Sequences

Number of symmetric foldings of a strip of n blank stamps.

Number of ways to fold a strip of n blank stamps.

Erroneous version of A040082.

Jordan-Polya numbers: products of factorial numbers A000142.

Sixth powers: a(n) = n^6.

Seventh powers: a(n) = n^7.

Eighth powers: a(n) = n^8.

Ninth powers: a(n) = n^9.

Powers of 8: a(n) = 8^n.

Powers of 9: a(n) = 9^n.

Powers of 11: a(n) = 11^n.

Powers of 12.

Powers of 13: a(n) = 13^n.

Powers of 14.

Powers of 15.

Powers of 16: a(n) = 16^n.

Powers of 17: a(n) = 17^n.

Powers of 18.

E.g.f. satisfies A'(x) = 1 + A(A(x)), A(0)=0.

Powers of 19.

Fixed under 1 -> 21, 2 -> 211.

Goldbach conjecture: a(n) = number of decompositions of 2n into sum of two primes (counting 1 as a prime).

Numbers k such that sum of squares of k consecutive integers >= 1 is a square.

Numbers n such that the sum of the squares of n consecutive positive odd numbers x^2 + (x+2)^2 + ... + (x+2n-2)^2 = k^2 for some integer k. The least values of x and k for each n are in A056131 and A056132, respectively.

Orders of noncyclic simple groups (without repetition).

Number of partially ordered sets ("posets") with n labeled elements (or labeled acyclic transitive digraphs).

Partial sums of A001037, omitting A001037(1).

Number of degree-n irreducible polynomials over GF(2); number of n-bead necklaces with beads of 2 colors when turning over is not allowed and with primitive period n; number of binary Lyndon words of length n.

Invertible Boolean functions with GL(n,2) acting on the domain and range.

a(n) = (p^p-1)/(p-1) where p = prime(n).

a(n+1) = n*a(n) + a(n-1) with a(0)=0, a(1)=1.

a(0)=12; thereafter a(n) = 12 times the product of the first n primes.

a(n) = a(n-1)^2 - a(n-2)^2.

Numbers that are the sum of 2 successive primes.

a(n) = (n!)^2.

Jacobsthal sequence (or Jacobsthal numbers): a(n) = a(n-1) + 2*a(n-2), with a(0) = 0, a(1) = 1; also a(n) = nearest integer to 2^n/3.

a(n) = n*(n-1)*a(n-1)/2 + a(n-2), a(0) = a(1) = 1.

a(n) = 3^n - 2^n.

a(n) = n! + (n-1)!.

Numbered stops in Manhattan on the Lexington Avenue subway.

Number of letters in n (in Finnish).

Number of subgroups of order n in orthogonal group O(3).

a(n) = n*(n-1)*a(n-1)/2 + a(n-2), a(0) = 1, a(1) = 2.

a(n+1) = n*a(n) + a(n-1) with a(0)=1, a(1)=0.

a(n) = a(n-1)*a(n-2) - 1.

The multiplicative partition function: number of ways of factoring n with all factors greater than 1 (a(1) = 1 by convention).

a(n) = a(n-1)*a(n-2) + 1, a(0) = 1, a(1) = 3.

Canonical enumeration of integers: interleaved positive and negative integers with zero prepended.

1-digit numbers in reverse alphabetical order, then 2-digit numbers, etc.

Number of doubly labeled heap-ordered trees.