# Programs for A250000-A299999

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)*binomia