(13).
  • A281860 (program): Curious identities based on the Armstrong number 371 = A005188(12).
  • A281861 (program): Riordan transform of the Fibonacci sequence with the Riordan matrix A053121.
  • A281862 (program): Riordan transform of the triangular number sequence A000217 with the Chebyshev S matrix A049310.
  • A281863 (program): Alternating powers of 60 and 10 times powers of 60.
  • A281881 (program): Triangle read by rows: T(n,k) (n>=1, 2<=k<=n+1) is the number of k-sequences of balls colored with at most n colors such that exactly one ball is of a color seen previously in the sequence.
  • A281899 (program): a(n) = n + 6*floor(n/3).
  • A281908 (program): a(n) = (Sum_{k=1..n} C(n,k) mod k) mod n.
  • 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.
  • A281946 (program): Number of sequences of balls colored with at most n colors such that exactly two balls are of a color seen earlier in the sequence.
  • A281949 (program): Number of nX2 0..1 arrays with no element unequal to more than four of its king-move neighbors and with new values introduced in order 0 sequentially upwards.
  • A281957 (program): a(n) = largest k such that n has at least k partitions each containing at least k parts.
  • A281959 (program): a(n) = sigma_25(n), the sum of the 25th powers of the divisors of n.
  • A281964 (program): Real part of n!*Sum_{k=1..n} i^(k-1)/k, where i is sqrt(-1).
  • A281981 (program): a(n) = 4*Sum_{i=1..n-1} Sum_{j=1..m} floor((j*i)/n)) - (m-1)*m*(n-1) where m is floor(sqrt(n)).
  • A281997 (program): a(n) = (n-1)^n * n^n.
  • A281999 (program): Half of the height of the right trapezoidal gnomon (of the derivative of Y=X^5).
  • A282002 (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 413”, based on the 5-celled von Neumann neighborhood.
  • A282003 (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 413”, based on the 5-celled von Neumann neighborhood.
  • 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.
  • A282010 (program): Number of ways to partition Turan graph T(2n,n) into connected components.
  • A282011 (program): Number T(n,k) of k-element subsets of [n] having an even sum; triangle T(n,k), n>=0, 0<=k<=n, read by rows.
  • 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).
  • A282035 (program): Sum of quadratic residues of (n-th prime == 3 mod 4).
  • A282036 (program): a(n) is the sum of quadratic nonresidues of A002145(n) (the n-th prime == 3 mod 4).
  • A282039 (program): Let p = n-th prime == 7 mod 8; a(n) = sum of quadratic residues mod p that are < p/2.
  • A282041 (program): Let p = n-th prime == 7 mod 8; a(n) = sum of quadratic residues mod p.
  • A282043 (program): Let p = n-th prime == 7 mod 8; a(n) = sum of quadratic nonresidues mod p.
  • A282044 (program): Reduced Kronecker coefficients for the case a=2, b=3, i=4.
  • 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 n*4^k - 1 and n*4^k + 1 do not form a twin prime pair.
  • A282060 (program): Coefficients in q-expansion of E_4*(E_2*E_4 - E_6)/720, where E_2, E_4, E_6 are the Eisenstein series shown in A006352, A004009, A013973, respectively.
  • A282062 (program): Expansion of (x + Sum_{p prime, k>=1} x^(p^k))^2.
  • A282077 (program): Number of 9-element subsets of [n+9] having an even sum.
  • A282078 (program): Number of 10-element subsets of [n+10] having an even sum.
  • A282079 (program): Number of n-element subsets of [n+2] having an even sum.
  • A282080 (program): Number of n-element subsets of [n+4] having an even sum.
  • A282081 (program): Number of n-element subsets of [n+5] having an even sum.
  • A282082 (program): Number of n-element subsets of [n+6] having an even sum.
  • A282083 (program): Number of n-element subsets of [n+7] having an even sum.
  • A282084 (program): Number of n-element subsets of [n+8] having an even sum.
  • A282085 (program): Number of n-element subsets of [n+9] having an even sum.
  • A282086 (program): Number of n-element subsets of [n+10] having an even sum.
  • A282087 (program): Number of length-n ternary strings that do not contain both “00” and “11”.
  • 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 (3*E_2*E_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_2^2*E_4 - 2*E_2*E_6 + E_4^2)/1728, where E_2, E_4, E_6 are the Eisenstein series shown in A006352, A004009, A013973, respectively.
  • A282121 (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 430”, based on the 5-celled von Neumann neighborhood.
  • 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.
  • A282131 (program): Records in A240542.
  • A282132 (program): Imaginary part of n!*Sum_{k=1..n} i^(k-1)/k, where i is sqrt(-1).
  • A282137 (program): Expansion of (24x^2-10x-1)/(16x^3-16x^2+x-1).
  • 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 - 2*x + 3*x^2)/((1 - x)*(1 - 2*x)*(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.
  • A282165 (program): Partial products of A061017.
  • 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.
  • A282169 (program): a(n) is the minimal product of a positive integer sequence of length n with no duplicate substrings of length greater than 1, and every number different from its neighbors.
  • A282179 (program): E.g.f.: exp(exp(x) - 1)*(exp(3*x) - 2*exp(x) + 1).
  • A282194 (program): a(n) = smallest positive k such that 2*n + 2^k + 1 is composite.
  • A282211 (program): Coefficients in q-expansion of (6*E_2^2*E_4 - 8*E_2*E_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_2^3*E_4 - 3*E_2^2*E_6 + 3*E_2*E_4^2 - E_4*E_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.
  • A282234 (program): a(n) = Fibonacci(n) represented in bijective base-3 numeration.
  • A282235 (program): a(n) = Fibonacci(n) represented in bijective base-4 numeration.
  • A282236 (program): a(n) = Fibonacci(n) represented in bijective base-5 numeration.
  • A282237 (program): a(n) = Fibonacci(n) represented in bijective base-6 numeration.
  • A282238 (program): a(n) = Fibonacci(n) represented in bijective base-7 numeration.
  • A282239 (program): a(n) = Fibonacci(n) represented in bijective base-8 numeration.
  • A282252 (program): Exponential Riordan array [Bessel_I(0,2*x)^2, x].
  • A282254 (program): Coefficients in q-expansion of (3*E_4^3 + 2*E_6^2 - 5*E_2*E_4*E_6)/1584, where E_2, E_4, E_6 are the Eisenstein series shown in A006352, A004009, A013973, respectively.
  • A282282 (program): Remainder when sum of squares of the first n primes is divided by n-th square pyramidal number.
  • A282284 (program): Least common multiple of 3*n+1 and 3*n-1.
  • A282285 (program): Least common multiple of 5*n+1 and 5*n-1.
  • A282286 (program): Least common multiple of 7*n+1 and 7*n-1.
  • A282310 (program): Number of n X 2 0..1 arrays with no 1 equal to more than four of its king-move neighbors.
  • A282321 (program): Lesser of twin primes congruent to 11 (mod 30).
  • A282322 (program): Greater of twin primes congruent to 13 (mod 30).
  • A282323 (program): Lesser of twin primes congruent to 17 (mod 30).
  • A282324 (program): Greater of twin primes congruent to 19 (mod 30).
  • A282326 (program): Greater of twin primes congruent to 1 (mod 30).
  • A282327 (program): Expansion of exp( Sum_{n>=1} sigma_3(2*n)*x^n/n ) in powers of x.
  • A282329 (program): Start with 2, then successively subtract the primes 3, 5, 7, …
  • A282371 (program): Number of n X 2 0..1 arrays with no 1 equal to more than four of its king-move neighbors, with the exception of exactly two elements.
  • A282380 (program): Number of ways to write n as a sum of two unordered nonsquarefree numbers.
  • A282385 (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 462”, based on the 5-celled von Neumann neighborhood.
  • A282386 (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 462”, based on the 5-celled von Neumann neighborhood.
  • A282387 (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 462”, based on the 5-celled von Neumann neighborhood.
  • A282388 (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 462”, based on the 5-celled von Neumann neighborhood.
  • 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.
  • A282412 (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 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.
  • A282415 (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 469”, based on the 5-celled von Neumann neighborhood.
  • A282416 (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 469”, 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.
  • A282418 (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 469”, based on the 5-celled von Neumann neighborhood.
  • A282429 (program): List of distinct terms of A282026.
  • A282432 (program): Number of primes of the form n - 3^k.
  • A282442 (program): a(n) is the smallest step size that does not occur on a staircase of n steps when following the following procedure: Take steps of length 1 up a staircase until you can’t step any further, then take steps of length 2 down until you can’t step any further, and so on.
  • A282443 (program): a(n) is the largest step size that is taken on a staircase of n steps when following the following procedure: Take steps of length 1 up a staircase until you can’t step any further, then take steps of length 2 down until you can’t step any further, and so on.
  • A282451 (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 475”, based on the 5-celled von Neumann neighborhood.
  • A282452 (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 475”, 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.
  • A282459 (program): Number of composite numbers of the form 2*n - 2^k + 1 (k > 0, 2^k < 2*n + 1).
  • 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.
  • A282467 (program): Number of partitions of n which are not the partitions into (one or more) consecutive parts.
  • A282473 (program): Multiples of 9 which cannot be expressed as the difference between a natural number k and its digit sum s(k).
  • A282498 (program): a(n) = nearest integer to Pi*prime(n).
  • A282500 (program): Expansion of 1/(1 - Sum_{k = i^j, i>=1, j>=2} x^k).
  • A282502 (program): Expansion of 1/(1 - Sum_{k>=0} x^(3*k*(k+1)/2+1)).
  • A282504 (program): Expansion of 1/(1 - Sum_{k>=0} x^(2*k*(k+1)+1)).
  • A282507 (program): Triangular array read by rows. T(n,k) is the number of chain topologies on an n-set with exactly k open sets where one of the open sets is a single point set, n>=2, 3<=k<=n+1.
  • A282513 (program): a(n) = floor((3*n + 2)^2/24 + 1/3).
  • A282518 (program): Number of n-element subsets of [n+1] having a prime element sum.
  • A282522 (program): Number of nX2 0..1 arrays with no 1 equal to more than two of its king-move neighbors.
  • 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.
  • A282544 (program): Expansion of (phi(x)^4 + 3*phi(x^3)^4) / 4 in powers of x where phi() is a Ramanujan theta function.
  • A282548 (program): Expansion of phi_{12, 1}(x) where phi_{r, s}(x) = Sum_{n, m>0} m^r * n^s * x^{m*n}.
  • A282552 (program): Difference between the multiplicative orders of 2 modulo p^2 and 2 modulo p, where p = prime(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.
  • A282566 (program): Number of compositions (ordered partitions) of n into deficient numbers (A005100).
  • A282569 (program): Number of compositions (ordered partitions) of n into multiplicatively perfect numbers (A007422).
  • A282570 (program): Number of ways to write n as an ordered sum of two multiplicatively perfect numbers (A007422).
  • A282574 (program): The final position on a staircase of n steps during the following routine: Take steps of length 1 up a staircase until you can’t step any further, then take steps of length 2 down until you can’t step any further, and so on.
  • 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.
  • A282582 (program): Number of compositions (ordered partitions) of n into tetrahedral (or triangular pyramidal) numbers (A000292).
  • A282583 (program): Number of compositions (ordered partitions) of n into quarter-squares (A002620).
  • A282584 (program): Number of compositions (ordered partitions) of n into decimal palindromes (A002113).
  • 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.
  • A282601 (program): a(n) = Sum_(k=1..phi(n)/2) 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.
  • A282614 (program): Number of inequivalent 3 X 3 matrices with entries in {1,2,3,..,n} up to vertical and horizontal reflections.
  • 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 - 3*x*y - 1.
  • A282627 (program): Exponential expansion of the square of the real root y = y(x) of y^3 - 3*x*y - 1.
  • A282628 (program): Triangle T(n, k) read by rows: row n gives for n >= 0 the coefficients of the exponential numerator polynomial used for the exponential generating function of {Sum_{j=1..m} (1 + 2*j)^n}_{m>=0}.
  • A282630 (program): Number of steps to reach 1 when starting from n and iterating the map x -> x - A055396(x).
  • A282641 (program): Number of nX2 0..1 arrays with no 1 equal to more than one of its king-move neighbors.
  • A282668 (program): Numbers m whose greatest divisor <= sqrt(m) is prime.
  • 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_1*x + c_2*x^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_1*x + c_2*x^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.
  • A282708 (program): a(n) = binomial(2*n,n) - ceiling(2^(2*n)/(n+1)).
  • A282711 (program): a(n) = number of terms of A003052 that are <= n.
  • A282717 (program): Number of nonzero entries in row n of A282716.
  • A282718 (program): Satisfies the tribonacci recurrence: a(n) = a(n-1) + a(n-2) + a(n-3).
  • A282720 (program): Number of nonzero terms in first n rows of the base-2 generalized Pascal triangle P_2 (see A282714).
  • A282723 (program): Let p = n-th prime == 3 mod 8; a(n) = sum of quadratic residues mod p.
  • A282726 (program): Let p = n-th prime == 3 mod 8; a(n) = sum of quadratic nonresidues mod p .
  • A282727 (program): Let p = n-th prime == 3 mod 8; a(n) = (sum of quadratic residues mod p that are < p/2) + (sum of all quadratic residues mod p).
  • A282730 (program): Sequence of integers defined by 3-expansion of Pi-3.
  • A282731 (program): Partial sums of A282717.
  • A282732 (program): Satisfies the recurrence a(n) = 3*a(n-1)-a(n-2)+a(n-3)-2*a(n-4)+2*a(n-5).
  • A282737 (program): Expansion of (x^6 - x^4 + x^3 - x - 1)/((x - 1)^3*(x + 1)^2).
  • A282738 (program): First differences of A282737.
  • A282743 (program): Irregular triangle read by rows, giving coefficients arising when solving g(n) = f(n)+ f(n-1) + f(n-2) for f(n).
  • 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.
  • A282781 (program): Expansion of phi_{8, 3}(x) where phi_{r, s}(x) = Sum_{n, m>0} m^r * n^s * x^{m*n}.
  • A282782 (program): Numbers that are equal to a product of powers of digits where the exponents from left to right decrease with 1 and the exponent for the units digit is 1.
  • A282795 (program): Start with n. If n is 1 or a prime, stop. Otherwise, add the prime factors of n (with repetition) to n, and repeat until reaching a prime, when we stop. If no prime is ever reached, a(n) = -1.
  • A282796 (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 505”, based on the 5-celled von Neumann neighborhood.
  • A282797 (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 505”, based on the 5-celled von Neumann neighborhood.
  • 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.
  • A282800 (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 507”, based on the 5-celled von Neumann neighborhood.
  • A282801 (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 507”, 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.
  • A282803 (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 507”, based on the 5-celled von Neumann neighborhood.
  • A282804 (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 513”, based on the 5-celled von Neumann neighborhood.
  • A282805 (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 513”, based on the 5-celled von Neumann neighborhood.
  • A282806 (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 513”, based on the 5-celled von Neumann neighborhood.
  • A282807 (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 513”, based on the 5-celled von Neumann neighborhood.
  • A282808 (program): a(1)=3; for n>=2, a(n) is the smallest m>a(n-1) such that odd part of a(1) + … + a(n-1) + m is prime.
  • 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.
  • A282818 (program): Number of inequivalent ways to color the edges of a tetrahedron using at most n colors so that no two adjacent edges have the same color.
  • 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.
  • A282844 (program): n-th even semiprime plus n-th odd semiprime.
  • A282847 (program): Given n people seated at a table, a(n) is the minimum number of swaps that must occur in order for everybody to have sat next to every other person.
  • A282848 (program): a(n) = 2*n + 1 + n mod 4.
  • A282850 (program): 38-gonal numbers: a(n) = n*(18*n-17).
  • A282851 (program): 35-gonal numbers: a(n) = n*(33*n-31)/2.
  • A282852 (program): 37-gonal numbers: a(n) = n*(35*n-33)/2.
  • A282853 (program): 36-gonal numbers: a(n) = n*(17*n-16).
  • A282854 (program): 34-gonal numbers: a(n) = n*(32*n-30)/2.
  • A282856 (program): Number of nX2 0..1 arrays with no 1 equal to more than one of its horizontal, vertical and antidiagonal neighbors.
  • A282876 (program): Expansion of ((1 + 4*x + 8*x^2)^(3/2) - (1 + 6*x + 18*x^2 + 20*x^3)) / (2*x^4) in powers of x.
  • A282892 (program): The difference between the number of partitions of n into odd parts (A000009) and the number of partitions of n into even parts (A035363).
  • A282893 (program): The difference between the number of partitions of 2n into odd parts (A000009) and the number of partitions of 2n into even parts (A035363).
  • A282898 (program): Numerator of the coefficients of the series expansion of the Riemann-Siegel theta function at infinity.
  • A282904 (program): Concatenation of the numbers of elements of P{1}, P{1, 2}, P{1, 2, 3}, …, P{1, 2, 3, …, n}; where P{A} denote the power set of set A ordered by the size of the subsets, and in each subset, following the increasing order.
  • A282911 (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 526”, based on the 5-celled von Neumann neighborhood.
  • A282912 (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 526”, based on the 5-celled von Neumann neighborhood.
  • A282913 (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 526”, based on the 5-celled von Neumann neighborhood.
  • A282914 (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 526”, based on the 5-celled von Neumann neighborhood.
  • A282937 (program): a(n) = A000728(5*n).
  • A282939 (program): Maximum number of straight lines required to draw the boundary of any polyomino with n squares.
  • A282942 (program): Expansion of Product_{k>=1} (1 - q^k)^8/(1 - q^(7*k)) in powers of q.
  • A282990 (program): Number of nX2 0..1 arrays with no 1 equal to more than one of its horizontal and vertical neighbors.
  • 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.
  • A283032 (program): Number of inequivalent 5 X 5 matrices with entries in {1,2,3,…,n} up to vertical and horizontal reflections.
  • A283049 (program): Numbers of configurations of A’Campo forests with co-dimension 1 and degree n>0.
  • A283050 (program): Integers that are divisible by the square of their least prime factor.
  • A283054 (program): Triangle read by rows: T(n,k) = T(n,k-1) + T(n-1,k), T(n,0)=1, T(n,n) = T(n,n-1) + 1.
  • A283070 (program): Sierpinski tetrahedron or tetrix numbers: a(n) = 2*4^n + 2.
  • A283077 (program): Expansion of Product_{n>=1} (1 - x^(7*n))/(1 - x^n)^8 in powers of x.
  • A283078 (program): a(n) = sigma(7*n).
  • A283104 (program): Second differences of Stern’s diatomic sequence (A002487).
  • A283107 (program): Numbers n such that tau(4*(n - 1)) is prime.
  • A283118 (program): a(n) = sigma(5*n).
  • A283119 (program): Expansion of exp( Sum_{n>=1} sigma(6*n)*x^n/n ) in powers of x.
  • A283120 (program): Expansion of exp( Sum_{n>=1} sigma(8*n)*x^n/n ) in powers of x.
  • A283121 (program): Expansion of exp( Sum_{n>=1} sigma(9*n)*x^n/n ) in powers of x.
  • A283122 (program): a(n) = sigma(8*n).
  • A283123 (program): a(n) = sigma(9*n).
  • A283124 (program): Number of nX2 0..1 arrays with no 1 equal to more than two of its horizontal and vertical neighbors.
  • A283149 (program): Largest k such that (p-1)! == -1 (mod p^k), where p = prime(n).
  • A283163 (program): Expansion of exp( Sum_{n>=1} -sigma(4*n)*x^n/n ) in powers of x.
  • A283164 (program): Expansion of exp( Sum_{n>=1} -sigma(6*n)*x^n/n ) in powers of x.
  • A283165 (program): a(0) = 0; a(1) = 1; a(2*n) = 2*a(n), a(2*n+1) = 2*a(n) + (-1)^a(n+1).
  • A283168 (program): Expansion of exp( Sum_{n>=1} -sigma(8*n)*x^n/n ) in powers of x.
  • A283169 (program): Expansion of exp( Sum_{n>=1} -sigma(9*n)*x^n/n ) in powers of x.
  • A283183 (program): Number of partitions of n into a prime and a square of an arbitrary integer.
  • A283188 (program): A periodic sequence of 8-bit binary numbers for single-bit multi-frequency generation.
  • A283190 (program): a(n) is the number of different values n mod k for 1 <= k <= floor(n/2).
  • A283208 (program): Minimal exponent integer sequence associated with Vietoris sequence.
  • A283214 (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 597”, based on the 5-celled von Neumann neighborhood.
  • A283215 (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 597”, based on the 5-celled von Neumann neighborhood.
  • A283216 (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 597”, based on the 5-celled von Neumann neighborhood.
  • A283217 (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 597”, based on the 5-celled von Neumann neighborhood.
  • A283224 (program): Expansion of exp( Sum_{n>=1} sigma_2(2*n)*x^n/n ) in powers of x.
  • A283233 (program): 2*A000201.
  • A283234 (program): 2*A001950.
  • A283237 (program): a(n) = sigma_2(3*n).
  • A283238 (program): Expansion of exp( Sum_{n>=1} sigma_2(3*n)*x^n/n ) in powers of x.
  • A283242 (program): Expansion of exp( Sum_{n>=1} -sigma_2(2*n)*x^n/n ) in powers of x.
  • A283243 (program): Expansion of exp( Sum_{n>=1} -sigma_2(3*n)*x^n/n ) in powers of x.
  • A283244 (program): Expansion of exp( Sum_{n>=1} sigma_3(3*n)*x^n/n ) in powers of x.
  • A283262 (program): Numbers n such that tau(n^2) is a prime.
  • A283263 (program): Expansion of exp( Sum_{n>=1} -sigma_3(n)*x^n/n ) in powers of x.
  • A283264 (program): Expansion of exp( Sum_{n>=1} -sigma_4(n)*x^n/n ) in powers of x.
  • A283265 (program): a(n) = 1 if n is neither 2 nor a lesser or greater twin prime (in A001097), 0 otherwise.
  • A283271 (program): Expansion of exp( Sum_{n>=1} -sigma_5(n)*x^n/n ) in powers of x.
  • A283298 (program): Diagonal of the Euler-Seidel matrix for the Catalan numbers.
  • A283301 (program): Numerators of coefficients at even powers in Taylor series expansion of log(x/sin(x)).
  • 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.
  • A283317 (program): Image of 0 under repeated applications of the morphism 0 -> 0,0,0,0,1, 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.
  • A283321 (program): Triangle read by rows: T(n,k) (0 <= k <= n) = number of elements of alternating semigroup A_n of height k.
  • A283322 (program): Row sums of triangle in A283321.
  • A283323 (program): a(n) = 4*a(n-2)+1 with initial terms 1,3,7.
  • A283324 (program): Number of ON cells at generation n in the reversible cellular automaton RCA(2) when started with a single ON cell at generation 0.
  • A283325 (program): Lengths of runs of successive zeros in A283683.
  • A283329 (program): a(n) = (1 + Sum_{j=1..K-1} a(n-j) + a(n-1)*a(n-K+1))/a(n-K) with a(1),…,a(K)=1, where K=4.
  • A283330 (program): a(n) = (1 + Sum_{j=1..K-1} a(n-j) + a(n-1)*a(n-K+1))/a(n-K) with a(1),…,a(K)=1, where K=5.
  • A283334 (program): G.f.: 1/(1 - x*d/dx log(eta(x))), where eta(x) is Dedekind’s eta(q) function without the q^(1/24) factor.
  • A283335 (program): Expansion of exp( Sum_{n>=1} -A062796(n)/n*x^n ) in powers of x.
  • A283336 (program): Expansion of exp( Sum_{n>=1} -sigma_6(n)*x^n/n ) in powers of x.
  • A283337 (program): Expansion of exp( Sum_{n>=1} -sigma_7(n)*x^n/n ) in powers of x.
  • A283338 (program): Expansion of exp( Sum_{n>=1} -sigma_8(n)*x^n/n ) in powers of x.
  • A283339 (program): Expansion of exp( Sum_{n>=1} -sigma_9(n)*x^n/n ) in powers of x.
  • A283340 (program): Expansion of exp( Sum_{n>=1} -sigma_10(n)*x^n/n ) in powers of x.
  • A283348 (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 617”, based on the 5-celled von Neumann neighborhood.
  • A283350 (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 617”, based on the 5-celled von Neumann neighborhood.
  • 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.
  • A283355 (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 621”, based on the 5-celled von Neumann neighborhood.
  • A283356 (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 621”, based on the 5-celled von Neumann neighborhood.
  • A283357 (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 621”, based on the 5-celled von Neumann neighborhood.
  • A283358 (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 621”, based on the 5-celled von Neumann neighborhood.
  • A283362 (program): a(n) = (floor(2*n/3))! mod (2n-1).
  • A283363 (program): Absolute values of first differences of A090396.
  • A283369 (program): a(n) = Sum_{d|n} d^(4*d + 1).
  • A283393 (program): a(n) = gcd(n^2-1, n^2+9).
  • A283394 (program): a(n) = 3*n*(3*n + 7)/2 + 4.
  • A283409 (program): Number of n X 2 0..1 arrays with no 1 equal to more than three of its horizontal, vertical and antidiagonal neighbors.
  • A283419 (program): a(n) is the multiplicative inverse of 3 modulo the n-th prime (n > 3).
  • A283424 (program): Number T(n,k) of blocks of size >= k in all set partitions of [n], assuming that every set partition contains one block of size zero; triangle T(n,k), n>=0, 0<=k<=n, read by rows.
  • A283428 (program): Starting with a(1)=3, a(2)=4, a(n)=sum of digits of a(n-1) + sum of digits of a(n-2).
  • 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).
  • A283456 (program): Row n=4 of A144048.
  • A283457 (program): Row n=5 of A144048.
  • A283475 (program): a(n) = A019565(A005187(n)).
  • A283477 (program): If 2n = 2^e1 + 2^e2 + … + 2^ek [e1 .. ek distinct], then a(n) = A002110(e1) * A002110(e2) * … * A002110(ek).
  • A283483 (program): Sums of distinct nonzero terms of A003462: a(n) = Sum_{k>=0} A030308(n,k)*A003462(1+k).
  • A283486 (program): Number of k such that sigma(k) = 2n where sigma(m) = A000203(m) is the sum of the divisors of m.
  • A283498 (program): a(n) = Sum_{d|n} d^(d+1).
  • A283499 (program): Expansion of exp( Sum_{n>=1} -A283498(n)/n*x^n ) in powers of x.
  • A283504 (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 641”, based on the 5-celled von Neumann neighborhood.
  • A283505 (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 641”, based on the 5-celled von Neumann neighborhood.
  • 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.
  • A283510 (program): Expansion of exp( Sum_{n>=1} A283369(n)/n*x^n ) in powers of x.
  • A283514 (program): Concatenation of the numbers from n down to 3.
  • 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)).
  • A283533 (program): a(n) = Sum_{d|n} d^(2*d + 1).
  • A283534 (program): Expansion of exp( Sum_{n>=1} -A283533(n)/n*x^n ) in powers of x.
  • A283535 (program): a(n) = Sum_{d|n} d^(3*d + 1).
  • A283536 (program): Expansion of exp( Sum_{n>=1} -A283535(n)/n*x^n ) in powers of x.
  • A283551 (program): a(n) = -1 + 5*n/6 + n^3/6.
  • A283555 (program): Even numbers that cannot be expressed as p+3, p+5, or p+7, with p prime.
  • A283556 (program): Digital root of the sum of the first n primes.
  • A283557 (program): The number of positive integer sequences of length n with no duplicate substrings and a minimal product (i.e., the product of the sequence is A282164(n)).
  • A283579 (program): Expansion of exp( Sum_{n>=1} A283533(n)/n*x^n ) in powers of x.
  • A283580 (program): Expansion of exp( Sum_{n>=1} A283535(n)/n*x^n ) in powers of x.
  • A283589 (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 657”, based on the 5-celled von Neumann neighborhood.
  • A283590 (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 657”, based on the 5-celled von Neumann neighborhood.
  • 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.
  • A283608 (program): Numbers whose largest decimal digit is 5.
  • A283609 (program): Numbers whose largest decimal digit is 6.
  • A283610 (program): Numbers n whose largest decimal digit is 7.
  • A283611 (program): Numbers whose largest decimal digit is 8.
  • 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.
  • A283648 (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 705”, based on the 5-celled von Neumann neighborhood.
  • A283649 (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 705”, 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.
  • A283651 (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 705”, based on the 5-celled von Neumann neighborhood.
  • A283667 (program): Number of Motzkin prefixes of length 2n and height n.
  • A283670 (program): The single square referenced in A190641 (Numbers having exactly one non-unitary prime factor).
  • A283671 (program): Square root of the single square referenced in A190641 (Numbers having exactly one non-unitary prime factor).
  • A283678 (program): Number of possible draws of 2n pairs of consecutive cards from a set of 4n + 1 cards, so that the card that initially occupies the central position is not selected.
  • 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.
  • A283692 (program): Number of 2 X n 0..1 arrays with no 1 equal to more than two of its horizontal, diagonal and antidiagonal neighbors.
  • 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.
  • A283708 (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 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.
  • A283710 (program): The smallest square referenced in A124809.
  • A283711 (program): Square root of the smallest square referenced in A124809 (Numbers of the form (square + 1) that are not squarefree).
  • A283716 (program): Row n=3 of A283674.
  • A283718 (program): Numbers m such that sum of digits of 27*m is 27.
  • A283733 (program): a(n) = a(n-1) + 1 + floor(n*golden ratio), with a(0) = 1.
  • A283737 (program): Numbers with digit sum 13 that are multiples of 13.
  • A283742 (program): Numbers with digit sum 11 that are multiples of 11.
  • A283750 (program): a(n) = n^2 XOR (n + 1)^2.
  • A283754 (program): The smallest number k such that k*2^n mod 3^n = 1.
  • A283760 (program): Expansion of (Sum_{i>=1} x^prime(i))*(Sum_{j>=1} x^(j^3)).
  • A283765 (program): Numbers k such that L(k) is even, where L = A000201 = lower Wythoff sequence.
  • A283766 (program): Numbers k such that L(k) is odd, where L = A000201 = lower Wythoff sequence.
  • A283767 (program): Numbers k such that U(k) is even, where U = A001950 = upper Wythoff sequence.
  • A283768 (program): Numbers k such that U(k) is odd, where U = A001950 = upper Wythoff sequence.
  • A283769 (program): Numbers k such that L(k) = 0 mod 3, where L = A000201 = lower Wythoff sequence.
  • A283770 (program): Numbers k such that L(k) = 1 mod 3, where L = A000201 = lower Wythoff sequence.
  • A283771 (program): Numbers k such that L(k) = 2 mod 3, where L = A000201 = lower Wythoff sequence.
  • A283772 (program): Numbers k such that U(k) = 0 mod 3, where U = A001950 = upper Wythoff sequence.
  • A283773 (program): Numbers k such that U(k) = 1 mod 3, where U = A001950 = upper Wythoff sequence.
  • A283774 (program): Numbers k such that U(k) == 2 mod 3, where U = A001950 = upper Wythoff sequence.
  • A283775 (program): Numbers k such that floor(k*sqrt(3)) is even.
  • A283776 (program): Numbers k such that floor(k*sqrt(3)) is odd.
  • A283777 (program): Numbers k such that floor(k*e) is even.
  • A283778 (program): Numbers k such that floor(k*e) is odd.
  • A283794 (program): Positions of 1 in A288375; complement of A288625.
  • A283799 (program): Number of dispersed Dyck prefixes of length 2n and height n.
  • A283800 (program): Numbers such that the sum of trits of its balanced ternary representation is 1 or -1.
  • A283803 (program): Expansion of exp( Sum_{n>=1} -A283369(n)/n*x^n ) in powers of x.
  • A283806 (program): Odd numbers which are uniquely decomposable into the sum of a prime and a power of two.
  • 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.
  • A283835 (program): Number of length-n binary vectors beginning with 0, ending with 1, and avoiding 5 consecutive 0’s and 5 consecutive 1’s.
  • A283836 (program): Number of length-n binary vectors beginning with 0, ending with 1, and avoiding 6 consecutive 0’s and 6 consecutive 1’s.
  • A283837 (program): Number of length-n binary vectors beginning with 0, ending with 1, and avoiding 7 consecutive 0’s and 7 consecutive 1’s.
  • A283842 (program): Expansion of x^3*(2-3*x)/((1-x)^2*(1-2*x)*(1-5*x+5*x^2)).
  • A283843 (program): a(n) = A063776(n) + 1.
  • A283844 (program): a(n) = A063776(2*n) + 1.
  • 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)}.
  • A283847 (program): Number of n-gonal inositol homologs with 2 kinds of achiral proligands.
  • A283858 (program): Number of 2 X n 0..1 arrays with no 1 equal to more than three of its horizontal, diagonal and antidiagonal neighbors.
  • 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.
  • A283906 (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 771”, based on the 5-celled von Neumann neighborhood.
  • A283907 (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 771”, based on the 5-celled von Neumann neighborhood.
  • A283908 (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 771”, based on the 5-celled von Neumann neighborhood.
  • A283909 (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 771”, based on the 5-celled von Neumann neighborhood.
  • A283919 (program): The smallest square referenced in A013929 (Numbers that are not squarefree).
  • A283958 (program): a(n) = (Sum_{j=1..h-1} a(n-j) + a(n-1)*a(n-h+1))/a(n-h) with a(1), …, a(h)=1, where h = 4.
  • A283959 (program): a(n) = (Sum_{j=1..h-1} a(n-j) + a(n-1)*a(n-h+1))/a(n-h) with a(1), …, a(h)=1, where h = 5.
  • A283963 (program): Fixed point of the morphism 0 -> 1, 1 -> 1010.
  • A283964 (program): Positions of 0 in A283963; complement of A283965.
  • A283965 (program): Positions of 1 in A283963; complement of A283964.
  • A283966 (program): Fixed point of the morphism 0 -> 1, 1 -> 10101.
  • A283967 (program): Positions of 0 in A283966; complement of A284015.
  • 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(4*n + 2) = 2*n + 1.
  • A283972 (program): a(n) = n minus (product of lengths of 1-runs in binary representation of n) = n - A227349(n).
  • A283980 (program): a(n) = A003961(n)*A006519(n).
  • A283981 (program): a(n) = A029931(n) - A280700(n).
  • A283982 (program): a(0) = 0, and for n > 0, a(n) = A070939(n) - A280700(n).
  • A283984 (program): Sums of distinct nonzero terms of A007489: a(n) = Sum_{k>=0} A030308(n,k)*A007489(1+k).
  • A283985 (program): Sums of distinct terms of A143293: a(n) = Sum_{k>=0} A030308(n,k)*A143293(k).
  • A283995 (program): Least number with same prime signature as the n-th divisorial: a(n) = A046523(A007955(n)).
  • A283996 (program): a(n) = n OR A005187(floor(n/2)), where OR is bitwise-or (A003986).
  • A283997 (program): a(n) = n XOR A005187(floor(n/2)), where XOR is bitwise-xor (A003987).
  • A283998 (program): a(n) = n AND A005187(floor(n/2)), where AND is bitwise-and (A004198).
  • A284001 (program): a(n) = A005361(A283477(n)).
  • A284002 (program): a(n) = A072411(A283477(n)).
  • A284003 (program): a(n) = A007913(A283477(n)) = A019565(A006068(n)).
  • A284004 (program): a(n) = A046523(A284003(n)).
  • A284005 (program): a(0) = 1, and for n > 1, a(n) = (1 + A000120(n))*a(floor(n/2)); also a(n) = A000005(A283477(n)).
  • A284013 (program): a(n) = n - A002487(n).
  • A284015 (program): Positions of 1 in A283966; complement of A283967.
  • A284016 (program): a(-1)=-1; a(n) = 2*A000108(n) for n >= 0.
  • A284020 (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 779”, based on the 5-celled von Neumann neighborhood.
  • A284021 (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 779”, based on the 5-celled von Neumann neighborhood.
  • A284022 (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 779”, based on the 5-celled von Neumann neighborhood.
  • A284023 (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 779”, based on the 5-celled von Neumann neighborhood.
  • A284028 (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 790”, based on the 5-celled von Neumann neighborhood.
  • A284029 (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 790”, based on the 5-celled von Neumann neighborhood.
  • A284031 (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 790”, based on the 5-celled von Neumann neighborhood.
  • A284036 (program): Positive integers n such that (n^2 - 3)/2 and (n^2 + 1)/2 are twin primes.
  • A284039 (program): Wiener index of the n-permutation star graph.
  • A284059 (program): The absolute values of A275966.
  • A284061 (program): Triangle read by rows: T(n,k) = pi(prime(k) * prime(n+1)).
  • A284062 (program): Numbers whose smallest decimal digit is 1.
  • A284063 (program): Numbers whose smallest decimal digit is 2.
  • A284064 (program): Numbers whose smallest decimal digit is 3.
  • A284065 (program): Numbers whose smallest decimal digit is 4.
  • A284066 (program): Numbers whose smallest decimal digit is 5.
  • A284067 (program): Numbers whose smallest decimal digit is 6.
  • A284068 (program): Numbers whose smallest decimal digit is 7.
  • A284087 (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 798”, based on the 5-celled von Neumann neighborhood.
  • A284088 (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 798”, based on the 5-celled von Neumann neighborhood.
  • A284090 (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 798”, based on the 5-celled von Neumann neighborhood.
  • A284095 (program): Expansion of Product_{k>=0} (1 + x^(8*k+1)).
  • A284096 (program): a(n) is the nearest integer to prime(n)*exp(prime(n)).
  • A284097 (program): a(n) = Sum_{d|n, d=1 mod 5} d.
  • A284098 (program): a(n) = Sum_{d|n, d==1 (mod 6)} d.
  • A284099 (program): a(n) = Sum_{d|n, d==1 (mod 7)} d.
  • A284100 (program): a(n) = Sum_{d|n, d==1 (mod 8)} 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.
  • A284105 (program): a(n) = Sum_{d|n, d=6 mod 7} d.
  • A284115 (program): Hosoya triangle of Lucas type.
  • A284117 (program): Sum of proper prime power divisors of n.
  • A284118 (program): Sum of nonprime squarefree divisors of n.
  • 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).
  • A284127 (program): Hosoya triangle of Pell type, read by rows.
  • A284128 (program): Hosoya triangle of Fermat Lucas type, read by rows.
  • A284150 (program): Sum_{d|n, d==1 or 4 mod 5} d.
  • A284151 (program): Sum_{d|n, d=1 or 6 mod 7} d.
  • A284152 (program): a(n) = Sum_{d|n, d == 2 or 3 mod 5} d.
  • A284204 (program): Eighth column of Euler’s difference table in A068106.
  • A284205 (program): Ninth column of Euler’s difference table in A068106.
  • A284206 (program): Tenth column of Euler’s difference table in A068106.
  • A284230 (program): Number of self-avoiding planar walks starting at (0,0), ending at (n,0), remaining in the first quadrant and using steps (0,1), (1,0), (1,1), (-1,1), and (1,-1) with the restriction that (0,1) is never used below the diagonal and (1,0) is never used above the diagonal.
  • A284232 (program): Binary representation of generation n in the reversible cellular automaton RCA(2) when started with a single ON cell at generation 0.
  • A284233 (program): Sum of odd prime power divisors of n (not including 1).
  • A284234 (program): Decimal representation of generation n in the reversible cellular automaton RCA(2) when started with a single ON cell at generation 0.
  • A284235 (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 833”, based on the 5-celled von Neumann neighborhood.
  • A284236 (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 833”, based on the 5-celled von Neumann neighborhood.
  • 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.
  • A284238 (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 833”, based on the 5-celled von Neumann neighborhood.
  • A284247 (program): Binary representation of generation n in the reversible cellular automaton RCA(1) when started with a single ON cell at generation 0.
  • A284248 (program): Every binary string w of length n has a subword of length a(n) that appears at least twice in w.
  • A284252 (program): a(n) = smallest prime dividing n which is larger than the square of smallest prime dividing n, or 1 if no such prime exists, a(1) = 1.
  • A284253 (program): a(n) = n / A284252(n).
  • A284254 (program): Largest divisor of n such that all its prime factors are greater than the square of smallest prime factor of n, a(1) = 1.
  • A284255 (program): Largest divisor of n such that all its prime factors are less than the square of the smallest prime factor of n, a(1) = 1.
  • A284256 (program): a(n) = number of prime factors of n that are > the square of smallest prime factor of n (counted with multiplicity), a(1) = 0.
  • A284257 (program): a(n) = number of prime factors of n that are < the square of smallest prime factor of n (counted with multiplicity), a(1) = 0.
  • A284259 (program): a(n) = number of distinct prime factors of n that are < the square of smallest prime factor of n, a(1) = 0.
  • A284260 (program): Greatest prime dividing n which is less than A020639(n)^2, where A020639(n) is the smallest prime dividing n, a(1) = 1.
  • A284263 (program): a(n) = A252459(2*A000040(n)), a(0) = 0 by convention.
  • A284280 (program): Sum_{d|n, d = 2 mod 5} d.
  • A284281 (program): Sum_{d|n, d = 3 mod 5} d.
  • A284286 (program): Expansion of eta(q^2)^4 / eta(q)^8 in powers of q.
  • A284288 (program): Numbers n such that the average of the strong divisors of n is an integer.
  • A284290 (program): Primes containing a digit 4.
  • A284291 (program): Primes containing a digit 6.
  • A284292 (program): Primes containing a digit 8.
  • A284293 (program): Numbers using only digits 1 and 6.
  • A284294 (program): Numbers using only digits 1 and 9.
  • A284307 (program): Permutation of the natural numbers partitioned into quadruples [4k-3, 4k, 4k-2, 4k-1], k > 0.
  • A284312 (program): Expansion of Product_{k>=0} (1 - x^(3*k+1)) in powers of x.
  • A284313 (program): Expansion of Product_{k>=0} (1 - x^(4*k+1)) in powers of x.
  • A284314 (program): Expansion of Product_{k>=0} (1 - x^(5*k+1)) in powers of x.
  • A284315 (program): Expansion of Product_{k>=0} (1 - x^(3*k+2)) in powers of x.
  • A284316 (program): Expansion of Product_{k>=0} (1 - x^(4*k+3)) in powers of x.
  • A284317 (program): Expansion of Product_{k>=0} (1 - x^(5*k+4)) in powers of x.
  • A284319 (program): Expansion of Product_{k>=0} (1 - x^(5*k+2)) in powers of x.
  • A284320 (program): Expansion of Product_{k>=0} (1 - x^(5*k+3)) in powers of x.
  • A284321 (program): Expansion of Product_{k>=0} (1 - x^(5*k+1))*(1 - x^(5*k+4)) in powers of x.
  • A284322 (program): Expansion of Product_{k>=0} (1 - x^(5*k+2))*(1 - x^(5*k+3)) in powers of x.
  • A284323 (program): Numbers n such that product of digits of n is a power of 4.
  • A284326 (program): Sum of the divisors of n that are not divisible by 6.
  • A284341 (program): Sum of the divisors of n that are not divisible by 8.
  • A284344 (program): Sum of the divisors of n that are not divisible by 10.
  • 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.
  • A284352 (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 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 (2*n+2 terms by row). Every row is 2*n + 1 followed by 2*n + 1 times 2*n + 2.
  • A284361 (program): Sum_{d|n, d = 0, 1, or 4 mod 5} d.
  • A284362 (program): Sum_{d|n, d = 0, 1, or 5 mod 6} d.
  • A284364 (program): Fixed point of the morphism 0->1, 1->101010.
  • A284365 (program): Positions of 0 in A284364; complement of A284366.
  • A284366 (program): Positions of 1 in A284364; complement of A284365.
  • A284368 (program): Fixed point of the morphism 0->1, 1->1011.
  • A284369 (program): Fixed point of the morphism 0->1, 1->1001.
  • A284370 (program): Positions of 0 in A284369; complement of A284371.
  • A284371 (program): Positions of 1 in A284369; complement of A284370.
  • A284372 (program): Sum_{d|n, d = 0, 1, or 11 mod 12} d.
  • A284375 (program): Numbers whose product of digits is a power of 0.
  • A284379 (program): Numbers n with digits 3 and 5 only.
  • A284380 (program): Numbers n with digits 5 and 7 only.
  • A284381 (program): Numbers n with digits 5 and 8 only.
  • A284382 (program): Numbers n with digits 5 and 9 only.
  • A284386 (program): Fixed point of the morphism 0->1, 1->1101.
  • A284387 (program): {010->2}-transform of the infinite Fibonacci word A003849.
  • A284388 (program): 0-limiting word of the morphism 0 -> 1, 1 -> 001.
  • A284389 (program): Positions of 0 in A284388; complement of A284390.
  • A284390 (program): Positions of 1 in A284388; complement of A284389.
  • A284391 (program): 1-limiting word of the morphism 0 -> 1, 1 -> 001.
  • A284392 (program): Positions of 0 in A284391; complement of A284393.
  • A284393 (program): Positions of 1 in A284391; complement of A284392.
  • A284394 (program): {101->2}-transform of the infinite Fibonacci word A003849.
  • 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.
  • A284404 (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 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.
  • A284432 (program): The number of positive integer sequences of length n with no duplicate substrings (forward or backward) and a minimal sum (i.e., the sum of the sequence is A282168(n)).
  • A284435 (program): The number of positive integer sequences of length n with no duplicate substrings (forward or backward) and a minimal product (i.e., the product of the sequence is A282193(n)).
  • A284438 (program): a(n) = phi(n)^n.
  • 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.
  • A284447 (program): Permutation of the positive integers: a(n) = A258996(A092569(n)) = A092569(A258996(n)).
  • A284458 (program): Number of pairs (f,g) of endofunctions on [n] such that the composite function gf has no fixed point.
  • A284459 (program): Permutation of the positive integers: this permutation transforms the enumeration system of positive irreducible fractions A002487/A002487’ (Calkin-Wilf) into the enumeration system A245327/A245328, and A162911/A162912 (Drib) into A020651/A020650 (Yu-Ting inverted).
  • A284460 (program): Permutation of the positive integers: this permutation transforms the enumeration system of positive irreducible fractions A245327/A245328 into the enumeration system A002487/A002487’ (Calkin-Wilf), and A020651/A020650 (Yu-Ting inverted) into A162911/A162912(Drib).
  • A284461 (program): Number of self-avoiding planar walks starting at (0,0), ending at (n,n), remaining in the first quadrant and using steps (0,1), (1,0), (1,1), (-1,1), and (1,-1) with the restriction that (0,1) is never used below the diagonal and (1,0) is never used above the diagonal.
  • A284467 (program): Expansion of Product_{k>=1} (1 + x^(2*k-1))^(2*k-1)/(1 + x^(2*k))^(2*k).
  • A284474 (program): Expansion of Product_{k>=1} (1 + x^(2*k))^(2*k)/(1 + x^(2*k-1))^(2*k-1).
  • A284475 (program): Total number of parts in all partitions of n into equal parts, minus the total number of parts in all partitions of n into consecutive parts.
  • A284479 (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 950”, based on the 5-celled von Neumann neighborhood.
  • A284480 (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 950”, based on the 5-celled von Neumann neighborhood.
  • A284481 (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 950”, based on the 5-celled von Neumann neighborhood.
  • A284482 (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 950”, based on the 5-celled von Neumann neighborhood.
  • A284484 (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 961”, based on the 5-celled von Neumann neighborhood.
  • A284485 (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 961”, based on the 5-celled von Neumann neighborhood.
  • A284487 (program): 0-limiting word of the morphism 0->1, 1->0011.
  • A284488 (program): Positions of 0 in A284487; complement of A284489.
  • A284489 (program): Positions of 1 in A284487; complement of A284488.
  • A284490 (program): 1-limiting word of the morphism 0->1, 1->0011.
  • A284491 (program): Positions of 0 in A284490; complement of A284492.
  • A284492 (program): Positions of 1 in A284490; complement of A284491.
  • A284494 (program): a(n) = A284016(n)^2.
  • A284499 (program): Expansion of Product_{k>=0} (1 - x^(7*k+1)) in powers of x.
  • A284500 (program): Expansion of Product_{k>=0} (1 - x^(7*k+2)) in powers of x.
  • A284501 (program): Expansion of Product_{k>=0} (1 - x^(7*k+3)) in powers of x.
  • A284503 (program): Expansion of Product_{k>=0} (1 - x^(7*k+5)) in powers of x.
  • A284505 (program): Fixed point of the morphism 0->1, 1->1100.
  • A284506 (program): Positions of 0 in A284505; complement of A284507.
  • A284507 (program): Positions of 1 in A284505; complement of A284506.
  • A284517 (program): Periodic with period [1, 4, 3, 4, 1, 6] of length 6.
  • A284518 (program): Periodic with period [1, 10, 9, 16, 1, 18, 1, 16, 9, 10, 1, 24] of length 12.
  • A284521 (program): Sum of largest prime power factors of numbers <= n.
  • A284533 (program): 0-limiting word of the morphism 0->1, 1->0101.
  • A284534 (program): Positions of 0 in A284533; complement of A284535.
  • A284535 (program): Positions of 1 in A284533; complement of A284534.
  • A284540 (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 974”, based on the 5-celled von Neumann neighborhood.
  • A284542 (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 974”, based on the 5-celled von Neumann neighborhood.
  • A284551 (program): Triangular array read by rows, demonstrating that the difference between a pentagonal number (left edge of triangle) and a square (right edge) is a triangular number.
  • A284552 (program): a(n) = A065621(n) modulo n.
  • A284555 (program): Positions of zeros in A284557.
  • A284556 (program): Sequence c of the mutual recurrence pair: b(0) = 0, b(1) = 1, b(2n) = c(n), b(2n+1) = b(n) + b(n+1), c(0) = c(1) = 0, c(2n) = b(n), c(2n+1) = c(n) + c(n+1).
  • A284557 (program): a(n) = A048727(n) mod 3.
  • A284565 (program): Bisection of A000360.
  • A284566 (program): Odd bisection of A284556.
  • A284570 (program): a(n) = A000005((n+1)^2) - A000005(n^2).
  • A284574 (program): a(n) = A048724(n) mod 3.
  • A284575 (program): a(n) = A048725(n) mod 3.
  • A284580 (program): Carryless base-2 product (A048720) of lengths of runs of 1-bits in binary representation of n.
  • A284584 (program): a(1) = 0; for n > 1, if n is not squarefree, then a(n) = A057627(n), otherwise a(n) = A013928(n).
  • A284585 (program): Expansion of Product_{k>=0} (1 - x^(6*k+1)) in powers of x.
  • A284586 (program): Expansion of Product_{k>=0} (1 - x^(6*k+5)) in powers of x.
  • A284587 (program): Sum of the divisors of n that are not divisible by 13.
  • A284588 (program): 1-limiting word of the morphism 0->1, 1->0101.
  • A284589 (program): Positions of 0 in A284588; complement of A284590.
  • A284590 (program): Positions of 1 in A284588; complement of A284589.
  • A284600 (program): a(n) = n/(largest prime power dividing n).
  • A284604 (program): Quadratic recurrence: a(n+2) = a(n+1)^2 + a(n)^2 + 1, with a(0) = a(1) = 1.
  • A284607 (program): Expansion of (eta(q^3)eta(q^6)/(eta(q)eta(q^2)))^4 in powers of q.
  • 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.
  • A284628 (program): Expansion of Product_{k>=1} 1/(1+x^(2*k-1))^(2*k-1).
  • A284630 (program): a(1)=1, a(2)=2; for n > 1, a(n+1) = (a(n-1) mod n) + n.
  • A284632 (program): Numbers n with digits 2 and 6 only.
  • A284633 (program): Numbers n with digits 3 and 6 only.
  • A284634 (program): Numbers with digits 4 and 6 only.
  • A284635 (program): Numbers with digits 6 and 8 only.
  • A284636 (program): Numbers with digits 6 and 9 only.
  • A284647 (program): Number of nonisomorphic unfoldings in an n-gonal Archimedean antiprism.
  • A284664 (program): Number of proper colorings of the 2n-gon with 2 instances of each of n colors under rotational symmetry.
  • A284674 (program): 0-limiting word of the morphism 0->1, 1-> 0111.
  • A284675 (program): Positions of 0 in A284674; complement of A284676.
  • A284676 (program): Positions of 1 in A284674; complement of A284675.
  • A284677 (program): 1-limiting word of the morphism 0->1, 1-> 0111.
  • A284678 (program): Positions of 0 in A284677; complement of A284679.
  • A284679 (program): Positions of 1 in A284677; complement of A284678.
  • A284680 (program): Fixed point of the morphism 0->1, 1->1000.
  • A284681 (program): Positions of 0 in A284680; complement of A284682.
  • A284682 (program): Positions of 1 in A284680; complement of A284681.
  • A284683 (program): Fixed point of the morphism 0 -> 01, 1 -> 0000
  • A284694 (program): Least prime number appearing in the prime tower factorization of n (when n > 1); a(1) = 1.
  • A284695 (program): Greatest prime number appearing in the prime tower factorization of n (when n > 1); a(1) = 1.
  • A284699 (program): Number of dominating sets in the n-antiprism graph.
  • A284709 (program): Number of maximal matchings in the wheel graph on n nodes.
  • A284712 (program): Number of indecomposable permutations avoiding the pattern 4321.
  • A284716 (program): Number of indecomposable permutations avoiding the pattern 2143.
  • A284720 (program): Number of indecomposable permutations avoiding the vincular pattern 1 2_ 3_.
  • 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.
  • A284745 (program): Fixed point of the morphism 0 -> 01, 1 -> 000.
  • A284746 (program): Positions of 0 in A284745; complement of A191263.
  • A284747 (program): Number of proper colorings of the 2n-gon with 2 instances of each of n colors under dihedral (rotational and reflectional) symmetry.
  • A284749 (program): {001->2}-transform of the infinite Fibonacci word A003849.
  • A284750 (program): a(n) = least k > 0 such that k * n in factorial base representation contains only 0’s and 1’s.
  • A284751 (program): Fixed point of the morphism 0 -> 01, 1 -> 0001.
  • A284752 (program): Positions of 0 in A284751; complement of A284753.
  • A284753 (program): Positions of 1 in A284751; complement of A284752.
  • A284759 (program): a(n) = (Sum_{i=1..n-1} i^(n-2)) mod n^3.
  • A284760 (program): a(n) = Sum_{i=1..n-1}(i^(n-2)) mod n^4.
  • A284761 (program): a(n) = gcd(A279513(n), A279513(n+1)).
  • A284772 (program): Fixed point of the morphism 0 -> 01, 1 -> 0010.
  • A284773 (program): Positions of 0 in A284772; complement of A284774.
  • A284774 (program): Positions of 1 in A284772; complement of A284773.
  • 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.
  • A284778 (program): Number of self-avoiding planar walks of length n+1 starting at (0,0), ending at (n,0), remaining in the first quadrant and using steps (0,1), (1,0), (1,1), (-1,1), and (1,-1) with the restriction that (0,1) is never used below the diagonal and (1,0) is never used above the diagonal.
  • A284787 (program): Even numbers representable in at least two ways as the sum of two odd composites.
  • A284789 (program): {1001->0}-transform of the Thue-Morse word A010060.
  • A284790 (program): Positions of 0 in A284789; complement of A284791.
  • A284791 (program): Positions of 1 in A284789; complement of A284790.
  • A284792 (program): {1001->1}-transform of the Thue-Morse word A010060.
  • A284793 (program): Difference sequence of A284775.
  • A284794 (program): Positions of -1 in A284793.
  • A284795 (program): Positions of 0’s in A284793.
  • A284796 (program): Positions of 1’s in A284793.
  • A284797 (program): Write in base k, complement, reverse. Case k = 3.
  • A284798 (program): Fixed points of the transform A284797.
  • A284799 (program): Write in base k, complement, reverse. Case k = 4.
  • A284800 (program): Fixed points of the transform A284799.
  • A284801 (program): Write in base k, complement, reverse. Case k = 5.
  • A284803 (program): Write in base k, complement, reverse. Case k = 6.
  • A284804 (program): Fixed points of the transform A284803.
  • A284805 (program): Write in base k, complement, reverse. Case k = 7.
  • A284807 (program): Write in base k, complement, reverse. Case k = 8.
  • A284808 (program): Fixed points of the transform A284807.
  • A284809 (program): Write in base k, complement, reverse. Case k = 9.
  • 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.
  • A284838 (program): Number of edges in the n-Keller graph.
  • A284840 (program): Number of quinternary strings avoiding consecutive digits i,i+1 and i,i+2.
  • A284843 (program): Number of permutations on [n+2] with no circular 2-successions.
  • A284844 (program): Number of permutations on [n+3] with no circular 3-successions.
  • A284845 (program): Number of permutations on [n+4] with no circular 4-successions.
  • A284850 (program): a(n) = 4^n - 3^n - n.
  • A284851 (program): Fixed point of the morphism 0 -> 01, 1 -> 0100.
  • A284852 (program): Positions of 0 in A284851; complement of A284853.
  • A284853 (program): Positions of 1 in A284851; complement of A284852.
  • A284855 (program): Array read by antidiagonals: T(n,k) = number of necklaces with n beads and k colors that are the same when turned over.
  • A284859 (program): Row sums of the Sheffer triangle (exp(x), exp(3*x)-1) given in A282629.
  • A284861 (program): Triangle read by rows: T(n, k) = S23,1*k! with the Sheffer triangle S2[3,1] = (exp(x), exp(3*x) -1) given in A282629.
  • A284864 (program): Row sums of Sheffer triangle S2[3,2] given by A225466.
  • A284878 (program): Fixed point of the morphism 0 -> 01, 1 -> 0110.
  • A284879 (program): Positions of 0 in A284878; complement of A284880.
  • A284880 (program): Positions of 1 in A284878; complement of A284879.
  • A284881 (program): Difference sequence of A284878.
  • A284882 (program): Positions of -1 in A284881.
  • A284883 (program): Positions of 0 in A284881.
  • A284884 (program): Positions of 1’s in A284881.
  • A284885 (program): (A284883)/2.
  • A284890 (program): a(1)=2, and then a(n+1) = a(n) + k where prime(k) is the least prime dividing a(n).
  • A284891 (program): Concatenation of the numbers from 3 to n.
  • A284892 (program): Numbers n > 1 such that all Hopf algebras of dimension n over algebraically closed fields of characteristic 0 are semisimple.
  • A284893 (program): Fixed point of the morphism 0 -> 01, 1 -> 0111.
  • A284894 (program): Positions of 0 in A284893; complement of A284895.
  • A284895 (program): Positions of 1 in A284893; complement of A284894.
  • A284896 (program): Expansion of Product_{k>=1} 1/(1+x^k)^(k^2) in powers of x.
  • A284897 (program): Expansion of Product_{k>=1} 1/(1+x^k)^(k^3) in powers of x.
  • A284898 (program): Expansion of Product_{k>=1} 1/(1+x^k)^(k^4) in powers of x.
  • A284899 (program): Expansion of Product_{k>=1} 1/(1+x^k)^(k^5) in powers of x.
  • A284900 (program): a(n) = Sum_{d|n} (-1)^(n/d+1)*d^4.
  • A284901 (program): Fixed point of the morphism 0 -> 01, 1 -> 1000.
  • A284902 (program): Positions of 0 in A284901; complement of A284903.
  • A284903 (program): Positions of 1 in A284901; complement of A284902.
  • A284905 (program): Fixed point of the morphism 0 -> 01, 1 -> 1001.
  • A284906 (program): Positions of 0 in A284905; complement of A284907.
  • A284907 (program): Positions of 1 in A284905; complement of A284906.
  • A284912 (program): Fixed point of the morphism 0 -> 01, 1 -> 1010.
  • A284913 (program): Positions of 0 in A284912; complement of A284914.
  • A284914 (program): Positions of 1 in A284912; complement of A284913.
  • A284920 (program): Numbers with digits 2 and 4 only.
  • A284921 (program): Numbers with digits 2 and 7 only.
  • A284922 (program): Numbers with digits 2 and 8 only.
  • A284923 (program): Numbers with digits 2 and 9 only.
  • A284926 (program): a(n) = Sum_{d|n} (-1)^(n/d+1)*d^5.
  • A284927 (program): a(n) = Sum_{d|n} (-1)^(n/d+1)*d^6.
  • A284929 (program): Fixed point of the morphism 0 -> 01, 1 -> 1011.
  • A284930 (program): Positions of 0 in A284929; complement of A284931.
  • A284931 (program): Positions of 1 in A284929; complement of A284930.
  • A284933 (program): Positions of 0 in A284792; complement of A284934.
  • A284934 (program): Positions of 1 in A284792; complement of A284933.
  • A284935 (program): Fixed point of the morphism 0 -> 01, 1 -> 1100.
  • A284936 (program): Positions of 0 in A284935; complement of A284937.
  • A284937 (program): Positions of 1 in A284935; complement of A284936.
  • A284938 (program): Triangle read by rows: coefficients of the edge cover polynomial for the n-path graph P_n.
  • A284939 (program): Fixed point of the morphism 0 -> 01, 1 -> 1101, starting with 0.
  • A284941 (program): Positions of 1 in A284939; complement of A080580.
  • A284944 (program): Fixed point of the morphism 0 -> 01, 1 -> 1110.
  • A284945 (program): Positions of 0 in A284944; complement of A284946.
  • A284946 (program): Positions of 1 in A284944; complement of A284945.
  • A284947 (program): Irregular triangle read by rows: coefficients of the cycle polynomial of the n-complete graph K_n.
  • A284948 (program): 1-limiting word of the morphism 0 -> 10, 1 -> 00
  • A284963 (program): Numbers with digits 3 and 8 only.
  • A284964 (program): Numbers with digits 3 and 9 only.
  • A284965 (program): a(n) is the number of self-conjugate partitions of n which represent Chomp positions with Sprague-Grundy value 1.
  • A284966 (program): Triangle read by rows: coefficients of the scaled Lucas polynomials x^(n/2) L(n, sqrt(x)) for n >= 0.
  • 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.
  • A284971 (program): Numbers with digits 4 and 7 only.
  • A284972 (program): Numbers with digits 4 and 8 only.
  • A284973 (program): Numbers with digits 4 and 9 only.
  • A284985 (program): a(0)=0, a(1)=24; for n>=2, a(n)=576*a(n-1)-a(n-2).
  • A285008 (program): Numerator of (3/4)^n * binomial(2*n,n).
  • A285009 (program): Subset sums (see Comments).
  • A285011 (program): Numbers with digits 7 and 9 only.
  • A285014 (program): Number of integers b with 1 < b < c such that b^(c-1) == 1 (modulo c), where c is the n-th composite number.
  • A285018 (program): Denominator of (-1/3)^n*sqrt(Pi)/(Gamma(1/2 - n)*Gamma(1 + n)).
  • A285019 (program): Numerator of (-1/3)^n*sqrt(Pi)/(Gamma(1/2 - n)*Gamma(1 + n)).
  • A285020 (program): Numerator of binomial(2*n,n)/20^n.
  • A285021 (program): Denominator of binomial(2*n,n)/20^n.
  • A285043 (program): Expansion of cosh(3*arctanh(2*sqrt(x))).
  • A285044 (program): Expansion of cosh(5*arctanh(2*sqrt(x))).
  • A285045 (program): Expansion of cosh(7*arctanh(2*sqrt(x))).
  • A285046 (program): Expansion of cosh(9*arctanh(2*sqrt(x))).
  • A285048 (program): Expansion of Product_{k>=0} 1/(1-x^(4*k+1))^(4*k+1).
  • A285050 (program): Expansion of Product_{k>=0} (1-x^(3*k+1))^(3*k+1).
  • 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.
  • A285057 (program): a(n) = lcm(n, A001177(n)).
  • A285064 (program): Row sums of Sheffer triangle S2[4,1] = A285061.
  • A285066 (program): Triangle read by rows: T(n, m) = A285061(n, m)*m!, 0 <= m <= n.
  • A285067 (program): Row sums of triangle A285066.
  • A285068 (program): Denominators of the generalized Bernoulli numbers B[3,1] = 3^n*B(n, 1/3).
  • A285069 (program): Expansion of Product_{k>=1} (1 - x^(2*k-1))^(2*k-1).
  • A285070 (program): Expansion of Product_{k>=0} (1-x^(4*k+1))^(4*k+1).
  • A285072 (program): Triangle read by rows: coefficients of the Laplacian polynomial of the n-path graph P_n.
  • 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.
  • A285099 (program): a(n) is the zero-based index of the second least significant 1-bit in the base-2 representation of n, or 0 if there are fewer than two 1-bits in n.
  • A285109 (program): a(n) = n multiplied by its smallest prime factor; a(1) = 1.
  • A285119 (program): Min(|d(k+1-i) - d(i)|, for i = 1..k, where d(1)..d(k) are the divisors of n^3.
  • 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.
  • A285123 (program): Min(|d(k+1-i) - d(i)|, for i = 1..k, where d(1),..,d(k) are the divisors of prime(n) - 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.
  • A285126 (program): Positions of 0 in A285125; complement of A285127.
  • A285127 (program): Positions of 1 in A285125; complement of A285126.
  • A285129 (program): Positions of 0 in A285128; complement of A285130.
  • A285130 (program): Positions of 1 in A285128; complement of A285139.
  • A285131 (program): Expansion of Product_{k>=0} 1/(1-x^(4*k+3))^(4*k+3).
  • A285139 (program): 0-limiting word of the morphism 0->10, 1-> 0010.
  • A285140 (program): Positions of 0 in A285139; complement of A285141.
  • A285141 (program): Positions of 1 in A285139; complement of A285140.
  • A285142 (program): 1-limiting word of the morphism 0->10, 1->0010.
  • A285143 (program): Positions of 0 in A285142; complement of A285144.
  • A285144 (program): Positions of 1 in A285142; complement of A285143.
  • 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.
  • A285185 (program): Expansion of (2*x+4*x^2) / (1-2*x-2*x^2+2*x^3).
  • A285186 (program): Expansion of (x+2*x^2) / (1-2*x-2*x^2+2*x^3).
  • A285187 (program): a(n) = Sum(psi(k-1)*psi(n-k-1),k=0..n)+(1-(-1)^n)/2, where psi(k) = A000931(k+6).
  • A285188 (program): a(n) = Sum_{k=1..n} (k^2*floor(k/2)).
  • A285192 (program): Array read by antidiagonals: T(n,k) = n*k*(3+n*k)/2 (n >= 0, k >= 0).
  • A285193 (program): Expansion of 1/(1+x+2*x^2) mod 3.
  • A285194 (program): Expansion of (1+x^2)/(1+x+x^4) 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.
  • A285197 (program): Expansion of (1-6*x+11*x^2-5*x^3) / ((1-x)*(1-3*x)*(1-3*x+x^2)).
  • A285198 (program): Binomial coefficients C(9,n).
  • A285199 (program): Product of n! and the n-th Legendre polynomial evaluated at 2.
  • 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.
  • A285205 (program): 0-limiting word of the morphism 0->10, 1-> 0100.
  • A285206 (program): Positions of 0 in A285205; complement of A285207.
  • A285207 (program): Positions of 1 in A285205; complement of A285206.
  • A285208 (program): 1-limiting word of the morphism 0->10, 1-> 0100.
  • A285209 (program): Positions of 0 in A285208; complement of A285210.
  • A285210 (program): Positions of 1 in A285208; complement of A285209.
  • A285212 (program): Expansion of Product_{k>=0} (1-x^(3*k+2))^(3*k+2).
  • A285213 (program): Expansion of Product_{k>=0} (1-x^(4*k+3))^(4*k+3).
  • A285231 (program): Number of entries in the third cycles of all permutations of [n].
  • A285232 (program): Number of entries in the fourth cycles of all permutations of [n].
  • A285233 (program): Number of entries in the fifth cycles of all permutations of [n].
  • A285234 (program): Number of entries in the sixth cycles of all permutations of [n].
  • A285235 (program): Number of entries in the seventh cycles of all permutations of [n].
  • A285262 (program): Expansion of Product_{k>=1} ((1-x^(4*k))/(1-x^k))^k.
  • A285268 (program): Triangle read by rows: T(m,n) = Sum_{i=1..n} P(m,i) where P(m,n) = m!/(m-n)! is the number of permutations of m items taken n at a time, for 1 <= n <= m.
  • A285269 (program): Number of (odd) primes between 2*n^2 and 2*(n+1)^2.
  • A285270 (program): a(n) = H_n(n), where H_n is the physicist’s n-th Hermite polynomial.
  • A285287 (program): Expansion of Product_{k>=0} 1/(1 + x^(4*k+1))^(4*k+1).
  • A285288 (program): Expansion of Product_{k>=0} (1 + x^(4*k+1))^(4*k+1).
  • A285301 (program): Fixed point of the morphism 0 -> 10, 1 -> 1000.
  • A285302 (program): Positions of 0 in A285301, complement of A086398.
  • 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.
  • A285309 (program): Sum of nonsquare divisors of n.
  • A285311 (program): Expansion of Product_{k>=0} 1/(1 + x^(4*k+3))^(4*k+3).
  • A285326 (program): a(0) = 0, for n > 0, a(n) = n + A006519(n).
  • A285329 (program): a(n) = A013928(A007947(n)).
  • A285335 (program): Odd bisection of A048675 divided by two: a(n) = A048675((2*n)-1)/2.
  • A285339 (program): Expansion of Product_{k>=0} (1 + x^(4*k+3))^(4*k+3).
  • A285341 (program): Fixed point of the morphism 0 -> 10, 1 -> 1011.
  • A285342 (program): Positions of 0 in A285341; complement of A285343.
  • A285343 (program): Positions of 1 in A285341; complement of A285342.
  • A285344 (program): (A285342)/2.
  • A285345 (program): Fixed point of the morphism 0 -> 10, 1 -> 1100.
  • A285346 (program): Positions of 0 in A285345; complement of A285347.
  • A285347 (program): Positions of 1 in A285345; complement of A285346.
  • A285351 (program): a(n) = 2n + 1 - A285346(n).
  • A285353 (program): Positions of 0 in A285351; complement of A285354.
  • A285354 (program): Positions of 1 in A285351; complement of A285353.
  • A285358 (program): Fixed point of the morphism 0 -> 10, 1 -> 1101.
  • A285359 (program): Positions of 0 in A285358; complement of A285360.
  • A285360 (program): Positions of 1 in A285358; complement of A285359.
  • A285361 (program): The number of tight 3 X n pavings.
  • A285363 (program): Sum of the entries in the first blocks of all set partitions of [n].
  • A285373 (program): Fixed point of the morphism 0 -> 10, 1 -> 1110.
  • A285374 (program): Positions of 0 in A285373; complement of A285375.
  • A285375 (program): Positions of 1 in A285373; complement of A285374.
  • A285376 (program): (A285374)/2.
  • A285382 (program): Sum of entries in the last cycles of all permutations of [n].
  • A285383 (program): Limiting 0-word of the morphism 0 -> 11, 1 -> 01.
  • A285384 (program): Limiting 1-word of the morphism 0 -> 11, 1 -> 01.
  • A285385 (program): Positions of 1 in A285384; complement of A072939.
  • A285388 (program): a(n) = numerator of ((1/n) * Sum_{k=0..n^2-1} binomial(2k,k)/4^k).
  • A285389 (program): Denominator of Sum_{k=0..n^2-1} (-1)^k*sqrt(Pi)/(Gamma(1/2-k)*Gamma(1+k))/n.
  • A285391 (program): Start with a single cell at coordinates (0, 0), then iteratively subdivide the grid into 3 X 3 cells and remove the cells whose sum of modulo 2 coordinates is 2; a(n) is the number of cells after n iterations.
  • A285392 (program): Start with a single cell at coordinates (0, 0), then iteratively subdivide the grid into 3 X 3 cells and remove the cells whose sum of modulo 2 coordinates is 0; a(n) is the number of cells after n iterations.
  • A285393 (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 2 or 3; a(n) is the number of cells after n iterations.
  • A285394 (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 1; a(n) is the number of cells after n iterations.
  • 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.
  • A285402 (program): Positions of 1 in A285177; complement of A285401.
  • A285404 (program): Positions of 0 in A285403; complement of A285405.
  • A285405 (program): Positions of 1 in A285403; complement of A285404.
  • A285406 (program): Base-2 logarithm of denominator of Sum_{k=0..n^2-1}((-1)^k*sqrt(Pi)/(Gamma(1/2-k)*Gamma(1+k)))/n).
  • A285418 (program): 0-limiting word of the morphism 0->11, 1-> 011.
  • A285419 (program): Positions of 0 in A285418; complement of A285420.
  • A285420 (program): Positions of 1 in A285418; complement of A285419.
  • A285421 (program): 1-limiting word of the morphism 0->11, 1-> 011.
  • A285422 (program): Positions of 0 in A285421; complement of A285423.
  • A285423 (program): Positions of 1 in A285421; complement of A285422.
  • A285427 (program): Fixed point of the morphism 0->11, 1-> 100.
  • A285428 (program): Positions of 0 in A285427; complement of A285429.
  • A285429 (program): Positions of 1 in A285427; complement of A285428.
  • A285430 (program): Fixed point of the morphism 0->11, 1-> 101.
  • A285431 (program): Fixed point of the morphism 0->11, 1-> 110.
  • A285434 (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 22”, based on the 5-celled von Neumann neighborhood.
  • A285435 (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 22”, based on the 5-celled von Neumann neighborhood.
  • A285436 (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 22”, based on the 5-celled von Neumann neighborhood.
  • A285437 (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 22”, based on the 5-celled von Neumann neighborhood.
  • 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.
  • A285442 (program): Expansion of Product_{k>0} ((1-x^{5k-2}) * (1-x^{5k-3})/((1-x^{5k-1}) * (1-x^{5k-4})))^2 in powers of x.
  • A285443 (program): Expansion of Product_{k>0} ((1-x^{5k-2}) * (1-x^{5k-3})/((1-x^{5k-1}) * (1-x^{5k-4})))^3 in powers of x.
  • A285444 (program): Expansion of Product_{k>0} ((1-x^{5k-2}) * (1-x^{5k-3})/((1-x^{5k-1}) * (1-x^{5k-4})))^4 in powers of x.
  • A285470 (program): Numbers k where “2” appears as the second digit of the decimal representation.
  • 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.
  • A285477 (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 20”, based on the 5-celled von Neumann neighborhood.
  • A285478 (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 20”, based on the 5-celled von Neumann neighborhood.
  • A285479 (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 20”, based on the 5-celled von Neumann neighborhood.
  • A285480 (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 20”, based on the 5-celled von Neumann neighborhood.
  • A285489 (program): Sum of entries in the second cycles of all permutations of [n].
  • A285501 (program): 0-limiting word of the morphism 0->11, 1-> 0011.
  • A285502 (program): Positions of 0 in A285501; complement of A285503.
  • A285503 (program): Positions of 1 in A285501; complement of A285502.
  • A285504 (program): 1-limiting word of the morphism 0->11, 1-> 0011.
  • A285505 (program): Positions of 0 in A285504; complement of A285506.
  • A285506 (program): Positions of 1 in A285504; complement of A285505.
  • A285508 (program): Numbers with exactly three prime factors, not all distinct.
  • A285510 (program): Numbers k such that the average of the squarefree divisors of k is an integer.
  • A285515 (program): {00->0, 11->1}-transform of A285501.
  • A285516 (program): Positions of 0 in A285515; complement of A285517.
  • A285517 (program): Positions of 1 in A285515; complement of A285516.
  • A285518 (program): {00->0, 11->1}-transform of A285504.
  • A285519 (program): Positions of 0 in A285518; complement of A285520.
  • A285520 (program): Positions of 1 in A285518; complement of A285519.
  • A285524 (program): a(n) is the value d<n/2 maximizing the expression d!*(d + 1)!*(2^(n-2*d-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.
  • A285529 (program): Triangle read by rows: T(n,k) is the number of nodes of degree k counted over all simple labeled graphs on n nodes, n>=1, 0<=k<=n-1.
  • 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.
  • A285541 (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 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.
  • A285543 (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 35”, based on the 5-celled von Neumann neighborhood.
  • A285551 (program): Volume of each square prism building the next 3-dimensional box in A100538 where side lengths form the Padovan spiral number sequence (A134816), starting with 1 X 1 X 1, 1 X 1 X 2, 2 X 2 X 2, 2 X 2 X 3, 4 X 4 X 5, …
  • A285555 (program): Expansion of q^(-2/5) * (r(q^2) + r(q)^2) / 2 in powers of q where r() is the Rogers-Ramanujan continued fraction.
  • A285586 (program): Complete list of numbers n for which there exists no prime number between n and 9n/8 inclusive.
  • A285597 (program): Positions of 0 in A285596; complement of A285598.
  • A285598 (program): Positions of 1 in A285596; complement of A285597.
  • A285600 (program): Positions of 0 in A285599; complement of A285601.
  • A285601 (program): Positions of 1 in A285599; complement of A285600.
  • 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.
  • A285613 (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 62”, based on the 5-celled von Neumann neighborhood.
  • A285617 (program): Fixed point of the morphism 0->11, 1->1000.
  • A285618 (program): Positions of 0 in A285617; complement of A285619.
  • A285619 (program): Positions of 1 in A285617; complement of A285618.
  • A285621 (program): Fixed point of the morphism 0->11, 1->1001.
  • A285622 (program): Positions of 0 in A285621; complement of A285623.
  • A285623 (program): Positions of 1 in A285621; complement of A285622.
  • A285625 (program): Fixed point of the morphism 0->11, 1->1010.
  • A285626 (program): Positions of 0 in A285625; complement of A285627.
  • A285627 (program): Positions of 1 in A285625; complement of A285626.
  • A285639 (program): a(n) = n*A117366(n)/spf(n), where A117366(n) is the smallest prime larger than all prime factors of n, and spf is the smallest prime factor of n (or 1 if n = 1).
  • A285647 (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 73”, based on the 5-celled von Neumann neighborhood.
  • A285648 (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 73”, based on the 5-celled von Neumann neighborhood.
  • A285649 (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 73”, based on the 5-celled von Neumann neighborhood.
  • A285650 (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 73”, based on the 5-celled von Neumann neighborhood.
  • A285657 (program): Fixed point of the morphism 0->11, 1->1011.
  • A285658 (program): Positions of 0 in A285657; complement of A285659.
  • A285659 (program): Positions of 1 in A285657; complement of A285658.
  • A285661 (program): Fixed point of the morphism 0->11, 1->1100.
  • A285662 (program): Positions of 0 in A285661; complement of A285663.
  • A285663 (program): Positions of 1 in A285661; complement of A285662.
  • A285666 (program): Fixed point of the mapping 00->001, 1->010, starting with 00.
  • A285667 (program): Positions of 0 in A285666; complement of A286058.
  • A285668 (program): Fixed point of the morphism 0->11, 1->1101.
  • A285669 (program): Positions of 0 in A285668; complement of A285670.
  • A285670 (program): Positions of 1 in A285668; complement of A285669.
  • A285671 (program): Fixed point of the morphism 0->11, 1->1110.
  • A285675 (program): Expansion of Product_{n>0} ((1-x^n)/(1+x^n))^n in powers of x.
  • A285676 (program): Beatty sequence of (7 + sqrt(7))/6; complement of A022841.
  • A285678 (program): Positions of 0 in A285677.
  • A285679 (program): Positions of 2 in A285677.
  • A285681 (program): Positions of 0 in A285680.
  • A285682 (program): Positions of 1 in A285680.
  • A285683 (program): Positions of 2 in A285680.
  • A285684 (program): Characteristic sequence of the Beatty sequence, A022838, of sqrt(3).
  • A285685 (program): Characteristic sequence of the Beatty sequence, A022839, of sqrt(5).
  • A285686 (program): Characteristic sequence of the Beatty sequence, A022840, of sqrt(6).
  • A285699 (program): a(1) = 1; for n > 1, a(n) = n - A079277(n).
  • A285700 (program): a(n) = Number of iterations x -> 2x-1 needed to get a nonprime number, when starting with x = n.
  • A285702 (program): a(n) = A000010(A064216(n)).
  • A285703 (program): a(n) = A000203(A064216(n)).
  • A285704 (program): a(n) = A285703(n) - n = A000203(A064216(n)) - n.
  • A285705 (program): a(n) = 2*n - A285703(n) = 2*n - A000203(A064216(n)).
  • A285707 (program): a(n) = gcd(n, A079277(n)), a(1) = 1.
  • A285708 (program): a(n) = n / A285707(n).
  • A285709 (program): a(n) = A000010(n) - A285699(n).
  • A285710 (program): Numbers n for which A000010(n) = A285699(n); positions of zeros in A285709.
  • A285713 (program): a(n) = A046523(A245612(n)).
  • A285714 (program): a(1) = 0; for n > 1, a(n) = 1 + a(A285712(n)).
  • A285715 (program): a(n) = A000120(A245611(n)).
  • A285716 (program): a(n) = A080791(A245611(n)).
  • A285717 (program): a(n) = A007814(n) + A159918(n) = A007814(n) + A000120(n^2).
  • A285718 (program): a(1) = 0, and for n > 1, a(n) = the least squarefree number x such that n-x is also squarefree.
  • A285719 (program): a(1) = 1, and for n > 1, a(n) = the largest squarefree number k such that n-k is also squarefree.
  • A285725 (program): a(1) = 0; for n > 1, a(n) = A252735(n) - A000035(n).
  • A285726 (program): a(1) = a(2) = 0; for n > 2, a(n) = A252736(n) - (1-A000035(n)).
  • A285728 (program): a(1) = 0; for n > 1, if n is even, then a(n) = A252463(A000265(n)), otherwise a(n) = a(A064989(n)).
  • A285734 (program): a(1) = 0, and for n > 1, a(n) = the largest squarefree number x such that x < n-x, and n-x is also squarefree.
  • A285735 (program): a(1) = 1, and for n > 1, a(n) = the least squarefree number x such that x > n-x, and n-x is also squarefree.
  • A285736 (program): a(n) = A285735(n) - A285734(n) = n - 2*A285734(n).
  • A285738 (program): Greatest prime less than 2*n^2 for n > 1, a(1) = 1.
  • A285741 (program): a(0) = 1; a(2*n) = a(n), a(2*n+1) = a(n) + R(a(n)), where R() is the digit reversal.
  • A285766 (program): Maximum spillway height for a zero or one bend minimal area lake in a number square.
  • A285768 (program): Moebius transform of repunits (A002275).
  • A285771 (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 84”, based on the 5-celled von Neumann neighborhood.
  • A285772 (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 84”, based on the 5-celled von Neumann neighborhood.
  • A285773 (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 84”, based on the 5-celled von Neumann neighborhood.
  • A285774 (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 84”, based on the 5-celled von Neumann neighborhood.
  • A285775 (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 89”, based on the 5-celled von Neumann neighborhood.
  • A285776 (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 89”, based on the 5-celled von Neumann neighborhood.
  • A285777 (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 89”, based on the 5-celled von Neumann neighborhood.
  • A285778 (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 89”, based on the 5-celled von Neumann neighborhood.
  • A285779 (program): Parity index: number of integers z with 1 <= z <= n for which A010060(z) = A010060(n), negated if A010060(n) = 1.
  • A285786 (program): Number of primes p with 2(n-1)^2 < p <= 2n^2.
  • A285788 (program): Irregular triangle T(n,m): nonprime 1 <= k <= n such that n and k are coprime.
  • A285789 (program): Primes equal to a pentagonal number plus 1.
  • A285790 (program): Primes equal to a hexagonal number plus 1.
  • A285791 (program): Primes equal to a heptagonal number plus 1.
  • A285792 (program): Primes equal to an octagonal number plus 1.
  • A285794 (program): a(1)=1, a(2)=2, a(3)=3, a(n) = 3*a(n-3)+2*a(n-2)+a(n-1).
  • A285795 (program): Sum of the second entries in all cycles of all permutations of [n].
  • A285796 (program): Number of ways to write n as an ordered sum of two numbers that are the product of an even number of distinct primes (including 1).
  • A285797 (program): Number of ways to write n as an ordered sum of two numbers that are the product of an odd number of distinct primes.
  • A285798 (program): Number of partitions of n into parts with an even number of distinct prime divisors.
  • A285799 (program): Number of partitions of n into parts with an odd number of distinct prime divisors.
  • A285800 (program): Numbers having more than one odd prime factor to an odd power in their prime factorization.
  • A285801 (program): Numbers having at most one odd prime factor to an odd power in their prime factorization.
  • A285804 (program): Composite numbers of the form 12*k+5 or 12*k+7 for some k.
  • A285809 (program): Primes equal to a centered triangular number plus 1.
  • A285810 (program): Primes equal to a centered pentagonal number plus 1.
  • A285811 (program): Primes equal to a centered heptagonal number plus 1.
  • A285812 (program): Primes equal to a centered 9-gonal number plus 1.
  • A285850 (program): Number of ways n couples can sit in a row such that exactly one couple sits next to each other.
  • A285851 (program): Denominator of the ratio of alternate consecutive prime gaps: Denominator((prime(n + 3) - prime(n + 2))/(prime(n + 1) - prime(n))).
  • A285853 (program): Number of permutations of [n] with two ordered cycles such that equal-sized cycles are ordered with increasing least elements.
  • A285863 (program): Numerators of Bernoulli numbers 3^n*B(n), with B(n) = A027641(n)/A027642(n).
  • A285867 (program): Triangle T(n, k) read by rows: T(n, k) = S2(n, k)*k! + S2(n, k-1)*(k-1)! with the Stirling2 triangle S2 = A048993.
  • A285868 (program): Row sums of triangle A285867.
  • 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.
  • A285871 (program): Decimal expansion of 1/sqrt(2 - sqrt(2)) (reciprocal of A101464).
  • 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.
  • A285895 (program): Sum of divisors d of n such that n/d is not congruent to 0 mod 4.
  • A285896 (program): Sum of divisors d of n such that n/d is not congruent to 0 mod 5.
  • A285898 (program): Triangle read by row: T(n,k) = number of partitions of n into exactly k consecutive parts (1 <= k <= n).
  • 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.
  • A285901 (program): Total number of partitions of all positive integers <= n into an odd number of consecutive parts.
  • A285902 (program): Total number of partitions of all positive integers <= n into an even number of consecutive parts.
  • A285915 (program): Integers n such that A112528(n) - A103274(n) = 1.
  • A285917 (program): Number of ordered set partitions of [n] into two blocks such that equal-sized blocks are ordered with increasing least elements.
  • A285927 (program): Expansion of (Product_{k>0} (1 - x^(3*k)) / (1 - x^k))^3 in powers of x.
  • A285928 (program): Expansion of (Product_{k>0} (1 - x^(5*k)) / (1 - x^k))^5 in powers of x.
  • A285932 (program): Expansion of (Product_{k>0} (1 - x^k) / (1 - x^(5*k)))^5 in powers of x.
  • 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.
  • A285955 (program): Numbers a(n) = T(b(n))*sqrt(T(b(n))+1), where T(b(n)) is the triangular number of b(n)= A000217(b(n)) and b(n)=A006451(n). Also a(n) = y solutions of the Bachet Mordell equation y^2=x^3+K, where x= T(b(n)) = A006454(n) and K = (T(b(n)))^2= A285985(n).
  • A285956 (program): Number of orthogonal rectangles with vertices on an n X n square grid of points but with no vertices on the grid’s diagonals.
  • A285957 (program): {01->0}-transform of the Thue-Morse word A010060.
  • A285958 (program): Positions of 0 in A285957; complement of A285959.
  • A285959 (program): Positions of 1 in A285957; complement of A285958.
  • A285960 (program): {01->1}-transform of the Thue-Morse word A010060.
  • A285961 (program): Positions of 0 in A285960; complement of A285962.
  • A285962 (program): Positions of 1 in A285960; complement of A285961.
  • A285963 (program): {11->0}-transform of the Thue-Morse word A010060.
  • A285964 (program): Positions of 0 in A285963; complement of A285965.
  • A285965 (program): Positions of 1 in A285963; complement of A285964.
  • A285966 (program): {11->1}-transform of the Thue-Morse word A010060.
  • A285967 (program): Positions of 0 in A285966; complement of A285968.
  • A285968 (program): Positions of 1 in A285966; complement of A285967.
  • A285969 (program): {0110->0}-transform of the Thue-Morse word A010060.
  • A285970 (program): Positions of 0 in A285969; complement of A285971.
  • A285971 (program): Positions of 0 in A285969; complement of A285970.
  • A285972 (program): {10->1}-transform of the Thue-Morse word A010060.
  • A285973 (program): Positions of 0 in A285972; complement of A285974.
  • A285974 (program): Positions of 1 in A285972; complement of A285973.
  • A285975 (program): {00->0}-transform of the Thue-Morse word A010060.
  • A285976 (program): Positions of 0 in A285975; complement of A285977.
  • A285977 (program): Positions of 1 in A285975; complement of A285976.
  • A285978 (program): {00->1}-transform of the Thue-Morse word A010060.
  • A285979 (program): Positions of 0 in A285978; complement of A285980.
  • A285980 (program): Positions of 1 in A285978; complement of A285979.
  • 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)
  • A285989 (program): a(0) = 0, a(n) = Sum_{0<d|n, n/d odd} d^4 for n > 0.
  • A285991 (program): Expansion of Product_{n>0} ((1-x^n)/(1+x^n))^(n^4) in powers of x.
  • A285996 (program): Triangle read by rows, 1<=k<=n, T(n,k) = number of arrangements of n circles in the affine plane having k separated islands.
  • 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).
  • A286014 (program): Sum of smallest parts of all partitions of n into consecutive parts.
  • A286015 (program): Sum of largest parts of all partitions of n into consecutive parts.
  • 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.
  • A286038 (program): Number of (undirected) paths in the n-cocktail party graph.
  • A286043 (program): (1/2)*A285658.
  • A286044 (program): {011->0}-transform of the Thue-Morse word A010060.
  • A286045 (program): Positions of 0 in A286044; complement of A003157.
  • A286046 (program): {011->1}-transform of the Thue-Morse word A010060.
  • A286047 (program): Positions of 0 in A286046; complement of A286048.
  • A286048 (program): Positions of 1 in A286046; complement of A286047.
  • A286049 (program): {110->1}-transform of the Thue-Morse word A010060.
  • A286050 (program): Positions of 0 in A286049; complement of A286051.
  • A286051 (program): Positions of 1 in A286049; complement of A286050.
  • A286052 (program): {101->0}-transform of the Thue-Morse word A010060.
  • A286053 (program): Positions of 0 in A286052; complement of A286054.
  • A286054 (program): Positions of 1 in A286052; complement of A286053.
  • A286055 (program): {010->1}-transform of the Thue-Morse word A010060.
  • A286056 (program): Positions of 0 in A286055; complement of A286057.
  • A286057 (program): Positions of 1 in A286055; complement of A286056.
  • A286058 (program): Positions of 1 in A285666; complement of A285667.
  • A286059 (program): Fixed point of the mapping 00->001, 1->011, starting with 00.
  • A286060 (program): Positions of 0 in A286059; complement of A286061.
  • A286061 (program): Positions of 1 in A286059; complement of A286060.
  • 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.
  • A286065 (program): Positions of 0 in A286064; complement of A286066.
  • A286066 (program): Positions of 1 in A286064; complement of A286065.
  • A286096 (program): Triangle read by rows giving numerators of the Fourier expansion of cos^n(x).
  • A286098 (program): Square array read by antidiagonals: A(n,k) = T(n AND k, n OR k), where T(n,k) is sequence A001477 considered as a two-dimensional table, AND is bitwise-and (A004198) and OR is bitwise-or (A003986).
  • A286099 (program): Square array read by antidiagonals: A(n,k) = T(n OR k, n AND k), where T(n,k) is sequence A001477 considered as a two-dimensional table, AND is bitwise-and (A004198) and OR is bitwise-or (A003986).
  • 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.
  • A286108 (program): Square array read by antidiagonals: A(n,k) = T(2*(n AND k), n XOR k), where T(n,k) is sequence A001477 considered as a two-dimensional table, AND is bitwise-and (A004198) and XOR is bitwise-xor (A003987).
  • A286109 (program): Square array read by antidiagonals: A(n,k) = T(n XOR k, 2*(n AND k)), where T(n,k) is sequence A001477 considered as a two-dimensional table, AND is bitwise-and (A004198) and XOR is bitwise-xor (A003987).
  • A286175 (program): Sum of the n-th entries in all cycles of all permutations of [n+1].
  • A286182 (program): Number of connected induced (non-null) subgraphs of the prism graph with 2n nodes.
  • A286183 (program): Number of connected induced (non-null) subgraphs of the antiprism graph with 2n nodes.
  • A286184 (program): Number of connected induced (non-null) subgraphs of the helm graph with 2n+1 nodes.
  • A286185 (program): Number of connected induced (non-null) subgraphs of the Möbius ladder 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.
  • A286218 (program): Number of partitions of n into parts with an odd number of prime divisors (counted with multiplicity).
  • A286219 (program): Number of partitions of n into parts with an even number of prime divisors (counted with multiplicity).
  • A286224 (program): Number of compositions (ordered partitions) of n into parts with an odd number of distinct prime divisors.
  • A286226 (program): Number of compositions (ordered partitions) of n into parts with an odd number of prime divisors (counted with multiplicity).
  • A286227 (program): Number of compositions (ordered partitions) of n into parts with an even number of prime divisors (counted with multiplicity).
  • A286243 (program): Filter-sequence: a(n) = A278222(A064216(n)).
  • A286250 (program): Filter-sequence: a(n) = A278223(A064216(n)) = A046523((2*A064216(n))-1).
  • 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) = (2*n-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).
  • A286299 (program): First differences of A286298.
  • A286305 (program): Number of partitions of n into powerful parts (A001694).
  • A286307 (program): a(n) is the numerator of r(n), where r(n) = r(n-1) + r(n-2)/(2*(n-1)) with r(0) = 0, r(1) = 1.
  • A286308 (program): Numbers m such that gcd(m, F(m)) = 2, where F(m) denotes the m-th Fibonacci number.
  • A286311 (program): a(n) = 2*a(n-1) - a(n-2) + a(n-4), n>3, a(0)=0, a(1)=a(2)=1, a(3)=3.
  • A286323 (program): Beatty sequence of (8 + sqrt(8))/7; complement of A022842.
  • A286324 (program): a(n) is the number of bi-unitary divisors of n.
  • A286336 (program): {1101->0}-transform of the Thue-Morse word A010060.
  • A286337 (program): Positions of 0 in A286336; complement of A286338.
  • A286338 (program): Positions of 1 in A286336; complement of A286337.
  • A286339 (program): {1101->1}-transform of the Thue-Morse word A010060.
  • A286340 (program): Positions of 0 in A286339; complement of A286341.
  • A286341 (program): Positions of 1 in A286339; complement of A286340.
  • A286346 (program): Expansion of eta(q)^24 / eta(q^2)^12 in powers of q.
  • A286350 (program): a(n) = 2*a(n-1) - a(n-2) + a(n-4) for n>3, a(0)=0, a(1)=a(2)=2, a(3)=3.
  • A286355 (program): Beatty sequence of (10 + sqrt(10))/9; complement of A177102.
  • A286357 (program): One more than the exponent of the highest power of 2 dividing sigma(n): a(n) = A001511(A000203(n)).
  • A286361 (program): Least number with the same prime signature as {the largest divisor of n with only prime factors of the form 4k+1} has: a(n) = A046523(A170818(n)).
  • A286363 (program): Least number with the same prime signature as {the largest divisor of n with only prime factors of the form 4k+3} has: a(n) = A046523(A097706(n)).
  • A286374 (program): a(n) = A278222(n^2).
  • 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.
  • A286385 (program): a(n) = A003961(n) - A000203(n).
  • A286387 (program): a(n) = A002487(n^2).
  • A286389 (program): a(0) = 0; a(n) = n - a(floor(a(n-1)/2)).
  • A286390 (program): a(n) = a(n-2) - 2*a(n-3) + a(n-4) for n>3, a(0)=0, a(1)=2, a(2)=-1, a(3)=3.
  • A286398 (program): Denominator of A285388(n+1)/A285388(n).
  • A286400 (program): {1010->1}-transform of the Thue-Morse word A010060.
  • A286401 (program): Positions of 0 in A286400; complement of A286402.
  • A286402 (program): Positions of 1 in A286400; complement of A286401.
  • A286428 (program): Beatty sequence of (12 + sqrt(12))/11; complement of A194028.
  • 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.
  • A286433 (program): Number of entries in the second last blocks of all set partitions of [n].
  • 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.
  • A286469 (program): a(n) = maximum of {the index of least prime dividing n} and {the maximal gap between indices of the successive primes in the prime factorization of n}.
  • A286471 (program): If n is noncomposite, then a(n) = 0, otherwise 1 + difference between indices of the two smallest (not necessarily distinct) prime factors of n.
  • A286477 (program): Ordinal transform of A032742, starting from its first term a(1) = 1.
  • A286479 (program): a(n) = A046523(n+A000005(n)).
  • A286484 (program): {0010->0}-transform of the Thue-Morse word A010060.
  • A286485 (program): Positions of 0 in A286484; complement of A286486.
  • A286486 (program): Positions of 1 in A286484; complement of A286485.
  • A286487 (program): {0010->1}-transform of the Thue-Morse word A010060.
  • A286488 (program): Positions of 0 in A286487; complement of A286489.
  • A286489 (program): Positions of 1 in A286487; complement of A286488.
  • A286496 (program): Renyi-Ulam liar numbers: for k=1,2,3,… this is the maximum n such that k questions “Is x in subset S of {1,…,n}?” are guaranteed to determine x when at most one answer can be a lie.
  • 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).
  • A286530 (program): a(n) = d(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.
  • A286574 (program): Sum of the binary weights of the lengths of 1-runs in base-2 representation of n: a(n) = A000523(A286575(n)).
  • A286575 (program): Run-length transform of A001316.
  • A286576 (program): a(n) = A132971(n) mod 3.
  • A286577 (program): If n = 3k-1 then a(n) = a(k), otherwise a(n) = n.
  • A286578 (program): a(n) = A285712(A286577(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)).
  • A286586 (program): a(n) = A006047(A048673(n)).
  • A286587 (program): a(n) = A006047(A244154(n)).
  • A286596 (program): a(n) = A278222(A153141(n)).
  • A286598 (program): a(n) = A278222(A153142(n)).
  • A286601 (program): a(n) = A278222(A193231(n)).
  • A286604 (program): a(n) = n mod sum of digits of n in factorial base.
  • A286607 (program): Numbers that are not divisible by the sum of their factorial base digits (A034968).
  • A286613 (program): a(n) = A046523(A244154(n)).
  • A286624 (program): a(n) = (prime(1+n)*prime(n)) + prime(n) + 1.
  • A286629 (program): a(n) = (A000040(n)-1) * A002110(n).
  • A286630 (program): a(0) = 1; for n >= 1, a(n) = A000040(n) * A002110(n).
  • A286631 (program): a(n) = A278222(A254104(n)).
  • A286634 (program): Numerator of the ratio of alternate consecutive prime gaps: Numerator ((prime(n + 3) - prime(n + 2))/(prime(n + 1) - prime(n))).
  • A286636 (program): Even numbers that are a sum of two squares plus 1.
  • A286654 (program): Characteristic sequence of the Beatty sequence, A022841, of sqrt(7).
  • 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.
  • A286691 (program): {0->010, 1->110}-transform of the Pell word, A171588.
  • A286692 (program): Positions of 0 in A286691; complement of A286693.
  • A286693 (program): Positions of 1 in A286691; complement of A286692.
  • 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.
  • A286719 (program): Column k=4 of triangle A039755, Sheffer(exp(x), (exp(2*x) - 1)/2).
  • A286721 (program): Column k=2 of the triangle A286718; Sheffer ((1 - 3*x)^(-1/3), (-1/3)*log(1 - 3*x)).
  • A286722 (program): Column k=2 of the triangle A225470; Sheffer ((1 - 3*x)^(-2/3), (-1/3)*log(1 - 3*x)).
  • A286723 (program): Column k = 1 of the triangle A225471; Sheffer ((1 - 3*x)^(-3/4), (-1/4)*log(1 - 4*x)).
  • A286724 (program): Triangle read by rows. A generalization of unsigned Lah numbers, called L[2,1].
  • 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.
  • A286746 (program): {00->null}-transform of the infinite Fibonacci word A003849.
  • A286747 (program): Characteristic sequence of the Beatty sequence, A177102, of sqrt(10).
  • A286748 (program): Characteristic sequence of the Beatty sequence, A194028, of sqrt(12).
  • A286749 (program): {0100->null}-transform of the infinite Fibonacci word A003849.
  • 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.
  • A286755 (program): Möbius (or Moebius) partition function of partitions in graded reverse lexicographic ordering.
  • 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.
  • A286771 (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 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.
  • A286779 (program): Multiplicative with a(p^e) = 2e^2 + 2.
  • A286784 (program): Triangle T(n,k) read by rows: coefficients of polynomials P_n(t) defined in Formula section.
  • A286785 (program): Triangle T(n,k) read by rows: coefficients of polynomials P_n(t) defined in Formula section.
  • A286801 (program): {0->110, 1->010}-transform of the Pell word, A171588.
  • A286802 (program): Positions of 0 in A286801; complement of A286803.
  • A286803 (program): Positions of 1 in A286801; complement of A286802.
  • A286804 (program): {000->null}-transform of the Pell word, A171588.
  • A286805 (program): Positions of 0 in A286804; complement of A286806.
  • 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.
  • A286813 (program): Number of positive odd solutions to equation x^2 + 8*y^2 = 8*n + 9.
  • A286814 (program): Number of matchings in the n-helm graph.
  • A286820 (program): a(n) = smallest positive multiple of n whose factorial base representation contains only 0’s and 1’s.
  • A286838 (program): Digits of one of the two 13-adic integers sqrt(-1) (digits 0, 1, … , 9, 10, 11, 12 are used instead of 0, 1, … , 9, A, B, C).
  • A286839 (program): Digits of one of the two 13-adic integers sqrt(-1) (digits 0, 1, … , 9, 10, 11, 12 are used instead of 0, 1, … , 9, A, B, C).
  • A286840 (program): One of the two successive approximations up to 13^n for 13-adic integer sqrt(-1). Here the 5 (mod 13) case (except for n=0).
  • A286841 (program): One of the two successive approximations up to 13^n for 13-adic integer sqrt(-1). Here the 8 (mod 13) case (except for n=0).
  • 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.
  • A286875 (program): If n = Product (p_j^k_j) then a(n) = Sum (k_j >= 2, p_j^k_j).
  • A286877 (program): One of the two successive approximations up to 17^n for 17-adic integer sqrt(-1). Here the 4 (mod 17) case (except for n=0).
  • A286878 (program): One of the two successive approximations up to 17^n for 17-adic integer sqrt(-1). Here the 13 (mod 17) case (except for n=0).
  • A286887 (program): Number of irredundant sets in the path graph P_n.
  • A286888 (program): Floor of the average gap between consecutive primes among the first n primes, for n > 1.
  • A286896 (program): Number of blocks of size >= n in all set partitions of [2n].
  • A286900 (program): Sum of the numbers from n to nextprime(n).
  • A286901 (program): Sum of the numbers from prevprime(n) to n.
  • A286903 (program): {0->00}-transform of the Sturmian word A080764.
  • 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.
  • A286908 (program): Positions of 0 in A286907; complement of A286909.
  • A286909 (program): Positions of 1 in A286907; complement of A286908.
  • A286910 (program): Number of independent vertex sets and vertex covers in the n-antiprism graph.
  • A286911 (program): Number of edge covers in the ladder graph P_2 x P_n.
  • A286922 (program): {0->01}-transform of the Sturmian word A080764.
  • 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.
  • A286937 (program): {111->null}-transform of the Sturmian word A080764.
  • A286938 (program): Length of n-th iterate of the mapping 00->001, 1->10, as in A284932.
  • A286945 (program): Number of maximal matchings in the ladder graph P_2 X P_n.
  • A286952 (program): Expansion of Product_{j>=1} (1 - x^j)/(1 - x^(3*j))^3.
  • A286953 (program): Expansion of Product_{j>=1} (1 - x^j)/(1 - x^(4*j))^4.
  • A286956 (program): Main diagonal of A286950.
  • A286972 (program): Numbers k such that the average of the prime power divisors (not including 1) of k is an integer.
  • A286983 (program): a(n) is the smallest integer that can appear as the n-th term of two distinct nondecreasing sequences of positive integers that satisfy the Fibonacci recurrence relation.
  • A286984 (program): Decimal expansion of (2 + sqrt(5) + sqrt(15 - 6*sqrt(5)))/2.
  • A286985 (program): Number of connected dominating sets in the n-prism graph.
  • A286986 (program): Number of connected dominating sets in the n-antiprism graph.
  • A286987 (program): {111->1}-transform of the Sturmian word A080764.
  • A286988 (program): Positions of 0 in A286987; complement of A286989.
  • A286989 (program): Positions of 1 in A286987; complement of A286988.
  • A286990 (program): {0->010, 1->101}-transform of the Sturmian word A080764.
  • A286991 (program): Positions of 0 in A286990; complement of A286992.
  • A286992 (program): Positions of 1 in A286990; complement of A286991.
  • A286994 (program): Positions of 0 in A286993; complement of A286995.
  • A286995 (program): Positions of 1 in A286993; complement of A286994.
  • A286996 (program): {0->000, 11->null}-transform of the Sturmian word A080764.
  • A286997 (program): Positions of 0 in A286996; complement of A188383.
  • A286999 (program): Positions of 0 in A286998.
  • A287000 (program): Positions of 1 in A286998.
  • A287002 (program): Start with 0 and repeatedly substitute 0->01, 1->20, 2->1.
  • A287003 (program): Positions of 0 in A287002.
  • A287004 (program): Positions of 1 in A287002.
  • A287005 (program): Number of connected dominating sets on the n-Moebius ladder.
  • A287014 (program): Bell numbers written in base 2.
  • A287015 (program): Lucas numbers written in base 2.
  • A287016 (program): a(n) = smallest number k such that A071904(n) + k^2 is a perfect square.
  • A287018 (program): Primes that can be generated by the concatenation in base 2, in ascending order, of two consecutive integers read in base 10.
  • A287028 (program): {0->101, 1->010}-transform of the Sturmian word A080764.
  • A287057 (program): a(n) = 2*n^2 + n - (n+1) mod 2.
  • A287058 (program): Sum of decimal digits of 118^n.
  • A287063 (program): Number of dominating sets in the n-crown graph (for n > 1).
  • A287072 (program): Start with 0 and repeatedly substitute 0->01, 1->21, 2->0.
  • A287073 (program): Positions of 0 in A287072.
  • A287074 (program): Positions of 1 in A287072.
  • A287075 (program): Positions of 2 in A287072.
  • A287081 (program): Positions of 2 in A287002.
  • A287082 (program): Number of edge covers on the n-web graph.
  • A287087 (program): Positions of 0 in A287086.
  • A287088 (program): Positions of 1 in A287086.
  • A287089 (program): Positions of 2 in A287086.
  • A287104 (program): Start with 0 and repeatedly substitute 0->10, 1->12, 2->0.
  • A287105 (program): Positions of 0 in A287104.
  • A287106 (program): Positions of 1 in A287104.
  • A287107 (program): Positions of 2 in A287104.
  • A287114 (program): Positions of 1 in A287112.
  • A287115 (program): Positions of 2 in A287112.
  • A287128 (program): a(n) = 3*a(n-1) - 2*a(n-2) + 2*a(n-3) - 4*a(n-4) + 2*a(n-5), where a(0) = 2, a(1) =3, a(2) = 6, a(3)=13, a(4) = 29.
  • A287143 (program): Expansion of x*(1 + 3*x + x^2)/((1 - x)^5*(1 + x)^4).
  • A287168 (program): Number of non-attacking bishop positions on a cylindrical 3 X 2n chessboard.
  • A287169 (program): Number of non-attacking king positions on a cylindrical 3 X 2n chessboard.
  • A287170 (program): a(n) = number of runs of consecutive prime numbers among the prime divisors of n.
  • A287174 (program): 2-limiting word of the morphism 0->10, 1->20, 2->0.
  • A287175 (program): Positions of 0 in A287174.
  • A287176 (program): Positions of 1 in A287174.
  • A287177 (program): Positions of 2 in A287174.
  • 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.
  • A287196 (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 259”, based on the 5-celled von Neumann neighborhood.
  • 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.
  • A287199 (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 259”, based on the 5-celled von Neumann neighborhood.
  • A287209 (program): a(1)=4, a(2)=5, a(n) = sum of digits of a(n-1) + sum of digits of a(n-2), n>=3.
  • 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.
  • A287295 (program): a(2n-1) is concatenation of sequence (1,3,..,2n-3,2n-1,2n-3,..3,1) and a(2n) is concatenation of sequence (1,3,..,2n-3,2n-1,2n-1,2n-3,..3,1).
  • A287300 (program): Primes that can be generated by the concatenation in base 3, in ascending order, of two consecutive integers read in base 10.
  • A287302 (program): Primes that can be generated by the concatenation in base 4, in ascending order, of two consecutive integers read in base 10.
  • A287304 (program): Primes that can be generated by the concatenation in base 5, in ascending order, of two consecutive integers read in base 10.
  • A287308 (program): Primes that can be generated by the concatenation in base 7, in ascending order, of two consecutive integers read in base 10.
  • A287310 (program): Primes that can be generated by the concatenation in base 8, in ascending order, of two consecutive integers read in base 10.
  • A287312 (program): Primes that can be generated by the concatenation in base 9, in ascending order, of two consecutive integers read in base 10.
  • A287324 (program): a(n) = A008412(n-1) + A008412(n-2) for n>1, a(0)=0, a(1)=1.
  • A287326 (program): Triangle read by rows: T(n, k) = 6*k*(n-k) + 1; n >= 0, 0 <= k <= n.
  • A287327 (program): Number of independent vertex sets (and vertex covers) in the 2n-crossed prism graph.
  • A287330 (program): 7*x - 1 Collatz-type sequence starting with a(0) = 11.
  • A287335 (program): Nonnegative numbers k such that 3*k + 2 is a cube.
  • A287349 (program): Number of matchings in the n-gear graph.
  • A287350 (program): Number of independent vertex sets and vertex covers in the n-gear graph.
  • A287353 (program): a(0)=0; for n>0, a(n) = 10*a(n-1) + prime(n).
  • A287356 (program): Start with 0 and repeatedly substitute 0->11, 1->12, 2->0.
  • A287357 (program): Positions of 0 in A287356.
  • A287358 (program): Positions of 1 in A287356.
  • A287359 (program): Positions of 2 in A287356.
  • A287373 (program): Positions of 0 in A101666.
  • A287374 (program): Positions of 1 in A101666.
  • A287375 (program): Positions of 2 in A101666.
  • A287379 (program): Positions of 0 in A287931; complement of A287380.
  • A287380 (program): Positions of 1 in A287931; complement of A287379.
  • 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.
  • A287396 (program): a(n) = (7*(csc(2*Pi/7))^2)^n + (7*(csc(4*Pi/7))^2)^n + (7*(csc(8*Pi/7))^2)^n.
  • A287405 (program): a(n) = (7*(cot(1*Pi/7))^2)^n + (7*(cot(2*Pi/7))^2)^n + (7*(cot(4*Pi/7))^2)^n.
  • 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.
  • A287439 (program): a(n) = 2*a(n-2) + 2*a(n-3) for n >= 3, where a(0) = 2, a(2) = 4, a(3) = 7.
  • A287451 (program): Start with 0 and repeatedly substitute 0->012, 1->201, 2->120.
  • A287452 (program): Positions of 0 in A287451.
  • A287453 (program): Positions of 1 in A287451.
  • A287454 (program): Positions of 2 in A287451.
  • 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.
  • A287469 (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 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.
  • A287471 (program): Number of connected dominating sets in the n-crown graph.
  • A287474 (program): Number of dominating sets in the n-web graph.
  • A287479 (program): Expansion of (x + x^2)/(1 + 3*x^2).
  • A287485 (program): Number of independent vertex sets and vertex covers in the n-web graph.
  • A287498 (program): Number of maximal independent vertex sets (and minimal vertex covers) in the n-web graph.
  • A287523 (program): Fixed point starting with 1 of the morphism 0->01, 1->101.
  • A287525 (program): a(n) = a(n-1) + a(n-2) - a(n-3) +a(n-4) + a(n-5) for n >= 6, where a(0) = 2, a(1) = 4, a(2) = 7, a(3) = 12, a(4) = 19, a(5) = 31.
  • 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.
  • A287576 (program): Start with 0 and repeatedly substitute 0->0321, 1->3210, 2->2103, 3->1032.
  • A287577 (program): Positions of 0 in A287576.
  • A287578 (program): Positions of 1 in A287576.
  • A287579 (program): Positions of 2 in A287576.
  • A287580 (program): Positions of 3 in A287576.
  • A287594 (program): Number of independent vertex sets in the n-helm graph.
  • A287596 (program): a(n) is the denominator of r(n), where r(n) = r(n-1) + r(n-2)/(2*(n-1)) with r(0) = 0, r(1) = 1.
  • A287616 (program): Number of ways to write n as x(x+1)/2 + y(3y+1)/2 + z(5z+1)/2 with x,y,z nonnegative integers.
  • A287618 (program): Triangle read by rows: T(j,k) is the number of distinct edge segments in a j X k rectangular grid.
  • A287619 (program): Number of positive odd solutions to equation x^2 + 39y^2 = 8*(n + 5).
  • A287655 (program): Seven steps forward, six steps back.
  • 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.
  • A287663 (program): {0->1, 1->000}-transform of the infinite Fibonacci word A003849.
  • A287664 (program): Positions of 0’s in A287663; complement of A287665.
  • A287665 (program): Positions of 1’s in A287663; complement of A287664.
  • A287674 (program): {0->1, 1->001}-transform of the infinite Fibonacci word A003849.
  • A287675 (program): Positions of 0 in A287674; complement of A287676.
  • A287676 (program): Positions of 1 in A287674; complement of A287675.
  • A287699 (program): a(n) = (n!)^3 * [x^n] hypergeom([], [1, 1], x)^4.
  • A287702 (program): a(n) = (3!)^3 * [z^3] hypergeom([], [1,1], z)^n.
  • A287722 (program): {0->1, 1->010}-transform of the infinite Fibonacci word A003849.
  • A287723 (program): Positions of 0 in A287722; complement of A287724.
  • A287724 (program): Positions of 1 in A287722; complement of A287723.
  • A287725 (program): {0->1, 1->011}-transform of the infinite Fibonacci word A003849.
  • A287726 (program): Positions of 0 in A287725; complement of A287727.
  • A287727 (program): Positions of 1 in A287725; complement of A287726.
  • 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.
  • A287743 (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 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.
  • A287745 (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 342”, based on the 5-celled von Neumann neighborhood.
  • A287746 (program): First differences of A154293.
  • A287747 (program): Concatenation {n, n + 1,.., n + 9}.
  • A287765 (program): Period 4: repeat [1, 3, 5, 3].
  • A287769 (program): {0->1, 1->110}-transform of the infinite Fibonacci word A003849.
  • A287770 (program): Positions of 1 in A287769; complement of A276855.
  • A287772 (program): {0->1, 1->00}-transform of the infinite Fibonacci word A003849.
  • A287773 (program): {0->010, 1->101}-transform of the infinite Fibonacci word A003849.
  • A287774 (program): Positions of 0 in A287773; complement of A287777.
  • A287775 (program): Positions of 0 in A287772; complement of A050140 (conjectured and proved).
  • A287777 (program): Positions of 1 in A287773; complement of A287774.
  • A287790 (program): {0->001, 1->110}-transform of the infinite Fibonacci word A003849.
  • A287791 (program): Positions of 0 in A287790; complement of A287792.
  • A287792 (program): Positions of 1 in A287790; complement of A287791.
  • A287793 (program): Eight steps forward, seven steps back.
  • A287794 (program): Nine steps forward, eight steps back.
  • A287795 (program): {0->101, 1->010}-transform of the infinite Fibonacci word A003849.
  • A287796 (program): Ten steps forward, nine steps back
  • A287801 (program): {0->100, 1->001}-transform of the infinite Fibonacci word A003849.
  • A287802 (program): Positions of 0 in A287801; complement of A287803.
  • A287803 (program): Positions of 1 in A287801; complement of A287802.
  • A287804 (program): Number of quinary sequences of length n such that no two consecutive terms have distance 1.
  • A287805 (program): Number of quinary sequences of length n such that no two consecutive terms have distance 2.
  • A287806 (program): Number of senary sequences of length n such that no two consecutive terms have distance 1.
  • A287807 (program): Number of senary sequences of length n such that no two consecutive terms have distance 2.
  • A287809 (program): Number of septenary sequences of length n such that no two consecutive terms have distance 2.
  • A287810 (program): Number of septenary sequences of length n such that no two consecutive terms have distance 3.
  • A287811 (program): Number of septenary sequences of length n such that no two consecutive terms have distance 5.
  • A287812 (program): Number of octonary sequences of length n such that no two consecutive terms have distance 1.
  • A287813 (program): Number of octonary sequences of length n such that no two consecutive terms have distance 2.
  • A287814 (program): Number of octonary sequences of length n such that no two consecutive terms have distance 3.
  • A287815 (program): Number of octonary sequences of length n such that no two consecutive terms have distance 7.
  • A287818 (program): Number of nonary sequences of length n such that no two consecutive terms have distance 3.
  • A287819 (program): Number of nonary sequences of length n such that no two consecutive terms have distance 4.
  • A287826 (program): Number of sequences over the alphabet {0,1,…,9} such that no two consecutive terms have distance 2.
  • A287827 (program): Number of sequences over the alphabet {0,1,…,9} such that no two consecutive terms have distance 3.
  • A287828 (program): Number of sequences over the alphabet {0,1,…,9} such that no two consecutive terms have distance 4.
  • A287829 (program): Number of sequences over the alphabet {0,1,…,9} such that no two consecutive terms have distance 6.
  • A287830 (program): Number of sequences over the alphabet {0,1,…,9} such that no two consecutive terms have distance 7.
  • A287831 (program): Number of sequences over the alphabet {0,1,…,9} such that no two consecutive terms have distance 8.
  • A287834 (program): Number of words of length n over the alphabet {0,1,…,10} such that no two consecutive terms have distance 3.
  • A287835 (program): Number of words of length n over the alphabet {0,1,…,10} such that no two consecutive terms have distance 4.
  • A287836 (program): Number of words over the alphabet {0,1,…,10} such that no two consecutive terms have distance 5.
  • A287837 (program): Number of words over the alphabet {0,1,…,10} such that no two consecutive terms have distance 7.
  • A287838 (program): Number of words of length n over the alphabet {0,1,…,10} such that no two consecutive terms have distance 8.
  • A287839 (program): Number of words of length n over the alphabet {0,1,…,10} such that no two consecutive terms have distance 9.
  • 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.
  • A287865 (program): a(n) = gpf(2*a(n-1)+1), with a(1)=1, where gpf = A006530.
  • A287866 (program): n - A274933(n).
  • A287867 (program): Floor(n/2) - A287864(n).
  • A287869 (program): Wythoff array with one extra column, read by antidiagonals downwards.
  • A287870 (program): The extended Wythoff array (the Wythoff array with two extra columns) read by antidiagonals downwards.
  • A287893 (program): a(n) = floor(n*(n+2)/9).
  • A287894 (program): Sum of the digit sums of the n-th powers of the first n positive integers.
  • A287895 (program): Differences of A287894.
  • A287896 (program): a(n) = A002487(n)*A001511(n).
  • A287898 (program): Number of ways to go up and down n stairs, with fewer than 4 stairs at a time, stepping on each stair at least once.
  • A287919 (program): Square array T(0,n) = prime(n) and T(m+1,n) = T(m,n) + T(m,n+1), m >= 0, n >= 1, read by falling antidiagonals.
  • A287920 (program): Triangle T(n,k) read by rows: T(n,k) = floor(prime(n)/prime(k)), n >= k >= 1.
  • A287922 (program): a(n) = prime(1)^2 + prime(n)^2.
  • A287924 (program): Numbers k such that A287922(k) is a prime.
  • A287925 (program): a(n) = prime(1)^4 + prime(n)^4
  • A287933 (program): Coefficients in expansion of 1/E_8.
  • A287960 (program): Numbers that are the sum of two centered triangular numbers (A005448).
  • A287962 (program): Positive numbers that are the sum of the squares of distinct Fibonacci numbers (with a single type of 1).
  • A287964 (program): Coefficients in expansion of 1/E_14.
  • A287990 (program): Expansion of Jacobi theta constant (theta_2/2)^36.
  • A287991 (program): Expansion of Jacobi theta constant (theta_2/2)^48.
  • A287992 (program): Number of (undirected) paths in the prism graph Y_n.
  • A287996 (program): Position of second occurrence of first n terms in A287108.
  • A287997 (program): Expansion of 1/((1-x)(1-x^3)(1-x^5) … (1-x^13)).
  • A287998 (program): Expansion of 1/((1-x)(1-x^3)(1-x^5) … (1-x^15)).
  • A288000 (program): Expansion of 1/((1-x)(1-x^3)(1-x^5) … (1-x^17)).
  • A288001 (program): Expansion of 1/((1-x)(1-x^3)(1-x^5) … (1-x^19)).
  • A288002 (program): L-fusc, sequence l of the mutual diatomic recurrence pair: l(1)=0, r(1)=1, l(2n) = l(n), r(2n) = r(n), l(2n+1) = l(n)+r(n), r(2n+1) = l(n+1)+r(n+1), where r(n) = A288003(n).
  • A288003 (program): R-fusc, sequence r of the mutual diatomic recurrence pair: l(1)=0, r(1)=1, l(2n) = l(n), r(2n) = r(n), l(2n+1) = l(n)+r(n), r(2n+1) = l(n+1)+r(n+1), where l(n) = A288002(n).
  • A288007 (program): Expansion of 1/Product_{j>=1} Product_{i>=1} (1 + x^(i*j)).
  • A288021 (program): Prime p1 of consecutive primes p1, p2, where p2 - p1 = 4, and p1, p2 are in different decades.
  • A288022 (program): Prime p1 of consecutive primes p1, p2, where p2 - p1 = 6, and p1, p2 are in different decades.
  • 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.
  • A288029 (program): Number of minimal edge covers in the ladder graph P_2 X P_n.
  • 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.
  • A288098 (program): Convolution inverse of A006171.
  • A288119 (program): Lexicographically earliest sequence of distinct nonnegative terms such that, for any i and j >= 0, a(i+j) != a(i) + a(j).
  • A288122 (program): Number of partitions of n into prime Fibonacci numbers (A005478).
  • 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.
  • A288135 (program): Coefficients of 1/(Sum_{k>=0} (k+1)*r^k), where r = sqrt[7/3] and [ ] = floor.
  • 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.
  • A288165 (program): Expansion of x^4/((1-x^4)*(1-x^3)*(1-x^6)*(1-x^9)).
  • A288167 (program): Fixed point of the mapping 00->0010, 1->000, starting with 00.
  • A288168 (program): Positions of 0 in A288167; complement of A288169.
  • A288169 (program): Positions of 1 in A288167; complement of A288168.
  • A288170 (program): a(n) = 3*a(n-1) - a(n-2) - 4*a(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 .
  • A288176 (program): a(n) = 2*a(n-1) + 2*a(n-2) - 4*a(n-3) + a(n-4), where a(0) = 2, a(1) = 4, a(2) = 8, a(3) = 16.
  • A288194 (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 430”, based on the 5-celled von Neumann neighborhood.
  • 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) = 3*a(n-1) - a(n-2) - 3*a(n-3) + 2*a(n-4), where a(0) = 2, a(1) = 4, a(2) = 8, a(3) = 18.
  • A288209 (program): Numbers k such that prime(k) * prime(k+1) mod prime(k+2) is odd.
  • A288213 (program): Fixed point of the mapping 00->0010, 1->011, starting with 00.
  • A288214 (program): Positions of 0 in A288213; complement of A288215.
  • A288215 (program): Positions of 1 in A288213; complement of A288215.
  • A288219 (program): a(n) = a(n-1) + a(n-2) for n >= 3, where a(0) = 2, a(1) = 4, a(2) = 7.
  • A288229 (program): Coefficients of 1/(Sum_{k>=0} (k+1)*r^k), where r = Pi/2 and [ ] = floor.
  • A288230 (program): Coefficients of 1/(Sum_{k>=0} (k+1)*r^k), where r = Sqrt[5/2] and [ ] = floor.
  • A288232 (program): Coefficients in the expansion of 1/([r]-[2r]x+[3r]x^2-…); []=floor, r=3e/5.
  • A288233 (program): Coefficients in the expansion of 1/([r]-[2r]x+[3r]x^2-…); [ ]=floor, r=sqrt(8/3).
  • A288235 (program): Coefficients in the expansion of 1/([r]-[2r]x+[3r]x^2-…); [ ]=floor, r=sqrt(e).
  • A288236 (program): Coefficients in the expansion of 1/([r]-[2r]x+[3r]x^2-…); [ ]=floor, r=-4/5+sqrt(6).
  • A288246 (program): Numbers k such that 8*k^3 + 81 is prime.
  • A288260 (program): a(n) = 2*a(n-1) + 2*a(n-3) - 3*a(n-4), where a(0) = 2, a(1) = 4, a(2) = 8, a(3) = 16.
  • A288268 (program): Expansion of e.g.f.: exp(Sum_{k>=1} (k-1)*x^k/k).
  • A288269 (program): Expansion of e.g.f.: exp(Sum_{k>=1} (k-1)*k*x^k).
  • A288270 (program): E.g.f.: exp(Sum_{k>=1} (k-1)^2*x^k).
  • A288309 (program): a(n) = 2*a(n-1) + 2*a(n-2) - 3*a(n-3), where a(0) = 2, a(1) = 4, a(2) = 8.
  • A288311 (program): Number of steps, reduced mod n, to reach 1 in the Collatz 3x+1 problem, or -1 if 1 is never reached.
  • A288312 (program): Number of endofunctions on [2n] such that the image size equals n.
  • A288313 (program): Let b(k) denote A056240(k); the sequence lists numbers b(2n) where for all m > n, b(2m) > b(2n).
  • A288317 (program): a(n) = a(n-1) + 3*a(n-2) - 2*a(n-3) - a(n-4) for n >= 4, where a(0) = 2, a(1) = 4, a(2) = 7, a(3) = 12.
  • A288327 (program): Decuple factorial, 10-factorial, n!10, n!!!!!!!!!!.
  • A288341 (program): Expansion of 1 / ((1-x)^2*(1-x^2)*(1-x^3)*…*(1-x^6)).
  • A288342 (program): Expansion of 1 / ((1-x)^2*(1-x^2)*(1-x^3)*…*(1-x^7)).
  • A288343 (program): Expansion of 1 / ((1-x)^2*(1-x^2)*(1-x^3)*…*(1-x^8)).
  • A288344 (program): Expansion of 1 / ((1-x)^2*(1-x^2)*(1-x^3)*…*(1-x^9)).
  • A288349 (program): Partial sums of A059268.
  • A288373 (program): Positions of 0 in A288372; complement of A288316.
  • A288374 (program): Positions of 1 in A288372; complement of A288316.
  • A288375 (program): Fixed point of the mapping 00->1000, 10->1001, starting at 00.
  • A288380 (program): a(n) = 3*a(n-1) - 3*a(n-2) + 3*a(n-3) - 3*a(n-4) + a(n-5) for n >= 1, where a(0) = 2, a(1) = 4, a(2) = 7. a(3) = 11, a(4) = 20.
  • 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.
  • A288385 (program): Expansion of Product_{k>=1} (1 - x^k)^sigma(k).
  • A288389 (program): Expansion of Product_{k>=1} (1 - x^k)^(sigma_2(k)).
  • A288391 (program): Expansion of Product_{k>=1} 1/(1 - x^k)^(sigma_3(k)).
  • A288392 (program): Expansion of Product_{k>=1} (1 - x^k)^(sigma_3(k)).
  • A288414 (program): Expansion of Product_{k>=1} (1 + x^k)^(sigma_2(k)).
  • A288415 (program): Expansion of Product_{k>=1} (1 + x^k)^(sigma_3(k)).
  • A288417 (program): a(n) = Sum_{d|n} A000593(n/d).
  • A288418 (program): a(n) = Sum_{d|n} d^2*A000593(n/d).
  • A288419 (program): a(n) = Sum_{d|n} d^3*A000593(n/d).
  • A288420 (program): a(n) = Sum_{d|n} d^4*A000593(n/d).
  • A288421 (program): Expansion of Product_{k>=1} 1/(1 + x^k)^sigma(k).
  • A288422 (program): Expansion of Product_{k>=1} 1/(1 + x^k)^(sigma_2(k)).
  • A288423 (program): Expansion of Product_{k>=1} 1/(1 + x^k)^(sigma_3(k)).
  • A288425 (program): Minimal number of vertices that must be selected from an n X n square grid so that any square of 4 vertices, regardless of orientation, will include at least one selected vertex.
  • 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.
  • A288462 (program): Fixed point of the mapping 00->0101, 1->10, starting with 00.
  • A288463 (program): Positions of 0 in A288462; complement of A288464.
  • A288464 (program): Positions of 1 in A288462; complement of A288463.
  • 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).
  • A288470 (program): a(n) = Sum_{k=0..n} binomial(n,k)*binomial(2*n,2*k).
  • A288476 (program): a(n) = a(n-1) + 4*a(n-2) - 2*a(n-3), where a(0) = 2, a(1) = 4, a(2) = 8.
  • A288477 (program): a(n) = (2^49 - 2)*n/3 + 247371098957.
  • A288486 (program): Square rings obtained by adding four identical cuboids from A169938, a(n) = 4*n*(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.
  • A288523 (program): a(n) = a(n-1) + a(n-2) + a(n-3) - 2*a(n-4) for n >= 5, where a(0) = 2, a(1) = 4, a(2) = 5, a(3) = 8, a(4) = 11.
  • A288529 (program): a(n) is the minimum number of rows from the table described in A286000 that are required to represent the partitions of n into consecutive parts.
  • A288534 (program): a(n) = n*(2*n^2 + 3), n >= 1; a(0)=1.
  • A288566 (program): Partial sums of A087207.
  • A288570 (program): Partial sums of A019565.
  • A288571 (program): a(n) = Sum_{d|n} (-1)^(n/d+1)*tau(d), where tau = number of divisors (A000005).
  • A288572 (program): a(n) = smallest positive integer k such that (n^3)^k == 1 mod (n+1)^3.
  • A288575 (program): Partial sums of A104324.
  • A288581 (program): a(0)=1, a(1)=0; thereafter a(n) = 2^Fibonacci(n-1)*a(n-1) + a(n-2).
  • A288582 (program): A288581(n) written in base 2.
  • 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.
  • A288600 (program): Fixed point of the mapping 00->0101, 10->1001, starting with 00.
  • 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.
  • A288633 (program): Fixed point of the mapping 00->0110, 1->10, starting with 00.
  • A288634 (program): Positions of 0 in A288633; complement of A288635.
  • A288635 (program): Positions of 1 in A288633; complement of A288634.
  • A288636 (program): Height of power-tower factorization of n. Row lengths of A278028.
  • A288656 (program): a(n) = Sum_{k=1..n} Sum_{i=floor((k-1)/2)..k-1)} i * c(i), where c is the prime characteristic (A010051).
  • A288657 (program): Numbers whose squares have an odd number of digits.
  • A288658 (program): Numbers whose squares have an even number of digits.
  • A288659 (program): Numbers whose cubes have an odd number of digits.
  • A288660 (program): Numbers whose cubes have an even number of digits.
  • A288661 (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 493”, based on the 5-celled von Neumann neighborhood.
  • A288662 (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 493”, based on the 5-celled von Neumann neighborhood.
  • 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.
  • A288664 (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 493”, based on the 5-celled von Neumann neighborhood.
  • A288668 (program): a(n) = a(n-2) + 2*a(n-3) for n >= 3, where a(0) = 2, a(2) = 4, a(3) = 5.
  • A288687 (program): Number of n-digit biquanimous strings using digits {0,1,2,3}.
  • A288694 (program): Fixed point of the mapping 00->0110, 10->100, starting with 00.
  • A288695 (program): Positions of 0 in A288694; complement of A288696.
  • A288696 (program): Positions of 1 in A288694; complement of A288695.
  • 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.
  • A288698 (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 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.
  • A288703 (program): Number of (undirected) paths in the n-barbell graph.
  • A288707 (program): 0-limiting word of the mapping 00->1000, 10->00, starting with 00.
  • A288708 (program): Positions of 0 in A288707; complement of A288709.
  • 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.
  • A288712 (program): Positions of 0 in A288711; complement of A288713.
  • A288713 (program): Positions of 1 in A288711; complement of A288712.
  • A288720 (program): Detour index of the n-hypercube graph.
  • A288726 (program): a(n) = Sum_{i=floor((n-1)/2)..n-1} i * c(i), where c is the prime characteristic (A010051).
  • A288729 (program): 0-limiting word of the mapping 00->1000, 10->01, starting with 00.
  • A288730 (program): Positions of 0 in A288729; complement of A288731.
  • A288731 (program): Positions of 1 in A288729; complement of A288730.
  • A288732 (program): a(n) = a(n-1) + 2*a(n-4) - 2*a(n-5) for n >= 5, where a(0) = 2, a(1) = 4, a(2) = 6, a(3) = 8, a(4) = 10.
  • A288756 (program): Numerator of the volume of the “monic slice” of the d-th Chern-Vaaler star body.
  • A288757 (program): Denominator of the volume of the “monic slice” of the d-th Chern-Vaaler star body.
  • A288758 (program): Floor of the volume of the “monic slice” of the d-th Chern-Vaaler star body.
  • A288772 (program): a(n) is the minimum number of rows from the table described in A286000 that are required to represent the partitions of all positive integers <= n into consecutive parts.
  • 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.
  • A288777 (program): Triangle read by rows in which column k lists the positive multiples of the factorial of k, with 1 <= k <= n.
  • A288778 (program): Triangle read by rows (1<=k<=n): T(n,k) = (n-k+1)*k! - (k-1)!
  • A288780 (program): Zero together with the row sums of A288778.
  • A288785 (program): Number of blocks of size >= three in all set partitions of n.
  • A288786 (program): Number of blocks of size >= four in all set partitions of n.
  • A288787 (program): Number of blocks of size >= five in all set partitions of n.
  • A288788 (program): Number of blocks of size >= 6 in all set partitions of n.
  • A288789 (program): Number of blocks of size >= 7 in all set partitions of n.
  • A288790 (program): Number of blocks of size >= eight in all set partitions of n.
  • A288791 (program): Number of blocks of size >= nine in all set partitions of n.
  • A288792 (program): Number of blocks of size >= ten in all set partitions of n.
  • A288795 (program): a(n) = 4^n + 3^(n + 1) - 2.
  • A288805 (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 510”, based on the 5-celled von Neumann neighborhood.
  • A288806 (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 510”, based on the 5-celled von Neumann neighborhood.
  • A288807 (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 510”, based on the 5-celled von Neumann neighborhood.
  • A288808 (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 510”, based on the 5-celled von Neumann neighborhood.
  • A288810 (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 513”, based on the 5-celled von Neumann neighborhood.
  • A288812 (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 513”, based on the 5-celled von Neumann neighborhood.
  • A288816 (program): Coefficients in expansion of 1/E_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).
  • A288838 (program): a(n) = (1/4!)*3^(n+2)*(n+7)*(n+2)*(n+1)*(n).
  • A288841 (program): Number of matchings in the n-barbell graph.
  • A288842 (program): Triangle (sans apex) of coefficients of terms of the form (eM_1)^j*(eM_2)^k re construction of triangle A287768.
  • A288869 (program): Numerators of z-sequence for the Sheffer matrix T = P*Lah = A271703 = A007318*A271703 = (exp(t), t/(1-t)).
  • A288870 (program): Triangle T from array A(k,n) = (2*k+1)*2^n + 1, k >=0, n >= 0 read by downwards antidiagonals.
  • A288871 (program): Triangle t needed for the e.g.f.s of the column sequences of A288870 with leading zeros.
  • A288872 (program): Denominators for generalized Bernoulli numbers B5,j, for j=1..4, n >= 0.
  • A288873 (program): Numerators of scaled Bernoulli numbers 4^n*B(n), with B(n) = A027641(n)/A027642(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).
  • A288915 (program): Run lengths in A039704.
  • 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.
  • A288920 (program): Number of 6-cycles in the n X n king graph.
  • A288929 (program): Fixed point of the mapping 00->1000, 10->10011, starting with 00.
  • A288930 (program): Positions of 0 in A288929; complement of A288931.
  • A288931 (program): Positions of 1 in A288929; complement of A288930.
  • 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.
  • A288936 (program): Fixed point of the mapping 00->0010, 01->011, 10->011, starting with 00.
  • A288937 (program): Positions of 0 in A288936; complement of A288938.
  • A288938 (program): Positions of 1 in A288936; complement of A288937.
  • A288944 (program): Number of automorphisms in the n-halved cube graph.
  • A288950 (program): Number of relaxed compacted binary trees of right height at most one with empty initial and final sequence on level 0.
  • A288952 (program): Number of relaxed compacted binary trees of right height at most one with empty sequences between branch nodes on level 0.
  • A288953 (program): Number of relaxed compacted binary trees of right height at most one with minimal sequences between branch nodes except after the last branch node on level 0.
  • 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.
  • A288964 (program): Number of key comparisons to sort all n! permutations of n elements by quicksort.
  • A288966 (program): a(n) = the number of iterations the “HyperbolaTiles” algorithm takes to factorize n.
  • A288989 (program): Denominators of coefficients in expansion of E_14/E_12.
  • 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.
  • A289000 (program): Length of n-th iterate of the mapping 00->0010, 01->001, 10->001, starting with 00.
  • A289001 (program): Fixed point of the mapping 00->0010, 01->001, 10->010, starting with 00.
  • A289006 (program): Conversion to octal of the binary expansion given by the first n terms of the period-3 sequence A011655 (repeat 0, 1, 1).
  • A289011 (program): Fixed point of the mapping 00->0010, 01->001, 10->100, starting with 00.
  • A289012 (program): Positions of 0 in A289011; complement of A289013.
  • A289013 (program): Positions of 1 in A289011; complement of A289012.
  • A289031 (program): Number of perfect matchings on n+3 edges which represent RNA secondary folding structures characterized by the Reeder and Giegerich and the Lyngso and Pedersen families, but not the family characterized by Cao and Chen.
  • A289034 (program): Fixed point of the morphism 0->010, 1->10 starting with 1.
  • A289035 (program): Fixed point of the mapping 00->0010, 01->010, 10->010, starting with 00.
  • A289036 (program): Positions of 0 in A289035; complement of A289037.
  • A289037 (program): Positions of 1 in A289035; complement of A289036.
  • A289052 (program): a(1) = 1; a(n) = a(n-A006530(n-1)) + 1 for n > 1.
  • A289055 (program): Triangle read by rows: T(n,k) = (k+1)*A028815(n) for 0 <= k <= n.
  • A289060 (program): a(n) = 3*a(n-1) - 3*a(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.
  • A289070 (program): a(n) = c(2n-1), where c(n+2) = Sum_{k=0..n} binomial(n,k)c(k)c(n+1-k) with c(0)=0, c(1)=3.
  • A289071 (program): Fixed point of the mapping 00->0010, 01->010, 10->100, starting with 00.
  • A289072 (program): Positions of 0 in A289071; complement of A289073.
  • A289073 (program): Positions of 1 in A289071; complement of A289072.
  • A289096 (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 545”, based on the 5-celled von Neumann neighborhood.
  • A289097 (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 545”, based on the 5-celled von Neumann neighborhood.
  • 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.
  • A289099 (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 545”, based on the 5-celled von Neumann neighborhood.
  • A289107 (program): a(n) = 2*a(n-1) - a(n-3) for n >= 5, a(0) = 2, a(1) = 4, a(2) = 7, a(3) = 12, a(4) = 22.
  • A289108 (program): Triangle read by rows: T(n,k) = (k + 1)*prime(n) + k for n > 0, 0 <= k <= n, and with T(0,0) = 1.
  • A289111 (program): a(n) = (2^49 - 2)*n/3 + 444813635231.
  • A289115 (program): a(n) = 3*a(n-1) - 3*a(n-2) + 2*a(n-3) - 2*a(n-4) + a(n-5) for n >= 10, a(0) = 2, a(1) = 4, a(2) = 7, a(3) = 12, a(4) = 20, a(5) = 32, a(6) = 50, a(7) = 77, a(8) = 116, a(9) = 174.
  • A289120 (program): a(n) is the number of odd integers divisible by 7 in ]2*(n-1)^2, 2*n^2[.
  • A289121 (program): a(n) = (8 - 2*n + 11*n^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, 2*n^2[.
  • A289131 (program): a(n) = a(n-1) + 3*a(n-2) - 3*a(n-3) - 2*a(n-4) + 2*a(n-5) for n >= 6, a(0) = 2, a(1) = 4, a(2) = 7, a(3) = 11, a(4) = 18, a(5) = 28.
  • A289133 (program): a(n) is the number of odd integers divisible by 9 in ]2*(n-1)^2, 2*n^2[.
  • A289134 (program): a(n) = 21*n^2 - 33*n + 13.
  • A289139 (program): a(n) is the number of odd integers divisible by 7 in ]4*(n-1)^2, 4*n^2[.
  • A289142 (program): Numbers such that the sum of prime factors (taken with multiplicity) is divisible by 3.
  • A289144 (program): The difference between the second divisor of n and the penultimate divisor of n.
  • A289147 (program): Number of (n+1) X (n+1) binary matrices M with at most one 1 in each of the first n rows and each of the first n columns and M[n+1,n+1] = 0.
  • A289150 (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 597”, based on the 5-celled von Neumann neighborhood.
  • 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.
  • A289182 (program): Positions of odd semiprimes in A001358.
  • A289187 (program): The arithmetic function v_1(n,6).
  • A289189 (program): Upper bound for certain restricted sumsets.
  • A289190 (program): Numbers k such that k^2 with last digit deleted is a prime.
  • A289192 (program): A(n,k) = n! * Laguerre(n,-k); square array A(n,k), n>=0, k>=0, read by antidiagonals.
  • A289195 (program): a(n) is the number of odd integers divisible by 5 in ]4*(n-1)^2, 4*n^2[.
  • A289199 (program): a(n) is the number of odd integers divisible by 13 in the open interval (12*(n-1)^2, 12*n^2).
  • A289203 (program): Number of maximum independent vertex sets in the n X n knight graph.
  • A289207 (program): a(n) = max(0, n-2).
  • A289208 (program): Number of rooted essentially 4-connected toroidal triangulations with n vertices.
  • A289211 (program): a(n) = n! * Laguerre(n,-5).
  • A289212 (program): a(n) = n! * Laguerre(n,-6).
  • A289213 (program): a(n) = n! * Laguerre(n,-7).
  • A289214 (program): a(n) = n! * Laguerre(n,-8).
  • A289215 (program): a(n) = n! * Laguerre(n,-9).
  • A289216 (program): a(n) = n! * Laguerre(n,-10).
  • 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.
  • A289233 (program): Largest number of disjoint point triples that can be chosen from an n X n X n triangular point grid, each point triple forming a 2 X 2 X 2 triangle.
  • A289236 (program): Square array a(p,q) read by antidiagonals: a(p,q) = the number of line segments that constitute the trajectory of a billiard ball on a pool table with dimensions p X q, before the ball reaches a corner.
  • A289240 (program): Positions of 0 in A289239; complement of A289241.
  • A289241 (program): Positions of 1 in A289239; complement of A289240.
  • A289245 (program): Coefficients of 1/(Sum_{k>=0} (-1 + (k+1)*r^k), where r = (3 + sqrt(5))/2 = 1 + golden ratio and [ ] = floor.
  • A289246 (program): Coefficients in the expansion of 1/Sum_{k >= 0} ([r*(k + 1)] + [s*(k + 1)]) * (-x)^k, where [ ] = floor, r = (1+sqrt(5))/2, s = 1/r.
  • A289249 (program): Number of compositions of n if only the order of parts 1 and 2 matters.
  • A289250 (program): Primes p such that p + 4 is a semiprime.
  • A289254 (program): a(n) = 4^n - 3*n - 1.
  • A289255 (program): a(n) = 4^n - 2*n - 1.
  • A289260 (program): Coefficients in the expansion of 1/([r]-[2r]x+[3r]x^2-…); [ ]=floor, r=8/5.
  • A289265 (program): Decimal expansion of the real root of x^3 - x^2 - 2 = 0.
  • A289277 (program): a(n) = A005259(n) mod 2*n+1.
  • A289278 (program): a(n) = A005259(n) mod (2*n+1)^2.
  • A289279 (program): Number of odd composite numbers in ]2*(n-1)^2, 2*n^2[.
  • A289280 (program): a(n) = least integer k > n such that any prime factor of k is also a prime factor of n.
  • A289289 (program): a(n) = A005259(n) mod (n+1)^3.
  • A289296 (program): a(n) = (n - 1)*(2*floor(n/2) + 1).
  • A289306 (program): a(n) = Sum_{k >= 0}(-1)^k*binomial(n,5*k).
  • A289320 (program): a(n) = A289310(n)^2 + A289311(n)^2.
  • A289321 (program): a(n) = Sum_{k >= 0}(-1)^k*binomial(n,5*k+1).
  • A289328 (program): Coefficients in expansion of E_6^(5/12).
  • A289336 (program): a(n) = numerator of (sigma(n) / phi(n)).
  • A289341 (program): Partial sums of l-fusc A288002(n-1) + 1;
  • A289342 (program): Partial sums of r-fusc A288003(n-1) + 1;
  • A289345 (program): Coefficients in expansion of E_6^(7/12).
  • A289346 (program): Coefficients in expansion of E_6^(2/3).
  • A289347 (program): Coefficients in expansion of E_6^(3/4).
  • A289348 (program): Coefficients in expansion of E_6^(5/6).
  • A289349 (program): Coefficients in expansion of E_6^(11/12).
  • A289353 (program): Primes p such that (p,p+4) is a pair of cousin primes and p == 7 (mod 10).
  • 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.
  • A289381 (program): a(n) = numerator of Sum_{k=1..n} 1/(2*k-1)!!.
  • A289382 (program): a(n) = 2^n mod triangular(n).
  • A289383 (program): Total number of nonzero vectors over all subspaces of an n-dimensional vector space over the field with two elements.
  • A289387 (program): a(n) = Sum_{k>=0} (-1)^k*binomial(n, 5*k+2).
  • A289388 (program): a(n) = Sum_{k>=0} (-1)^k*binomial(n,5*k+3).
  • A289389 (program): a(n) = Sum_{k>=0} (-1)^k*binomial(n,5*k+4).
  • 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.
  • A289405 (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 566”, based on the 5-celled von Neumann neighborhood.
  • A289412 (program): a(n) = denominator of (sigma(n) / phi(n)).
  • A289413 (program): Primes p such that (p,p+4) is a pair of cousin primes and p == 3 (mod 10).
  • A289414 (program): a(n) = ((10-sqrt(10))^n + (10+sqrt(10))^n) / 2.
  • A289415 (program): a(n) = ((11-sqrt(11))^n + (11+sqrt(11))^n) / 2.
  • A289418 (program): Number of Dyck paths of semilength n and height exactly 5.
  • A289425 (program): a(n) = length of longest circuit code K(n,4).
  • A289426 (program): a(n) = length of longest circuit code K(n,5).
  • A289432 (program): Numbers b_n of Fibonacci-quilt legal decompositions of n.
  • A289433 (program): Numbers c_n of Fibonacci-quilt legal decompositions of n.
  • A289435 (program): The arithmetic function v_3(n,3).
  • A289436 (program): The arithmetic function v_1(n,4).
  • A289437 (program): The arithmetic function v_2(n,4).
  • A289438 (program): The arithmetic function v_4(n,4).
  • A289443 (program): a(0)=2, a(1)=6; thereafter a(n) = 3*n^2.
  • A289445 (program): a(n) = number of similarity classes of groups G with exactly n subgroups and such that G = G-tilde, where G-tilde is the unique subgroup of G left after factoring out the cyclic, central Sylow subgroups.
  • A289446 (program): Related to number of mesh patterns of length 2 that avoid the pattern 231.
  • A289447 (program): Related to number of mesh patterns of length 2 that avoid the pattern 231.
  • A289448 (program): Related to number of mesh patterns of length 2 that avoid the pattern 231.
  • A289449 (program): Related to number of mesh patterns of length 2 that avoid the pattern 231.
  • A289450 (program): Related to number of mesh patterns of length 2 that avoid the pattern 231.
  • A289451 (program): Related to number of mesh patterns of length 2 that avoid the pattern 231.
  • A289453 (program): Related to number of mesh patterns of length 2 that avoid the pattern 321.
  • A289460 (program): Number of units u in Z/nZ such that Phi(3,u) is a unit, where Phi is the cyclotomic polynomial.
  • A289472 (program): Number of gcds-sortable two-rooted graphs on n vertices.
  • A289488 (program): a(n) = denominator of Sum_{k=1..n} 1/(2*k-1)!!.
  • A289491 (program): a(n) = denominator of 1/(1 + 1/(1 + 2/(1 + … (1 + n)))).
  • A289493 (program): Number of primes in the interval [2n, 3n].
  • A289494 (program): Number of primes in the interval [3n, 4n].
  • A289495 (program): Number of primes in the interval [4n, 5n].
  • A289496 (program): Number of primes in the interval [5n, 6n].
  • A289497 (program): Number of primes in the interval [6n, 7n].
  • A289498 (program): Number of primes in the interval [7n, 8n].
  • A289499 (program): Number of primes in the interval [8n, 9n].
  • A289500 (program): Number of primes in the interval [9n, 10n].
  • A289504 (program): Decimal expansion of 2*(1+3^(3/2)/(2*Pi)).
  • A289506 (program): Write n as a product of primes p_{s_1}*p_{s_2}*p_{s_3}*… where p_i denotes the i-th prime; then a(n) = s_1^2 + s_2^2 + s_3^2 + …
  • A289508 (program): a(n) is the GCD of the indices j for which the j-th prime p_j divides n.
  • A289509 (program): Numbers k such that the gcd of the indices j for which the j-th prime prime(j) divides k is 1.
  • A289521 (program): Number of vertices in a planar Apollonian graph at iteration n.
  • A289553 (program): Numbers that are not the product of two distinct noncomposite numbers (A008578).
  • A289554 (program): Numbers that are the product of two distinct composite numbers (A002808).
  • A289555 (program): Numbers that are not the product of two distinct composite numbers (A002808).
  • A289557 (program): Expansion of Hypergeometric function F(1/12, 7/12; 1; 1728*x) in powers of x.
  • A289558 (program): Numbers with two distinct prime factors not divisible by a square larger than 4.
  • A289586 (program): Numbers k whose smallest multiple that is a Fibonacci number is Fibonacci(k).
  • A289588 (program): Related to number of mesh patterns of length 2 that avoid the pattern 321.
  • A289589 (program): Related to number of mesh patterns of length 2 that avoid the pattern 321.
  • A289590 (program): Related to number of mesh patterns of length 2 that avoid the pattern 321.
  • A289592 (program): Related to number of mesh patterns of length 2 that avoid the pattern 321.
  • A289593 (program): Related to number of mesh patterns of length 2 that avoid the pattern 321.
  • A289595 (program): Related to number of mesh patterns of length 2 that avoid the pattern 321.
  • A289596 (program): Related to number of mesh patterns of length 2 that avoid the pattern 321.
  • A289597 (program): Related to number of mesh patterns of length 2 that avoid the pattern 321.
  • A289598 (program): Related to number of mesh patterns of length 2 that avoid the pattern 321.
  • A289600 (program): Related to number of mesh patterns of length 2 that avoid the pattern 321.
  • A289601 (program): Related to number of mesh patterns of length 2 that avoid the pattern 321.
  • A289607 (program): Related to number of mesh patterns of length 2 that avoid the pattern 321.
  • A289609 (program): Related to number of mesh patterns of length 2 that avoid the pattern 321.
  • A289610 (program): Related to number of mesh patterns of length 2 that avoid the pattern 321.
  • A289611 (program): Related to number of mesh patterns of length 2 that avoid the pattern 321.
  • A289613 (program): Related to number of mesh patterns of length 2 that avoid the pattern 321.
  • A289614 (program): Related to number of mesh patterns of length 2 that avoid the pattern 321.
  • A289615 (program): A246604 (Catalan(n)-n) with initial terms 1,0,0,2 changed to 1,1,1,3.
  • A289616 (program): A246604 (Catalan(n)-n) with initial terms 1,0,0,2,10 changed to 1,1,1,2,11.
  • A289617 (program): a(n) = A005187(A001222(n)).
  • A289618 (program): a(n) = A289617(n) - A046645(n) = A005187(A001222(n)) - A046645(n).
  • A289619 (program): Positions of ones in A289618.
  • A289623 (program): a(n) = A055396(A048673(n)).
  • A289633 (program): a(n) = 6 * Sum_{d|n} d * A110163(d).
  • A289635 (program): Coefficients in expansion of -q*E’_2/E_2 where E_2 is the Eisenstein Series (A006352).
  • A289636 (program): Coefficients in expansion of -q*E’_4/E_4 where E_4 is the Eisenstein Series (A004009).
  • A289638 (program): Coefficients in expansion of -q*E’_8/E_8 where E_8 is the Eisenstein Series (A008410).
  • A289640 (program): Coefficients in expansion of -q*E’_14/E_14 where E_14 is the Eisenstein Series (A058550).
  • A289641 (program): a(n) = bigomega(n) - mu(n).
  • A289642 (program): Number of 2-digit numbers whose digits add up to n.
  • A289643 (program): n*(2*n+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.
  • A289654 (program): Related to number of mesh patterns of length 2 that avoid the pattern 321.
  • A289659 (program): “n-Value” of Big Collatz matrix for 2n+1.
  • A289666 (program): a(n) = number of weakly threshold graphs on n nodes.
  • A289679 (program): a(n) = Catalan(n-1)*Bell(n).
  • A289680 (program): a(n) = Catalan(n+1)*Bell(n).
  • A289682 (program): Catalan numbers read modulo 16.
  • A289683 (program): Mixing moments of the busy period of mean steady-state 1/2 in an M/M/1 waiting process.
  • A289684 (program): Mixing moments for the waiting time in a M/G/1 waiting queue.
  • A289692 (program): The number of partitions of [n] with exactly 2 blocks without peaks.
  • A289713 (program): The order of the semigroup of orientation-preserving partial transformations on n elements.
  • A289715 (program): The order of the semigroup of orientation-preserving full transformations on n elements.
  • A289718 (program): The order of the semigroup of orientation-preserving or reserving full transformations of n elements.
  • A289719 (program): a(n) = (n/2)*binomial(2*n, n) + 1.
  • A289720 (program): a(n) = 1 + n*binomial(2*n,n) - n^2*(n^2 - 2*n + 3)/2.
  • 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.
  • A289741 (program): a(n) = Kronecker symbol (-20/n).
  • 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.
  • A289762 (program): Triangular array T(m,k) = (m+1-k)^2 + k - 1 with m (row) >= 1 and k (column) >= 1, read by rows.
  • A289763 (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 597”, based on the 5-celled von Neumann neighborhood.
  • 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.
  • A289765 (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 597”, based on the 5-celled von Neumann neighborhood.
  • A289766 (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 598”, based on the 5-celled von Neumann neighborhood.
  • A289768 (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 598”, based on the 5-celled von Neumann neighborhood.
  • A289779 (program): p-INVERT of the squares, where p(S) = 1 - S - S^2.
  • A289780 (program): p-INVERT of the positive integers (A000027), where p(S) = 1 - S - S^2.
  • A289781 (program): p-INVERT of the positive Fibonacci numbers (A000045), where p(S) = 1 - S - S^2.
  • A289783 (program): p-INVERT of the (3^n), where p(S) = 1 - S - S^2.
  • A289784 (program): p-INVERT of the (4^n), where p(S) = 1 - S - S^2.
  • A289785 (program): p-INVERT of the (5^n), where p(S) = 1 - S - S^2.
  • A289786 (program): p-INVERT of the odd positive integers (A005408), where p(S) = 1 - S - S^2.
  • A289787 (program): p-INVERT of the even positive integers (A005843), where p(S) = 1 - S - S^2.
  • A289788 (program): a(n) = (1/2)*A289787(n).
  • A289789 (program): p-INVERT of A016777, where p(S) = 1 - S - S^2.
  • A289790 (program): p-INVERT of A016789, where p(S) = 1 - S - S^2.
  • A289792 (program): Number of 4-cycles in the n-tetrahedral graph.
  • A289795 (program): p-INVERT of (3n), where p(S) = 1 - S - S^2.
  • A289796 (program): a(n) = (1/3)*A289795(n).
  • A289797 (program): p-INVERT of the triangular numbers (A000217), where p(S) = 1 - S - S^2.
  • A289798 (program): p-INVERT of (-1 + 2^n), where p(S) = 1 - S - S^2.
  • A289801 (program): p-INVERT of the tetrahedral numbers (A000292), where p(S) = 1 - S - S^2.
  • A289803 (program): p-INVERT of the even bisection (A001906) of the Fibonacci numbers, where p(S) = 1 - S - S^2.
  • A289804 (program): p-INVERT of the even bisection (A001519) of the Fibonacci numbers, where p(S) = 1 - S - S^2.
  • A289806 (program): p-INVERT of (1,1,2,2,3,3,…) (A008619), where p(S) = 1 - S - S^2.
  • A289807 (program): p-INVERT of (1,2,2,3,3,4,4,…) (A080513), where p(S) = 1 - S - S^2.
  • A289812 (program): n for which a Factor Pair Latin Square of order n exists.
  • A289813 (program): A binary encoding of the ones in ternary representation of n (see Comments for precise definition).
  • A289814 (program): A binary encoding of the twos in ternary representation of n (see Comments for precise definition).
  • A289830 (program): a(n) satisfies the equation n/(n-1) + a(n)/n! = H(n), where H(n) is the n-th harmonic number.
  • A289831 (program): a(n) = A289813(n) + A289814(n).
  • A289833 (program): Fourier coefficients of -q*(Delta/q)’ where Delta is the normalized unique weight-twelve cusp form for the full modular group (the generating function of Ramanujan’s tau function).
  • A289834 (program): Number of perfect matchings on n edges which represent RNA secondary folding structures characterized by the Lyngso and Pedersen (L&P) family and the Cao and Chen (C&C) family.
  • A289835 (program): Number of units u in Z/(2n-1)Z such that Phi(4,u) is a unit, where Phi is the cyclotomic polynomial.
  • A289837 (program): Number of cliques in the n-tetrahedral graph.
  • A289839 (program): Primes of the form 8*n^2+8*n+31.
  • A289845 (program): p-INVERT of A079977, where p(S) = 1 - S - S^2.
  • A289846 (program): p-INVERT of (1,0,1,0,1,0,1,0,1,…) (A059841), where p(S) = 1 - S - S^2.
  • A289849 (program): Cardinality of the maximal set of ordered factor pairs such that a Quasi-Factor Pair Latin Square of order n exists.
  • A289864 (program): Number of cliques in the n-triangular honeycomb queen graph.
  • 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.
  • A289897 (program): Number of matchings in the n-triangular honeycomb rook graph.
  • A289898 (program): a(n) = floor((2^prime(n+1))/Sum_{k=0|n,2^prime(k)}).
  • A289900 (program): Number of maximal matchings in the n-triangular honeycomb rook graph.
  • A289909 (program): Numerator of r(n), where r(n) = 1/r(n-2) + r(n-1); r(1)=r(2)=1/2.
  • A289910 (program): The denominator of r(n), where r(n) = 1/r(n-2) + r(n-1); r(1)=r(2)=1/2.
  • A289914 (program): Coefficients of 1/(Sum_{k>=0} round((k+1)*r)(-x)^k), where r = 7/5.
  • A289915 (program): Decimal expansion of the limiting ratio of consecutive terms of A289914.
  • A289917 (program): Decimal expansion of the limiting ratio of consecutive terms of A289916.
  • A289918 (program): p-INVERT of (1,0,0,1,0,0,1,0,0,…), where p(S) = (1 - S^2).
  • A289919 (program): p-INVERT of (1,0,0,1,0,0,1,0,0,…), where p(S) = (1 - S)^2.
  • A289920 (program): p-INVERT of (1,0,0,1,0,0,1,0,0,…), where p(S) = 1 - S - S^2.
  • A289924 (program): p-INVERT of (n!), n >= 1 (A000142, shifted), where p(S) = 1 - S - S^2.
  • A289945 (program): a(n) = Sum_{k=1..n} k!^4.
  • A289946 (program): a(n) = Sum_{k=1..n} k!^6.
  • A289948 (program): a(n) = Sum_{k=0..n} k!^3.
  • A289949 (program): a(n) = Sum_{k=0..n} k!^4.
  • A289950 (program): Number of permutations of [n] having exactly two nontrivial cycles.
  • A289951 (program): Number of permutations of [n] having exactly three nontrivial cycles.
  • A289973 (program): p-INVERT of the lower Wythoff sequence (A000201), where p(S) = 1 - S.
  • A289974 (program): p-INVERT of the upper Wythoff sequence (A001950), where p(S) = 1 - S.
  • A289975 (program): p-INVERT of the Fibonacci numbers (A000045, including 0), where p(S) = 1 - S - S^2.
  • A289976 (program): p-INVERT of (0,0,1,2,3,5,8,…), the Fibonacci numbers preceded by two zeros, where p(S) = 1 - S - S^2.
  • A289999 (program): Sierpinski cuboctahedral numbers: a(n) = 16*4^n - 12*2^n + 9.
  • A290000 (program): a(n) = Product_{k=1..n-1} (3^k + 1).
  • A290011 (program): Number of ways to connect n nodes with n+1 edges to form a 2-edge-connected graph.
  • A290026 (program): Number of 3-cycles in the n-halved cube graph.
  • A290027 (program): Number of 4-cycles in the n-halved cube graph.
  • A290030 (program): Leading coefficients of numerators of Norlund’s B_{nu}^(n) polynomials (Nørlund, Tafel 5, p. 459).
  • A290031 (program): Number of 6-cycles in the n-hypercube graph.
  • A290055 (program): Expansion of x*(1 + 4*x + 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)*(3*n^3 + 5*n^2 - 6*n + 16).
  • A290070 (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 641”, based on the 5-celled von Neumann neighborhood.
  • A290071 (program): a(n) = (1/48)*n*(n+5)^2*(1*n^3 + 7*n^2 + 16*n + 28).
  • A290072 (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 641”, based on the 5-celled von Neumann neighborhood.
  • 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.
  • A290075 (program): Number of monomials in c(n) where c(1) = x, c(2) = y, c(n+2) = c(n+1) + c(n)^2.
  • A290077 (program): a(n) = A000010(A005940(1+n)).
  • A290079 (program): Characteristic function for A249721: a(n) = 1 if there are either no 1-digits at all in base-3 representation of n, or if there are exactly two 1’s next to each other, a(n) = 0 in any other cases.
  • A290080 (program): a(1) = 0; for n > 1, a(n) = sigma(bigomega(n)).
  • A290081 (program): a(n) = number of ways of writing n as the sum of two odd positive squares.
  • A290089 (program): Filter-sequence for the prime signature of cototient: a(1) = 0; for n > 1, a(n) = A101296(A051953(n)).
  • A290090 (program): a(n) is the number of proper divisors of n that are odious (A000069).
  • A290091 (program): Filter based on 1-digits of base-3 expansion: a(n) = A278222(A289813(n)).
  • A290092 (program): Filter based on 2-digits of base-3 expansion: a(n) = A278222(A289814(n)).
  • A290098 (program): Characteristic function for A003658 (fundamental discriminants of real quadratic fields).
  • A290099 (program): Multiplicative with a(2^e) = (-1)^e and a(p^e) = prevprime(p)^e for odd primes p.
  • A290106 (program): a(1) = 1; for n > 1, if n = Product prime(k)^e(k), then a(n) = Product (k)^(e(k)-1).
  • A290107 (program): a(1) = 1; for n > 1, a(n) = product of distinct exponents in the prime factorization of 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.
  • A290133 (program): Number of unique X-rays of n X n binary matrices with exactly n ones.
  • A290136 (program): Positive numbers that are not the sum of two nonprime squarefree numbers (A000469).
  • A290137 (program): Number of compositions (ordered partitions) of n into nonprime squarefree parts (A000469).
  • A290140 (program): The number of maximal subsemigroups of the Jones monoid on the set [1..n].
  • A290147 (program): Expansion of (1-sqrt(1-8*x-8*x^2))/(4*x).
  • 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.
  • A290158 (program): a(n) = n! * [x^n] exp(-n*x)/(1 + LambertW(-x)).
  • A290168 (program): If n is even then a(n) = n^2*(n+2)/8, otherwise a(n) = (n-1)*n*(n+1)/8.
  • A290186 (program): Expansion of (1+x)/ ((1+x)^3-7*x).
  • A290190 (program): Minimum sum of mutual Manhattan distances of n distinct grid points in a cubic lattice.
  • 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.
  • A290192 (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 705”, based on the 5-celled von Neumann neighborhood.
  • A290193 (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 705”, based on the 5-celled von Neumann neighborhood.
  • A290194 (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 705”, based on the 5-celled von Neumann neighborhood.
  • A290195 (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 705”, 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.
  • A290215 (program): a(n) = n! * [x^n] -exp(-n*x)*LambertW(-x).
  • A290219 (program): a(n) = n! * [x^n] exp(exp(x) - n*x - 1).
  • A290228 (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 771”, based on the 5-celled von Neumann neighborhood.
  • A290229 (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 771”, based on the 5-celled von Neumann neighborhood.
  • A290230 (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 771”, based on the 5-celled von Neumann neighborhood.
  • A290231 (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 771”, based on the 5-celled von Neumann neighborhood.
  • A290232 (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 773”, 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.
  • A290234 (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 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.
  • A290249 (program): Numbers that are the sum of distinct primorial numbers (A002110) (not including 1).
  • 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.
  • A290258 (program): Triangle read by rows: row n (>=2) contains in increasing order the integers for which the binary representation has length n and all runs of 1’s have even length.
  • A290259 (program): Triangle read by rows: row n (>=1) contains in increasing order the integers for which the binary representation has length n, the first run of 1’s has odd length, and all the other runs of 1’s have even length.
  • A290260 (program): a(n) = number of isolated 0’s in the binary representation of n.
  • A290268 (program): Number of terms in the fully expanded n-th derivative of x^(x^2).
  • A290273 (program): Number of minimal dominating sets in the n-pan graph.
  • A290288 (program): Sum of the differences of the larger and smaller parts in the partitions of 2n into two parts with the larger part prime.
  • A290294 (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 779”, based on the 5-celled von Neumann neighborhood.
  • A290295 (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 779”, based on the 5-celled von Neumann neighborhood.
  • A290296 (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 779”, based on the 5-celled von Neumann neighborhood.
  • A290297 (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 779”, based on the 5-celled von Neumann neighborhood.
  • A290310 (program): Irregular triangle read by rows. Row n gives the coefficients of the polynomial multiplying the exponential function in the e.g.f. of the (n+1)-th diagonal sequences of triangle A008459 (Pascal squares). T(n,k) for n >= 0 and k = 0..2*n.
  • A290312 (program): Third diagonal sequence of the Sheffer triangle A094816 (special Charlier).
  • A290313 (program): Fourth 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}.
  • A290342 (program): Number of ways to write n as x^2 + 2*y^2 + z*(z+1)/2, where x is a nonnegative integer, and y and z are positive integers.
  • A290344 (program): Denominators of the Kirchhoff (and Harary) index for the n-hypercube graph.
  • A290348 (program): Denominators of the Harary index for the n-halved cube graph.
  • A290360 (program): Number of 6-leaf rooted trees with n levels.
  • A290366 (program): Reduced denominators of the Kirchhoff index for the n-halved cube graph.
  • A290380 (program): Analog of Motzkin sums for Coxeter type D.
  • A290391 (program): Number of 5-cycles in the n-triangular honeycomb obtuse knight graph.
  • A290396 (program): a(n) = 3*2^n + 3*4^n + 6^(n+1) + 1.
  • A290398 (program): Number of tiles in distance d from a given heptagon in the truncated order-3 tiling of the heptagonal plane (a.k.a. the “hyperbolic soccerball”).
  • A290402 (program): Primes congruent to {7, 17} mod 24.
  • A290403 (program): Expansion of 256/(lambda(z)*(1 - lambda(z)))^2 in powers of nome q = exp(Pi*i*z) where lambda(z) is the elliptic modular function (A115977).
  • A290416 (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 790”, based on the 5-celled von Neumann neighborhood.
  • A290418 (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 790”, based on the 5-celled von Neumann neighborhood.
  • A290420 (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 798”, based on the 5-celled von Neumann neighborhood.
  • A290422 (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 798”, based on the 5-celled von Neumann neighborhood.
  • A290442 (program): a(n) = Catalan(n-1)*Motzkin(n).
  • A290443 (program): a(n) = Catalan(n)*Motzkin(n-1).
  • A290444 (program): a(n) = Bell(n)*Motzkin(n).
  • A290445 (program): a(n) = Bell(n-1)*Motzkin(n).
  • A290446 (program): a(n) = Bell(n)*Motzkin(n-1).
  • A290448 (program): Triangle read by rows: T(n,k) = (Eulerian(n+1,k)-binomial(n,k))/2, for 0 <= k <= n.
  • A290450 (program): Primes with property that the next prime has the same last digit.
  • A290452 (program): Triangle formed by reading the triangle of Eulerian numbers (A173018) mod 2.
  • A290453 (program): Triangle formed by reading the triangle of Eulerian numbers (A173018) mod 3.
  • A290454 (program): Triangle formed by reading the triangle of Eulerian numbers (A173018) mod 4.
  • A290455 (program): Triangle formed by reading the triangle of Eulerian numbers (A173018) mod 5.
  • A290456 (program): Triangle formed by reading the triangle of Eulerian numbers (A173018) mod 6.
  • A290457 (program): Triangle formed by reading the triangle of Eulerian numbers (A173018) mod 7.
  • A290458 (program): Triangle formed by reading the triangle of Eulerian numbers (A173018) mod 8.
  • A290459 (program): Triangle formed by reading the triangle of Eulerian numbers (A173018) mod 9.
  • A290460 (program): Triangle formed by reading the triangle of Eulerian numbers (A173018) mod 10.
  • A290478 (program): Triangle read by rows in which row n lists the sum of the divisors of each divisor of n.
  • A290479 (program): Product of nonprime squarefree divisors of n.
  • A290480 (program): Product of proper unitary divisors of n.
  • A290492 (program): Maximal number of binary vectors of length n such that the unions (or bitwise ORs) of any 3 distinct vectors are all distinct.
  • A290493 (program): Number of irredundant sets in the n-cycle graph.
  • A290494 (program): Number of irredundant sets in the n-wheel graph.
  • A290496 (program): First differences of A001751.
  • A290499 (program): Hypotenuses for which there exist exactly 8 distinct integer triangles.
  • A290500 (program): Hypotenuses for which there exist exactly 9 distinct integer triangles.
  • A290501 (program): Hypotenuses for which there exist exactly 11 distinct integer triangles.
  • A290502 (program): Hypotenuses for which there exist exactly 14 distinct integer triangles.
  • A290503 (program): Hypotenuses for which there exist exactly 15 distinct integer triangles.
  • A290504 (program): Hypotenuses for which there exist exactly 18 distinct integer triangles.
  • A290506 (program): Decimal expansion of 1 - 1/e^(1/2).
  • A290517 (program): Maximum value of the multinomial coefficients M(n;lambda), where lambda ranges over all partitions of n into distinct parts.
  • A290518 (program): Minimum value of Product_{i in lambda} i!, where lambda ranges over all partitions of n into distinct parts.
  • A290526 (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 833”, based on the 5-celled von Neumann neighborhood.
  • A290528 (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 833”, based on the 5-celled von Neumann neighborhood.
  • A290530 (program): Primes congruent to (11,17) mod 30.
  • A290532 (program): Irregular triangle read by rows in which row n lists the number of divisors of each divisor of n.
  • A290533 (program): Numerator of 2*n*(2*n+1) B_{2*n}, where B_n are the Bernoulli numbers.
  • A290534 (program): Denominator of 2*n*(2*n+1) B_{2*n}, where B_n are the Bernoulli numbers.
  • A290557 (program): One of the two successive approximations up to 7^n for the 7-adic integer sqrt(2). These are the numbers congruent to 3 mod 7 (except for the initial 0).
  • A290558 (program): Coefficients in 7-adic expansion of sqrt(2).
  • A290559 (program): One of the two successive approximations up to 7^n for the 7-adic integer sqrt(2). These are the numbers congruent to 4 mod 7 (except for the initial 0).
  • A290561 (program): a(n) = n + cos(n*Pi/2).
  • A290562 (program): a(n) = n - cos(n*Pi/2).
  • A290563 (program): Coefficients in 5-adic expansion of 3^(1/3).
  • A290564 (program): Number of primes between n^2 and 2*n^2.
  • A290566 (program): Coefficients in 5-adic expansion of 2^(1/3).
  • A290567 (program): The successive approximations up to 5^n for 5-adic integer 2^(1/3).
  • A290568 (program): The successive approximations up to 5^n for 5-adic integer 3^(1/3).
  • A290570 (program): Decimal expansion of Integral_{0..Pi/2} dtheta/(cos(theta)^3 + sin(theta)^3)^(2/3).
  • A290575 (program): Apéry-like numbers Sum_{k=0..n} (C(n,k) * C(2*k,n))^2.
  • A290583 (program): a(n) is the factor R(n) having prime factors < (2/3)*n^2 in A285388(n) = R(n)P(n).
  • A290584 (program): a(n) is the factor P(n) having prime factors between n^2 and 2*n^2 in A285388(n) = R(n)P(n) for n > 1, a(1)=1.
  • A290593 (program): Number of maximal independent vertex sets (and minimal vertex covers) in the n-antiprism graph.
  • A290596 (program): Triangle read by rows. A generalization of unsigned Lah numbers, called L[3,1].
  • A290598 (program): Triangle read by rows. A generalization of unsigned Lah numbers, called L[3,2].
  • A290599 (program): Number of numbers from 1 to A002808(n) - 1 that are non-coprime to A002808(n).
  • A290600 (program): Irregular triangle T(n, k) read by rows: positive numbers non-coprime to A002808(n) and smaller than A002808(n), sorted increasingly.
  • A290604 (program): a(0) = 2, a(1) = 2; for n > 1, a(n) = a(n-1) + 2*a(n-2) + 3.
  • A290605 (program): Square array A(n,k), n>=0, k>=0, read by antidiagonals, where column k is the expansion of 2/(1 + sqrt(1 - 4*k*x)).
  • A290608 (program): Number of maximal independent vertex sets (and minimal vertex covers) in the n-Moebius ladder graph.
  • A290612 (program): Number of maximal independent vertex sets (and minimal vertex covers) in the n-wheel graph.
  • A290616 (program): p-INVERT of (1,0,0,1,0,0,1,0,0,…), where p(S) = 1 - 2 S - S^2.
  • A290631 (program): a(n) = (n^2 + 1) * (2*n - 1).
  • A290641 (program): Multiplicative with a(p^e) = prime(p-1)^e.
  • A290648 (program): a(n) is the smallest number of faces of the triangular lattice required to enclose an area consisting of exactly n faces.
  • A290649 (program): The largest number z less than or equal to 3n+1 such that binomial(z,n) is odd.
  • A290650 (program): a(1) = 1. For n > 1, a(n) = a(n-1)/2 if a(n-1) is even, a(n) = a(n-1)*n otherwise.
  • 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.
  • A290661 (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 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.
  • A290680 (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 929”, 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.
  • A290690 (program): E.g.f.: exp(Sum_{k>=1} (k-1)^3*x^k).
  • A290697 (program): Size of largest triangle occurring in any of the possible dissections of an equilateral triangle into n equilateral triangles with integer sides, assuming gcd(s_1,s_2,…,s_n)=1, s_k being the side lengths.
  • 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.
  • A290720 (program): a(n) = 2*3^n + 4^n + 3*n.
  • 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.
  • A290753 (program): Semiprimes beginning with 1 such that deleting the 1 leaves a prime.
  • A290756 (program): Number of (non-null) connected induced subgraphs of the complete tripartite graph K_{n,n,n}.
  • 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).
  • A290770 (program): a(n) = Product_{k=1..n} k^(2*k).
  • A290775 (program): Number of 5-cycles in the n-triangular honeycomb bishop graph.
  • A290778 (program): Number of connected undirected unlabeled loopless multigraphs with 4 vertices and n edges.
  • A290781 (program): a(n) = 20*n + 15.
  • A290794 (program): Coefficients in 7-adic expansion of sqrt(-6).
  • A290795 (program): Coefficients in 7-adic expansion of sqrt(-6).
  • A290796 (program): Coefficients in 7-adic expansion of sqrt(-3).
  • A290797 (program): Coefficients in 7-adic expansion of sqrt(-3).
  • A290798 (program): Coefficients in 7-adic expansion of sqrt(-5).
  • A290799 (program): Coefficients in 7-adic expansion of sqrt(-5).
  • A290800 (program): One of the two successive approximations up to 7^n for the 7-adic integer sqrt(-6). These are the numbers congruent to 1 mod 7 (except for the initial 0).
  • A290802 (program): One of the two successive approximations up to 7^n for the 7-adic integer sqrt(-6). These are the numbers congruent to 6 mod 7 (except for the initial 0).
  • A290803 (program): One of the two successive approximations up to 7^n for the 7-adic integer sqrt(-3). These are the numbers congruent to 2 mod 7 (except for the initial 0).
  • A290804 (program): One of the two successive approximations up to 7^n for the 7-adic integer sqrt(-3). These are the numbers congruent to 5 mod 7 (except for the initial 0).
  • A290806 (program): One of the two successive approximations up to 7^n for the 7-adic integer sqrt(-5). These are the numbers congruent to 3 mod 7 (except for the initial 0).
  • A290807 (program): Number of partitions of n into Pell parts (A000129).
  • A290809 (program): One of the two successive approximations up to 7^n for the 7-adic integer sqrt(-5). These are the numbers congruent to 4 mod 7 (except for the initial 0).
  • A290813 (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 961”, based on the 5-celled von Neumann neighborhood.
  • A290819 (program): Number of rooted 4-regular one-face maps on genus g surface.
  • A290821 (program): Side length of largest equilateral triangle that can be made from n or fewer equilateral triangles with integer sides s_k, subject to gcd(s_1,s_2,…,s_n) = 1.
  • A290825 (program): Least base-3 digit of n.
  • A290827 (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 961”, based on the 5-celled von Neumann neighborhood.
  • A290828 (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 961”, based on the 5-celled von Neumann neighborhood.
  • 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.
  • A290834 (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 969”, based on the 5-celled von Neumann neighborhood.
  • A290835 (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 969”, based on the 5-celled von Neumann neighborhood.
  • A290836 (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 969”, based on the 5-celled von Neumann neighborhood.
  • A290837 (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 969”, based on the 5-celled von Neumann neighborhood.
  • A290840 (program): a(n) = n! * [x^n] exp(n*x)/(1 + LambertW(-x)).
  • A290845 (program): a(1) = 1; a(n) = Sum_{k=1..n} a(ceiling((n-1)/k)).
  • A290847 (program): Number of dominating sets in the n-triangular graph.
  • 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.
  • A290857 (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 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.
  • A290884 (program): Let S be the sequence generated by these rules: 0 is in S, and if z is in S, then z * (1+i) and (z-1) * (1+i) + 1 are in S (where i denotes the imaginary unit), and duplicates are deleted as they occur; a(n) = the real part of the n-th term of S.
  • A290885 (program): Let S be the sequence generated by these rules: 0 is in S, and if z is in S, then z * (1+i) and (z-1) * (1+i) + 1 are in S (where i denotes the imaginary unit), and duplicates are deleted as they occur; a(n) = the imaginary part of the n-th term of S.
  • A290890 (program): p-INVERT of the positive integers, where p(S) = 1 - S^2.
  • A290891 (program): p-INVERT of the positive integers, where p(S) = 1 - S^3.
  • A290892 (program): p-INVERT of the positive integers, where p(S) = 1 - S^4.
  • A290893 (program): p-INVERT of the positive integers, where p(S) = 1 - S^5.
  • A290894 (program): p-INVERT of the positive integers, where p(S) = 1 - S^6.
  • A290895 (program): p-INVERT of the positive integers, where p(S) = 1 - S^7.
  • A290896 (program): p-INVERT of the positive integers, where p(S) = 1 - S^8.
  • A290897 (program): p-INVERT of the positive integers, where p(S) = 1 - S - S^3.
  • A290900 (program): p-INVERT of the positive integers, where p(S) = 1 - S^2 - S^3.
  • 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.
  • A290904 (program): p-INVERT of the positive integers, where p(S) = 1 - 2*S^2.
  • A290905 (program): a(n) = (1/2)*A290904(n).
  • A290906 (program): p-INVERT of the positive integers, where p(S) = 1 - 3*S^2.
  • A290907 (program): a(n) = (1/3)*A290906(n).
  • A290908 (program): p-INVERT of the positive integers, where p(S) = 1 - 4*S^2.
  • A290909 (program): p-INVERT of the positive integers, where p(S) = 1 - 5*S^2.
  • A290910 (program): a(n) = (1/5)*A290909(n), n>= 0.
  • A290911 (program): p-INVERT of the positive integers, where p(S) = 1 - 6*S^2.
  • A290912 (program): a(n) = (1/6)*A290911(n).
  • A290913 (program): p-INVERT of the positive integers, where p(S) = 1 - 7*S^2.
  • A290914 (program): a(n) = (1/7)*A290913(n).
  • A290915 (program): p-INVERT of the positive integers, where p(S) = 1 - 8*S^2.
  • A290916 (program): a(n) = (1/8)*A290915(n).
  • A290917 (program): p-INVERT of the positive integers, where p(S) = (1 - S)^2.
  • A290918 (program): p-INVERT of the positive integers, where p(S) = (1 - S)^3.
  • A290919 (program): p-INVERT of the positive integers, where p(S) = (1 - S)^4.
  • A290920 (program): p-INVERT of the positive integers, where p(S) = (1 - S)^5.
  • A290921 (program): p-INVERT of the positive integers, where p(S) = (1 - S)^6.
  • A290922 (program): p-INVERT of the positive integers, where p(S) = 1 - S - 2*S^2.
  • A290923 (program): p-INVERT of the positive integers, where p(S) = 1 - 2*S - 2*S^2.
  • A290924 (program): a(n) = (1/2)*A290923(n).
  • A290925 (program): p-INVERT of the positive integers, where p(S) = 1 - 3*S - 2*S^2.
  • A290926 (program): p-INVERT of the positive integers, where p(S) = (1 - S^2)^2.
  • A290927 (program): p-INVERT of the positive integers, where p(S) = (1 - S^2)^3.
  • A290928 (program): p-INVERT of the positive integers, where p(S) = (1 - S^3)^2.
  • A290929 (program): p-INVERT of the positive integers, where p(S) = (1 - S)(1 - S^2).
  • A290930 (program): p-INVERT of the positive integers, where p(S) = (1 - S^2)(1 - 2*S^2).
  • A290939 (program): Number of 5-cycles in the n-triangular graph.
  • A290943 (program): Number of ways to write n as an ordered sum of 3 generalized pentagonal numbers (A001318).
  • 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.
  • A290968 (program): a(n) = a(n-1) + a(n-2) - a(n-3) + a(n-4) + a(n-5), with a(0)=a(1)=a(2)=1, a(3)=-1 and a(4)=1, a linear recurrence related to Fibonacci numbers.
  • A290974 (program): Alternating sum of row 2n of A022166.
  • A290980 (program): The arithmetic function v_3(n,6).
  • A290986 (program): Expansion of x^6/((1 - x)^2*(1 - 2*x + x^3 - x^4)).
  • A290987 (program): Expansion of (1 - 2*x + x^2 - x^4 + x^3 + x^5)/((1 - x)^2*(1 - 2*x + x^3 - x^4)).
  • A290988 (program): The arithmetic function v+-(n,3).
  • A290989 (program): Expansion of x^6*(1 + x^3)/(1 - 4*x + 5*x^2 - x^3 - 2*x^4 + x^6 + x^7 - 2*x^8 + x^9).
  • A290990 (program): p-INVERT of the nonnegative integers (A000027), where p(S) = 1 - S - S^2.
  • A290991 (program): p-INVERT of (0,0,1,2,3,4,5,…), the nonnegative integers A000027 preceded by one zero, where p(S) = 1 - S - S^2.
  • A290993 (program): p-INVERT of (1,1,1,1,1,…), where p(S) = 1 - S^6.
  • A290994 (program): p-INVERT of (1,1,1,1,1,…), where p(S) = 1 - S^7.
  • A290995 (program): p-INVERT of (1,1,1,1,1,…), where p(S) = 1 - S^8.
  • A290996 (program): p-INVERT of (1,1,1,1,1,…), where p(S) = 1 - S - S^4.
  • A290997 (program): p-INVERT of (1,1,1,1,1,…), where p(S) = 1 - S^3 - S^6.
  • A290998 (program): p-INVERT of (1,1,1,1,1,…), where p(S) = 1 - S^3 - S^4.
  • A290999 (program): p-INVERT of (1,1,1,1,1,…), where p(S) = 1 - 6*S^2.
  • A291000 (program): p-INVERT of (1,1,1,1,1,…), where p(S) = 1 - S - S^2 - S^3.
  • A291001 (program): p-INVERT of (1,1,1,1,1,…), where p(S) = 1 - 8*S^2.
  • A291002 (program): p-INVERT of (1,1,1,1,1,…), where p(S) = (1 - S)(1 - 2*S)(1 - 3*S).
  • A291004 (program): p-INVERT of (1,1,1,1,1,…), where p(S) = (1 - 3*S)^2.
  • A291005 (program): p-INVERT of (1,1,1,1,1,…), where p(S) = 1 - 2 S - 2 S^3.
  • A291006 (program): p-INVERT of (1,1,1,1,1,…), where p(S) = 1 - S - S^2 - S^3 - S^4.
  • A291007 (program): p-INVERT of (1,1,1,1,1,…), where p(S) = 1 - S - S^2 - S^3 - S^4 - S^5.
  • 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).
  • A291013 (program): p-INVERT of (1,1,1,1,1,…), where p(S) = (1 - S^2)^3.
  • A291014 (program): p-INVERT of (1,1,1,1,1,…), where p(S) = (1 - S^3)^2.
  • 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.
  • A291019 (program): p-INVERT of (1,1,1,1,1,…), where p(S) = 1 - S - S^2 - S^3 + S^4.
  • A291020 (program): p-INVERT of (1,1,1,1,1,…), where p(S) = 1 - S - S^2 - S^3 - S^4 + S^5.
  • A291021 (program): p-INVERT of (1,1,1,1,1,…), where p(S) = 1 - S - S^2 - S^3 + S^4 + S^5.
  • 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.
  • A291025 (program): p-INVERT of the positive integers, where p(S) = 1 - 3*S + S^2.
  • A291026 (program): p-INVERT of the positive integers, where p(S) = 1 - 4*S + S^2.
  • A291027 (program): p-INVERT of the positive integers, where p(S) = 1 - 5*S + S^2.
  • A291028 (program): p-INVERT of the positive integers, where p(S) = 1 - 6*S + S^2.
  • A291029 (program): p-INVERT of the positive integers, where p(S) = 1 - S - S^2 - S^3.
  • A291030 (program): p-INVERT of the positive integers, where p(S) = 1 - S - S^2 - S^3 - S^4.
  • 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.
  • A291035 (program): p-INVERT of (1,0,0,1,0,0,1,0,0,…), where p(S) = 1 - S - 2 S^2.
  • A291036 (program): p-INVERT of (1,0,0,1,0,0,1,0,0,…), where p(S) = 1 - 2 S - 2 S^2.
  • A291037 (program): a(n) = (1/2)*A291036(n).
  • A291038 (program): p-INVERT of (1,0,0,1,0,0,1,0,0,…), where p(S) = (1 - 2 S)^2.
  • A291039 (program): a(n) = (1/4)*A291038(n).
  • A291040 (program): The arithmetic function u(n,3,2).
  • A291050 (program): Decimal expansion of Pi^2 / 27.
  • A291064 (program): a(n) = 2^n*(n + 1) - 3*(n - 1).
  • A291066 (program): Number of edges in the n-Menger sponge graph.
  • A291076 (program): Number of prime 3-ary toroidal arrays with 2 rows and n columns.
  • A291080 (program): Irregular triangle read by rows: T(n,m) = number of lattice paths of type {A^H}_R terminating at point (n, m).
  • A291081 (program): Irregular triangle read by rows: T(n,m) = number of lattice paths of type A^H terminating at point (n, m).
  • A291082 (program): Irregular triangle read by rows: T(n,m) = number of lattice paths of type {A^Q}_R terminating at point (n, m).
  • A291083 (program): Irregular triangle read by rows: T(n,m) = number of lattice paths of type A^Q terminating at point (n, m).
  • A291088 (program): a(n) = A026520(2n).
  • A291089 (program): a(n) = A026520(2n+1).
  • A291090 (program): a(n) = A214938(2n).
  • A291091 (program): a(n) = A214938(2n+1).
  • A291092 (program): 1 followed by infinitely many 9’s.
  • A291096 (program): Number of rooted gluings of octahedra with n square vertices.
  • A291097 (program): a(n) = 2^n*(n/8 + 1) - n.
  • A291107 (program): Number of irredundant sets in the n-pan graph.
  • A291108 (program): Expansion of Sum_{k>=2} k^2*x^(2*k)/(1 - x^k).
  • A291109 (program): Numbers that are not the sum of the squarefree divisors of some natural number.
  • A291140 (program): Sum of the n-th powers of the first n primes.
  • A291142 (program): a(n) = (1/4)*A291024(n).
  • A291143 (program): p-INVERT of (1,1,1,1,1,…), where p(S) = (1 - S^3)^3.
  • A291154 (program): Red numbers on the roulette wheel.
  • A291165 (program): Disconnected Haar graph numbers.
  • A291166 (program): Connected Haar graph numbers.
  • A291171 (program): Black numbers on the roulette wheel.
  • A291181 (program): p-INVERT of the positive integers, where p(S) = 1 - 8*S.
  • A291182 (program): p-INVERT of the positive integers, where p(S) = 1 - 3*S + 2*S^2.
  • A291183 (program): p-INVERT of the positive integers, where p(S) = 1 - 4*S + 2*S^2.
  • A291184 (program): p-INVERT of the positive integers, where p(S) = 1 - 4*S + 3*S^2.
  • A291186 (program): a(n) = numerator of (pod(n) / tau(n)).
  • A291208 (program): Number of noncube divisors of n.
  • A291217 (program): p-INVERT of (0,1,0,1,0,1,…), where p(S) = 1 - S^3.
  • A291218 (program): p-INVERT of (0,1,0,1,0,1,…), where p(S) = 1 - S^5.
  • A291219 (program): p-INVERT of (0,1,0,1,0,1,…), where p(S) = 1 - S - S^3.
  • A291222 (program): p-INVERT of (0,1,0,1,0,1,…), where p(S) = 1 - S^2 - S^3.
  • A291224 (program): p-INVERT of (0,1,0,1,0,1,…), where p(S) = (1 - S)^4.
  • A291225 (program): p-INVERT of (0,1,0,1,0,1,…), where p(S) = (1 - S)^5.
  • A291226 (program): p-INVERT of (0,1,0,1,0,1,…), where p(S) = (1 - S)^6.
  • A291227 (program): p-INVERT of (0,1,0,1,0,1,…), where p(S) = 1 - S - 2*S^2.
  • A291228 (program): p-INVERT of (0,1,0,1,0,1,…), where p(S) = 1 - 2 S - 2 S^2.
  • A291229 (program): p-INVERT of (0,1,0,1,0,1,…), where p(S) = (1 - S)(1 - 2 S).
  • A291232 (program): p-INVERT of (0,1,0,1,0,1,…), where p(S) = (1 - 3 S)^2.
  • A291233 (program): p-INVERT of (0,1,0,1,0,1,…), where p(S) = 1 - S - S^2 - S^3.
  • A291234 (program): p-INVERT of (0,1,0,1,0,1,…), where p(S) = 1 - S - S^2 - S^3 - S^4.
  • A291236 (program): p-INVERT of (0,1,0,1,0,1,…), where p(S) = (1 - S)(1 - 3 S).
  • A291239 (program): p-INVERT of (0,1,0,1,0,1,…), where p(S) = (1 - S^2) (1 - 2 S).
  • A291241 (program): p-INVERT of (0,1,0,1,0,1,…), where p(S) = 1 - S - S^2 + S^3.
  • A291242 (program): p-INVERT of (0,1,0,1,0,1,…), where p(S) = 1 - 2 S - S^2 + S^3.
  • A291243 (program): p-INVERT of (0,1,0,1,0,1,…), where p(S) = 1 - 3 S + S^2.
  • A291244 (program): p-INVERT of (0,1,0,1,0,1,…), where p(S) = 1 - 4 S + S^2.
  • A291245 (program): p-INVERT of (0,1,0,1,0,1,…), where p(S) = 1 - 5 S + S^2.
  • A291246 (program): p-INVERT of (0,1,0,1,0,1,…), where p(S) = 1 - 6 S + S^2.
  • A291250 (program): p-INVERT of (0,1,0,1,0,1,…), where p(S) = 1 - S - 2 S^2 + 2 S^3.
  • A291257 (program): a(n) = (1/2)*A291228(n).
  • A291264 (program): p-INVERT of (0,1,0,1,0,1,…), where p(S) = (1 - 2 S)^2.
  • A291265 (program): a(n) = (1/3)*A291232(n).
  • A291267 (program): The arithmetic function v_2(n,3).
  • A291268 (program): The arithmetic function v_3(n,2).
  • A291270 (program): The arithmetic function v_4(n,3).
  • A291271 (program): The arithmetic function v_4(n,2).
  • A291285 (program): Expansion of G(x)^4 where G(x) = g.f. for A291096.
  • A291286 (program): a(0)=1, a(1)=2, thereafter a(n) = n*a(n-1)+(n-1)*(n-2)*a(n-2).
  • A291287 (program): a(0)=a(1)=1, a(2)=3, thereafter a(n) = n*a(n-1)+(n-1)*(n-2)*a(n-2).
  • A291288 (program): a(n) = binomial(n+3, 3)*(1 + binomial(n+2, 3)/4).
  • A291289 (program): The Padovan sequence A000931 doubled.
  • A291290 (program): a(n) = n/3 if n == 0 mod 3, floor((n+1)/2) if n == 1 mod 3, otherwise n-2.
  • A291292 (program): Necklace Catalan numbers.
  • A291294 (program): Total domination number of Fibonacci cube Gamma_n.
  • A291295 (program): Domination number of n-Fibonacci cube graph.
  • A291296 (program): 2-packing number of Fibonacci cube Gamma_n.
  • A291297 (program): Independent domination number of Fibonacci cube Gamma_n.
  • A291299 (program): Partial domination number of Fibonacci cube Gamma_n.
  • A291300 (program): Signed 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).
  • A291311 (program): Expansion of (1 - x^2)/(1 - 2 x + x^3 - x^4 + x^5 + x^6).
  • 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.
  • A291325 (program): The arithmetic function v+-(n,6).
  • A291326 (program): The arithmetic function v+-(n,7).
  • A291327 (program): The arithmetic function v+-(n,8).
  • A291328 (program): The arithmetic function v+-(n,9).
  • A291329 (program): The arithmetic function v+-(n,10).
  • A291330 (program): The arithmetic function v_4(n,1).
  • A291337 (program): p-INVERT of (1,1,1,1,1,…), where p(S) = 1 - 2 S - 2 S^3.
  • 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).
  • A291365 (program): Number of closed Sturmian words of length n.
  • 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).
  • A291369 (program): The arithmetic function u(n,3,7).
  • A291370 (program): The arithmetic function u(n,3,8).
  • A291379 (program): p-INVERT of (1,1,0,0,0,0,…), where p(S) = 1 - S^4.
  • A291380 (program): p-INVERT of (1,1,0,0,0,0,…), where p(S) = 1 - S^5.
  • A291381 (program): p-INVERT of (1,1,0,0,0,0,…), where p(S) = 1 - S^6.
  • A291382 (program): p-INVERT of (1,1,0,0,0,0,…), where p(S) = 1 - 2 S - S^2.
  • A291383 (program): p-INVERT of (1,1,0,0,0,0,…), where p(S) = 1 - 2 S - 2 S^2.
  • A291384 (program): a(n) = (1/2)*A291383(n).
  • A291385 (program): a(n) = (1/4)*A073388(n+1).
  • A291386 (program): a(n) = (1/3)*A099432(n+1).
  • A291387 (program): p-INVERT of (1,1,0,0,0,0,…), where p(S) = (1 - 4 S)^2.
  • A291388 (program): a(n) = (1/8)*A291387(n).
  • A291389 (program): p-INVERT of (1,1,0,0,0,0,…), where p(S) = (1 - 5 S)^2.
  • A291390 (program): a(n) = (1/5)*A291389(n).
  • A291391 (program): p-INVERT of (1,1,0,0,0,0,…), where p(S) = (1 - 6 S)^2.
  • A291392 (program): a(n) = (1/12)*A291391(n).
  • A291393 (program): p-INVERT of (1,1,0,0,0,0,…), where p(S) = (1 - S)(1 - 2 S).
  • A291394 (program): p-INVERT of (1,1,0,0,0,0,…), where p(S) = (1 - S)(1 - 3 S).
  • A291395 (program): p-INVERT of (1,1,0,0,0,0,…), where p(S) = (1 - 2 S)(1 - 3 S).
  • A291396 (program): p-INVERT of (1,1,0,0,0,0,…), where p(S) = (1 - S)(1 - 2 S)(1 - 3 S).
  • A291397 (program): p-INVERT of (1,1,0,0,0,0,…), where p(S) = 1 - S - S^3.
  • A291398 (program): p-INVERT of (1,1,0,0,0,0,…), where p(S) = 1 - S^2 - S^3.
  • A291408 (program): p-INVERT of (1,1,0,0,0,0,…), where p(S) = (1 - S)(1 - S^2).
  • A291409 (program): p-INVERT of (1,1,0,0,0,0,…), where p(S) = (1 - S^2)(1 - S)^2.
  • A291410 (program): p-INVERT of (1,1,0,0,0,0,…), where p(S) = 1 - S - S^2 - 2 S^3.
  • A291411 (program): p-INVERT of (1,1,0,0,0,0,…), where p(S) = 1 - 2 S - S^2 + S^3.
  • A291412 (program): p-INVERT of (1,1,0,0,0,0,…), where p(S) = 1 - S - 2 S^2 + S^3.
  • A291413 (program): p-INVERT of (1,1,0,0,0,0,…), where p(S) = 1 - 3 S + S^2 + S^3.
  • A291414 (program): p-INVERT of (1,1,0,0,0,0,…), where p(S) = 1 - 2 S + S^3.
  • A291415 (program): p-INVERT of (1,1,0,0,0,0,…), where p(S) = 1 - 3 S + S^2.
  • A291416 (program): p-INVERT of (1,1,0,0,0,0,…), where p(S) = 1 - 4 S + S^2.
  • A291417 (program): p-INVERT of (1,1,0,0,0,0,…), where p(S) = 1 - 4 S + 2 S^2.
  • A291423 (program): The arithmetic function u(n,4,2).
  • A291424 (program): The arithmetic function u(n,4,3).
  • A291425 (program): The arithmetic function u(n,4,4).
  • A291426 (program): The arithmetic function u(n,4,5).
  • A291427 (program): The arithmetic function u(n,4,6).
  • A291428 (program): The arithmetic function u(n,4,7).
  • A291429 (program): The arithmetic function u(n,4,8).
  • A291430 (program): The arithmetic function u(n,5,2).
  • A291454 (program): Number of half tones between successive pitches in a major scale.
  • A291456 (program): a(n) = (n!)^6 * Sum_{i=1..n} 1/i^6.
  • A291462 (program): a(n) = (1/2)*A291417(n)..
  • A291463 (program): a(n) is the product of n-th prime number with the distance to the next prime.
  • A291482 (program): Expansion of e.g.f. arcsin(x)*exp(x).
  • A291483 (program): Expansion of e.g.f. arcsinh(x)*exp(x).
  • 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).
  • A291502 (program): The arithmetic function uhat(n,1,8).
  • A291505 (program): a(n) = (n!)^7 * Sum_{i=1..n} 1/i^7.
  • A291506 (program): a(n) = (n!)^8 * Sum_{i=1..n} 1/i^8.
  • A291507 (program): a(n) = (n!)^9 * Sum_{i=1..n} 1/i^9.
  • A291508 (program): a(n) = (n!)^10 * Sum_{i=1..n} 1/i^10.
  • A291509 (program): The arithmetic function uhat(n,2,4).
  • A291510 (program): The arithmetic function uhat(n,2,5), negated.
  • A291511 (program): The arithmetic function uhat(n,2,6).
  • 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.
  • A291534 (program): Expansion of the series reversion of x/((1 + x)*(1 - x^2)).
  • A291537 (program): a(n) = 8^n - 3*2^n + 5.
  • A291542 (program): a(n) = prime(n)^3 - prime(n) * prime(n^2).
  • A291557 (program): a(n) = 23*2^n - 1.
  • A291561 (program): Diagonal in triangle A291560: a(n) = -A291560(n+1, n) for n>=1.
  • A291563 (program): Number of partitions of 2n into two prime parts or two nonprime parts.
  • A291564 (program): Number of partitions of 2n into two parts such that one part is prime and the other is nonprime.
  • 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).
  • A291585 (program): a(n) = ((2n-1)!!)^3 * Sum_{i=1..n} 1/(2*i-1)^3.
  • A291586 (program): a(n) = ((2n-1)!!)^4 * Sum_{i=1..n} 1/(2*i-1)^4.
  • A291587 (program): a(n) = ((2n-1)!!)^5 * Sum_{i=1..n} 1/(2*i-1)^5.
  • A291625 (program): Numbers k such that 0 is the smallest decimal digit of k^2.
  • A291626 (program): Numbers k such that 1 is the smallest decimal digit of k^2.
  • A291627 (program): Numbers k such that 2 is the smallest decimal digit of k^2.
  • A291628 (program): Numbers k such that 3 is the smallest decimal digit of k^2.
  • A291629 (program): Numbers k such that 4 is the smallest decimal digit of k^2.
  • A291632 (program): Column 1 of A122832.
  • A291639 (program): Numbers k such that 0 is the smallest decimal digit of k^3.
  • A291640 (program): Numbers k such that 1 is the smallest decimal digit of k^3.
  • A291641 (program): Numbers k such that 2 is the smallest decimal digit of k^3.
  • A291642 (program): Numbers k such that 3 is the smallest decimal digit of k^3.
  • A291655 (program): Expansion of Product_{k>=1} 1/(1-x^(k^2))^(k^2).
  • A291658 (program): a(n) is the sum of all integers from 5^n to 5^(n+1)-1.
  • A291660 (program): a(n) = 2*a(n-1) - a(n-2) + a(n-4) for n>3, a(0)=2, a(1)=3, a(2)=5, a(3)=7, a sequence related to Lucas numbers.
  • 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))).
  • A291668 (program): Numbers k such that 0 is the smallest decimal digit of k^4.
  • A291669 (program): Numbers k such that 1 is the smallest decimal digit of k^4.
  • A291670 (program): Numbers k such that 2 is the smallest decimal digit of k^4.
  • A291675 (program): a(n) = a(n-1) + 2*a(n-2) + 8*Fibonacci(n) + 2*Fibonacci(n-1); a(1) = 4, a(2) = 14.
  • A291681 (program): First differences of A067046.
  • A291696 (program): Expansion of Product_{k>=1} (1-x^(k^2))^(k^2).
  • A291699 (program): a(n) = n^n*(2*n)!/(n!*(n + 1)!).
  • A291703 (program): Number of connected dominating sets in the complete tripartite graph K_{n,n,n}.
  • A291706 (program): Number of connected dominating sets in the n-ladder graph.
  • A291708 (program): Number of partitions of n into two prime parts or two nonprime parts.
  • A291711 (program): The minimum number of coins needed to pay for n units in the currency system of values 1, 3, 8, 21, 55, 144, …, Fibonacci(2k), …
  • A291723 (program): p-INVERT of (1,0,1,0,0,0,0,…), where p(S) = 1 - S^3.
  • A291724 (program): p-INVERT of (1,0,1,0,0,0,0,…), where p(S) = 1 - S^5.
  • A291725 (program): p-INVERT of (1,0,1,0,0,0,0,…), where p(S) = (1 - S)^2.
  • A291726 (program): p-INVERT of (1,0,1,0,0,0,0,…), where p(S) = (1 - S)^3.
  • A291727 (program): p-INVERT of (1,0,1,0,0,0,0,…), where p(S) = (1 - S)^4.
  • A291728 (program): p-INVERT of (1,0,1,0,0,0,0,…), where p(S) = 1 - S - S^2.
  • A291729 (program): p-INVERT of (1,0,1,0,0,0,0,…), where p(S) = 1 - 2 S - S^2.
  • A291730 (program): p-INVERT of (1,0,1,0,0,0,0,…), where p(S) = 1 - 2 S - 2 S^2.
  • A291731 (program): a(n) = (1/2)*A291730(n)..
  • A291732 (program): p-INVERT of (1,0,1,0,0,0,0,…), where p(S) = (1 - 2 S)^2.
  • A291733 (program): a(n) = (1/4)*A291732(n).
  • A291734 (program): p-INVERT of (1,0,1,0,0,0,0,…), where p(S) = (1 - S)(1 - 2 S).
  • A291740 (program): p-INVERT of (1,0,1,0,0,0,0,…), where p(S) = (1 - S)(1 - S^2).
  • A291741 (program): p-INVERT of (1,0,1,0,0,0,0,…), where p(S) = (1 - S)(1 + S^2).
  • A291745 (program): Nonprimes of the form 3*k + 1.
  • A291746 (program): Nonprimes of the form 5*k + 1.
  • A291747 (program): Nonprimes of the form 7*k + 1.
  • A291759 (program): Binary encoding of 2-digits in ternary representation of A048673(n).
  • A291763 (program): Binary encoding of 2-digits in ternary representation of A245612(n).
  • A291770 (program): A binary encoding of the zeros in ternary representation of n.
  • A291771 (program): Filter based on runlengths of 0-digits in base-3 expansion of n: a(n) = A278222(A291770(n)).
  • 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).
  • A291782 (program): Let f_k(n) be the result of applying phi (the Euler totient function A000010) k times to n; a(n) = n*Product_{k=1..oo} f_k(n).
  • A291783 (program): Partial sums of A064415(k)^2.
  • A291784 (program): a(n) = (psi(n) + phi(n))/2.
  • A291822 (program): A diagonal of triangle A291820.
  • A291823 (program): Number of ordered rooted trees with n non-root nodes and all outdegrees <= eight.
  • A291824 (program): Number of ordered rooted trees with n non-root nodes and all outdegrees <= nine.
  • A291825 (program): Number of ordered rooted trees with n non-root nodes and all outdegrees <= ten.
  • A291832 (program): Numbers k such that k^6 is sum of two positive 7th powers.
  • A291856 (program): a(0) = -1, a(1) = 1, a(n) = a(n-1) + (n-1)*a(n-2) for n > 1.
  • A291876 (program): Consider the graph with one central vertex connected to three outer vertices (a star graph). Then, a(n) is the minimum number of moves required to transfer a stack of n pegs from one outer vertex to another outer vertex, moving pegs to adjacent vertices, following the rules of the Towers of Hanoi.
  • A291884 (program): Complement of A039691.
  • A291898 (program): (n+1)^2*a(n+1) = -(9*n^2 + 9*n + 3)*a(n) - 27*n^2*a(n-1), with a(0) = 1 and a(1) = -3.
  • A291900 (program): Sum of the divisors of 24*n - 1, divided by 24, minus n.
  • A291907 (program): Numbers such that the nonzero digits in the base 3 expansion consists of two 1s and one 2.
  • A291910 (program): Number of 4-cycles in the n X n rook complement graph.
  • A291911 (program): Number of 5-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.
  • A291933 (program): a(1)=2; a(n) is the sum of prime(n) and the last digit of previous term.
  • A291937 (program): G.f.: Sum_{n=-oo..+oo} n * x^n * (1 - x^n)^n.
  • 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.
  • A291946 (program): Powers of 11111.
  • A291962 (program): Decimal repunits written in base 2.
  • A291973 (program): a(n) = (3*n)! * [z^(3*n)] exp(exp(z)/3 + 2*exp(-z/2)*cos(z*sqrt(3)/2)/3 - 1).
  • A291978 (program): Triangle read by rows, T(n, k) = (-1)^(n-k)*n!*t^k for 0<=k<=n.
  • A291979 (program): a(n) = (-1)^n*n!*[x^n] exp(-x)/(1 + log(1+x)).
  • A291980 (program): Triangle read by rows, T(n, k) = n!*[t^k] ([x^n] exp(x*t)/(1 - log(1+x))) for 0<=k<=n.
  • A291981 (program): a(n) = n! * [x^n] exp(x)/(1 - log(1+x)).
  • A291983 (program): Expansion of 1/((1+x)*(1+x^2)*(1+x^3)).
  • A291984 (program): Expansion of 1/((1+x)*(1+x^2)*(1+x^3)*(1+x^4)).
  • A291986 (program): Expansion of 1/((1-x)*(1-2*x^2)*(1-3*x^3)).
  • 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).
  • A292029 (program): Wiener index of the n-folded cube graph.
  • A292030 (program): Table read by ascending antidiagonals: T(n,k) = A000045(k+1)*n + A000045(k).
  • A292034 (program): Linear divisibility sequence based on Salem number of order 4 (case t=6, see formula).
  • A292035 (program): Linear divisibility sequence based on Salem number of order 4 (case t=7, see formula).
  • 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.
  • A292055 (program): Wiener index of the n-Mycielski graph.
  • A292056 (program): Wiener index of the n-Keller 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.
  • A292062 (program): Wiener index of the n-transposition graph.
  • 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).
  • A292118 (program): G.f.: 1 + 2*Sum_{k >= 1} (-1)^k*q^A003159(k).
  • A292144 (program): a(n) is the greatest k < n such that k*n is square.
  • A292145 (program): A permutation of the natural numbers: A292144(A013929(n)).
  • A292164 (program): Expansion of Product_{k>=1} (1 - k^2*x^k).
  • A292185 (program): One-fifth of the rolling arithmetic mean of the fifth powers of the natural numbers taken five at a time.
  • A292202 (program): The n-th iteration of A062028 starting with n.
  • A292203 (program): Primes as they appear in A003188.
  • A292204 (program): Primes as they appear in A006068.
  • A292209 (program): Number of cliques in the n-Menger sponge graph.
  • A292219 (program): Triangle read by rows. A generalization of unsigned Lah numbers, called L[4,3].
  • A292220 (program): Expansion of the exponential generating function (1/2)*(1 + 4*x)*(1 - (1 + 4*x)^(-1/2))/x.
  • A292221 (program): Expansion of the exponential generating function (1/2)*(1 + 4*x)*(1 - (1 + 4*x)^(-3/2))/x.
  • A292227 (program): Numerators of partial sums of the series 1 + 2*Sum_{k >= 1} 1/(4*k^4 + 1).
  • A292228 (program): Denominators of partial sums of the series 1 + 2*Sum_{k >= 1} 1/(4*k^4 + 1).
  • 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).
  • A292252 (program): Number of trailing 2-digits in ternary representation of A048673(n).
  • A292257 (program): a(n) is the total number of 1’s in binary expansion of all proper divisors of n.
  • A292261 (program): The 3-adic valuation of A245612(n).
  • A292262 (program): Number of trailing 2-digits in ternary representation of A245612(n).
  • A292263 (program): a(n) = A292264(A243071(n)).
  • A292264 (program): a(n) = n - A292944(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^n*F(n)*F(n+1), where F = A000045.
  • A292278 (program): a(n) = (Fibonacci(3*n-1) + 1)/2 for n >= 1.
  • A292281 (program): Number of magic labelings of the prism graph I X C_6 having magic sum n.
  • A292282 (program): a(n) = 2*(n-1)^3*n^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.
  • A292292 (program): Number of vertices of type C at level n of the hyperbolic Pascal pyramid.
  • A292293 (program): Number of vertices of type D at level n of the hyperbolic Pascal pyramid.
  • A292294 (program): Number of vertices of type E 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} k*phi(k)*x^k/(1 - x^k), where phi() is the Euler totient function (A000010).
  • A292305 (program): a(n) = [x^n] Product_{k>=1} (1 + n^k*x^k).
  • A292309 (program): Numbers equal to the sum of three triangular numbers in arithmetic progression.
  • A292310 (program): Triangular numbers that are equidistant from two other triangular numbers.
  • A292312 (program): Expansion of Product_{k>=1} (1 - k^k*x^k).
  • A292313 (program): Numbers that are the sum of three squares in arithmetic progression.
  • A292314 (program): Numbers equal to the sum of three oblong numbers in arithmetic progression.
  • A292315 (program): Positive integers not divisible by any number of the form 2^n + 1 for n >= 0.
  • A292316 (program): Oblong numbers equidistant from two other oblong numbers.
  • A292323 (program): p-INVERT of (1,0,0,1,0,0,1,0,0,…), where p(S) = (1 - S)(1 + S^2).
  • A292324 (program): p-INVERT of (1,0,0,1,0,0,0,0,0,…), where p(S) = (1 - S)^2.
  • A292325 (program): p-INVERT of (1,0,0,0,1,0,0,0,0,0,…), where p(S) = (1 - S)^2.
  • A292327 (program): p-INVERT of the Fibonacci sequence (A000045), where p(S) = (1 - S)^2.
  • A292329 (program): p-INVERT of the Fibonacci sequence (A000045), where p(S) = 1 - S^3.
  • A292342 (program): Number of singletons in the integer partition having viabin number n.
  • 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).
  • A292347 (program): Möbius function of absolute order.
  • 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).
  • A292370 (program): A binary encoding of the zeros in base-4 representation of n.
  • A292371 (program): A binary encoding of 1-digits in the base-4 representation of n.
  • A292372 (program): A binary encoding of 2-digits in base-4 representation of n.
  • A292373 (program): A binary encoding of 3-digits in base-4 representation of n.
  • A292380 (program): Base-2 expansion of a(n) encodes the steps where multiples of 4 are encountered when map x -> A252463(x) is iterated down to 1, starting from x=n.
  • A292382 (program): Base-2 expansion of a(n) encodes the steps where numbers of the form 4k+2 are encountered when map x -> A252463(x) is iterated down to 1, starting from x=n.
  • A292386 (program): Expansion of Product_{k>=1} (1 - x^k)^(k*(k+1)/2).
  • A292387 (program): Expansion of Product_{k>=1} (1 - x^k)^(k*(k+1)*(k+2)/6).
  • A292399 (program): p-INVERT of (1,2,3,5,8,…) (distinct Fibonacci numbers), where p(S) = (1 - S)^2.
  • A292400 (program): p-INVERT of (1,2,2,2,2,2,2,…) (A040000), where p(S) = (1 - S)^2.
  • A292401 (program): p-INVERT of (1,0,2,0,2,0,2,0,2,0,…), where p(S) = (1 - S)^2.
  • A292402 (program): p-INVERT of (1,0,0,1,0,0,0,0,0,0,…), where p(S) = 1 - S^2.
  • A292403 (program): p-INVERT of (1,0,0,0,0,1,0,0,0,0,0,0,…), where p(S) = 1 - S^2.
  • A292404 (program): p-INVERT of (1,0,0,1,0,0,0,0,0,0,…), where p(S) = 1 - S^4.
  • A292410 (program): Difference between (2n+1)^2 and highest power of 2 less than or equal to (2n+1)^2.
  • A292411 (program): a(n) = ((prime(n) - 1)/2)^2 modulo prime(n).
  • A292412 (program): Numbers of the form Fibonacci(2*k-1) or Lucas(2*k-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.
  • A292425 (program): The smallest positive number of the form 3^n-2^a-2^b.
  • A292432 (program): Number of normal multisets that cannot be expressed as the multiset-union of a set of sets.
  • A292438 (program): Characteristic function of non-isolated nonprimes.
  • A292440 (program): Expansion of (1 - x + sqrt(1 - 2*x - 3*x^2))/2 in powers of x.
  • A292441 (program): Largest m such that m^2 divides A000984(n).
  • A292442 (program): a(n) = A292441(n)^2.
  • A292443 (program): a(n) = (5/32)*A000045(6*n)^2.
  • A292444 (program): Number of non-isomorphic finite multisets that cannot be expressed as the multiset-union of a set of sets.
  • A292460 (program): Expansion of (1 - x - x^2 - sqrt((1 - x - x^2)^2 - 4*x^3))/(2*x^3) in powers of x.
  • A292461 (program): Expansion of (1 - x - x^2 + sqrt((1 - x - x^2)^2 - 4*x^3))/2 in powers of x.
  • A292463 (program): Number of partitions of n with n kinds of 1.
  • A292465 (program): a(n) = n*F(n)*F(n+1), where F = A000045.
  • A292478 (program): p-INVERT of A010892, where p(S) = 1 - S - S^3.
  • A292479 (program): p-INVERT of the positive squares, where p(S) = 1 - S^2.
  • A292480 (program): p-INVERT of the odd positive integers, where p(S) = 1 - S^2.
  • A292482 (program): p-INVERT of the odd positive integers, where p(S) = (1 - S)^2.
  • A292483 (program): p-INVERT of the odd positive integers, where p(S) = (1 - S)^3.
  • A292484 (program): p-INVERT of the odd positive integers, where p(S) = 1 + S - S^2.
  • A292485 (program): p-INVERT of the odd positive integers, where p(S) = 1 - S - 2 S^2.
  • A292486 (program): p-INVERT of the odd positive integers, where p(S) = 1 - S - 3 S^2.
  • A292487 (program): p-INVERT of the odd positive integers, where p(S) = 1 - S - 4 S^2.
  • A292488 (program): p-INVERT of the odd positive integers, where p(S) = 1 - S - 5 S^2.
  • A292489 (program): p-INVERT of the odd positive integers, where p(S) = 1 - S - 6 S^2.
  • A292490 (program): p-INVERT of the odd positive integers, where p(S) = 1 - S - 7 S^2.
  • A292491 (program): p-INVERT of the odd positive integers, where p(S) = 1 + S - 2 S^2.
  • A292493 (program): p-INVERT of the odd positive integers, where p(S) = 1 + S - 3 S^2.
  • A292499 (program): a(n) equals the sum of the Gaussian binomial coefficients [n,k] at q=n for n>=0.
  • A292507 (program): Number of partitions of n with up to n distinct kinds of 1.
  • A292509 (program): Primes of the form n^2 + 23*n + 23.
  • 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.
  • A292518 (program): Expansion of Product_{k>=1} (1 - x^(k*(k+1)/2)).
  • A292520 (program): Expansion of Product_{k>=1} 1/(1 + x^(k^2)).
  • A292521 (program): a(n) = a(n-2) - 2a(n-3) + a(n-4) for n>3, with a(0)=2, a(1)=0, a(2)=1, a(3)=-1, a sequence related to Pellian numbers.
  • A292524 (program): Interpret the values of the Moebius function mu(k) for k = 1 to n as a balanced ternary number.
  • A292527 (program): Decimal expansion of the aliquot constant (negated).
  • 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.
  • A292535 (program): p-INVERT of the squares (A000290), where p(S) = 1 + S - 2 S^2.
  • A292536 (program): p-INVERT of the squares (A000290), where p(S) = 1 + S - 3 S^2.
  • 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.
  • A292551 (program): Expansion of x*(1 - 2*x + x^2 + 7*x^3 - x^4)/((1 - x)^4*(1 + x)^3).
  • A292552 (program): Nontotients of the form 10^k - 2.
  • A292560 (program): Expansion of Product_{k>=1} 1/(1 + x^(k^3)).
  • A292561 (program): Expansion of Product_{k>=1} (1 - mu(k)^2*x^k), where mu() is the Moebius function (A008683).
  • 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.
  • A292578 (program): Primes of the form 11*n^2 + 55*n + 43.
  • A292586 (program): a(n) = A002110(A001221(n)) = product of first omega(n) primes.
  • A292589 (program): a(n) = A046523(A003557(n)) = A003557(A046523(n)); the least representative of the prime signature of {n divided by largest squarefree divisor of n}.
  • 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).
  • A292602 (program): a(n) = floor(A005940(1+n)/4).
  • A292603 (program): Doudna-tree reduced modulo 4: a(n) = A005940(1+n) mod 4.
  • A292608 (program): a(n) = 2*n + 1 + valuation(n, 2) with valuation(n, 2) = A007814(n).
  • A292610 (program): Take 3 triangle numbers, skip 1 triangle number, take 4 triangle numbers, skip 2 triangle numbers, take 5 triangle numbers, skip 3 triangle numbers, …
  • 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, …
  • A292612 (program): a(n) = F(n)^2 + 4*(-1)^n = F(n+3)*F(n-3), where F = A000045.
  • A292613 (program): a(n) = [x^n] 1/(1-x)^n * Product_{k=1..n} 1/(1-x^k).
  • A292616 (program): a(n) = 3*a(n-2) - a(n-4) for n > 3, with a(0)=4, a(1)=3, a(2)=a(3)=6, a sequence related to bisections of Fibonacci numbers.
  • A292621 (program): a(n) = a(n-1) + a(floor(log(n))) with a(1) = 1, a(2) = 2.
  • A292629 (program): a(n) = n! * [x^n] exp(n*x)*BesselI(1,2*x).
  • A292630 (program): Square array A(n,k), n>=0, k>=0, read by antidiagonals, where column k is the expansion of e.g.f. exp(k*x)*(BesselI(0,2*x) + BesselI(1,2*x)).
  • A292631 (program): a(n) = n! * [x^n] exp(n*x)*(BesselI(0,2*x) + BesselI(1,2*x)).
  • A292632 (program): a(n) = n! * [x^n] exp((n+2)*x)*(BesselI(0,2*x) - BesselI(1,2*x)).
  • A292633 (program): a(n) = n! * [x^n] -exp(n*x)*LambertW(-x).
  • A292636 (program): Rank of (3-r)*n when all the numbers (3-r)*j and (3+r)*k, where r = sqrt(2), j>=1, k>=1, are jointly ranked.
  • A292637 (program): Rank of (3+r)*n when all the numbers (3-r)*j and (3+r)*k, where r = sqrt(2), j>=1, k>=1, are jointly ranked.
  • 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.
  • A292640 (program): Rank of (4-r)*n when all the numbers (4-r)*j and (4+r)*k, where r = sqrt(2), j>=1, k>=1, are jointly ranked.
  • A292641 (program): Rank of (4+r)*n when all the numbers (4-r)*j and (4+r)*k, where r = sqrt(2), j>=1, k>=1, are jointly ranked.
  • A292642 (program): Rank of (5-r)*n when all the numbers (5-r)*j and (5+r)*k, where r = sqrt(2), j>=1, k>=1, are jointly ranked.
  • A292643 (program): Rank of (5+r)*n when all the numbers (5-r)*j and (5+r)*k, where r = sqrt(2), j>=1, k>=1, are jointly ranked.
  • A292644 (program): Rank of (6-r)*n when all the numbers (6-r)*j and (6+r)*k, where r = sqrt(2), j>=1, k>=1, are jointly ranked.
  • A292645 (program): Rank of (6+r)*n when all the numbers (6-r)*j and (6+r)*k, where r = sqrt(2), j>=1, k>=1, are jointly ranked.
  • A292646 (program): Rank of e*n when all the numbers e*j and (e+1)*k, for j>=1, k>=1, are jointly ranked.
  • A292647 (program): Rank of (e+1)*n when all the numbers e*j and (e+1)*k, for j>=1, k>=1, are jointly ranked.
  • A292648 (program): Rank of Pi*n when all the numbers Pi*j and (Pi+1)*k, for j>=1, k>=1, are jointly ranked.
  • A292649 (program): Rank of (Pi+1)*n when all the numbers Pi*j and (Pi+1)*k, for j>=1, k>=1, are jointly ranked.
  • A292650 (program): Rank of n*e when all the numbers j*e and k*Pi, for j>=1, k>=1, are jointly ranked.
  • A292651 (program): Rank of n*Pi when all the numbers j*e and k*Pi, for j>=1, k>=1, are jointly ranked.
  • A292652 (program): Rank of n*cos(1) when all the numbers j*cos(1) and k*sin(1), for j>=1, k>=1, are jointly ranked.
  • A292653 (program): Rank of n*sin(1) when all the numbers j*cos(1) and k*sin(1), for j>=1, k>=1, are jointly ranked.
  • A292663 (program): Rank of n*(e-1) when all the numbers j*(e+1) and k*e, for j>=1, k>=1, are jointly ranked.
  • A292664 (program): Rank of n*e when all the numbers j*(e+1) and k*e, for j>=1, k>=1, are jointly ranked.
  • A292665 (program): Rank of n*(e-1) when all the numbers j*(e-1) and k*(e+1), for j>=1, k>=1, are jointly ranked.
  • A292666 (program): Rank of n*(e+1) when all the numbers j*(e-1) and k*(e+1), for j>=1, k>=1, are jointly ranked.
  • A292680 (program): Rule 6: 000, …, 111 -> 0, 1, 1, 0, 0, 0, 0, 0.
  • A292681 (program): Rule 6: (000, …, 111) -> (0, 1, 1, 0, 0, 0, 0, 0), without extending to the right of input bit 0.
  • A292682 (program): Rule 230: (000, …, 111) -> (0, 1, 1, 0, 0, 1, 1, 1), without extending to the right of input bit 0.
  • A292688 (program): Antidiagonals of the Sierpinski carpet (as binary numbers).
  • A292689 (program): Decimal values of the antidiagonals of the Sierpinski carpet considered as binary numbers.
  • A292696 (program): a(n) = L(n)^2 - 5*(-1)^n = L(n+1)*L(n-1), where L = A000032.
  • A292706 (program): a(n) = 1/2*((-1)^n*E(2*n-1,n) - E(2*n-1,0)), where E(n,x) is the Euler polynomial.
  • A292716 (program): a(n) = [x^n] 1/(1 - n*x - n*x^2/(1 - n*x - n*x^2/(1 - n*x - n*x^2/(1 - n*x - n*x^2/(1 - …))))), a continued fraction.
  • A292717 (program): Square array A(n,k), n >= 0, k >= 0, read by antidiagonals, where column k is the expansion of e.g.f. -log(1 - x)/(1 - x)^k.
  • A292744 (program): a(0) = 1; a(n) = Sum_{k=1..n} prime(k+1)*a(n-k).
  • A292751 (program): a(n) = n!*A063019(n).
  • A292752 (program): Dimensions of centralizer algebras of groups associated with Z_4-codes.
  • A292756 (program): E.g.f.: exp(x)*(tan(x)+sec(x))^2.
  • A292758 (program): E.g.f.: (tan x + sec x)^3.
  • A292759 (program): E.g.f.: exp(x)*(tan x + sec x)^3.
  • A292762 (program): Numbers of the form p^k or 2*p^k, where p is a prime == 3 mod 4 and k is odd.
  • A292763 (program): Numbers m such that sigma(m)+phi(m) == 2 mod 4.
  • A292768 (program): Partial sums of A065387.
  • A292769 (program): Partial sums of A051612.
  • A292770 (program): If sigma(n)+phi(n) is even then (sigma(n)+phi(n))/2 otherwise -1.
  • A292771 (program): If sigma(n)-phi(n) is even then (sigma(n)-phi(n))/2 otherwise -1.
  • A292777 (program): First differences of A100290.
  • A292778 (program): INVERT transform of double factorials.
  • A292779 (program): Interpret the values of the Moebius function mu(k) for k = n to 1 as a balanced ternary number.
  • A292782 (program): a(n) = E(2n,n)/2, where E(n,x) is the Euler polynomial.
  • A292783 (program): Square array A(n,k), n>=0, k>=0, read by antidiagonals, where column k is the expansion of e.g.f. 1/sqrt(1 - 2*k*x).
  • A292784 (program): a(n) = n! * [x^n] 1/sqrt(1 - 2*n*x).
  • A292786 (program): a(n) = psi(n) - phi(n).
  • A292787 (program): For n > 1, a(n) = least positive k, not a power of n, such that the digital sum of k in base n equals the digital sum of k^2 in base n.
  • A292797 (program): 2-Hankel transform of ((2*n - 1)!!, 2^n * n).
  • A292798 (program): a(n) = [x^n] 1/(1 - x - n*x/(1 - x - n*x/(1 - x - n*x/(1 - x - n*x/(1 - x - n*x/(1 - …)))))), a continued fraction.
  • A292816 (program): b(0) = 1, b(2*n-1) = 1/(1+1^2/(1+1^2/(1+2^2/(1+2^2/(…+(n-1)^2/(1+n^2)))))) and b(2*n) = 1/(1+1^2/(1+1^2/(1+2^2/(1+2^2/(…+n^2/(1+n^2)))))). a(n) is the numerator of b(n).
  • A292817 (program): b(0) = 1, b(2*n-1) = 1/(1+1^2/(1+1^2/(1+2^2/(1+2^2/(…+(n-1)^2/(1+n^2)))))) and b(2*n) = 1/(1+1^2/(1+1^2/(1+2^2/(1+2^2/(…+n^2/(1+n^2)))))). a(n) is the denominator of b(n).
  • A292830 (program): a(1) = 1, for n>=2, a(n) = B(2*n-1, n), where B(n, x) is the Bernoulli polynomial.
  • A292831 (program): Expansion of 1 - 2*x - 2*x^2/(1 - 3*x - 4*x^2/(1 - 4*x - 6*x^2/(1 - 5*x - 8*x^2/(1 - 6*x - 10*x^2/(…))))), a continued fraction.
  • A292854 (program): Expansion of 1/(1 + x + x/(1 + x^2 + x^2/(1 + x^3 + x^3/(1 + x^4 + x^4/(1 + …))))), a continued fraction.
  • A292878 (program): Number of ascending ballistic random walks of length n in 3-dimensions.
  • A292880 (program): Number of sequences of balls colored with at most n colors such that exactly three balls are of a color seen earlier in the sequence.
  • A292893 (program): Expansion of e.g.f. exp(x * (1 - exp(x))).
  • A292897 (program): a(n) = -Sum_{k=1..3}(-1)^(n-k)*hypergeom([k, k-n-3], [], 1).
  • A292913 (program): Square array A(n,k), n >= 0, k >= 0, read by antidiagonals, where column k is the expansion of e.g.f. exp(exp(k*x)-1).
  • A292914 (program): a(n) = n! * [x^n] exp(exp(n*x)-1).
  • A292916 (program): a(n) = n! * [x^n] exp(n*x)/(2 - exp(x)).
  • 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.
  • A292919 (program): Sum of n-th powers of odd divisors of n.
  • A292926 (program): a(n) = prime(n)*prime(n+1) + prime(n+2).
  • A292930 (program): Triangle read by rows: T(n,k) (n>=1, 3<=k<=n+2) is the number of k-sequences of balls colored with at most n colors such that exactly three balls are the same color as some other ball in the sequence
  • A292932 (program): Number of quasitrivial semigroups on an arbitrary n-element set.
  • A292933 (program): E.g.f.: x/(x+3-2*exp(x)).
  • A292934 (program): E.g.f.: x^2/(x+3-2*exp(x)).
  • A292935 (program): E.g.f.: exp(exp(-x) - 1).
  • 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.
  • A292943 (program): a(n) = A292944(A243071(n)); Base-2 expansion of a(n) encodes the steps where numbers of the form 6k+3 are encountered when map x -> A252463(x) is iterated down to 1, starting from x=n.
  • A292944 (program): a(n) = A292272(A004754(n)) - 2*A053644(n).
  • A292952 (program): E.g.f.: exp(-x * exp(x)).
  • A292966 (program): a(n) = (2*n)! * [x^(2*n)] exp(n*(cosh(x)-1)).
  • A292976 (program): a(n) = n! * [x^n] exp(n*x)*(sec(x) + tan(x)).
  • A292977 (program): Square array A(n,k), n >= 0, k >= 0, read by antidiagonals, where column k is the expansion of e.g.f. exp(-k*x)/(1 - x).
  • 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 2*x^5 - 9*x^4 + 13*x^3 - 11*x^2 + 5*x - 1; complement of A292987.
  • A292995 (program): Sum of digits of 3^n (A004166) divided by 9.
  • A292998 (program): Number of sequences of balls colored with at most n colors such that exactly three balls are the same color as some other ball in the sequence.
  • 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 2*x^2*(x+1) / (2*x^3-3*x+1).
  • A293007 (program): Expansion of 2*x^2 / (1-2*x-2*x^2).
  • A293008 (program): Primes of the form 2^q * 3^r * 7^s + 1.
  • A293013 (program): a(n) = n! * [x^n] exp(x/(1 - x)^n).
  • 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.
  • A293025 (program): E.g.f.: exp(exp(x) - Sum_{i=0..5} x^i/i!).
  • A293037 (program): E.g.f.: exp(1 + x - exp(x)).
  • A293038 (program): E.g.f.: exp(1 + x + x^2/2! - exp(x)).
  • A293042 (program): Number of even permutations p of {1,…,n} such that p(i) is not i or i+1.
  • A293043 (program): Number of odd permutations p of {1,…,n} such that p(i) is not i or i+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.
  • A293049 (program): E.g.f.: exp(x^3/(1 - x)).
  • A293050 (program): E.g.f.: exp(x^4/(1 - x)).
  • A293055 (program): a(n) = n! * [x^n] Product_{k>0} exp(binomial(n+k-1,n)*x^k).
  • A293057 (program): Solution of the complementary equation a(n) = a(n-1) + a(n-2) + b(n-2) + 2, where a(0) = 1, a(1) = 3, b(0) = 2, b(1) = 4.
  • A293058 (program): Solution of the complementary equation a(n) = a(n-1) + a(n-2) + b(n-2) + 3, where a(0) = 1, a(1) = 3, b(0) = 2, b(1) = 4.
  • 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).
  • A293068 (program): Sum of values of vertices of type D at level n of the hyperbolic Pascal pyramid PP_(4,5).
  • A293069 (program): Sum of values of vertices of type E at level n of the hyperbolic Pascal pyramid PP_(4,5).
  • A293070 (program): Sum of values of vertices at level n of the hyperbolic Pascal pyramid PP_(4,5).
  • A293073 (program): Number of matchings in the n-cocktail party graph.
  • A293076 (program): Solution of the complementary equation a(n) = a(n-1) + a(n-2) + b(n-2), where a(0) = 1, a(1) = 3, b(0) = 2, b(1) = 4.
  • 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).
  • A293116 (program): E.g.f.: exp(x/(x-1)).
  • A293117 (program): E.g.f.: exp(x^2/(x-1)).
  • A293118 (program): E.g.f.: exp(x^3/(x-1)).
  • A293120 (program): E.g.f.: exp(x^2/(1+x)).
  • A293121 (program): E.g.f.: exp(x^3/(1+x)).
  • A293122 (program): E.g.f.: exp(-x^2/(1+x)).
  • A293123 (program): E.g.f.: exp(-x^3/(1+x)).
  • A293125 (program): Expansion of e.g.f.: exp(-x/(1+x)).
  • A293126 (program): Number of matchings in the 2n-crossed prism graph.
  • A293137 (program): a(0) = 0, and a(n) = floor(2*sqrt(n)) - 1 for n >= 1.
  • A293140 (program): E.g.f.: Product_{m>0} (1-x^m).
  • A293143 (program): Number of vertex points in a Sierpinski Carpet grid subdivided into squares: a(n+1) = 8*a(n) - 8*(3^n+1), a(0) = 4.
  • A293145 (program): a(n) = n! * [x^n] exp(n*x/(1 - x)).
  • A293146 (program): a(n) = n! * [x^n] exp(x/(1 - n*x)).
  • A293156 (program): Number of linear chord diagrams with n+2 chords such that every chord has length at least n.
  • 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)).
  • A293170 (program): Number of distinct subsequences of the binary expansion of n.
  • A293171 (program): Triangle read by rows: T(n,k) = number of colored weighted Motzkin paths ending at (n,k).
  • A293172 (program): Triangle read by rows: T(n,k) = number of colored weighted Motzkin paths ending at (n,k).
  • A293191 (program): a(n) = n! * [x^n] exp(n*arcsin(x)).
  • A293192 (program): a(n) = n! * [x^n] exp(n*arctan(x)).
  • A293193 (program): a(n) = n! * [x^n] exp(n*arctanh(x)).
  • A293205 (program): Numbers n > 0 such that 2*n = (4*k-2)^m where k, m > 0.
  • A293206 (program): a(n) = prime(n) + prime(n+1) * prime(n+2).
  • A293227 (program): a(n) is the number of proper divisors of n that are squarefree.
  • A293228 (program): a(n) is the sum of proper divisors of n that are squarefree.
  • A293229 (program): a(0) = 0; and for n > 0, a(n) = a(n-1) + (A008966(4n+3) - A008966(4n+1)).
  • A293233 (program): a(1) = 1; and for n > 1, a(n) = mu(n) * a(floor(n/2)), where mu is the Moebius function A008683.
  • A293234 (program): a(n) is the number of proper divisors of n that are square.
  • A293235 (program): a(n) is the sum of proper divisors of n that are square.
  • A293239 (program): Number of terms in the fully expanded n-th derivative of x^x.
  • A293243 (program): Numbers that cannot be written as a product of distinct squarefree numbers.
  • A293262 (program): a(n) = floor(prime(n)*(e-2)).
  • A293270 (program): a(n) = n^n*binomial(2*n-1, n).
  • A293290 (program): a(n) = Product_{1 <= j <= k <= n} (k^2 + j^2).
  • A293292 (program): Numbers with last digit less than 5 (in base 10).
  • A293295 (program): a(n) = Sum_{k=1..n} (-1)^(n-k)*hypergeom([k, k-2-n], [], 1).
  • A293296 (program): a(n) = 2*n^2 - floor(n/4).
  • A293297 (program): Row sums of A293472.
  • A293300 (program): E.g.f.: Product_{m>0} 1/(1 + x^m).
  • A293313 (program): Greatest integer k such that k/2^n < (1+sqrt(5))/2 (the golden ratio).
  • A293314 (program): Least integer k such that k/2^n > (1+sqrt(5))/2 (the golden ratio).
  • A293315 (program): The integer k that minimizes |k/2^n - r|, where r = golden ratio.
  • A293316 (program): Solution of the complementary equation a(n) = a(n-1) + a(n-2) + b(n-2) + 1, where a(0) = 1, a(1) = 3, b(0) = 2, b(1) = 4.
  • A293317 (program): Solution of the complementary equation a(n) = a(n-1) + a(n-2) + b(n-2) - 1, where a(0) = 1, a(1) = 3, b(0) = 2, b(1) = 4.
  • A293319 (program): Greatest integer k such that k/2^n < tau^2, where tau = (1+sqrt(5))/2 = golden ratio.
  • A293320 (program): Least integer k such that k/2^n > tau^2, where tau = (1+sqrt(5))/2 = golden ratio.
  • A293321 (program): The integer k that minimizes |k/2^n - tau^2|, where tau = (1+sqrt(5))/2 = golden ratio.
  • 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.
  • A293324 (program): The integer k that minimizes |k/2^n - 1/tau|, where tau = (1+sqrt(5))/2 = golden ratio.
  • A293325 (program): Least integer k such that k/2^n > sqrt(3).
  • A293326 (program): The integer k that minimizes |k/2^n - sqrt(3))|.
  • A293327 (program): Least integer k such that k/2^n > sqrt(1/3).
  • A293328 (program): Least integer k such that k/2^n > sqrt(1/3).
  • A293329 (program): The integer k that minimizes |k/2^n - sqrt(1/3))|.
  • A293331 (program): Greatest integer k such that k/2^n < sqrt(5).
  • A293332 (program): Least integer k such that k/2^n > sqrt(5).
  • A293333 (program): The integer k that minimizes |k/2^n - sqrt(5))|.
  • A293334 (program): Greatest integer k such that k/2^n < sqrt(1/5).
  • A293335 (program): Least integer k such that k/2^n > sqrt(1/5).
  • A293336 (program): The integer k that minimizes |k/2^n - sqrt(1/5))|.
  • A293337 (program): Least integer k such that k/2^n > e.
  • A293338 (program): The integer k that minimizes |k/2^n - e|.
  • A293339 (program): Greatest integer k such that k/2^n < 1/e.
  • A293340 (program): Least integer k such that k/2^n > 1/e.
  • A293341 (program): The integer k that minimizes |k/2^n - 1/e|.
  • A293342 (program): Least integer k such that k/2^n > Pi.
  • A293349 (program): Solution of the complementary equation a(n) = a(n-1) + a(n-2) + b(n-2) + n, where a(0) = 1, a(1) = 3, b(0) = 2, b(1) = 4.
  • A293350 (program): Solution of the complementary equation a(n) = a(n-1) + a(n-2) + b(n-2) + 2n, where a(0) = 1, a(1) = 3, b(0) = 2, b(1) = 4.
  • A293351 (program): Solution of the complementary equation a(n) = a(n-1) + a(n-2) + b(n-2) + n -1, where a(0) = 1, a(1) = 3, b(0) = 2, b(1) = 4.
  • A293357 (program): Solution of the complementary equation a(n) = a(n-1) + a(n-2) + b(n-2) + n +1, where a(0) = 1, a(1) = 3, b(0) = 2, b(1) = 4.
  • A293358 (program): Solution of the complementary equation a(n) = a(n-1) + a(n-2) + b(n-1), where a(0) = 1, a(1) = 3, b(0) = 2, b(1) = 4.
  • A293359 (program): Greatest integer k such that k/2^n < e^2.
  • A293360 (program): Least integer k such that k/2^n > e^2.
  • A293361 (program): The integer k that minimizes |k/2^n - e^2|.
  • A293362 (program): Greatest integer k such that k/2^n < log 2.
  • A293363 (program): Least integer k such that k/2^n > log 2.
  • A293364 (program): The integer k that minimizes |k/2^n - log 2|.
  • A293378 (program): Expansion of (eta(q^6)/(eta(q)eta(q^2)eta(q^3))^2 in powers of q.
  • A293387 (program): Expansion of (eta(q^2)^2/(eta(q)eta(q^3)))^2 in powers of q.
  • 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).
  • A293406 (program): Solution of the complementary equation a(n) = a(n-1) + a(n-2) + b(n-1) + 1, where a(0) = 1, a(1) = 3, b(0) = 2, b(1) = 4.
  • 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).
  • A293409 (program): Decimal expansion of the minimum ripple factor for a fifth-order, reflectionless, Chebyshev filter.
  • 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.
  • A293412 (program): Greatest integer k such that k/n^2 < e.
  • A293413 (program): Least integer k such that k/n^2 > e.
  • A293414 (program): The integer k that minimizes |k/n^2 - e|.
  • A293418 (program): a(n) is the greatest integer k such that k/Fibonacci(n) < sqrt(2).
  • A293419 (program): a(n) is the least integer k such that k/Fibonacci(n) > sqrt(2).
  • A293420 (program): a(n) is the integer k that minimizes |k/Fibonacci(n) - sqrt(2)|.
  • A293426 (program): Expansion of Product_{k>0} ((1 - q^(3*k))^3*(1 - q^(6*k))^3)/((1 - q^k)^5*(1 - q^(2*k))^3).
  • A293429 (program): a(0) = 0; and for n > 0, a(n) = a(n-1) + (A008966(4n-1) - A008966(4n+1)).
  • A293430 (program): Persistently squarefree numbers for base-2 shifting: Numbers n such that all terms in finite set [n, floor(n/2), floor(n/4), floor(n/8), …, 1] are squarefree.
  • A293431 (program): a(n) is the number of Jacobsthal numbers dividing n.
  • A293432 (program): Sum of Jacobsthal numbers that divide n.
  • A293433 (program): a(n) is the number of the proper divisors of n that are Jacobsthal numbers (A001045).
  • A293434 (program): a(n) is the sum of the proper divisors of n that are Jacobsthal numbers (A001045).
  • A293435 (program): a(n) is the number of the proper divisors of n that are Fibonacci numbers (A000045).
  • A293436 (program): a(n) is the sum of the proper divisors of n that are Fibonacci numbers (A000045).
  • A293447 (program): Fully additive with a(p^e) = e * A000225(PrimePi(p)), where PrimePi(n) = A000720(n) and A000225(n) = (2^n)-1.
  • A293449 (program): Characteristic function for A056166, numbers that have no nonprime exponents present in their prime factorization n = p_1^e_1 * … * p_k^e_k.
  • A293451 (program): Number of proper divisors of form 4k+1.
  • 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.
  • A293464 (program): a(n) = Sum_{k=0..n} (-1)^k * 2^k * p(k), where p(k) is the partition function A000041.
  • A293466 (program): a(n) = Sum_{k=0..n} 2^k * q(k), where q(k) is A000009 (partitions into distinct parts).
  • A293468 (program): a(n) = Sum_{k=0..n} k!*binomial(2*n-k, n).
  • A293469 (program): a(n) = Sum_{k=0..n} (2*k-1)!!*binomial(2*n-k, n).
  • A293470 (program): a(n) = [x^n] (1/(1 - x/(1 - 2*x/(1 - 3*x/(1 - 4*x/(1 - 5*x/(1 - 6*x/(1 - …))))))))^n, a continued fraction.
  • A293472 (program): Triangle read by rows, coefficients of polynomials in t = log(x) of the n-th derivative of x^x, evaluated at x = 1. T(n, k) with n >= 0 and 0 <= k <= n.
  • A293475 (program): a(n) = (3*n + 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).
  • A293482 (program): The number of 5th powers in the multiplicative group modulo n.
  • A293483 (program): The number of 6th powers in the multiplicative group modulo n.
  • A293484 (program): The number of 7th powers in the multiplicative group modulo n.
  • A293485 (program): The number of 8th powers in the multiplicative group modulo n.
  • A293487 (program): E.g.f.: Product_{m>0} (1 + x^(2*m-1)).
  • A293490 (program): a(n) = Sum_{k=0..n} binomial(2*k, k)*binomial(2*n-k, n).
  • A293491 (program): a(n) = n! * [x^n] exp((n+2)*x)*BesselI(0,2*x).
  • A293493 (program): E.g.f.: exp(x/(1 - x^3)).
  • A293494 (program): E.g.f.: exp(x^2/(1 - x^3)).
  • A293497 (program): Triangular array read by rows: row n >= 1 is the list of integers from 0 to 2n-1.
  • A293499 (program): Number of unlabeled hereditary semiorders on n points.
  • 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|.
  • A293506 (program): Decimal expansion of real root of x^5 - x^4 - x^2 - 1.
  • A293507 (program): E.g.f.: exp(x/(1 - x^4)).
  • A293508 (program): Decimal expansion of the positive real root of x^6 - x^5 - x^4 + x^2 - 1.
  • A293509 (program): Decimal expansion of real root of x^5 - x^3 - x^2 - x - 1.
  • A293511 (program): Numbers that can be written as a product of distinct squarefree numbers in exactly one way.
  • A293513 (program): Number of proper divisors of form 4k+3.
  • A293516 (program): a(n) = phi(n) - 2*phi(phi(n)), where phi = Euler totient function, A000010.
  • A293526 (program): E.g.f.: exp(x^3/(1 - x^4)).
  • A293532 (program): E.g.f.: exp(x/(x^2 - 1)).
  • A293533 (program): E.g.f.: 1/Product_{m > 0, m mod 3 > 0} exp(x^m).
  • 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|.
  • A293548 (program): Expansion of Product_{k>=2} 1/(1 - x^k)^omega(k), where omega(k) is the number of distinct primes dividing k (A001221).
  • A293549 (program): Expansion of Product_{k>=2} 1/(1 - x^k)^bigomega(k), where bigomega(k) is the number of prime divisors of k counted with multiplicity (A001222).
  • A293550 (program): a(n) = Sum_{k=0..n} k^3*binomial(2*n-k,n).
  • 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|.
  • A293557 (program): Decimal expansion of real root of x^7 - x^6 - x^5 + x^2 - 1.
  • A293560 (program): Decimal expansion of real root of 1 - x - x^3 - x^5.
  • A293561 (program): Column 3 of A142249.
  • A293565 (program): E.g.f.: Product_{m>=0} exp(-x^(3*m+1)).
  • A293566 (program): E.g.f.: Product_{m>=0} exp(-x^(4*m+1)).
  • A293567 (program): E.g.f.: exp(x^2/(x^3 - 1)).
  • A293568 (program): E.g.f.: exp(x^3/(x^4 - 1)).
  • A293571 (program): E.g.f.: exp(x/(1 + x + x^2)).
  • A293574 (program): a(n) = Sum_{k=0..n} n^(n-k)*binomial(n+k-1,k).
  • A293575 (program): Difference between the number of proper divisors of n and the number of squares dividing n.
  • A293579 (program): Number of compositions of n where each part i is marked with a word of length i over a binary alphabet whose letters appear in alphabetical order and both letters occur at least once in the composition.
  • A293588 (program): E.g.f.: exp(x + x^6/6).
  • A293600 (program): G.f. A(x,y) = Sum_{-oo..+oo} (x - y^n)^(n+1), as a flattened rectangular array of coefficients T(n,k) of x^n * y^(k*(n+k-1)) in A(x,y) for n>=1.
  • A293604 (program): E.g.f.: exp(x * (1 - x)).
  • A293606 (program): Number of unlabeled antichains of weight n.
  • A293607 (program): Number of unlabeled clutters of weight n.
  • A293608 (program): a(n) = (3*n + 7)*Pochhammer(n, 5) / 4!.
  • A293611 (program): a(n) = (25*n + 41)*Pochhammer(n, 5) / 6!.
  • A293614 (program): a(n) = (8*n + 18)*Pochhammer(n, 6) / 6!.
  • 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.
  • A293703 (program): a(n) is the length of the longest palindromic subsequence in the first differences of the list of the first n negative and positive roots of floor(tan(k))=1.
  • A293706 (program): a(n) is the shift of the longest palindromic subsequence within the first differences of the concatenation of the first n negative and positive roots of floor(tan(k)) = 1.
  • A293710 (program): Expansion of x^2/(1 - 4*x - 4*x^2 - x^3).
  • A293716 (program): E.g.f.: exp(x + 2*x^2 + 3*x^3).
  • A293720 (program): E.g.f.: exp(x + 4*x^2).
  • A293721 (program): E.g.f.: exp(x + 4*x^2 + 9*x^3).
  • A293722 (program): Number of distinct nonempty subsequences of the binary expansion of n.
  • A293727 (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 sqrt(2).
  • 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).
  • A293761 (program): Numbers k such that (d(k), d(k+1)) = (0,0) in the base-2 digits d(i) of sqrt(2).
  • A293762 (program): Numbers k such that (d(k), d(k+1)) = (0,1) in the base-2 digits d(i) of sqrt(2).
  • A293763 (program): Numbers k such that (d(k), d(k+1)) = (1,0) in the base-2 digits d(i) of sqrt(2).
  • A293764 (program): Numbers k such that (d(k), d(k+1)) = (1,1) in the base-2 digits d(i) of sqrt(2).
  • A293765 (program): Solution of the complementary equation a(n) = a(n-1) + a(n-2) + b(n-1) + 2, where a(0) = 1, a(1) = 3, b(0) = 2, b(1) = 4.
  • A293766 (program): Solution of the complementary equation a(n) = a(n-1) + a(n-2) + b(n-1) + 3, where a(0) = 1, a(1) = 3, b(0) = 2, b(1) = 4.
  • A293767 (program): Solution of the complementary equation a(n) = a(n-1) + a(n-2) + b(n-1) - 1, where a(0) = 1, a(1) = 3, b(0) = 2, b(1) = 4.
  • A293787 (program): Numbers k such that (d(k), d(k+1)) = (0,0) in the base-2 digits d(i) of sqrt(3).
  • A293788 (program): Numbers k such that (d(k), d(k+1)) = (0,1) in the base-2 digits d(i) of sqrt(3).
  • A293789 (program): Numbers k such that (d(k), d(k+1)) = (1,0) in the base-2 digits d(i) of sqrt(3).
  • A293790 (program): Numbers k such that (d(k), d(k+1)) = (1,1) in the base-2 digits d(i) of sqrt(3).
  • A293793 (program): Numbers k such that (d(k), d(k+1)) = (0,1) in the base-2 digits d(i) of e.
  • A293794 (program): Numbers k such that (d(k), d(k+1)) = (1,0) in the base-2 digits d(i) of e.
  • A293795 (program): Numbers k such that (d(k), d(k+1)) = (1,1) in the base-2 digits d(i) of e.
  • 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.
  • A293828 (program): Numbers k such that (d(k), d(k+1)) = (0,0) in the base-2 digits d(i) of Pi.
  • A293829 (program): Numbers k such that (d(k), d(k+1)) = (0,1) in the base-2 digits d(i) of Pi.
  • A293830 (program): Numbers k such that (d(k), d(k+1)) = (1,0) in the base-2 digits d(i) of Pi.
  • A293838 (program): “Look once to the left” sequence starting with 1,2 (see comment).
  • A293847 (program): E.g.f.: exp(Sum_{n>=1} n!*x^n).
  • A293848 (program): E.g.f.: exp(Sum_{n>=1} n^n*x^n).
  • A293849 (program): Expansion of e.g.f.: exp(Sum_{n>=1} n^(n-1)*x^n).
  • A293860 (program): a(0) = 0, a(1) = 1; a(n) = n! * [x^n] exp(n*x)*Sum_{k=1..n-1} a(k)*x^k/k!.
  • A293895 (program): Number of proper divisors of the form 3k+1.
  • A293896 (program): Number of proper divisors of the form 3k+2.
  • A293897 (program): Sum of proper divisors of the form 3k+1.
  • A293898 (program): Sum of proper divisors of the form 3k+2.
  • A293899 (program): Number of proper divisors of form 3k+1 minus number of proper divisors of form 3k+2.
  • A293901 (program): Sum of proper divisors of form 4k+1.
  • A293903 (program): Sum of proper divisors of form 4k+3.
  • A293914 (program): Number of linear chord diagrams having n chords and minimal chord length one.
  • A293928 (program): Totients having one or more solutions to phi(m)^(k+1) = phi(phi(m)^k*m), k >= 1, m >= 1.
  • A293954 (program): First differences of A055612.
  • A293955 (program): Partial sums of A055612.
  • 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.
  • A293959 (program): Construct a triangle T(n,k) (0 <= k <= n) of strings of integers, where T(0,0) = {0}, T(n,n) = {n}, and otherwise T(n,k) is the concatenation of T(n-1,k-1) and T(n-1,k). The sequence is obtained by reading across the rows of the triangle, concatenating the successive strings.
  • A293962 (program): Number of linear chord diagrams having n chords and maximal chord length n, a(0)=1.
  • A293974 (program): Row sums of antidiagonals of the Sierpinski carpet A153490.
  • A293975 (program): If n is even, divide by 2; otherwise, add the next larger prime.
  • A293976 (program): a(2n) = a(2n-1) + a(n) for n >= 1, a(2n+1) = a(2n) + 1, a(0) = 0.
  • A293985 (program): Square array A(n,k), n >= 0, k >= 0, read by antidiagonals, where column k is the expansion of e.g.f.: exp(x/(1-x))/(1-x)^k.
  • A293986 (program): E.g.f.: exp((1/(1-x)^7 - 1)/7).
  • A293987 (program): E.g.f.: exp((1/(1-x)^8 - 1)/8).
  • A293988 (program): E.g.f.: exp((1/(1-x)^9 - 1)/9).
  • A293990 (program): a(n) = (3*n + ((n-2) mod 4))/2.
  • A293995 (program): Number of linear chord diagrams having n chords and no chord length larger than three.
  • 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.
  • A294022 (program): Sum of the differences of the larger and smaller parts in the partitions of n into two parts with the larger part prime.
  • 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.
  • A294032 (program): Triangle read by rows, T(n, k) = Pochhammer(3, k)*Stirling2(3 + n, 3 + k) for n >= 0 and 0 <= k <= n.
  • A294035 (program): a(n) = 3^n*hypergeom([-n/3, (1-n)/3, (2-n)/3], [1, 1], -1).
  • A294039 (program): a(n) = e*Gamma(2*n,1).
  • A294040 (program): a(n) = e*(Gamma(2*n,1) - Gamma(n,1)).
  • A294049 (program): Number of binary strings of length n avoiding substrings 1000, 1011, 1101, or 1111.
  • A294050 (program): E.g.f.: exp(1/(1-x)^4 - 1).
  • A294051 (program): E.g.f.: exp(1/(1-x)^5 - 1).
  • A294052 (program): Number of set partitions of [n] such that the maximal absolute difference between consecutive elements within a block equals three.
  • 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.
  • A294061 (program): Sum of the differences of the larger and smaller parts in the partitions of n into two parts with the larger 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.
  • A294063 (program): Sum of the differences of the larger and smaller parts in the partitions of 2n into two parts with the larger part squarefree.
  • A294070 (program): a(n) = (1/4)*(n^2 - 2*n)^2 + (9/4)*(n^2 - 2*n) + 6.
  • A294072 (program): Number of noncube divisors of n^3.
  • A294082 (program): Square array read by antidiagonals: T(m,n) = T(m,n-1)^2 - T(m,n-2)^2 + T(m,n-2) with T(1,n) = 1, T(m,0) = 1, and T(m,1) = m.
  • A294084 (program): Number of indecomposable intervals in the Tamari lattices.
  • A294085 (program): a(n) is the number of self-symmetric anonymous and neutral equivalence classes of preference profiles with 3 alternatives and n agents (IANC model).
  • A294091 (program): Numbers k such that (k - 1)/2 is prime that are not congruent to -1 mod 8.
  • A294092 (program): Numbers k == 119 (mod 120) such that 2^((k-1)/2), 3^((k-1)/2) and 5^((k-1)/2) are congruent to 1 (mod k).
  • A294097 (program): Number of partitions of 2n into two parts such that both parts are either squarefree or nonsquarefree.
  • A294098 (program): Number of partitions of 2n into two parts such that one part is squarefree and the other part is nonsquarefree.
  • A294099 (program): Rectangular array read by (upward) antidiagonals: A(n,k) = Sum_{j=0..k} (-1)^floor(j/2)*binomial(k-floor((j+1)/2), floor(j/2))*n^(k-j), n >= 1, k >= 0.
  • A294100 (program): Number of partitions of n into two squarefree parts or two nonsquarefree positive integer parts.
  • A294101 (program): Number of partitions of n into two parts such that one is squarefree and the other is nonsquarefree.
  • A294106 (program): Sum of products of terms in all partitions of 3*n into distinct powers of 3.
  • A294107 (program): Maximum of the number of primes appearing among the smaller parts and the number of primes appearing among the larger parts of the partitions of n into two parts.
  • A294108 (program): Minimum of the number of primes appearing among the smaller parts and the number of primes appearing among the larger parts of the partitions of n into two parts.
  • A294109 (program): Sum of the larger parts of the partitions of n into two parts with smaller part prime.
  • A294111 (program): Sum of the smaller parts of the partitions of n into two parts with larger part prime.
  • A294113 (program): Sum of the smaller parts of the partitions of 2n into two parts with larger part prime.
  • A294114 (program): Sum of the larger parts of the partitions of 2n into two parts with smaller part prime.
  • A294116 (program): Fibonacci sequence beginning 2, 21.
  • A294117 (program): a(n) = (n!)^2 * Sum_{k=1..n} binomial(n,k) / k^2.
  • A294119 (program): Expansion of e.g.f.: exp(2*((1+x)^2 - 1)).
  • A294120 (program): E.g.f.: exp(3*((1+x)^3 - 1)).
  • 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.
  • A294139 (program): Sum of the areas of the distinct rectangles (and the areas of the squares on their sides) with positive integer sides such that L + W = n, W < L.
  • A294140 (program): Number of total dominating sets in the n-crown graph.
  • A294143 (program): Sum of the larger parts of the partitions of 2n into two parts with smaller part squarefree.
  • A294144 (program): Sum of the smaller parts of the partitions of 2n into two parts with larger part squarefree.
  • A294145 (program): Sum of the smaller parts of the partitions of n into two parts with larger part squarefree.
  • A294146 (program): Sum of the larger parts of the partitions of n into two parts with smaller part squarefree.
  • A294152 (program): Chromatic invariant of the n-antiprism graph.
  • A294157 (program): Fibonacci sequence beginning 2, 8.
  • A294159 (program): Alternating row sums of triangle A291844.
  • A294172 (program): Maximum value of the cyclic convolution of first n positive integers with themselves.
  • A294175 (program): a(n) = 2^(n-1) + ((1+(-1)^n)/4)*binomial(n, n/2) - binomial(n, floor(n/2)).
  • A294178 (program): a(2n) = 2*n + 1, a(2n+1) = 6*n + 3.
  • A294180 (program): The 3-symbol Pell word.
  • A294187 (program): Numbers k == 77 (mod 120) such that (2*k-1)*2^((k-1)/2), (2*k-1)*3^((k-1)/2) and (2*k-1)*5^((k-1)/2) are congruent to 1 (mod k).
  • A294189 (program): E.g.f.: exp(2*(1/(1-x)^2 - 1)).
  • A294193 (program): a(n) = sum of integers between n!+1 and (n+1)!.
  • A294198 (program): Labeled trees on n nodes with at least one node of degree two.
  • A294199 (program): Number of partitions of n into powers of 2 such that 1 and 2 cannot both be parts of a particular partition, and 4 and 8 cannot both be parts of a particular partition, and 16 and 32, and so on.
  • A294211 (program): Sum of the parts in the partitions of n into two squarefree parts or two nonsquarefree parts.
  • A294213 (program): E.g.f.: exp(1/((1-x)*(1-x^2)) - 1).
  • A294232 (program): Number of partitions of n into two parts with smaller part squarefree and larger part nonsquarefree.
  • A294233 (program): Number of partitions of n into two parts with smaller part nonsquarefree and larger part squarefree.
  • A294234 (program): Number of partitions of n into two parts such that the smaller part is nonsquarefree.
  • A294235 (program): Number of partitions of n into two parts such that the larger part is nonsquarefree.
  • A294236 (program): Sum of the smaller parts of the partitions of n into two parts with larger part nonsquarefree.
  • A294237 (program): Sum of the larger parts of the partitions of n into two parts with smaller part nonsquarefree.
  • A294238 (program): Sum of the parts in the partitions of n into two parts with smaller part nonsquarefree.
  • A294239 (program): Sum of the parts in the partitions of n into two parts with larger part nonsquarefree.
  • A294242 (program): Number of partitions of 2n into two parts with the larger part nonsquarefree.
  • A294243 (program): Sum of the larger parts of the partitions of 2n into two parts with smaller part nonsquarefree.
  • A294244 (program): Sum of the smaller parts of the partitions of 2n into two parts with larger part nonsquarefree.
  • A294245 (program): Sum of the larger parts of the partitions of 2n into two parts with larger part nonsquarefree.
  • A294246 (program): Sum of the smaller parts of the partitions of 2n into two parts with smaller part nonsquarefree.
  • A294247 (program): Sum of the parts in the partitions of n into exactly two distinct squarefree parts.
  • A294248 (program): Number of partitions of 2n into two distinct squarefree parts.
  • A294255 (program): E.g.f.: exp((1-x)*(1-x^2) - 1).
  • A294259 (program): a(n) = n*(n^3 + 2*n^2 - 5*n + 10)/8.
  • A294262 (program): a(n) = 3*a(n-1) + 5*a(n-2) + a(n-3), with a(0) = a(1) = 1 and a(2) = 7, a linear recurrence which is a trisection of A005252.
  • A294263 (program): Sum of the larger parts of the partitions of n into two parts with smaller part squarefree > 1.
  • 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.
  • A294270 (program): Sum of the cubes of the parts in the partitions of n into two parts.
  • A294271 (program): Sum of the fourth powers of the parts in the partitions of n into two parts.
  • A294272 (program): Sum of the fifth powers of the parts in the partitions of n into two parts.
  • A294273 (program): Sum of the sixth powers of the parts in the partitions of n into two parts.
  • A294274 (program): Sum of the seventh powers of the parts in the partitions of n into two parts.
  • A294275 (program): Sum of the eighth powers of the parts in the partitions of n into two parts.
  • A294276 (program): Sum of the ninth powers of the parts in the partitions of n into two parts.
  • A294277 (program): Numbers k such that omega(k) < omega(k+1) (where omega(m) = A001221(m), the number of distinct primes dividing m).
  • A294278 (program): Numbers n such that omega(n) > omega(n+1) (where omega(m) = A001221(m), the number of distinct primes dividing m).
  • A294279 (program): Sum of the tenth powers of the parts in the partitions of n into two parts.
  • A294283 (program): Sum of the larger parts of the partitions of n into two distinct parts with smaller part squarefree.
  • A294284 (program): Sum of the smaller parts of the partitions of n into two distinct parts with larger part squarefree.
  • A294285 (program): Sum of the larger parts of the partitions of n into two distinct parts with larger part squarefree.
  • 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) = ((9*n + 8)*10^n - 8)/9.
  • A294328 (program): a(n) = ((9*n + 8)*10^n - 8)/81.
  • A294329 (program): a(n) = 8*((9*n + 8)*10^n - 8)/81.
  • A294344 (program): a(n) = ((-9*n + 82)*10^n - 1)/81.
  • A294345 (program): Sum of the products of the smaller and larger parts of the Goldbach partitions of n into two distinct parts.
  • A294349 (program): Product of first n terms of the binomial transform of the Lucas numbers (A000032).
  • A294350 (program): Product of first n terms of the binomial transform of the partition function (A000041).
  • A294352 (program): Product of first n terms of the binomial transform of the factorial.
  • A294353 (program): Product of first n terms of the binomial transform of n^n (A086331).
  • A294361 (program): E.g.f.: exp(Sum_{n>=1} sigma(n) * x^n).
  • A294362 (program): E.g.f.: exp(Sum_{n>=1} sigma_2(n) * x^n).
  • A294363 (program): E.g.f.: exp(Sum_{n>=1} d(n) * x^n), where d(n) is the number of divisors of n.
  • A294364 (program): Linear recurrence with signature (1,1,-1,1,1), where the first terms are powers of 2 (1,2,4,8,16).
  • A294365 (program): Solution of the complementary equation a(n) = a(n-1) + a(n-2) + b(n-1) + n, where a(0) = 1, a(1) = 3, b(0) = 2, b(1) = 4.
  • A294366 (program): Solution of the complementary equation a(n) = a(n-1) + a(n-2) + b(n-1) + 2n, where a(0) = 1, a(1) = 3, b(0) = 2, b(1) = 4.
  • A294367 (program): Solution of the complementary equation a(n) = a(n-1) + a(n-2) + b(n-1) + n - 1, where a(0) = 1, a(1) = 3, b(0) = 2, b(1) = 4.
  • A294371 (program): Lexicographically earliest sequence of distinct positive numbers such that, for any n > 0, a(3*n) = 2*a(n).
  • A294372 (program): Expansion of (1-x)^4/(x^2 + 4*x + 1).
  • A294373 (program): Product of first n Bell numbers.
  • A294383 (program): Solution of the complementary equation a(n) = a(n-1)*b(n-2) + 1, where a(0) = 1, a(1) = 3, b(0) = 2, b(1) = 4.
  • A294387 (program): Expansion of chi(q^3) / chi^3(q) in powers of q where chi() is a Ramanujan theta function.
  • A294389 (program): a(n) = 2^(n-3) mod n, for n >= 3.
  • A294390 (program): a(n) = 2^(n-4) mod n, for n >= 4.
  • A294392 (program): E.g.f.: exp(Sum_{n>=1} A001227(n) * x^n).
  • A294394 (program): E.g.f.: exp(Sum_{n>=1} A000593(n) * x^n).
  • A294397 (program): Solution of the complementary equation a(n) = a(n-1) + b(n-2) + 1, where a(0) = 1, a(1) = 3, b(0) = 2, b(1) = 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.
  • A294402 (program): E.g.f.: exp(-Sum_{n>=1} d(n) * x^n), where d(n) is the number of divisors of n.
  • A294403 (program): E.g.f.: exp(-Sum_{n>=1} sigma(n) * x^n).
  • A294404 (program): E.g.f.: exp(-Sum_{n>=1} sigma_2(n) * x^n).
  • A294405 (program): Number of connected weakly regular graphs on n nodes.
  • A294406 (program): Positive odd numbers k such that both (sigma(m) - 2*m) and (2*m - sigma(m)) are never equal to k, where sigma(.) is the sum of divisors function A000203 (conjectured).
  • A294409 (program): a(n) = n! * [x^n] exp(n*x)*BesselI(0,2*n*x).
  • A294417 (program): Solution of the complementary equation a(n) = a(n-1) + a(n-2) + b(n-1) + b(n-2) - n, where a(0) = 1, a(1) = 3, b(0) = 2, b(1) = 4.
  • A294422 (program): Solution of the complementary equation a(n) = a(n-1) + a(n-2) + b(n-1) - b(n-2) + 1, where a(0) = 1, a(1) = 3, b(0) = 2, b(1) = 4.
  • A294423 (program): Solution of the complementary equation a(n) = a(n-1) + a(n-2) + b(n-1) - b(n-2) + n, where a(0) = 1, a(1) = 3, b(0) = 2, b(1) = 4.
  • A294424 (program): Solution of the complementary equation a(n) = a(n-1) + a(n-2) + b(n-1) - b(n-2) - 1, where a(0) = 1, a(1) = 3, b(0) = 2, b(1) = 4.
  • A294426 (program): Solution of the complementary equation a(n) = a(n-1) + a(n-2) + 2*b(n-1) - b(n-2) - 2, where a(0) = 1, a(1) = 3, b(0) = 2, b(1) = 4.
  • A294431 (program): Rank of the inverse semigroup D_n of all difunctional relations on an n-element set.
  • A294433 (program): Expansion of (1+11*x+24*x^2+11*x^3+x^4)/(1-x)^5.
  • A294434 (program): a(0)=0; for n>0, a(n) = (A163778(n)-1)/2.
  • A294435 (program): a(n) = Sum_{m=0..n} (Sum_{k=0..m} binomial(n,k))^4.
  • A294436 (program): a(n) = Sum_{m=0..n} (Sum_{k=0..m} binomial(n,k))^5.
  • A294442 (program): Kepler’s tree of fractions, read across rows (the fraction i/j is represented as the pair i,j).
  • A294445 (program): a(n) = (2*n + 4)!*(n^2 + 11*n + 2)/(2*(n-1)!*(n+6)!).
  • A294448 (program): Discrepancy of the Kolakoski sequence A000002.
  • A294453 (program): Array read by antidiagonals: T(0,k) = A000045(k+1) for k >= 0. T(n,0) = 1 for n >= 0; thereafter T(n,k) = T(n-1,k-1)+T(n-1,k) for n, k >= 1.
  • A294456 (program): a(1)=0, a(2)=1; thereafter a(n) = a(floor(n/2)) + a(ceiling(n/2)) + 2.
  • A294458 (program): E.g.f.: Product_{n>=1} (1 - x^(2*n-1))^(1/(2*n-1)).
  • A294459 (program): E.g.f.: exp(-Sum_{n>=1} A001227(n) * x^n).
  • A294462 (program): E.g.f.: Product_{k>0} (1-k*x^k)^(-1/k).
  • A294463 (program): E.g.f.: Product_{k>0} (1-k*x^k)^(1/k).
  • A294464 (program): E.g.f.: Product_{k>0} (1+k*x^k)^(1/k).
  • A294465 (program): E.g.f.: Product_{k>0} (1+k*x^k)^(-1/k).
  • A294467 (program): Binomial transform of A088311.
  • A294468 (program): Inverse binomial transform of A088311.
  • 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.
  • A294487 (program): Sum of the lengths of the distinct rectangles with prime length and integer width such that L + W = n, W < L.
  • A294491 (program): Number of length 2n n-ary words that can be built by repeatedly inserting doublets into the initially empty word.
  • A294496 (program): Number of distinct minimal period lengths of periodic infinite words on n symbols having the constant gap property.
  • A294499 (program): Inverse binomial transform of the number of overpartitions (A015128).
  • A294500 (program): Binomial transform of the number of planar partitions (A000219).
  • A294501 (program): Inverse binomial transform of the number of planar partitions (A000219).
  • A294502 (program): Binomial transform of A026007.
  • A294507 (program): Sum(m^p, m=1..p-1) / p^2 as p runs through the odd primes.
  • A294512 (program): Denominators of partial sums of the reciprocals of octagonal numbers.
  • A294513 (program): Denominators of the partial sums of the reciprocals of twice the pentagonal numbers.
  • A294515 (program): Denominators of partial sums of the reciprocals of the decagonal numbers.
  • A294516 (program): Numerators of the partial sums of the reciprocals of (k+1)*(4*k+3) = A033991(k+1), for k >= 0.
  • A294517 (program): Denominators of the partial sums of the reciprocals of (k+1)*(4*k+3) = A033991(k+1), for k >= 0.
  • A294519 (program): Convolution triangle for Chebyshev S polynomials (rising powers).
  • A294520 (program): Numerators of the partial sums of the reciprocals of the dodecagonal numbers (k + 1)*(5*k + 1) = A051624(k+1), for k >= 0.
  • A294521 (program): Denominators of the partial sums of the reciprocals of the dodecagonal numbers (k + 1)*(5*k + 1) = A051624(k+1), for k >= 0.
  • A294527 (program): Number of Dyck paths of length 2n with exactly 2 hills.
  • A294529 (program): Binomial transform of A001156.
  • A294530 (program): Binomial transform of A023871.
  • A294532 (program): Solution of the complementary equation a(n) = a(n-1) + a(n-2) + b(n-2), where a(0) = 1, a(1) = 2, b(0) = 3.
  • A294533 (program): Solution of the complementary equation a(n) = a(n-1) + a(n-2) + b(n-2) + 1, where a(0) = 1, a(1) = 2, b(0) = 3.
  • A294534 (program): Solution of the complementary equation a(n) = a(n-1) + a(n-2) + b(n-2) + 2, where a(0) = 1, a(1) = 2, b(0) = 3.
  • A294535 (program): Solution of the complementary equation a(n) = a(n-1) + a(n-2) + b(n-2) + 3, where a(0) = 1, a(1) = 2, b(0) = 3.
  • A294536 (program): Solution of the complementary equation a(n) = a(n-1) + a(n-2) + b(n-2) - 1, where a(0) = 1, a(1) = 2, b(0) = 3.
  • A294537 (program): Solution of the complementary equation a(n) = a(n-1) + a(n-2) + b(n-2) + n, where a(0) = 1, a(1) = 2, b(0) = 3.
  • A294538 (program): Solution of the complementary equation a(n) = a(n-1) + a(n-2) + b(n-2) + 2n, where a(0) = 1, a(1) = 2, b(0) = 3.
  • A294539 (program): Solution of the complementary equation a(n) = a(n-1) + a(n-2) + b(n-2) + n - 1, where a(0) = 1, a(1) = 2, b(0) = 3.
  • A294540 (program): Solution of the complementary equation a(n) = a(n-1) + a(n-2) + b(n-2) + 2*n - 1, where a(0) = 1, a(1) = 2, b(0) = 3.
  • A294541 (program): Solution of the complementary equation a(n) = a(n-1) + a(n-2) + b(n-1), where a(0) = 1, a(1) = 2, b(0) = 3, and (a(n)) and (b(n)) are increasing complementary sequences.
  • A294542 (program): Solution of the complementary equation a(n) = a(n-1) + a(n-2) + b(n-1) + 1, where a(0) = 1, a(1) = 2, b(0) = 3, and (a(n)) and (b(n)) are increasing complementary sequences.
  • A294543 (program): Solution of the complementary equation a(n) = a(n-1) + a(n-2) + b(n-1) + 2, where a(0) = 1, a(1) = 2, b(0) = 3, and (a(n)) and (b(n)) are increasing complementary sequences.
  • A294544 (program): Solution of the complementary equation a(n) = a(n-1) + a(n-2) + b(n-1) + 3, where a(0) = 1, a(1) = 2, b(0) = 3, and (a(n)) and (b(n)) are increasing complementary sequences.
  • A294545 (program): Solution of the complementary equation a(n) = a(n-1) + a(n-2) + b(n-1) - 1, where a(0) = 1, a(1) = 2, b(0) = 3, and (a(n)) and (b(n)) are increasing complementary sequences.
  • A294546 (program): Solution of the complementary equation a(n) = a(n-1) + a(n-2) + b(n-1) + n, where a(0) = 1, a(1) = 2, b(0) = 3, and (a(n)) and (b(n)) are increasing complementary sequences.
  • A294547 (program): Solution of the complementary equation a(n) = a(n-1) + a(n-2) + b(n-1) + 2n, where a(0) = 1, a(1) = 2, b(0) = 3, and (a(n)) and (b(n)) are increasing complementary sequences.
  • A294548 (program): Solution of the complementary equation a(n) = a(n-1) + a(n-2) + b(n-1) + n - 1, where a(0) = 1, a(1) = 2, b(0) = 3, and (a(n)) and (b(n)) are increasing complementary sequences.
  • A294549 (program): Solution of the complementary equation a(n) = a(n-1) + a(n-2) + b(n-1) + n + 1, where a(0) = 1, a(1) = 2, b(0) = 3, and (a(n)) and (b(n)) are increasing complementary sequences.
  • A294562 (program): Solution of the complementary equation a(n) = a(n-1) + a(n-2) + b(n-1) - b(n-2) + 1, where a(0) = 1, a(1) = 2, b(0) = 3, and (a(n)) and (b(n)) are increasing complementary sequences.
  • A294564 (program): Solution of the complementary equation a(n) = a(n-1) + a(n-2) + 2*b(n-1) - b(n-2) - 1, where a(0) = 1, a(1) = 2, b(0) = 3, and (a(n)) and (b(n)) are increasing complementary sequences.
  • 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.
  • A294567 (program): a(n) = Sum_{d|n} d^(1 + 2*n/d).
  • A294568 (program): Decimal expansion of 1/18779.
  • A294573 (program): a(n) = n! * [x^n] exp((n+1)*x)*BesselI(1,2*x)/x.
  • A294574 (program): Numbers having exactly one representation as sum of squares of primes.
  • A294601 (program): Numbers with exactly one odd decimal digit.
  • A294602 (program): a(n) = pi(n-1) - pi(floor(n/2)), where pi is A000720.
  • A294606 (program): Expansion of Product_{k>=1} (1 - k*x^k)^(k^k).
  • A294608 (program): a(n) = Sum_{d|n} d^(d + 1 + n/d).
  • A294610 (program): Expansion of Product_{k>=1} 1/(1 - k*x^k)^(k^k).
  • A294612 (program): Denominator of the contraharmonic mean of the first n primes.
  • 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.
  • A294620 (program): Expansion of Product_{k>0} (1 - k^2*x^k)^(1/k).
  • A294627 (program): Expansion of x*(1 + x)/((1-2*x)*(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.
  • A294642 (program): a(n) = n! * [x^n] exp(n*x)*BesselI(1,2*sqrt(2)*x)/(sqrt(2)*x).
  • A294643 (program): Length (= size) of the orbit of n under the “3x+1” map A006370: x -> x/2 if even, 3x+1 if odd. a(n) = -1 in case the orbit would be infinite.
  • A294644 (program): Decimal expansion of the real positive solution to x^3 = x + 3.
  • A294645 (program): a(n) = Sum_{d|n} d^(n+1).
  • A294646 (program): a(n) = (1/2)^(2*n) mod (2*n+1).
  • A294647 (program): Differential variant of the Kolakoski sequence, with initial terms 1, 1.
  • A294649 (program): a(n) = numerator(A206369(n))/n.
  • A294650 (program): a(n) = denominator(A206369(n))/n.
  • A294652 (program): Positive integers k such that the sum of decimal digits of (4^k - 1) equals 3*k.
  • A294665 (program): Numbers n such that the largest digit of n^3 is 5.
  • A294670 (program): Decimal expansion of the sum sqrt(2) + sqrt(5).
  • A294671 (program): Decimal expansion of the sum of sqrt(2) and sqrt(5) with no positional regrouping.
  • A294673 (program): Order of the “inside-out” permutation on 2n+1 letters.
  • A294674 (program): Numbers that are the product of any number of consecutive odd primes.
  • A294689 (program): Collatz cycle of negative numbers starting with -17.
  • A294697 (program): Number of permutations of [n] avoiding {1342, 2143, 3412}.
  • A294700 (program): Number of permutations of [n] avoiding {1324, 2143, 3421}.
  • A294701 (program): Number of permutations of [n] avoiding {4231, 2143, 1342}.
  • A294702 (program): Number of permutations of [n] avoiding {1324, 2143, 3412}.
  • A294704 (program): Expansion of Product_{k>=1} (1 - k^k*x^k)^(k^k).
  • A294709 (program): Number of permutations of [n] avoiding {2143, 3412, 1234}.
  • A294725 (program): Number of permutations of [n] avoiding {4231, 3412, 1234}.
  • A294731 (program): Smallest average of a twin prime pair divisible by the n-th prime, i.e. A090530(n), divided by 6*prime(n).
  • A294732 (program): Maximal diameter of the connected cubic graphs on 2*n vertices.
  • A294733 (program): Maximal diameter of connected (2*k)-regular graphs on 2*n+1 nodes written as triangular array T(n,k), 1 <= k <= n.
  • A294757 (program): Expansion of Product_{k>=1} 1/(1 - k^k*x^k)^(k^k).
  • A294764 (program): Number of permutations of [n] avoiding {2143, 3142, 1234}.
  • A294767 (program): Number of permutations of [n] avoiding {4213, 1432, 1324}.
  • A294769 (program): Number of permutations of [n] avoiding {2143, 1423, 1234}.
  • A294772 (program): Number of permutations of [n] avoiding {4132, 4123, 1243}.
  • A294773 (program): a(n) = Sum_{d|n} d^(d+n+1).
  • A294774 (program): a(n) = 2*n^2 + 2*n + 5.
  • A294790 (program): Subtract n from partial sums of partial sums of Catalan numbers.
  • A294796 (program): Number of permutations of [n] avoiding {1234, 1324, 3412}.
  • A294800 (program): Number of permutations of [n] avoiding {1324, 2341, 3421}.
  • A294801 (program): Number of permutations of [n] avoiding {4231, 1324, 2341}.
  • A294802 (program): Number of permutations of [n] avoiding {3412, 3421, 1324}.
  • A294803 (program): Number of permutations of [n] avoiding {1324, 2413, 3421}.
  • A294804 (program): Number of permutations of [n] avoiding {1324, 3142, 4231}.
  • A294809 (program): Expansion of Product_{k>=1} (1 - k^k*x^k)^k.
  • A294810 (program): a(n) = Sum_{d|n} d^(n+2).
  • A294813 (program): Expansion of Product_{k>=1} 1/(1 - k^k*x^k)^k.
  • A294814 (program): Number of permutations of [n] avoiding {1324, 1342, 3412}.
  • A294817 (program): Number of permutations of [n] avoiding {1324, 2431, 3241}.
  • A294818 (program): Number of permutations of [n] avoiding {1324, 2314, 2431}.
  • A294824 (program): Number of permutations of [n] avoiding {1324, 2413, 2431}.
  • A294826 (program): Numerators of the partial sums of the reciprocals of twice the heptagonal numbers (k + 1)*(5*k + 2) = A135706(k+1) = 2*A000566(k+1), for k >= 0.
  • A294827 (program): Denominators of the partial sums of the reciprocals of twice the heptagonal numbers (k + 1)*(5*k + 2) = A135706(k+1) = 2*A000566(k+1), for k >= 0.
  • A294828 (program): Numerators of the partial sums of the reciprocals of the numbers (k + 1)*(5*k + 3) = A147874(k+2), for k >= 0.
  • A294829 (program): Denominators of the partial sums of the reciprocals of the numbers (k + 1)*(5*k + 3) = A147874(k+2), for k >= 0.
  • A294831 (program): Numerators of the partial sums of the reciprocals of the numbers (k + 1)*(5*k + 4) = 2*A005476(k+1), for k >= 0.
  • A294832 (program): Denominators of the partial sums of the reciprocals of the numbers (k + 1)*(5*k + 4) = 2*A005476(k+1), for k >= 0.
  • A294834 (program): Numerators of the partial sums of the reciprocals of the positive tetradecagonal numbers (k + 1)*(6*k + 1) = A051866(k+1).
  • A294835 (program): Denominators of the partial sums of the reciprocals of the positive tetradecagonal numbers (k + 1)*(6*k + 1) = A051866(k+1), for k >= 0.
  • A294885 (program): a(n) = A004125(n) mod n = [Sum_{i=1..n} (n mod i)] mod n.
  • A294886 (program): Sum of deficient proper divisors of n.
  • A294888 (program): Sum of nonabundant proper divisors of n.
  • A294889 (program): Sum of abundant proper divisors of n.
  • A294896 (program): a(n) = gcd(A000203(n), A005187(n)).
  • A294898 (program): a(n) = A005187(n) - A000203(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), (2*n-1)*(2^((n-1)/2)), (4*ceiling((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), (2*n-1)*(2^((n-1)/2)), (4*ceiling((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.
  • A294928 (program): Number of proper divisors of n that are nonabundant (A263837).
  • 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.
  • A294948 (program): Expansion of Product_{n>=1} (1 - n^n*x^n)^(1/n).
  • A294953 (program): Expansion of Product_{k>=1} (1 - k^(2*k)*x^k)^k.
  • A294954 (program): Expansion of Product_{k>=1} 1/(1 - k^(2*k)*x^k)^k.
  • A294955 (program): a(n) = Sum_{d|n} d^(2*n+2).
  • A294956 (program): a(n) = Sum_{d|n} d^(d + n/d).
  • A294957 (program): Expansion of Product_{k>=1} 1/(1 - k*x^k)^(k^(k-1)).
  • A294964 (program): Numerators of the partial sums of the reciprocals of the positive numbers (k + 1)*(6*k + 5) = A049452(k+1).
  • A294965 (program): Denominators of the partial sums of the reciprocals of the numbers (k + 1)*(6*k + 5) = A049452(k+1).
  • A294969 (program): Decimal expansion of sqrt(14)/2 = sqrt(7/2) = A010471/2.
  • A294970 (program): Numerators of the partial sums for the Catalan constant A006752: Sum_{k=0..n} ((-1)^k)/(2*k+1)^2, n >= 0.
  • A294971 (program): Denominators of the partial sums for the Catalan constant A006752: Sum_{k=0..n} ((-1)^k)/(2*k+1)^2, n >= 0.
  • A294972 (program): Numerators of continued fraction convergents to sqrt(7)/2.
  • A294973 (program): Denominators of the continued fraction convergents to sqrt(7)/2.
  • A294980 (program): a(n) is the total number of elements after n-th stage in a hybrid cellular automaton formed by Y-toothpicks and V-toothpicks (see Comments lines for precise definition).
  • A294982 (program): Number of compositions (ordered partitions) of 1 into exactly 3n+1 powers of 1/(n+1).
  • A294991 (program): Let S be the sequence of integer sets defined by the following rules: S(0) = {0}, S(1) = {1} and for any k > 0, S(2*k) = {2*k} U S(k) and S(2*k+1) = {2*k+1} U S(k) U S(k+1) (where X U Y denotes the union of the sets X and Y); a(n) = the number of elements of S(n).
  • A294993 (program): Numbers n > 1 such that all of 2^(n-1), 3^(n-1), 5^(n-1), (2*n-1)*(2^((n-1)/2)), 4*ceiling((3/4)*n)-2, and (2^((n+1)/2) + floor(n/4)*2^((n+3)/2)) are congruent to 1 (mod n).
  • A294996 (program): Numbers n such that the largest digit of n^3 is 6.
  • A294997 (program): Numbers n such that the largest digit of n^3 is 7.
  • A294998 (program): Numbers n such that the largest digit of n^3 is 8.
  • A294999 (program): Numbers n such that the largest digit of n^3 is 9.
  • A295005 (program): Numbers n such that the largest digit of n^2 is 5.
  • A295006 (program): Numbers n such that the largest digit of n^2 is 6.
  • A295007 (program): Numbers n such that the largest digit of n^2 is 7.
  • A295008 (program): Numbers whose square has largest digit 8.
  • A295009 (program): Numbers kn such that the largest digit of k^2 is 9.
  • A295012 (program): a(n) = sigma(12n - 1)/12, where sigma = sum of divisors (A000203).
  • A295015 (program): Squares whose largest digit is 5.
  • A295016 (program): Squares whose largest digit is 6.
  • A295017 (program): Squares whose largest digit is 7.
  • A295018 (program): Squares whose largest digit is 8.
  • A295019 (program): Squares whose largest digit is 9.
  • A295021 (program): Cubes whose largest digit is 6.
  • A295022 (program): Cubes whose largest digit is 7.
  • A295023 (program): Cubes whose largest digit is 8.
  • A295024 (program): Cubes whose largest digit is 9.
  • A295025 (program): Cubes whose largest digit is 5.
  • A295041 (program): The Grundy number of restricted Nim with a pass move.
  • A295045 (program): Number of n X 2 0..1 arrays with each 1 horizontally or vertically adjacent to 0 or 2 1s.
  • A295056 (program): Solution of the complementary equation a(n) = 2*a(n-1) + b(n-1), where a(0) = 1, a(1) = 4, b(0) = 2, and (a(n)) and (b(n)) are increasing complementary sequences.
  • A295059 (program): Solution of the complementary equation a(n) = 2*a(n-1) + b(n-2), where a(0) = 1, a(1) = 4, b(0) = 2, b(1) = 3, and (a(n)) and (b(n)) are increasing complementary sequences.
  • A295074 (program): Numerator of the coefficient of the n-th term of the power expansion near x = 0 of sqrt(1+1/sqrt(1-x))/sqrt(2).
  • A295076 (program): Numbers n > 1 such that n and sigma(n) have the same smallest prime factor.
  • A295077 (program): a(n) = 2*n*(n-1) + 2^n - 1.
  • A295084 (program): Number of sqrt(n)-smooth numbers <= n.
  • A295085 (program): Numbers k such that {k*phi} < 0.25 or {k*phi} > 0.75, where phi is the golden ratio (1 + sqrt(5))/2 and { } denotes fractional part.
  • A295089 (program): a(n) = 3*n^2 + n + 3.
  • A295091 (program): Number of n X 2 0..1 arrays with each 1 horizontally or vertically adjacent to 1 or 3 1s.
  • A295099 (program): a(n) = n! * [x^n] exp(n*x)/sqrt(1 - 2*x).
  • A295100 (program): a(n) = n! * [x^n] exp(n*x)/(1 - 2*x).
  • A295112 (program): a(n) = Sum_{k=0..n} binomial(n,2*k)*binomial(2*k,k)/(2*k-1).
  • A295126 (program): Denominator of Sum_{d|n} mu(n/d)/d, where mu is the Möbius function A008683.
  • A295127 (program): Numerator of Sum_{d|n} mu(n/d)/d, where mu is the Möbius function A008683.
  • A295130 (program): a(n) = 3*n*(64*n^2 + 1).
  • A295133 (program): Solution of the complementary equation a(n) = 3*a(n-1) + b(n-1), where a(0) = 1, a(1) = 2, b(0) = 3, and (a(n)) and (b(n)) are increasing complementary sequences.
  • A295134 (program): Solution of the complementary equation a(n) = 3*a(n-1) + b(n-1) - 1, where a(0) = 1, a(1) = 2, b(0) = 3, and (a(n)) and (b(n)) are increasing complementary sequences.
  • A295135 (program): Solution of the complementary equation a(n) = 3*a(n-1) + b(n-1) - 2, where a(0) = 1, a(1) = 2, b(0) = 3, and (a(n)) and (b(n)) are increasing complementary sequences.
  • A295136 (program): Solution of the complementary equation a(n) = 3*a(n-1) + b(n-1) - 3, where a(0) = 1, a(1) = 2, b(0) = 3, and (a(n)) and (b(n)) are increasing complementary sequences.
  • A295137 (program): Solution of the complementary equation a(n) = 3*a(n-1) + b(n-1) - n, where a(0) = 1, a(1) = 2, b(0) = 3, and (a(n)) and (b(n)) are increasing complementary sequences.
  • A295143 (program): Solution of the complementary equation a(n) = 2*a(n-1) + a(n-2) + b(n-1), where a(0) = 1, a(1) = 2, b(0) = 3, b(1) = 4, and (a(n)) and (b(n)) are increasing complementary sequences.
  • A295144 (program): Solution of the complementary equation a(n) = 2*a(n-1) + a(n-2) + b(n-1), where a(0) = 1, a(1) = 3, b(0) = 2, b(1) = 4, and (a(n)) and (b(n)) are increasing complementary sequences.
  • A295145 (program): Solution of the complementary equation a(n) = a(n-1) + 2*a(n-2) + b(n-2), where a(0) = 1, a(1) = 2, b(0) = 3, b(1) = 4, and (a(n)) and (b(n)) are increasing complementary sequences.
  • A295147 (program): Solution of the complementary equation a(n) = a(n-1) + 2*a(n-2) + b(n-1), where a(0) = 1, a(1) = 2, b(0) = 3, b(1) = 4, and (a(n)) and (b(n)) are increasing complementary sequences.
  • A295148 (program): Solution of the complementary equation a(n) = a(n-1) + 2*a(n-2) + b(n-1), where a(0) = 1, a(1) = 3, b(0) = 2, b(1) = 4, and (a(n)) and (b(n)) are increasing complementary sequences.
  • A295150 (program): Numbers that have exactly two representations as a sum of five nonnegative squares.
  • A295151 (program): Numbers that have exactly three representations as a sum of five nonnegative squares.
  • A295167 (program): Expansion of Product_{k>0} 1/(1 + k^k*x^k)^(1/k).
  • A295168 (program): Chromatic invariant of the 2n-crossed prism graph.
  • A295181 (program): Square array A(n,k), n >= 0, k >= 0, read by antidiagonals, where column k is the expansion of e.g.f. exp(-k*x)/(1 - x)^k.
  • A295182 (program): a(n) = n! * [x^n] exp(-n*x)/(1 - x)^n.
  • A295183 (program): a(n) = n! * [x^n] exp(n*x)/(1 - x)^n.
  • A295200 (program): Number of nX3 0..1 arrays with each 1 horizontally or vertically adjacent to 2 or 4 1s.
  • A295220 (program): a(n) = Sum_{i=1..floor(n/2)} floor((n+i)/i) - floor((n-i-1)/i).
  • A295232 (program): Denominator of (-1)^(n+1) * (2*n)! * (2^(2*n)+1)/(B_{2*n} * 2^(4*n-1)), where B_{n} is the Bernoulli number.
  • A295234 (program): Expansion of Product_{k>=1} (1 - k*x^k)^(k^(k-1)).
  • A295240 (program): Expansion of e.g.f. 1/(1 - x*exp(x)/(1 - 2*x*exp(x)/(1 - 3*x*exp(x)/(1 - 4*x*exp(x)/(1 - …))))), a continued fraction.
  • A295243 (program): Sums of two numbers that are both consecutive and squarefree.
  • A295247 (program): Number of n X 2 0..1 arrays with each 1 horizontally or vertically adjacent to 0, 1 or 3 1s.
  • 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.
  • A295292 (program): Sum of the products of the smaller and larger parts of the partitions of n into two parts with the larger part odd.
  • A295293 (program): Sum of the products of the smaller and larger parts of the partitions of n into two parts with the larger part even.
  • 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.
  • A295298 (program): Numbers n for which sum of the divisors (A000203) and the binary weight of n (A000120) have the same parity.
  • A295299 (program): Numbers k such that the sum of the divisors (A000203) and the binary weight of k (A000120) have different parity.
  • 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.
  • A295303 (program): a(n) = +1 if n > phi(sigma(n)), -1 if n < phi(sigma(n)), and 0 if n = phi(sigma(n)), where phi = A000010 and sigma = A000203.
  • A295304 (program): a(n) = +1 if sigma(phi(n)) > n, -1 if sigma(phi(n)) < n, and 0 if sigma(phi(n)) = n, where phi = A000010 and sigma = A000203.
  • A295305 (program): a(n) = tau(sigma(n)) - tau(n), where tau is the number of divisors (A000005) and sigma is the sum of divisors of n (A000203).
  • A295306 (program): a(n) = +1 if tau(sigma(n)) > tau(n), -1 if n < tau(sigma(n)) < tau(n), and 0 if tau(sigma(n)) = tau(n), where tau = A000005 and sigma = A000203.
  • A295307 (program): Numbers k such that k > phi(sigma(k)), 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))).
  • A295312 (program): a(n) = A062401(n) / A295310(n) = phi(sigma(n)) / gcd(n, phi(sigma(n))).
  • A295313 (program): a(n) = gcd(sigma(n), phi(sigma(n))).
  • A295314 (program): a(n) = sigma(n) / gcd(sigma(n), phi(sigma(n))).
  • A295315 (program): a(n) = phi(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.
  • A295320 (program): Sum of the products of the smaller and larger parts of the partitions of n into two distinct parts with the larger part odd.
  • A295321 (program): Sum of the products of the smaller and larger parts of the partitions of n into two distinct parts with the larger part even.
  • A295330 (program): Decimal expansion of sqrt(13)/2.
  • A295331 (program): Numerators of continued fraction convergents to sqrt(13)/2 = A295330.
  • A295332 (program): Denominators of the continued fraction convergents to sqrt(13)/2 = A295330.
  • A295333 (program): Numerators of continued fraction convergents to sqrt(10)/2 = sqrt(5/2) = A020797 + 1.
  • A295334 (program): Denominators of continued fraction convergents to sqrt(10)/2 = sqrt(5/2) = A020797 + 1.
  • A295336 (program): Numerators of the convergents to sqrt(14)/2 = A294969.
  • A295337 (program): Denominators of the convergents to sqrt(14)/2 = A294969.
  • A295340 (program): Numbers congruent to 11 or 13 mod 15.
  • A295341 (program): The number of partitions of n in which at least one part is a multiple of 3.
  • A295342 (program): The number of partitions of n in which at least one part is a multiple of 4.
  • A295368 (program): For any number n > 0 with s divisors, say d_1, d_2, …, d_s such that d_1 = 1 < d_2 < … < d_s = n, the binary representation of a(n) is (d_1 mod 2, d_2 mod 2, …, d_s mod 2).
  • A295371 (program): a(n) = (1/(2n))*Sum_{k=0..n-1} C(n-1, k)*C(n+k, k)*C(2k, k)*(k+2)*(-3)^(n-1-k).
  • A295381 (program): Square array A(n,k), n >= 0, k >= 0, read by antidiagonals, where column k is the expansion of e.g.f. exp(-k*x/(1 - x))/(1 - x).
  • A295382 (program): Expansion of e.g.f. exp(-2*x/(1 - x))/(1 - x).
  • A295383 (program): a(n) = (2*n)! * [x^(2*n)] (-x/(1 - x))^n/((1 - x)*n!).
  • A295384 (program): a(n) = n!*Sum_{k=0..n} (-1)^k*binomial(2*n,n-k)*n^k/k!.
  • A295385 (program): a(n) = n!*Sum_{k=0..n} binomial(2*n,n-k)*n^k/k!.
  • 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.
  • A295389 (program): Numbers whose sum of digits is squarefree.
  • A295405 (program): a(n) = 1 if n^2+1 is prime, 0 otherwise.
  • A295406 (program): a(n) = n! * Laguerre(n, 2*n, -n).
  • A295407 (program): a(n) = n! * Laguerre(n, 3*n, -n).
  • A295408 (program): a(n) = n! * Laguerre(n, 4*n, -n).
  • A295409 (program): a(n) = n! * Laguerre(n, n^2, -n).
  • A295418 (program): a(n) = n! * Laguerre(n, n*(n-1), -n).
  • A295420 (program): Number of total dominating sets in the n-Moebius ladder.
  • A295421 (program): Decimal expansion of the sum of the reciprocals of the dodecahedral numbers (A006566).
  • A295425 (program): a(n) = smallest number > a(n-1) such that the number of preceding terms in the sequence dividing a(n) is divisible by 4; a(1) = 2.
  • A295430 (program): a(n) is the least nontrivial multiple of n that begins with 3.
  • A295473 (program): a(0) = 0; for n>0, a(n) = 9*n!.
  • A295501 (program): a(n) = phi(4^n-1), where phi is Euler’s totient function (A000010).
  • A295505 (program): a(n) = Sum_{d|n} mu(n/d)*4^(d-1).
  • A295506 (program): a(n) = Sum_{d|n} mu(n/d)*5^(d-1).
  • 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).
  • A295525 (program): Number of n X 2 0..1 arrays with each 1 horizontally or vertically adjacent to 1, 2 or 4 1s.
  • A295552 (program): a(n) = n! * [x^n] exp(x*exp(n*x)).
  • A295553 (program): Expansion of 1/(1 - Sum_{k>=1} (2*k-1)!!*x^k).
  • 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).
  • A295561 (program): Prefixal-derivation of A092782.
  • A295568 (program): Irregular triangle, read by rows: the Catalan generating tree, read from left to right, row by row, starting at the root.
  • A295574 (program): a(n) = Sum_{1 <= j <= n/2, gcd(j,n)=1} j^2.
  • A295575 (program): a(n) = Sum_{1 <= j <= n/2, gcd(j,n)=1} j^3.
  • A295576 (program): a(n) = Sum_{1 <= j <= n/2, gcd(j,n)=1} j^4.
  • A295579 (program): Maximal value of a length-n “minimal good sequence” in the sense of Cavenagh et al. (2006).
  • A295581 (program): Maximal value of a length-n “minimal cyclically good sequence” in the sense of Cavenagh et al. (2006).
  • A295610 (program): a(n) = Sum_{k=0..n} (n!/(n - k)!)^k.
  • A295611 (program): a(n) = Sum_{k=0..n} (-1)^k*binomial(n,k)^k.
  • A295612 (program): a(n) = Sum_{k=0..n} binomial(n+k,k)^k.
  • A295619 (program): a(n) = a(n-1) + 3*a(n-2) - 2*a(n-3) - 2*a(n-4), where a(0) = 1, a(1) = 2, a(2) = 3, a(3) = 4.
  • A295622 (program): Number of nonequivalent dissections of an n-gon into 3 polygons by nonintersecting diagonals rooted at a cell up to rotation.
  • A295623 (program): a(n) = n! * [x^n] exp(n*x*exp(x)).
  • A295629 (program): Number of partitions of n into two parts such that not both are prime.
  • A295630 (program): Number of partitions of n into two distinct parts that are not both prime.
  • 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.
  • A295655 (program): a(n) = A000203(n) / A294896(n) = A000203(n) / gcd(A000203(n), A005187(n)).
  • A295656 (program): a(n) = A005187(n) / A294896(n) = A005187(n) / gcd(A000203(n), A005187(n)).
  • A295657 (program): Multiplicative with a(p^e) = p^floor((e-1)/2).
  • A295659 (program): Number of exponents larger than 2 in the prime factorization of n.
  • A295660 (program): Binary weight of Euler phi: a(n) = A000120(A000010(n)).
  • A295661 (program): Numbers with at least one odd exponent larger than one in their prime factorization.
  • A295662 (program): Number of odd exponents larger than one in the canonical prime factorization of n.
  • A295663 (program): a(n) = A295664(n) - A056169(n); 2-adic valuation of tau(n) minus the number of unitary prime divisors of 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).
  • A295671 (program): a(n) = a(n-1) + a(n-3) + a(n-4), where a(0) = 1, a(1) = 1, a(2) = 1, a(3) = -1.
  • A295672 (program): a(n) = a(n-1) + a(n-3) + a(n-4), where a(0) = 1, a(1) = 1, a(2) = 1, a(3) = -2.
  • A295673 (program): a(n) = a(n-1) + a(n-3) + a(n-4), where a(0) = 4, a(1) = 3, a(2) = 2, a(3) = 1.
  • A295674 (program): a(n) = a(n-1) + a(n-3) + a(n-4), where a(0) = 1, a(1) = 2, a(2) = 4, a(3) = 8.
  • A295675 (program): a(n) = a(n-1) + a(n-3) + a(n-4), where a(0) = 1, a(1) = 1, a(2) = 2, a(3) = -2.
  • A295676 (program): a(n) = a(n-1) + a(n-3) + a(n-4), where a(0) = 1, a(1) = 1, a(2) = 3, a(3) = -3.
  • A295677 (program): a(n) = a(n-1) + a(n-3) + a(n-4), where a(0) = 1, a(1) = 1, a(2) = 4, a(3) = -3.
  • A295678 (program): a(n) = a(n-1) + a(n-3) + a(n-4), where a(0) = 1, a(1) = 2, a(2) = 1, a(3) = 3.
  • 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.
  • A295681 (program): a(n) = a(n-1) + a(n-3) + a(n-4), where a(0) = 0, a(1) = 1, a(2) = 0, a(3) = 2.
  • A295682 (program): a(n) = a(n-1) + a(n-3) + a(n-4), where a(0) = 0, a(1) = 2, a(2) = 0, a(3) = 1.
  • A295683 (program): a(n) = a(n-1) + a(n-3) + a(n-4), where a(0) = 2, a(1) = 1, a(2) = 0, a(3) = 1.
  • A295684 (program): a(n) = a(n-1) + a(n-3) + a(n-4), where a(0) = 2, a(1) = 0, a(2) = 1, a(3) = 1.
  • A295685 (program): a(n) = a(n-1) + a(n-3) + a(n-4), where a(0) = 2, a(1) = 1, a(2) = 1, a(3) = 1.
  • A295686 (program): a(n) = a(n-1) + a(n-3) + a(n-4), where a(0) = 2, a(1) = 1, a(2) = 2, a(3) = 1.
  • A295687 (program): a(n) = a(n-1) + a(n-3) + a(n-4), where a(0) = 1, a(1) = 2, a(2) = 2, a(3) = 1.
  • A295688 (program): a(n) = a(n-1) + a(n-3) + a(n-4), where a(0) = 2, a(1) = 1, 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
  • A295690 (program): a(n) = a(n-1) + a(n-3) + a(n-4), where a(0) = 2, a(1) = 2, a(2) = 1, a(3) = 1.
  • A295691 (program): a(n) = a(n-1) + a(n-3) + a(n-4), where a(0) = 2, a(1) = 2, a(2) = 2, a(3) = 1.
  • A295717 (program): a(n) = a(n-1) + 3*a(n-2) -2*a(n-3) - 2*a(n-4), where a(0) = 1, a(1) = 3, a(2) = 5, a(3) = 7.
  • A295718 (program): a(n) = a(n-1) + 3*a(n-2) -2*a(n-3) - 2*a(n-4), where a(0) = 1, a(1) = 3, a(2) = 4, a(3) = 5.
  • A295719 (program): a(n) = a(n-1) + 3*a(n-2) -2*a(n-3) - 2*a(n-4), where a(0) = 1, a(1) = 3, a(2) = 6, a(3) = 10.
  • A295720 (program): a(n) = a(n-1) + 3*a(n-2) -2*a(n-3) - 2*a(n-4), where a(0) = 1, a(1) = 4, a(2) = 9, a(3) = 16.
  • A295721 (program): a(n) = a(n-1) + 3*a(n-2) -2*a(n-3) - 2*a(n-4), where a(0) = -1, a(1) = 2, a(2) = 3, a(3) = 4.
  • A295722 (program): a(n) = a(n-1) + 3*a(n-2) -2*a(n-3) - 2*a(n-4), where a(0) = -1, a(1) = -1, a(2) = 2, a(3) = 3.
  • A295723 (program): a(n) = a(n-1) + 3*a(n-2) -2*a(n-3) - 2*a(n-4), where a(0) = 0, a(1) = 1, a(2) = 2, a(3) = 3.
  • A295724 (program): a(n) = a(n-1) + 3*a(n-2) -2*a(n-3) - 2*a(n-4), where a(0) = 0, a(1) = 0, a(2) = 1, a(3) = 2.
  • A295725 (program): a(n) = a(n-1) + 3*a(n-2) -2*a(n-3) - 2*a(n-4), where a(0) = 0, a(1) = 0, a(2) = -1, a(3) = 1.
  • A295726 (program): a(n) = a(n-1) + 3*a(n-2) -2*a(n-3) - 2*a(n-4), where a(0) = 0, a(1) = -1, a(2) = 1, a(3) = 1.
  • A295727 (program): a(n) = a(n-1) + 3*a(n-2) -2*a(n-3) - 2*a(n-4), where a(0) = -1, a(1) = 1, a(2) = 1, a(3) = 1.
  • A295728 (program): a(n) = a(n-1) + 3*a(n-2) -2*a(n-3) - 2*a(n-4), where a(0) = 1, a(1) = -1, a(2) = 1, a(3) = 1.
  • A295729 (program): a(n) = a(n-1) + 3*a(n-2) -2*a(n-3) - 2*a(n-4), where a(0) = -1, a(1) = 0, a(2) = 1, a(3) = 1.
  • A295730 (program): a(n) = a(n-1) + 3*a(n-2) -2*a(n-3) - 2*a(n-4), where a(0) = -1, a(1) = 0, a(2) = 0, a(3) = 1.
  • A295731 (program): a(n) = a(n-1) + 3*a(n-2) -2*a(n-3) - 2*a(n-4), where a(0) = -1, a(1) = -1, a(2) = 0, a(3) = 1.
  • A295732 (program): a(n) = a(n-1) + 3*a(n-2) -2*a(n-3) - 2*a(n-4), where a(0) = -1, a(1) = -1, a(2) = -1, a(3) = 1.
  • A295733 (program): a(n) = a(n-1) + 3*a(n-2) -2*a(n-3) - 2*a(n-4), where a(0) = 0, a(1) = -1, a(2) = -1, a(3) = 1.
  • A295734 (program): a(n) = a(n-1) + 3*a(n-2) -2*a(n-3) - 2*a(n-4), where a(0) = 0, a(1) = 0, a(2) = -1, a(3) = 2.
  • A295735 (program): a(n) = a(n-1) + 3*a(n-2) -2*a(n-3) - 2*a(n-4), where a(0) = 0, a(1) = -1, a(2) = 0, a(3) = 1.
  • A295736 (program): a(n) = a(n-1) + 3*a(n-2) -2*a(n-3) - 2*a(n-4), where a(0) = 1, a(1) = -2, a(2) = -2, a(3) = 1.
  • A295737 (program): a(n) = a(n-1) + 3*a(n-2) -2*a(n-3) - 2*a(n-4), where a(0) = 1, a(1) = -1, a(2) = -1, a(3) = 2.
  • A295771 (program): a(n) is the minimum size of a planar additive basis for the square [0,n]^2.
  • A295772 (program): a(n) = Sum_{k=0..n} binomial((n-k)*k, k).
  • 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.
  • A295782 (program): Square array A(n,k), n >= 1, k >= 1, read by antidiagonals, where A(n,k) is the number of coprime pairs (a,b) with -n <= a <= n, -k <= b <= k.
  • A295792 (program): Expansion of e.g.f. Product_{k>=1} ((1 + x^k)/(1 - x^k))^(1/k).
  • A295796 (program): The only integers that cannot be partitioned into a sum of seven positive squares.
  • A295819 (program): Number of nonnegative solutions to (x,y) = 1 and x^2 + y^2 = n.
  • A295820 (program): Number of nonnegative solutions to (x,y) = 1 and x^2 + y^2 <= n.
  • 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.
  • A295833 (program): Expansion of e.g.f. Product_{k>=1} (1 + x^k)^((-1)^k/k).
  • A295834 (program): Expansion of e.g.f. Product_{k>=1} (1 + x^k)^((-1)^(k+1)/k).
  • A295835 (program): Numbers k == 3 (mod 4) such that 2^((k-1)/2), 3^((k-1)/2) and 5^((k-1)/2) are congruent to 1 (mod k).
  • A295838 (program): Largest value corresponding to a string of n printable ASCII characters.
  • A295839 (program): a(n) is the number of ways of inserting parentheses into the expression i^i^i^…^i with n i’s such that the result is a real value.
  • A295841 (program): Number of n X 2 0..1 arrays with each 1 adjacent to 1 or 2 king-move neighboring 1s.
  • A295850 (program): a(n) = a(n-1) + 3*a(n-2) -2*a(n-3) - 2*a(n-4), where a(0) = 0, a(1) = 0, a(2) = 2, a(3) = 1.
  • A295851 (program): a(n) = a(n-1) + 3*a(n-2) -2*a(n-3) - 2*a(n-4), where a(0) = 0, a(1) = -1, a(2) = 2, a(3) = 1.
  • A295852 (program): a(n) = a(n-1) + 3*a(n-2) -2*a(n-3) - 2*a(n-4), where a(0) = -1, a(1) = -1, a(2) = 2, a(3) = 1.
  • A295853 (program): a(n) = a(n-1) + 3*a(n-2) -2*a(n-3) - 2*a(n-4), where a(0) = -2, a(1) = -1, a(2) = 2, a(3) = 1.
  • A295854 (program): a(n) = a(n-1) + 3*a(n-2) -2*a(n-3) - 2*a(n-4), where a(0) = -2, a(1) = -2, a(2) = 2, a(3) = 1.
  • A295855 (program): a(n) = a(n-1) + 3*a(n-2) -2*a(n-3) - 2*a(n-4), where a(0) = 1, a(1) = -2, a(2) = 2, a(3) = 1.
  • A295856 (program): a(n) = a(n-1) + 3*a(n-2) -2*a(n-3) - 2*a(n-4), where a(0) = 0, a(1) = 0, a(2) = 3, a(3) = 1.
  • A295857 (program): a(n) = a(n-1) + 3*a(n-2) -2*a(n-3) - 2*a(n-4), where a(0) = 0, a(1) = 0, a(2) = 2, a(3) = 3.
  • A295858 (program): a(n) = a(n-1) + 3*a(n-2) -2*a(n-3) - 2*a(n-4), where a(0) = -2, a(1) = 0, a(2) = 0, a(3) = 1.
  • A295859 (program): a(n) = a(n-1) + 3*a(n-2) -2*a(n-3) - 2*a(n-4), where a(0) = -2, a(1) = 0, a(2) = 1, a(3) = 1.
  • A295860 (program): a(n) = a(n-1) + 3*a(n-2) -2*a(n-3) - 2*a(n-4), where a(0) = -2, a(1) = 1, a(2) = 0, a(3) = 1.
  • A295861 (program): a(n) = a(n-1) + 3*a(n-2) -2*a(n-3) - 2*a(n-4), where a(0) = -2, a(1) = -1, a(2) = 0, a(3) = 1.
  • A295864 (program): a(n) = hypergeom([-n, -n], [1], 1) * n! / (floor(n/2)!)^2.
  • A295866 (program): Number of decimal digits in the number of partitions of n.
  • A295868 (program): Initial digit of the number of partitions of n.
  • A295869 (program): Numbers not divisible by 2, 3 or 5 (A007775) with digital root 8.
  • A295870 (program): a(n) = binomial(3n,n)*CQC(n), where CQC(n) = A005721(n) = A005190(2n) is a central quadrinomial coefficient.
  • A295871 (program): a(n) = numerator(hypergeom([-n, 1/2], [1], 1)*hypergeom([-floor(n/2), (-1)^n/2], [1], 1)).
  • A295873 (program): Number of permutations of length n which avoid the patterns 1342, 2413, 3124 and 3142.
  • A295875 (program): Let p = A295895(n) = parity of the binary weight of A005940(1+n). If A005940(1+n) is a square or twice a square (in A028982) then a(n) = 1 - p, otherwise a(n) = p.
  • A295879 (program): Multiplicative with a(p) = 1, a(p^e) = prime(e-1) if e > 1.
  • A295883 (program): Number of exponents that are 3 in the prime factorization of n.
  • 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).
  • A295894 (program): Binary weight of the contents of node n in Doudna-tree (A005940).
  • A295895 (program): Parity of the binary weight of the contents of node n in Doudna-tree (A005940).
  • 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.
  • A295897 (program): Numbers in whose binary expansion there are no 1-runs of odd length followed by a 0 to their right.
  • 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.
  • A295909 (program): Number of (not necessarily maximum) cliques in the n X n black bishop graph.
  • A295910 (program): Number of (not necessarily maximum) cliques in the n X n white bishop graph.
  • A295911 (program): Number of (not necessarily maximal) cliques in the n-Hanoi graph.
  • A295913 (program): Number of n X 3 0..1 arrays with each 1 adjacent to 0 or 3 king-move neighboring 1s.
  • A295920 (program): Number of twice-factorizations of n of type (P,R,R).
  • A295921 (program): Number of (not necessarily maximum) cliques in the n-folded cube graph.
  • A295925 (program): Number of bilaterally asymmetric 8-hoops with n symbols.
  • A295926 (program): Number of (not necessarily maximum) cliques in the n-cube-connected cycle graph.
  • A295931 (program): Number of ways to write n in the form n = (x^y)^z where x, y, and z are positive integers.
  • A295932 (program): Number of (not necessarily maximum) cliques in the n-Sierpinski carpet graph.
  • A295933 (program): Number of (not necessarily maximum) cliques in the n-Sierpinski sieve graph.
  • A295934 (program): Number of (not necessarily maximum) cliques in the n-odd graph.
  • A295937 (program): Number of n X 2 0..1 arrays with each 1 adjacent to 1 or 3 king-move neighboring 1s.
  • A295979 (program): Number of n X 2 0..1 arrays with each 1 adjacent to 2 or 3 king-move neighboring 1s.
  • A295986 (program): Number of maximal cliques in the n-halved cube graph.
  • A295989 (program): Irregular triangle T(n, k), read by rows, n >= 0 and 0 <= k < A001316(n): T(n, k) is the (k+1)-th nonnegative number m such that n AND m = m (where AND denotes the bitwise AND operator).
  • A296020 (program): Number of primes of the form 4*k+3 <= 4*n+3.
  • A296021 (program): Number of primes of the form 4*k+1 <= 4*n+1.
  • A296028 (program): Characteristic function of primes in the nonmultiples of 3.
  • A296033 (program): Number of n X 2 0..1 arrays with each 1 adjacent to 2 or 4 king-move neighboring 1s.
  • A296043 (program): a(n) = [x^n] Product_{k>=1} ((1 + x^(2*k-1))/(1 + x^(2*k)))^n.
  • A296044 (program): a(n) = [x^n] Product_{k>=1} ((1 + x^(2*k))/(1 - x^(2*k-1)))^n.
  • A296048 (program): Expansion of e.g.f. Product_{k>=1} ((1 - x^k)/(1 + x^k))^(1/k).
  • 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.
  • A296064 (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 an integer. Preference is given to positive values of a(n).
  • 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.
  • A296073 (program): Filter combining A296071(n) and A296072(n), related to the deficiencies of proper divisors of n.
  • A296074 (program): Sum of deficiencies of the proper divisors of n.
  • A296075 (program): Sum of deficiencies of divisors of n.
  • A296078 (program): Least number with the same prime signature as 1+phi(n), where phi = A000010, Euler totient function.
  • A296079 (program): a(n) = 1 if 1+phi(n) is prime, 0 otherwise, where phi = A000010, Euler totient function.
  • A296081 (program): a(n) = gcd(tau(n)-1, sigma(n)-1), where tau = A000005 and sigma = A000203.
  • A296082 (program): a(1) = 0; for n > 1, a(n) = A032741(n) / gcd(A039653(n),A032741(n)).
  • A296083 (program): a(1) = 0; for n > 1, a(n) = A039653(n) / gcd(A039653(n),A032741(n)).
  • A296084 (program): a(1) = 0 and for n > 1, a(n) = 1 if tau(n)-1 divides sigma(n)-1, 0 otherwise. Here tau = A000005, sigma = A000203.
  • A296091 (program): a(1) = 1 and for n > 1, the least number with the same prime signature as sigma(n)-1.
  • A296092 (program): Least number with the same prime signature as sigma(n)+1.
  • A296102 (program): Number of total dominating sets in the n-prism graph.
  • A296109 (program): Number of n X 2 0..1 arrays with each 1 adjacent to 3 or 4 king-move neighboring 1s.
  • 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.
  • A296162 (program): a(n) = [x^n] Product_{k>=1} ((1 - x^(3*k))/(1 - x^k))^n.
  • 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.
  • A296189 (program): Harary index for the n-Keller graph.
  • 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.
  • A296204 (program): Numbers k such that Product_{d|k, gcd(d,k/d) is prime} gcd(d,k/d) = k; the fixed points of A295666.
  • A296205 (program): Numbers k such that Product_{d|k^2, gcd(d,k^2/d) is prime} gcd(d,k^2/d) = k^2.
  • A296209 (program): a(n) = 1 if n is a pentanacci number, 0 otherwise; characteristic function for A001591.
  • 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.
  • A296229 (program): Triangle read by rows: Eulerian triangle that produces sums of even powers.
  • A296239 (program): a(n) = distance from n to nearest Fibonacci number.
  • A296243 (program): Numbers k such that the multiplicative order of 2 modulo k is even.
  • A296299 (program): Dimension of the n-th component of a certain graded Lie algebra.
  • A296304 (program): Numbers whose absolute difference from a square is never a prime.
  • A296306 (program): a(n) = A001157(n)/A050999(n).
  • A296307 (program): Array read by upwards antidiagonals: f(n,k) = (n+1)*ceiling(n/(k-1)) - 1.
  • A296309 (program): Number of n X 4 0..1 arrays with each 1 adjacent to 3 or 6 king-move neighboring 1s.
  • A296329 (program): Number of n X 2 0..1 arrays with each 1 horizontally, vertically or antidiagonally adjacent to 0 or 2 neighboring 1s.
  • A296349 (program): Position where binary expansion of n starts in the binary Champernowne sequence A030190.
  • A296350 (program): List of numbers k such that the determinant of the Bordered Lights Out matrix BL_k is nonzero.
  • A296352 (program): List of numbers k such that the determinant of the Unordered Lights Out matrix UBL_k is nonzero.
  • A296354 (program): Official position where binary expansion of n starts in the list of binary numbers in the binary Champernowne sequence A076478.
  • A296357 (program): a(n) = ceiling of n/Pi.
  • A296359 (program): Number of monohedral disk tilings of type C^t_{2n+1,2}.
  • A296363 (program): a(1)=0; for n>1, a(n) = 4*n^3 - 3*n^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.
  • A296371 (program): Number of integer partitions of n using Jacobsthal numbers.
  • A296376 (program): Natural numbers x such that 7*y^2 = x^2 + x + 1 has a solution in natural numbers.
  • A296377 (program): Natural numbers y such that 7y^2 = x^2 + x + 1 has a solution in natural numbers.
  • A296397 (program): a(n) = a(n-1) * a(n-2) + a(n-3) * Product_{k=0..n-4} a(k)^2, with a(0) = a(1) = 1, a(2) = 2.
  • A296420 (program): Period of last digit of multiples of n.
  • A296442 (program): Initial digit of n-th Mersenne number.
  • A296507 (program): Numbers m such that m^2 - 13 is a prime.
  • A296509 (program): Duplicate of A238005.
  • A296515 (program): Number of edges in a maximal planar graph with n vertices.
  • A296519 (program): Denominator of n*Sum_{k=1..n} 1/(n+k).
  • A296522 (program): Number of disjoint covering systems of cardinality n with gcd of the moduli equal to 1.
  • A296550 (program): Number of n X 4 0..1 arrays with each 1 horizontally, vertically or antidiagonally adjacent to 3 or 6 neighboring 1s.
  • A296579 (program): Numbers that are not the sum of 3 squares and a nonnegative 9th power.
  • A296589 (program): a(n) = Product_{k=0..n} binomial(2*n, k).
  • A296590 (program): a(n) = Product_{k=0..n} binomial(2*n - k, k).
  • A296601 (program): L.g.f.: -log(Product_{k>=1} (1 - k*x^k)^k) = Sum_{n>=1} a(n)*x^n/n.
  • A296606 (program): Numbers k such that d*k does not contain the digit d for any d in {1,2,3,4,5,6,7,8,9}.
  • A296612 (program): Square array read by antidiagonals upwards: T(n,k) equals k times the number of compositions (ordered partitions) of n, with n >= 0 and k >= 1.
  • 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.
  • A296617 (program): Expansion of 1/Sum_{k>=0} (k+1)^(k+1)*x^k.
  • A296618 (program): Expansion of the e.g.f. exp(-x)/sqrt(1-4*x).
  • A296619 (program): The number of nonnegative walks of n steps with step sizes 1 and 2, starting at 0 and ending at 2.
  • A296645 (program): Number of n X 2 0..1 arrays with each 1 adjacent to 0, 1 or 3 king-move neighboring 1s.
  • A296660 (program): Expansion of the e.g.f. exp(-2*x)/(1-4*x).
  • A296661 (program): a(n) = (exp(k)*Gamma(1+n, k) - exp(-k)*Gamma(1+n, -k))/k! for k = 3.
  • A296663 (program): Row sums of A296664.
  • A296665 (program): Row sums of A296666.
  • A296668 (program): Number of n X 2 0..1 arrays with each 1 adjacent to 0, 2 or 3 king-move neighboring 1s.
  • A296715 (program): a(n) = [x^n] 1/Sum_{k=0..n} k^k*x^k.
  • A296716 (program): Numbers congruent to {7, 11, 13, 29} mod 30.
  • A296719 (program): Number of n X 2 0..1 arrays with each 1 adjacent to 0, 2 or 4 king-move neighboring 1s.
  • A296726 (program): Expansion of e.g.f. arcsin(x)/(1 - x).
  • A296727 (program): Expansion of e.g.f. arcsinh(x)/(1 - x).
  • A296760 (program): Numbers n whose base-16 digits d(m), d(m-1), …, d(0) have #(rises) > #(falls); see Comments.
  • A296764 (program): Numbers n whose base-20 digits d(m), d(m-1), …, d(0) have #(rises) < #(falls); see Comments.
  • A296767 (program): Numbers n whose base-60 digits d(m), d(m-1), …, d(0) have #(rises) < #(falls); see Comments.
  • A296769 (program): Row sums of A296662.
  • A296770 (program): Row sums of A050158.
  • A296771 (program): Row sums of A050157.
  • A296775 (program): Expansion of 1/Sum_{k>=0} A000326(k+1)*x^k.
  • A296779 (program): Detour index of the n X n grid graph.
  • A296780 (program): Detour index of the n X n X n grid graph.
  • A296784 (program): Detour index for the n X n torus grid graph.
  • A296785 (program): Detour index for the n-transposition graph.
  • A296798 (program): Number of n X 2 0..1 arrays with each 1 adjacent to 1, 3 or 4 king-move neighboring 1s.
  • A296805 (program): Sum of the larger parts in the partitions of n into two distinct parts with the larger part even.
  • A296817 (program): Expansion of 1/Sum_{k>=0} (2*k+1)^2*x^k.
  • A296819 (program): Maximum detour index of any bipartite graph on n nodes.
  • A296888 (program): Numbers n whose base-12 digits d(m), d(m-1), …, d(0) have #(pits) = #(peaks); see Comments.
  • A296891 (program): Numbers n whose base-13 digits d(m), d(m-1), …, d(0) have #(pits) = #(peaks); see Comments.
  • A296902 (program): Numbers n whose base-16 digits d(m), d(m-1), …, d(0) have #(pits) < #(peaks); see Comments.
  • A296905 (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.
  • A296908 (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) = 4*n-2*(-1)^n.
  • A296911 (program): Partial sums of A296910.
  • A296920 (program): Rational primes that decompose in the quadratic field Q(sqrt(-11)).
  • A296922 (program): Primes p such that Legendre(-5,p) = 0 or 1.
  • A296923 (program): Primes p such that Legendre(-5,p) = -1.
  • A296924 (program): Primes p such that Legendre(-6,p) = 0 or 1.
  • A296933 (program): Primes p such that Legendre(3,p) = 0 or 1.
  • A296943 (program): Number of bisymmetric and quasitrivial operations on an arbitrary n-element set.
  • A296944 (program): Expansion of (2*x*exp(x)-3)/(1-x).
  • A296946 (program): Number of n X 2 0..1 arrays with each 1 adjacent to 1, 3 or 5 king-move neighboring 1s.
  • 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 + 4*x^2) / ((1 - x)*(1 - 2*x)).
  • A296955 (program): Sum of the smaller parts of the partitions of n into two distinct parts such that the smaller part divides the larger.
  • A296957 (program): Number of n X 2 0..1 arrays with each 1 adjacent to 2, 3 or 5 king-move neighboring 1s.
  • A296964 (program): Expansion of (x*exp(x)-1)/(1-x).
  • A296965 (program): Expansion of x*(1 - x + 2*x^2) / ((1 - x)*(1 - 2*x)).
  • A296966 (program): Sum of all the parts in the partitions of n into two distinct parts such that the smaller part divides the larger.
  • A296968 (program): Number of n X 2 0..1 arrays with each 1 adjacent to 2, 4 or 5 king-move neighboring 1s.
  • A296984 (program): Number of n X 2 0..1 arrays with each 1 adjacent to 3, 4 or 5 king-move neighboring 1s.
  • A296997 (program): Number of ways to place 3 points on an n X n point grid so that no point is equally distant from two other points on the same row or the same column.
  • A297002 (program): Completely multiplicative with a(prime(k)) = prime(2 * k) (where prime(k) denotes the k-th prime).
  • 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.
  • A297025 (program): Number of iterations of A220096 required to reach 0 starting from n.
  • A297030 (program): Number of pieces in the list d(m), d(m-1), …, d(0) of base-2 digits of n; see Comments.
  • A297038 (program): Number of pieces in the list d(m), d(m-1), …, d(0) of base-10 digits of n; see Comments.
  • A297039 (program): Number of pieces in the list d(m), d(m-1), …, d(0) of base-11 digits of n; see Comments.
  • A297040 (program): Number of pieces in the list d(m), d(m-1), …, d(0) of base-12 digits of n; see Comments.
  • A297041 (program): Number of pieces in the list d(m), d(m-1), …, d(0) of base-13 digits of n; see Comments.
  • A297042 (program): Number of pieces in the list d(m), d(m-1), …, d(0) of base-14 digits of n; see Comments.
  • A297043 (program): Number of pieces in the list d(m), d(m-1), …, d(0) of base-15 digits of n; see Comments.
  • A297044 (program): Number of pieces in the list d(m), d(m-1), …, d(0) of base-16 digits of n; see Comments.
  • A297045 (program): Number of pieces in the list d(m), d(m-1), …, d(0) of base-20 digits of n; see Comments.
  • A297047 (program): Number of edge covers in the n-wheel graph.
  • A297053 (program): Sum of the larger parts of the partitions of n into two parts such that the smaller part does not divide the larger.
  • A297054 (program): The coefficients of the product (1-x^2)(1-x^3)(1-x^4)… / (1+x).
  • A297086 (program): a(n) = 1 if gcd(n, phi(n)) == 1 otherwise 0.
  • A297108 (program): If n is prime(k)^e, e >= 1, then a(n) = 2^(k-1), otherwise 0; Möbius transform of A048675.
  • A297109 (program): If n is prime(k)^e, e >= 1, then a(n) = k, otherwise 0.
  • A297111 (program): Möbius transform of A005187, where A005187(n) = 2n - (number of 1’s in binary representation of n).
  • A297112 (program): Möbius transform of A156552.
  • A297113 (program): a(1) = 0, a(2) = 1, after which, a(n) = a(n/2) if n is of the form 4k+2, and otherwise a(n) = 1+a(A252463(n)).
  • A297114 (program): Möbius transform of A294898, where A294898(n) = A005187(n) - A000203(n).
  • A297115 (program): Möbius transform of A000120, binary weight of n.
  • A297116 (program): Odd bisection of A297115, Möbius transform of A000120 (binary weight of n).
  • A297117 (program): Möbius transform of A011371, n minus (number of 1’s in binary expansion of n).
  • A297124 (program): Numbers having an up-first zigzag pattern in base 3; see Comments.
  • A297126 (program): Numbers whose base-3 digits d(m), d(m-1),…, d(0) have m=0 or else d(i) = d(i+1) for some i in {0,1,…,m-1}.
  • A297130 (program): Numbers whose base-4 digits d(m), d(m-1),…, d(0) have m=0 or else d(i) = d(i+1) for some i in {0,1,…,m-1}.
  • A297133 (program): Numbers whose base-5 digits d(m), d(m-1),…, d(0) have m=0 or else d(i) = d(i+1) for some i in {0,1,…,m-1}.
  • A297142 (program): Numbers whose base-8 digits d(m), d(m-1),…, d(0) have m=0 or else d(i) = d(i+1) for some i in {0,1,…,m-1}.
  • A297150 (program): Let b(k) denote A292081(k); the sequence lists numbers b(2n) where for all m > n, b(2m) > b(2n).
  • A297151 (program): a(n) = Sum_{i=0..n} Sum_{j=0..n} Sum_{k=0..n} binomial(n,i)*binomial(n,j)*binomial(n,k)*max(i,j,k).
  • 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)).
  • A297159 (program): a(n) = 3*n - 2*phi(n) - sigma(n); Difference between the deficiency of n and its Moebius-transform.
  • A297163 (program): Permutation of natural numbers: a(n) = A156552(1+A005940(1+n)).
  • A297164 (program): Permutation of nonnegative integers: a(n) = A156552(A005940(1+n)-1).
  • A297167 (program): a(1) = 0, for n > 1, a(n) = -1 + the excess of n (A046660) + the index of the largest prime factor (A061395).
  • A297168 (program): Difference between A156552 and its Moebius transform: a(n) = A156552(n) - A297112(n).
  • A297170 (program): a(n) = gcd(phi(n), sigma(n)-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.
  • A297189 (program): Expansion of (x + 3*x^2 - 2*x^3 - 3*x^4)/(1 - 8*x^2 + 9*x^4).
  • A297191 (program): Irregular triangle read by rows formed by taking every other row of the Delannoy array (A008288) regarded as a triangle.
  • A297192 (program): Left-hand half of triangle A297191.
  • A297193 (program): Irregular triangle read by rows: rows are partial alternating sums of rows of A297191.
  • A297194 (program): Left-hand half of triangle A297193.
  • A297208 (program): a(0)=0; for n >= 1, a(n) = a(n-1-A023416(n)) + A000120(n).
  • A297219 (program): Number of n X 3 0..1 arrays with every 1 horizontally or antidiagonally adjacent to 1 neighboring 1s.
  • A297220 (program): Number of n X 4 0..1 arrays with every 1 horizontally or antidiagonally adjacent to 1 neighboring 1s.
  • A297232 (program): Up-variation of the base-11 digits of n; see Comments.
  • A297235 (program): Up-variation of the base-12 digits of n; see Comments.
  • A297249 (program): Numbers whose base-3 digits have greater down-variation than up-variation; see Comments.
  • 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.
  • A297252 (program): Numbers whose base-4 digits have greater down-variation than up-variation; see Comments.
  • A297253 (program): Numbers whose base-4 digits having equal up-variation and down-variation; see Comments.
  • A297256 (program): Numbers whose base-5 digits have equal down-variation and up-variation; see Comments.
  • A297259 (program): Numbers whose base-6 digits have equal down-variation and up-variation; see Comments.
  • A297265 (program): Numbers whose base-8 digits have equal down-variation and up-variation; see Comments.
  • A297270 (program): Numbers whose base-10 digits have greater down-variation than up-variation; see Comments.
  • A297271 (program): Numbers whose base-10 digits have equal down-variation and up-variation; see Comments.
  • A297272 (program): Numbers whose base-10 digits have greater up-variation than down-variation; see Comments.
  • A297287 (program): Numbers whose base-15 digits have greater up-variation than down-variation; see Comments.
  • A297290 (program): Numbers whose base-16 digits have greater up-variation than down-variation; see Comments.
  • A297296 (program): Number of n X 5 0..1 arrays with every 1 horizontally or antidiagonally adjacent to 2 neighboring 1s.
  • A297300 (program): Number of 3 X n 0..1 arrays with every 1 horizontally or antidiagonally adjacent to 2 neighboring 1s.
  • A297333 (program): Number of n X 3 0..1 arrays with every 1 horizontally or antidiagonally adjacent to 0 or 2 neighboring 1s.
  • A297339 (program): Number of 2 X n 0..1 arrays with every 1 horizontally or antidiagonally adjacent to 0 or 2 neighboring 1s.
  • 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.
  • A297369 (program): Number of n X 3 0..1 arrays with every 1 horizontally or antidiagonally adjacent to 0, 1 or 2 neighboring 1s.
  • A297381 (program): Numerator of -A023900(n)/2.
  • A297382 (program): Denominator of -A023900(n)/2.
  • A297384 (program): Number of Eulerian cycles in the n-antiprism graph.
  • A297390 (program): Number of n X 3 0..1 arrays with every 1 horizontally, diagonally or antidiagonally adjacent to 1 neighboring 1.
  • A297396 (program): Number of 3 X n 0..1 arrays with every 1 horizontally, diagonally or antidiagonally adjacent to 1 neighboring 1.
  • A297401 (program): Non-sphenic numbers with exactly 8 divisors.
  • A297402 (program): a(n) = gcd_{k=1..n} (prime(k+1)^n-1)/2.
  • A297404 (program): A binary representation of the positive exponents that appear in the prime factorization of a number, shown in decimal.
  • A297405 (program): Binary “cubes”; numbers whose binary representation consists of three consecutive identical blocks.
  • A297432 (program): Number of 2 X n 0..1 arrays with every 1 horizontally, diagonally or antidiagonally adjacent to 2 neighboring 1s.
  • A297439 (program): Number of maximum independent vertex sets and minimum vertex covers in the n-web graph.
  • A297443 (program): a(n) = a(n-1) + 2*a(n-2) - 2*a(n-3) + 3*a(n-4) - 3*a(n-5), where a(0) = 1, a(1) = 3, a(2) = 6, a(3) = 11, a(4) = 20, a(5) = 33.
  • A297444 (program): a(n) = a(n-1) + 9*a(n-2) - 9*a(n-3), where a(0) = 1, a(1) = 3, a(2) = 6, a(3) = 33.
  • A297445 (program): a(n) = a(n-1) + 9*a(n-2) - 9*a(n-3), where a(0) = 1, a(1) = 5, a(2) = 11.
  • A297446 (program): a(1) = 1; a(n) = (2^n - 1)*((3^n - 1)/(2^n - 1) mod 1), n >= 2. Unreduced numerators of fractional parts of (3^n - 1)/(2^n - 1).
  • A297458 (program): Number of 2 X n 0..1 arrays with every 1 horizontally, diagonally or antidiagonally adjacent to 0 or 2 neighboring 1s.
  • A297464 (program): Solution (a(n)) of the system of 4 complementary equations in Comments.
  • A297465 (program): Solution (b(n)) of the system of 4 complementary equations in Comments.
  • A297466 (program): Solution (c(n)) of the system of 4 complementary equations in Comments.
  • A297469 (program): Solution (bb(n)) of the system of 3 complementary equations in Comments.
  • A297470 (program): Number of maximal matchings in the n-barbell graph.
  • A297474 (program): Number of maximal matchings in the n-cocktail party graph.
  • A297491 (program): a(n) = (1/2) * Sum_{|k|<=2*sqrt(p)} k^4*H(4*p-k^2) where H() is the Hurwitz class number and p is n-th prime.
  • A297520 (program): Number of 2 X n 0..1 arrays with every 1 horizontally, diagonally or antidiagonally adjacent to 1 or 3 neighboring 1s.
  • A297554 (program): a(n) = a(n-2) + 4*a(n-3) - 4*a(n-5), where a(0) = 1, a(1) = 4, a(2) = 7, a(3) = 12, a(4) = 19, a(5) = 28.
  • A297555 (program): a(n) = a(n-1) + 16*a(n-3) - 16*a(n-4), where a(0) = 1, a(1) = 4, a(2) = 8, a(3) = 12, a(4) = 76.
  • A297556 (program): a(n) = a(n-1) + 16*a(n-3) - 16*a(n-4), where a(0) = 1, a(1) = 4, a(2) = 7, a(3) = 19.
  • A297575 (program): Numbers whose sum of divisors is divisible by 10.
  • A297583 (program): Number of 2 X n 0..1 arrays with every 1 horizontally, diagonally or antidiagonally adjacent to 1 or 4 neighboring 1s.
  • A297616 (program): a(n) is the number of connected components in the graph with vertices 1..n and adjacency criterion i and j not coprime.
  • A297619 (program): a(n) = 2*a(n-1) + 2*a(n-2) - 4*a(n-3), a(1) = 0, a(2) = 0, a(3) = 8.
  • A297661 (program): a(n) = n + 2*cos((n*Pi)/3) + Lucas(n).
  • A297662 (program): Number of chordless cycles in the complete tripartite graph K_n,n,n.
  • A297663 (program): a(n) = 5*n + 2^n.
  • A297665 (program): Number of chordless cycles in the n-web graph.
  • A297667 (program): Number of chordless cycles in the n-Moebius ladder.
  • A297670 (program): Number of chordless cycles in the n-triangular graph.
  • A297675 (program): a(n) = 3*(n^2+n-4)/2.
  • A297695 (program): Number of 2Xn 0..1 arrays with every 1 horizontally, diagonally or antidiagonally adjacent to 0, 2 or 4 neighboring 1s.
  • A297701 (program): Decimal expansion of 1 + sqrt(2) + sqrt(3).
  • A297704 (program): Triangle read by rows, T(n,k) = binomial(n, k)*hypergeom2F1(k - n, n + 1, k + 2, -2) for n >= 0 and 0 <= k <= n.
  • A297705 (program): a(n) = Sum_{k=0..n} binomial(n, k)*hypergeom([k - n, n + 1], [k + 2], -4).
  • A297708 (program): Number of permutations p of [n] such that p(p(i)) = i for all i or p(n+1-p(i)) = n+1-i for all i.
  • A297734 (program): Number of 2Xn 0..1 arrays with every 1 horizontally, diagonally or antidiagonally adjacent to 2 or 4 neighboring 1s.
  • A297763 (program): Number of 2Xn 0..1 arrays with every 1 horizontally, diagonally or antidiagonally adjacent to 2, 3 or 4 neighboring 1s.
  • A297778 (program): Number of distinct runs in base-10 digits of n.
  • 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.
  • A297809 (program): Number of n X 2 0..1 arrays with every element equal to 2 or 3 king-move adjacent elements, with upper left element zero.
  • A297830 (program): Solution of the complementary equation a(n) = a(1)*b(n-1) - a(0)*b(n-2) + 2*n, where a(0) = 1, a(1) = 2, b(0) = 3, b(1) = 4, and (b(n)) is the increasing sequence of positive integers not in (a(n)). See Comments.
  • A297831 (program): Solution of the complementary equation a(n) = a(1)*b(n-1) - a(0)*b(n-2) + 2*n - 1, where a(0) = 1, a(1) = 2, b(0) = 3, b(1) = 4, and (b(n)) is the increasing sequence of positive integers not in (a(n)). See Comments.
  • A297832 (program): Solution of the complementary equation a(n) = a(1)*b(n-1) - a(0)*b(n-2) + 2*n - 2, where a(0) = 1, a(1) = 2, b(0) = 3, b(1) = 4, and (b(n)) is the increasing sequence of positive integers not in (a(n)). See Comments.
  • A297833 (program): Solution of the complementary equation a(n) = a(1)*b(n-1) - a(0)*b(n-2) + 2*n - 3, where a(0) = 1, a(1) = 2, b(0) = 3, b(1) = 4, and (b(n)) is the increasing sequence of positive integers not in (a(n)). See Comments.
  • A297834 (program): Solution of the complementary equation a(n) = a(1)*b(n-1) - a(0)*b(n-2) + 2*n - 4, where a(0) = 1, a(1) = 2, b(0) = 3, b(1) = 4, and (b(n)) is the increasing sequence of positive integers not in (a(n)). See Comments.
  • A297841 (program): a(n) = Sum_{d|n} max(d, n/d)^2.
  • A297842 (program): a(n) = Sum_{d|n} max(d, n/d)^3.
  • A297843 (program): a(n) = Sum_{d|n} max(d, n/d)^4.
  • A297844 (program): a(n) = Sum_{d|n} max(d, n/d)^5.
  • A297860 (program): Number of n X 2 0..1 arrays with every element equal to 2, 3 or 4 king-move adjacent elements, with upper left element zero.
  • A297870 (program): Number of nX2 0..1 arrays with every element equal to 2, 3 or 5 king-move adjacent elements, with upper left element zero.
  • A297898 (program): Triangle read by rows, T(n, k) = (-1)^(n-k)*binomial(n,k)*hypergeom([k - n, n + 1], k + 1, 2), for n >= 0 and 0 <= k <= n.
  • A297899 (program): Triangle read by rows, T(n, k) = binomial(n, k)*hypergeom([k-n, n+1], [k+2], -4), for n >= 0 and 0 <= k <= n.
  • A297909 (program): Number of n X 2 0..1 arrays with every element equal to 0, 2, 3 or 4 king-move adjacent elements, with upper left element zero.
  • A297924 (program): Number of set partitions of [2n] in which the size of the last block is n.
  • A297925 (program): Even numbers k such that k - 5 is prime but k - 3 is not prime.
  • A297926 (program): Number of set partitions of [2n] in which the size of the first block is n.
  • A297928 (program): a(n) = 2*4^n + 3*2^n - 1.
  • A297937 (program): Number of nX2 0..1 arrays with every element equal to 0, 2, 3 or 5 king-move adjacent elements, with upper left element zero.
  • A297953 (program): Number of n X 2 0..1 arrays with every element equal to 1, 2, 4 or 5 king-move adjacent elements, with upper left element zero.
  • A297965 (program): a(n) = Fibonacci(binomial(n+3, 3)).
  • A297966 (program): a(n) = 3^n mod prime(n).
  • A297967 (program): a(n) = 5^n mod prime(n).
  • A297970 (program): Numbers that are not the sum of 3 squares and a nonnegative 7th power.
  • A297972 (program): Number of n X 2 0..1 arrays with every element equal to 2, 3, 4 or 5 king-move adjacent elements, with upper left element zero.
  • A297980 (program): Number of n X 2 0..1 arrays with every element equal to 0, 2, 3 or 6 king-move adjacent elements, with upper left element zero.
  • 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).
  • A298000 (program): Solution of the complementary equation a(n) = a(1)*b(n) - a(0)*b(n-1) + 2*n, where a(0) = 1, a(1) = 2, b(0) = 3, b(1) = 4, b(2) = 5, and (b(n)) is the increasing sequence of positive integers not in (a(n)). See Comments.
  • A298003 (program): Solution b( ) of the complementary equation a(n) = a(1)*b(n-1) - a(0)*b(n-2) + 2*n, where a(0) = 1, a(1) = 2, b(0) = 3, b(1) = 4, and (b(n)) is the increasing sequence of positive integers not in (a(n)). See Comments.
  • A298006 (program): Solution b( ) of the complementary equation a(n) = a(1)*b(n-1) - a(0)*b(n-2) + 2*n - 1, where a(0) = 1, a(1) = 2, b(0) = 3, b(1) = 4, and (b(n)) is the increasing sequence of positive integers not in (a(n)). See Comments.
  • A298007 (program): Solution b( ) of the complementary equation a(n) = a(1)*b(n-1) - a(0)*b(n-2) + 2*n - 2, where a(0) = 1, a(1) = 2, b(0) = 3, b(1) = 4, and (b(n)) is the increasing sequence of positive integers not in (a(n)). See Comments.
  • A298008 (program): a(n) = f(n-1,n) + 10*(n-1), where f(a,b) is the number of primes in the range [10*a,10*b].
  • 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.
  • A298018 (program): Partial sums of A298015.
  • 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+3*x^3+6*x^2+3*x+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.
  • A298071 (program): Number of primes between floor(3*n/2) and 2*n (inclusive).
  • A298078 (program): a(n) = 7*n^2 - 7*n - 43.
  • A298095 (program): Number of nX3 0..1 arrays with every element equal to 3, 4, 5 or 6 king-move adjacent elements, with upper left element zero.
  • A298101 (program): Expansion of x*(1 + x)/((1 - x)*(1 - 322*x + x^2)).
  • A298108 (program): Solution b( ) of the complementary equation a(n) = a(1)*b(n-1) - a(0)*b(n-2) + 2*n - 3, where a(0) = 1, a(1) = 2, b(0) = 3, b(1) = 4, and (b(n)) is the increasing sequence of positive integers not in (a(n)). See Comments.
  • A298109 (program): Solution b( ) of the complementary equation a(n) = a(1)*b(n-1) - a(0)*b(n-2) + 2*n - 4, where a(0) = 1, a(1) = 2, b(0) = 3, b(1) = 4, and (b(n)) is the increasing sequence of positive integers not in (a(n)). See Comments.
  • A298111 (program): Solution b( ) of the complementary equation a(n) = a(1)*b(n) - a(0)*b(n-1) + 2*n, where a(0) = 1, a(1) = 2, b(0) = 3, b(1) = 4, b(2) = 5, and (b(n)) is the increasing sequence of positive integers not in (a(n)). See Comments.
  • A298125 (program): The hex numbers (A003215) together with 3.
  • A298158 (program): a(n) = a(n-1) + 3*a(n-2) -2*a(n-3) - 2*a(n-4), where a(0) = -1, a(1) = -2, a(2) = 1, a(3) = 1.
  • A298179 (program): Number of nX4 0..1 arrays with every element equal to 3, 5, 6 or 8 king-move adjacent elements, with upper left element zero.
  • A298198 (program): Number of Eulerian cycles in the graph Cartesian product of C_n and a double edge.
  • A298207 (program): Numbers that are a product of zero, one, or three (not necessarily distinct) prime numbers.
  • A298210 (program): Smallest n such that A001542(a(n)) == 0 (mod n), i.e., x=A001541(a(n)) and y=A001542(a(n)) is the fundamental solution of the Pell equation x^2 - 2*(n*y)^2 = 1.
  • A298211 (program): Smallest n such that A001353(a(n)) == 0 (mod n), i.e., x=A001075(a(n)) and y=A001353(a(n)) is the fundamental solution of the Pell equation x^2 - 3*(n*y)^2 = 1.
  • A298212 (program): Smallest n such that A060645(a(n)) = 0 (mod n), i.e., x=A023039(a(n)) and y=A060645(a(n)) is the fundamental solution of the Pell equation x^2 - 5*(n*y)^2 = 1.
  • A298231 (program): Fixed point of the morphism 1->1221, 2->122.
  • A298234 (program): Number of nX2 0..1 arrays with every element equal to 0, 2, 3, 4 or 5 king-move adjacent elements, with upper left element zero.
  • A298242 (program): Decimal expansion of BesselI(1,1/2)/BesselI(0,1/2).
  • A298247 (program): Expansion of Product_{k>=1} (1 - x^(k*(k+1)*(k+2)/6)).
  • 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 - 322*x + x^2)).
  • A298296 (program): Solution b( ) of the complementary equation a(n) = a(0)*b(n) + a(1)*b(n-1), where a(0) = 1, a(1) = 2, b(0) = 3, b(1) = 4, b(2) = 5, and (b(n)) is the increasing sequence of positive integers not in (a(n)). See Comments.
  • A298300 (program): Analog of Motzkin numbers for Coxeter type D.
  • A298311 (program): Expansion of Product_{k>=1} 1/((1 - x^(2*k))*(1 - x^(2*k-1))^3).
  • A298338 (program): a(n) = a(n-1) + a(n-2) + a([n/2]), where a(0) = 1, a(1) = 1, a(2) = 1.
  • A298339 (program): a(n) = a(n-1) + a(n-2) + a([n/2]), where a(0) = 1, a(1) = 2, a(2) = 3.
  • A298340 (program): a(n) = a(n-1) + a(n-2) + a([n/3]), where a(0) = 1, a(1) = 1, a(2) = 1.
  • A298341 (program): a(n) = a(n-1) + a(n-2) + a([n/3]), where a(0) = 1, a(1) = 2, a(2) = 3.
  • A298342 (program): a(n) = a(n-1) + a(n-2) + a([2n/3]), where a(0) = 1, a(1) = 1, a(2) = 1.
  • A298343 (program): a(n) = a(n-1) + a(n-2) + a([2n/3]), where a(0) = 1, a(1) = 2, a(2) = 3.
  • A298346 (program): a(n) = a(n-1) + a(n-2) + 2 a([n/2]), where a(0) = 1, a(1) = 1, a(2) = 1.
  • A298347 (program): a(n) = a(n-1) + a(n-2) + 2 a([n/2]), where a(0) = 1, a(1) = 2, a(2) = 3.
  • A298348 (program): a(n) = a(n-1) + a(n-2) + a([(n+1)/2]), where a(0) = 1, a(1) = 1, a(2) = 1.
  • A298349 (program): a(n) = a(n-1) + a(n-2) + a([(n+1)/2]), where a(0) = 1, a(1) = 2, a(2) = 3.
  • A298350 (program): a(n) = a(n-1) + a(n-2) + 2 a(ceiling(n/2)), where a(0) = 1, a(1) = 1, a(2) = 1.
  • A298351 (program): a(n) = a(n-1) + a(n-2) + 2 a(ceiling(n/2)), where a(0) = 1, a(1) = 2, a(2) = 3.
  • A298352 (program): a(n) = a(n-1) + a(n-2) + a([(n-1)/2]), where a(0) = 1, a(1) = 1, a(2) = 1.
  • A298353 (program): a(n) = a(n-1) + a(n-2) + a([(n-1)/2]), where a(0) = 1, a(1) = 2, a(2) = 3.
  • A298354 (program): a(n) = a(n-1) + a(n-2) + 2 a([(n-1)/2]), where a(0) = 1, a(1) = 1, a(2) = 1.
  • A298355 (program): a(n) = a(n-1) + a(n-2) + 2 a([(n-1)/2]), where a(0) = 1, a(1) = 2, a(2) = 3.
  • 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.
  • A298366 (program): Even numbers n such that n-5 and n-3 are both composite.
  • A298368 (program): Triangle read by rows: T(n, k) = floor((n-1)/2)*floor(n/2)*floor((k-1)/2)*floor(k/2).
  • A298371 (program): a(n) = Sum_{m=0..n} Sum_{i=0..m} i*C(m-i,i)*C(m-i,n-m-i).
  • A298372 (program): a(n), in decimal base, is the number of numbers k >= 0 with no more digits than n such that k + n can be computed without carry.
  • A298373 (program): a(n) = n! * [x^n] exp(n*x - exp(x) + 1).
  • A298375 (program): Partial sums of A230584.
  • A298397 (program): Pentagonal numbers divisible by 4.
  • A298402 (program): a(n) = 2*a(n-1) - a(n-3) + a(floor(n/2)), where a(0) = 1, a(1) = 1, a(2) = 1.
  • A298403 (program): a(n) = 2*a(n-1) - a(n-3) + a(floor(n/2)), where a(0) = 1, a(1) = 2, a(2) = 3.
  • A298404 (program): a(n) = 2*a(n-1) - a(n-3) + a(ceiling(n/2)), where a(0) = 1, a(1) = 1, a(2) = 1.
  • A298405 (program): a(n) = 2*a(n-1) - a(n-3) + a(ceiling(n/2)), where a(0) = 1, a(1) = 2, a(2) = 3.
  • A298411 (program): Coefficients of q^(-1/24)*eta(4q)^(1/2).
  • A298412 (program): a(n) = 2*a(n-1) + a(n-2) + a([n/2]), where a(0) = 1, a(1) = 1, a(2) = 1.
  • A298414 (program): a(n) = 2*a(n-1) - a(n-2) + a([n/2]), where a(0) = 1, a(1) = 1, a(2) = 1.
  • A298415 (program): a(n) = a(n-1) + 2*a(n-2) + a([n/2]), where a(0) = 1, a(1) = 1, a(2) = 1.
  • A298416 (program): a(n) = 2*a(n-1) + 2*a(n-2) - a([n/2]), where a(0) = 1, a(1) = 1, a(2) = 1.
  • A298417 (program): a(n) = 2*a(n-1) + 2*a(n-2) + a([n/2]), where a(0) = 1, a(1) = 1, a(2) = 1.
  • A298420 (program): Expansion of f(x, x) * f(x, x^2) * f(x^2, x^4) in powers of x where f(, ) is Ramanujan’s general theta function.
  • A298434 (program): Expansion of Product_{k>=1} 1/(1 - x^(k^3))^2.
  • A298435 (program): Expansion of Product_{k>=1} 1/(1 - x^(k*(k+1)/2))^2.
  • A298436 (program): Expansion of Product_{k>=1} 1/(1 - x^prime(k))^2.
  • A298468 (program): Solution (aa(n)) of the system of 3 complementary equations in Comments.
  • A298473 (program): a(n) = n * lambda(n) * 2^omega(n).
  • A298474 (program): a(n) is the least k such that A090701(k) = n.
  • A298484 (program): Square array A(n,k), n >= 1, k >= 1, read by antidiagonals, where A(n,k) is defined by the following: A(1,k) = k and A(n,k) = A(n-1,k)*(A(n-1,k)+1) for n > 1.
  • A298485 (program): Triangle read by rows; row 0 is 1; the n-th row for n>0 contains the coefficients in the expansion of (2-x)*(1+x)^(n-1).
  • A298564 (program): a(n) = (3^(n+2)+11)/2 - 5*2^(n+1) + 2*n.
  • A298567 (program): a(n) = Sum_{k=0..2*n/3} C(n-k,2*k-n)^2.
  • A298569 (program): Number of nX2 0..1 arrays with every element equal to 0, 2, 4, 5 or 7 king-move adjacent elements, with upper left element zero.
  • A298596 (program): Expansion of Product_{k>=2} 1/(1 + x^k).
  • A298599 (program): Expansion of Product_{k>=2} (1 - x^k)^k.
  • A298600 (program): Expansion of Product_{k>=2} 1/(1 + x^(k^2)).
  • A298601 (program): Expansion of Product_{k>=2} (1 - x^(k^2)).
  • A298602 (program): Expansion of (1 - x)*Product_{k>=1} (1 - x^prime(k)).
  • A298603 (program): Number of partitions of n into odd prime parts (including 1).
  • A298604 (program): Number of partitions of n into distinct odd prime parts (including 1).
  • A298607 (program): Powers of 2 with the digit ‘0’ in their decimal expansion.
  • A298611 (program): Expansion of (1 - 6*x + x^2 - 8*x^3 + 16*x^4)^(-1/2).
  • A298612 (program): The number of concave polygon classes.
  • A298675 (program): Rectangular array A: first differences of row entries of array A294099, read by antidiagonals.
  • A298677 (program): a(n) = 110*a(n-1) - a(n-2) for n >= 2, a(0)=1, a(1)=111.
  • A298678 (program): Start with the hexagonal tile of the Shield tiling and recursively apply the substitution rule. a(n) is the number of hexagonal tiles after n iterations.
  • A298679 (program): Start with the hexagonal tile of the Shield tiling and recursively apply the substitution rule. a(n) is the number of square tiles after n iterations.
  • A298680 (program): Start with the triangle with 4 markings of the Shield tiling and recursively apply the substitution rule. a(n) is the number of triangles with 6 markings after n iterations.
  • A298681 (program): Start with the square tile of the Shield tiling and recursively apply the substitution rule. a(n) is the number of triangles with 6 markings after n iterations.
  • A298682 (program): Start with the triangle with 4 markings of the Shield tiling and recursively apply the substitution rule. a(n) is the number of triangles with 4 markings after n iterations.
  • A298683 (program): Start with the square tile of the Shield tiling and recursively apply the substitution rule. a(n) is the number of squares after n iterations.
  • A298695 (program): G.f.: Sum_{n>=0} binomial(n^2, n) * x^n / (1 + x)^(n^2).
  • A298696 (program): G.f.: Sum_{n>=0} binomial(n*(n+1), n)/(n+1) * x^n / (1 + x)^(n*(n+1)).
  • A298700 (program): a(n) = (n/2)*Sum_{k=1..n} C(n + k, n)*C(k, n - k)/k.
  • 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.
  • A298732 (program): Number of compositions (ordered partitions) of n into parts > 1 such that no two adjacent parts are equal (Carlitz compositions).
  • A298734 (program): a(n) = n-th term in periodic sequence repeating the divisors of n in decreasing order.
  • A298735 (program): Number of odd squares dividing n.
  • A298738 (program): Decimal expansion of (1/2)(1 + sqrt(7 + 2*sqrt(5))).
  • A298740 (program): Decimal expansion of (1/2)(1 + sqrt(1 + 4*sqrt(2))).
  • A298742 (program): Decimal expansion of (1/2)(1 + sqrt(5 + 4*sqrt(2))).
  • A298743 (program): Decimal expansion of (1/2)(1 + sqrt(1 + 4*sqrt(3))).
  • A298744 (program): Decimal expansion of (1/2)(1 + sqrt(-3 + 4*sqrt(3))).
  • A298745 (program): Decimal expansion of (1/2)*(1 + sqrt(5 + 4*sqrt(3))).
  • A298749 (program): Decimal expansion of (1/2)(1 + sqrt(1 + 4*sqrt(5))).
  • A298750 (program): Decimal expansion of (1/2)(1 + sqrt(5 + 4*sqrt(5))).
  • A298751 (program): Decimal expansion of (1/2)(1 + sqrt(-3 + 4*sqrt(5))).
  • A298752 (program): Decimal expansion of (1/2)(1 + sqrt(-7 + 4*sqrt(5))).
  • A298754 (program): Numerator of sigma_3(n)/sigma_2(n).
  • A298784 (program): Expansion of (1 + x^2)*(1 + 3*x + x^2) / ((1 - x)*(1 - x^3)).
  • A298785 (program): Partial sums of A298784.
  • A298786 (program): Expansion of (x^4 + 2*x^3 + 4*x^2 + 2*x + 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.
  • A298799 (program): Expansion of (1-27*x)^(-1/9).
  • A298802 (program): Growth series for group with presentation < S, T : S^4 = T^4 = (S*T)^4 = 1 >.
  • A298813 (program): Decimal expansion of the greatest real zero of x^4 - 2*x^2 - x + 1.
  • A298814 (program): Decimal expansion of the greatest real zero of x^8 - 2*x^4 - x + 1.
  • A298815 (program): Decimal expansion of the greatest real zero of x^8 - 4*x^6 + 6*x^4 - 4*x^2 - x + 1.
  • A298822 (program): Number of minimum edge covers in the n-dipyramidal graph.
  • A298823 (program): Number of minimal total dominating sets in the n-dipyramidal graph.
  • A298825 (program): Row sums of A298824.
  • A298826 (program): a(n) = A298825(n)/n.
  • A298852 (program): Decimal expansion of the greatest real zero of x^4 - 4*x^2 - x + 3.
  • A298853 (program): Decimal expansion of the greatest real zero of x^4 - 2*x^2 - x - 1.
  • A298855 (program): Squarefree semiprimes p*q for which the symmetric representation of sigma(p*q) has four parts, in increasing order.
  • A298856 (program): Triangular numbers n for which A240542(n) = A240542(n-1).
  • 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 3*p when all primes p and products 3*p are jointly ranked.
  • A298865 (program): The primes p and products 4*p in increasing order.
  • A298866 (program): Positions of primes p when all p and 4*p are arranged in increasing order.
  • A298867 (program): Positions of numbers 4*p when all primes p and products 4*p are arranged in increasing order.
  • A298879 (program): Numbers whose square is not odious.
  • A298881 (program): a(0) = 0; for n>0, a(n) = 6*n!.
  • A298897 (program): Number of nX3 0..1 arrays with every element equal to 3, 4, 5, 6 or 8 king-move adjacent elements, with upper left element zero.
  • A298919 (program): Number of nX3 0..1 arrays with every element equal to 1, 3, 5, 7 or 8 king-move adjacent elements, with upper left element zero.
  • A298931 (program): Expansion of psi(x^4) * c(x^3) / (3*x) where phi() is a Ramanujan theta function and c() is a cubic AGM theta function.
  • A298932 (program): Expansion of f(-x^3)^3 * phi(-x^12) / (f(-x) * chi(-x^4)) in powers of x where phi(), chi(), f() are Ramanujan theta functions.
  • A298933 (program): Expansion of f(x, x^2) * f(x, x^3) * f(x^2, x^4) in powers of x where f(, ) is Ramanujan’s general theta function.
  • A298944 (program): a(n) = 2^(c-1) mod c^2, where c is the n-th composite number.
  • A298946 (program): a(n) = binomial(2*c-1, c-1) (mod c^4), where c is the n-th composite number.
  • A298948 (program): Expansion of Product_{k>=1} (1 - x^prime(k))^2.
  • 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).
  • A298959 (program): Number of nX4 0..1 arrays with every element equal to 3, 5, 6, 7 or 8 king-move adjacent elements, with upper left element zero.
  • A298971 (program): Number of compositions of n that are proper powers of Lyndon words.
  • A298977 (program): Base-7 complementary numbers: n equals the product of the 7 complement (7-d) of its base-7 digits d.
  • A298992 (program): a(n) = (2*n-3-(-1)^n)*(22*n^2-21*n+5*n*(-1)^n)/96.
  • A298993 (program): Expansion of Product_{n>=1} 1/sqrt(1 + (4*x)^n).
  • A298994 (program): Expansion of Product_{n>=1} (1 + (4*x)^n)^(1/2).
  • A299017 (program): Intersection of A264041 and A000217.
  • A299019 (program): Expansion of Product_{k>=1} (1 - x^k)^(k+1).
  • A299020 (program): a(n) is the maximum digit in the factorial base expansion of 1/n.
  • A299034 (program): a(n) = n! * [x^n] Product_{k>=1} 1/(1 - x^k)^(n/k).
  • A299043 (program): G.f. Sum_{n>=0} Series_Reversion( x*(1-x)^n )^n.
  • A299044 (program): G.f. Sum_{n>=0} Series_Reversion( x/(1+x)^n )^n.
  • A299045 (program): Rectangular array: A(n,k) = Sum_{j=0..k} (-1)^floor(j/2)*binomial(k-floor((j+1)/2), floor(j/2))*(-n)^(k-j), n >= 1, k >= 0, read by antidiagonals.
  • A299069 (program): Expansion of Product_{k>=1} (1 + x^k)^phi(k), where phi() is the Euler totient function (A000010).
  • A299074 (program): Expansion of 1/((1-x)*(1-2*x)*(1-6*x)*(1-24*x)).
  • A299090 (program): Number of “digits” in the binary representation of the multiset of prime factors of n.
  • A299099 (program): Number of (n + 1, n + 2)-core partitions with odd parts and corresponding order ideals confined to the two outermost diagonals of P_{n + 1, n + 2}.
  • A299105 (program): Expansion of 1/(1 - x*Product_{k>=1} (1 - x^k)).
  • A299120 (program): a(n) = (n-1)*(n-2)*(n+3)*(n+2)/12.
  • A299121 (program): a(n) = Sum_{k=0..n} (k*(n-k))!.
  • A299143 (program): a(n) is the least k > n such that gcd(k,n) > 1 and gcd(k+1,n+1) > 1.
  • A299146 (program): Modified Pascal’s triangle read by rows: T(n,k) = C(n+1,k) - n, 1 <= k <= n.
  • A299149 (program): Numerators of the positive solution to n = Sum_{d|n} a(d) * a(n/d).
  • A299150 (program): Denominators of the positive solution to n = Sum_{d|n} a(d) * a(n/d).
  • A299167 (program): Expansion of 1/(1 - x*Product_{k>=1} (1 + x^k)^k).
  • A299174 (program): The even positive integers.
  • A299198 (program): a(n) = n^4/6 - 2*n^3/3 - n^2/6 + 5*n/3 + 1.
  • A299210 (program): Expansion of 1/(1 - x*Product_{k>=1} 1/(1 + k*x^k)).
  • A299211 (program): Expansion of 1/(1 - x*Product_{k>=1} (1 - x^k)^k).
  • A299212 (program): Expansion of 1/(1 - x*Product_{k>=1} 1/(1 + x^k)^k).
  • A299230 (program): a(n) = height of n-th {2,3}-power tower; see Comments.
  • 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.
  • A299233 (program): Ranks of {2,3}-power towers that end with 2; see Comments.
  • A299234 (program): Ranks of {2,3}-power towers that end with 3; see Comments.
  • A299250 (program): Numbers congruent to {9, 11, 21, 29} mod 30.
  • A299251 (program): a(n) = ((Sum_{k=1..floor((n+1)^2/4)} d(k)) - T(n)) / 2, where d(n) = number of divisors of n (A000005) and T(n) = the n-th triangular number (A000217).
  • 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.
  • A299296 (program): G.f. 1/(1-z*R(z*m(z))) where R(z) = (1-z-(z+1)*sqrt(1-4*z))/(2*z^2), m(z) = (3-z-sqrt(1-6*z+z^2))/2.
  • A299322 (program): Ranks of {2,3}-power towers without neither consecutive 2’s nor consecutive 3’s; see Comments.
  • 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).
  • A299399 (program): a(n) = a(n-1)*a(n-2)*a(n-3)*a(n-4); a(0..3) = (1, 1, 2, 3).
  • A299404 (program): a(n) = 1 + Sum_{m >= 1} (m + 1)^n/2^(m - 1).
  • A299406 (program): G.f.: Sum_{n>0} a(n)/n^s = ((zeta(s)*zeta(6*s))/((zeta(2*s)*zeta(3*s)).
  • A299407 (program): Solution b( ) of the complementary equation a(n) = b(n-1) + b(n-2), where a(0) = 1, a(1) = 4; see Comments.
  • A299411 (program): Solution b( ) of the complementary equation a(n) = b(n-1) + b(n-2), where a(0) = 2, a(1) = 3; see Comments.
  • A299412 (program): Pentagonal pyramidal numbers divisible by 3.
  • A299417 (program): Solution b( ) of the complementary equation a(n) = b(n-1) + b(n-2), where a(0) = 3, a(1) = 4; see Comments.
  • A299419 (program): Solution b( ) of the complementary equation a(n) = b(n-1) + b(n-2), where a(0) = 3, a(1) = 5; see Comments.
  • A299421 (program): Solution b( ) of the complementary equation a(n) = b(n-1) + b(n-2), where a(0) = 4, a(1) = 5; see Comments.
  • A299426 (program): E.g.f. Sum_{n>=0} Series_Reversion( x*exp(-n*x) )^n.
  • A299428 (program): a(n) = binomial((n+1)*(2*n+1), n) * (n+1)/(2*n+1).
  • A299429 (program): a(n) = binomial((n+1)*(2*n+1), n) / ((n+1)*(2*n+1)).
  • A299435 (program): G.f.: Sum_{n>=0} binomial((n+1)^2, n)/(n+1) * x^n / (1 + x)^((n+1)^2).
  • A299436 (program): G.f.: exp( Sum_{n>=1} A020696(n) * x^n/n ), where A020696(n) = Product_{d|n} (d + 1).
  • A299437 (program): G.f.: exp( Sum_{n>=1} A020696(n)/2 * x^n/n ), where A020696(n) = Product_{d|n} (d + 1).
  • A299443 (program): Expansion of (x^4 + 2*x^3 + 7*x^2 - 6*x + 1)^(-1/2).
  • A299444 (program): Triangle read by rows, T(n, k) = 2^k*binomial(n, k)*hypergeom([-k, k - n, k - n], [1, -n], 1/2) for n >= 0 and 0 <= k <= n.
  • A299473 (program): a(n) = 3*p(n), where p(n) is the number of partitions of n.
  • A299474 (program): a(n) = 4*p(n), where p(n) is the number of partitions of n.
  • A299475 (program): a(n) is the number of vertices in the diagram of partitions of n (see example).
  • A299480 (program): List of pairs (a,b) where in the n-th pair, a = number of odd divisors of n and b = number of even divisors of n.
  • A299482 (program): Numbers m such that in the diagram of the symmetric representation of sigma(k) described in A237593 there is no Dyck path that contains the point (m,m), where both k and m are positive integers.
  • A299485 (program): List of pairs (a,b) where in the n-th pair, a = number of even divisors of n and b = number of odd divisors of n.
  • A299499 (program): Triangle read by rows, T(n,k) = [x^k] Sum_{k=0..n} p_{n,k}(x) where p_{n,k}(x) = x^k*binomial(n, k)*hypergeom([-k, k-n, k-n], [1, -n], 1/x), for 0 <= k <= n.
  • A299500 (program): Triangle read by rows, T(n,k) = [x^k] Sum_{k=0..n} p_{n,k}(x) where p_{n,k}(x) = x^(n-k)*binomial(n,k)*hypergeom([-k, k-n, k-n], [1, -n], 1/x), for 0 <= k <= n.
  • A299501 (program): Expansion of (1 - 6*x + 7*x^2 - 2*x^3 + x^4)^(-1/2).
  • A299502 (program): Expansion of (1 - 6*x + x^2 + 8*x^3 + 16*x^4)^(-1/2).
  • A299503 (program): a(n) = (1/12) * Sum_{d|n} d * A288851(d).
  • A299504 (program): Triangle read by rows, T(n,k) = (k+1)^(n-k)*k! for 0 <= k <= n.
  • A299506 (program): a(n) = hypergeom([-n, n - 1/2], [1], -4).
  • A299507 (program): a(n) = (-1)^n*hypergeom([-n, n], [1], 4).
  • A299529 (program): Number of Johnson solids with exactly n types of faces.
  • A299530 (program): Number of regular-faced convex polyhedra (excluding prisms and antiprisms) with exactly n types of faces.
  • A299532 (program): Solution b( ) of the complementary equation a(n) = 2*b(n-1) + b(n-2), where a(0) = 1, a(1) = 2; see Comments.
  • A299534 (program): Solution b( ) of the complementary equation a(n) = b(n-1) + 2*b(n-2), where a(0) = 1, a(1) = 2; see Comments.
  • A299536 (program): Solution b( ) of the complementary equation a(n) = b(n-1) + b(n-3), where a(0) = 1, a(1) = 2, a(2) = 3; see Comments.
  • A299538 (program): Solution b( ) of the complementary equation a(n) = b(n-1) + b(n-3), where a(0) = 2, a(1) = 3, a(2) = 4; see Comments.
  • A299540 (program): Solution b( ) of the complementary equation a(n) = b(n-1) + b(n-3), where a(0) = 2, a(1) = 3, a(2) = 5; see Comments.
  • A299542 (program): Solution b( ) of the complementary equation a(n) = b(n-1) + b(n-3), where a(0) = 2, a(1) = 4, a(2) = 6; see Comments.
  • A299641 (program): Solution (d(n)) of the system of 5 complementary equations in Comments.
  • A299644 (program): a(n) = prime(prime(n+1)) + prime(prime(n)).
  • A299645 (program): Numbers of the form m*(8*m + 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.
  • A299700 (program): Squarefree part of 1!*2!*3!*…*n!: The product of factorials one through n divided by its largest square divisor.
  • A299741 (program): Array read by antidiagonals upwards: a(i,0) = 2, i >= 0; a(i,1) = i+2, i >= 0; a(i,j) = (i+2) * a(i,j-1) - a(i,j-2), for i >= 0, j > 1.
  • A299763 (program): a(n) = 1 + A182986(n).
  • A299766 (program): Greatest odd noncomposite divisor of n.
  • A299770 (program): a(n) is the total number of elements after n-th stage of a hybrid (and finite) cellular automaton on the infinite square grid, formed by toothpicks of length 2, D-toothpicks, toothpicks of length 1, and T-toothpicks.
  • A299771 (program): a(n) is the number of elements added at n-th stage in the structure of the finite cellular automaton of A299770.
  • A299788 (program): a(n) = denominator of Product_{d|n} (sigma(d)/d) where sigma(k) = the sum of the divisors of k (A000203).
  • 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).
  • A299824 (program): a(n) = (1/e^n)*Sum_{j >= 1} j^n * n^j / (j-1)!.
  • A299845 (program): a(n) = hypergeom([-n, n - 1], [1], -4).
  • A299854 (program): G.f. S(x) satisfies C(x)^(1/2) - S(x)^(1/2) = 1 such that C’(x)*S(x)^(1/2) = S’(x)*C(x)^(1/2) = 72*x.
  • A299855 (program): G.f. C(x)^(1/2) satisfies C(x)^(1/2) - S(x)^(1/2) = 1 such that C’(x)*S(x)^(1/2) = S’(x)*C(x)^(1/2) = 72*x.
  • A299864 (program): a(n) = (-1)^n*hypergeom([-n, n - 1/2], [1], 4).
  • A299913 (program): a(n) = a(n-1) + 2*a(n-2) if n even, or 3*a(n-1) + 4*a(n-2) if n odd, starting with 0, 1.
  • A299914 (program): a(n) = a(n-1) + 3*a(n-2) if n even, or 2*a(n-1) + 4*a(n-2) if n odd, starting with 0, 1.
  • A299915 (program): a(n) = A299914(2n).
  • A299916 (program): a(n) = A299914(2n+1).
  • A299918 (program): Motzkin numbers (A001006) mod 8.
  • A299919 (program): Motzkin numbers (A001006) mod 4.
  • A299920 (program): Motzkin numbers (A001006) mod 6.
  • A299921 (program): Squares that differ from a triangular number by 1.
  • A299927 (program): Number of permutations of length n that avoid the patterns 213 and 312 and have k double ascents, read by rows.
  • A299958 (program): Expansion of root of z^5 + 25*x*z - 1.
  • A299960 (program): a(n) = ( 4^(2*n+1) + 1 )/5.
  • A299963 (program): a(n) = greatest prime factor of the terms in the Collatz sequence starting at n; a(1) = 1.
  • A299965 (program): Number of triangles in a Star of David of size n.
  • A299990 (program): a(n) = A243822(n) - A000005(n).

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