Sequences

Number of n-input 3-output switching networks under action of S(n) and complementing group C(2,3) on inputs and outputs.

Numbers ending with a vowel in American English.

Number of n-input 2-output switching networks under action of AG(n,2) and complementing group C(2,2) on inputs and outputs.

Number of n-input 3-output switching networks under action of AG(n,2) and complementing group C(2,3) on inputs and outputs.

Deceptive nonprimes: composite numbers k that divide the repunit R_{k-1}.

Numbers beginning with letter 'o' in English.

2^n written in base 5.

Numbers beginning with letter 'f' in English.

Number of switching networks with C(2,n) acting on domain and GL(2,Z2) acting on range.

Number of switching networks with C(2,n) acting on domain and GL(3,Z2) acting on range.

Numbers beginning with letter 's' in English.

Number of switching networks with S(n) acting on the domain and GL(2,2) acting on the range.

Number of switching networks with S(n) acting on the domain and GL(3,2) acting on the range.

Numbers beginning with letter 'e' in English.

Number of switching networks with S(n) and C(2,2) acting on the domain and GL(2,2) acting on the range.

Number of switching networks with S(n) and C(2,2) acting on the domain and GL(3,2) acting on the range.

From a self-replicating tiling.

Number of switching networks with GL(n,2) acting on the domain and GL(2,2) acting on the range.

Number of switching networks with GL(n,2) acting on the domain and GL(3,2) acting on the range.

Number of primes < prime(n)^2.

Number of switching networks with AG(n,2) acting on the domain and GL(2,2) acting on the range.

Number of switching networks with AG(n,2) acting on the domain and GL(3,2) acting on the range.

Number of twin prime pairs <= product of first n primes.

Number of switching networks with C(2,n) acting on the domain and AG(2,2) acting on the range.

Number of switching networks with C(2,n) acting on the domain and AG(3,2) acting on the domain.

Number of twin prime pairs < square of n-th prime.

Number of switching networks with S(n,2) acting on the domain and AG(2,2) acting on the range where S(n,k) is the symmetric group acting on k variables.

Number of switching networks with S(n,2) acting on the domain and AG(3,2) acting on the range where S(n,k) is the symmetric group acting on k variables.

a(n) = (2*n)!^2 / ((n+1)!*n!^3).

Number of switching networks with S(n) and C(2,2) acting on the domain and AG(2,2) acting on the range.

Number of switching networks with S(n) and C(2,2) acting on the domain and AG(2,3) acting on the range.

a(n) = (2*n)!*(2*n+1)! / (n! * (n+1)!)^2.

Number of switching networks with GL(n,2) acting on the domain and AG(2,2) acting on the range.

Number of switching networks with GL(n,2) acting on the domain and AG(3,2) acting on the range.

a(n) = (2*n)!*(2*n+1)! /((n+1)! *n!^3).

Number of switching networks with AG(n,2) acting on the domain and AG(2,2) acting on the range.

Number of switching networks with AG(n,2) acting on the domain and AG(3,2) acting on the range.

a(n) = (4*n)! / ((2*n)!*n!^2).

a(n) = 2*(a(n-1) + (n-1)*a(n-2)) for n >= 2 with a(0) = 1.

Number of solutions to the rook problem on an n X n board having a certain symmetry group (see Robinson for details).

Number of solutions to the rook problem on an n X n board having a certain symmetry group (see Robinson for details).

Number of solutions to the rook problem on a 2n X 2n board having a certain symmetry group (see Robinson for details).

Expansion of e.g.f. (1/2)*(exp(2*x + x^2) + 1).

Number of inequivalent ways of placing n nonattacking rooks on n X n board up to rotations and reflections of the board.

a(n) = (n+1)*a(n-1) + (n+2)*a(n-2) + a(n-3); a(1)=0, a(2)=3, a(3)=13.

Hamilton numbers.

Exponential generating function: 2*(1+3*x)/(1-2*x)^(7/2).

Second-order reciprocal Stirling number (Fekete) a(n) = [[2n+2, n]]. The number of n-orbit permutations of a (2n+2)-set with at least 2 elements in each orbit. Also known as associated Stirling numbers of the first kind (e.g., Comtet).

Atom-rooted polyenoids with n edges with symmetry class C_s.

a(n) = (2*n)!*(2*n+1)! / n!^2.