Sequences

Sum of rows of triangle defined in A001404.

Number of n-step self-avoiding walks on square lattice.

Number of n-step self-avoiding walks on cubic lattice.

Number of 2n-step self-avoiding cycles on the cubic lattice.

Integer log of n: sum of primes dividing n (with repetition). Also called sopfr(n).

Number of ways of folding a 2 X n strip of stamps.

Number of ways of folding a 3 X n strip of stamps.

Number of ways of folding a 2 X 2 X ... X 2 n-dimensional map.

Number of ways of folding an n X n sheet of stamps.

Number of n-celled polyominoes with holes.

Number of fixed 2-dimensional triangular-celled animals with n cells (n-iamonds, polyiamonds) in the 2-dimensional hexagonal lattice.

a(n) = (6*n)!/((n!)^3*(3*n)!).

Numbers which are not the sum of distinct squares.

Number of semigroups of order n, considered to be equivalent when they are isomorphic or anti-isomorphic (by reversal of the operator).

Number of nonisomorphic and nonantiisomorphic groupoids with n elements.

Number of commutative groupoids with n elements.

Number of commutative semigroups of order n.

Number of regular semigroups of order n, considered to be equivalent when they are isomorphic or anti-isomorphic (by reversal of the operator).

Number of inverse semigroups of order n, considered to be equivalent when they are isomorphic or anti-isomorphic (by reversal of the operator).

Number of n-node connected unicyclic graphs.

Number of graphs with n nodes and n-2 edges.

Number of graphs with n nodes and n-3 edges.

Number of graphs with n nodes and n-4 edges.

Number of graphs with n nodes and n-1 edges.

Number of graphs with n nodes and n edges.

Number of connected graphs with n nodes and n+1 edges.

Number of connected graphs with n nodes, n+2 edges.

Number of connected graphs with n nodes and ceiling(n(n-1)/4) edges.

Maximal number of mutually orthogonal Latin squares (or MOLS) of order n.

Number of proper linear spaces of order n.

Number of symmetric Costas arrays of order n that are inequivalent under dihedral group.

Number of inequivalent Costas arrays of order n under dihedral group.

G-symmetric Costas arrays of order n that are inequivalent under dihedral group.

Number of strong starters in cyclic group of order 2n+1.

Bending a piece of wire of length n+1 (configurations that can only be brought into coincidence by turning the figure over are counted as different).

a(n) = (2^n + 2^[ n/2 ] )/2.

a(n) = (4^n + 4^[ n/2 ] )/2.

a(n) = (5^n + 5^floor(n/2))/2.

a(n) = binomial(4n,2n) or (4*n)!/((2*n)!*(2*n)!).

Binomial coefficients binomial(5n,n).

a(n) = binomial(5*n,2*n).

a(n) = (5*n)!/((3*n)!*n!*n!).

Number of 5-line partitions of n.

Catalan numbers - 1.

Number of permutations of length n with longest increasing subsequence of length 3.

Number of permutations of length n with longest increasing subsequence of length 4.

Number of permutations of length n with longest increasing subsequence of length 5.

Number of permutations of length n with longest increasing subsequence of length 6.

Number of permutations of length n with longest increasing subsequence of length 7.

a(n) = (5*n)!/((2*n)!*(2*n)!*n!).