Sequences

Numbers k for which 10k+1, 10k+3, 10k+7 and 10k+9 are primes.

Number of n-node Steinhaus graphs whose complements have at least one cut-vertex.

Number of planar Steinhaus graphs with n nodes.

Exponent of highest power of 2 dividing n, a.k.a. the binary carry sequence, the ruler sequence, or the 2-adic valuation of n.

Number of triangulations of cyclic 3-polytope C(3,n+3).

Number of abstract simplicial 2-complexes on {1,2,3,...,n+3} which triangulate the 2-sphere: C(n+3,2)*(4n+1)!/(3n+3)!.

Number of abstract simplicial 2-complexes on {1,2,3,...,n+4} which triangulate a Moebius band in such a way that all vertices lie on the boundary and are traversed in the order 1,2,3,... as one goes around the boundary.

Maximal number of bonds joining n nodes in simple cubic lattice.

a(n) = Sum_{j=1..n} binomial(n^2, j).

Stirling numbers of second kind S(2n,n).

Primes p such that pi(p) is not prime.

Number of symmetric foldings of 2n+1 stamps.

A007824(n)/16.

a(n) = f(a(n-1)), with f(m) = Sum i*b(i)*2^(i-1), m = Sum b(i)*2^i, and starting value 16.

Number of n step self-avoiding walks on 3 X infinity grid starting from (0,1).

Numbered stops on the Market-Frankford rapid transit (SEPTA) railway line in Philadelphia, PA USA.

Number of homeomorphically irreducible (or series-reduced) trees with n pendant nodes, or continua with n non-cut points, or leaves.

Largest t such that a spherical t-design with n points exists in 3 dimensions.

From random walks on complete directed triangle.

a(n) = (n+3)^n.

Number of edge-labeled series-reduced trees with n nodes.

Number of point labeled 5,6-free two-graphs with n nodes.

Number of point-labeled reduced two-graphs with n nodes.

Number of point labeled reduced 5-free two-graphs with n nodes.

Number of unordered sets of pairs (in-degree, out-degree) for nodes of directed trees on n unlabeled nodes (the edges are directed in arbitrary directions, the tree is unrooted).

Springer numbers associated with symplectic group.

Number of partitions of n-set with distinct block sizes.

Number of permutations of n elements with distinct cycle lengths.

Number of polynomials of degree n over GF(2) in which the degrees of all irreducible factors are distinct.

Number of factorizations of permutations of n letters into ordered cycles.

Number of factorizations of permutations of n letters into cycles in nondecreasing length order.

Largest determinant of 2n+1 X 2n+1 matrix with entries +-1 and 0 diagonal.

Least positive integer k for which 2^n divides k!.

Least positive integer k for which 3^n divides k!.

Least positive integer k for which 5^n divides k!.

There are three equivalent descriptions: 1. Number of (horizontally or vertically) connected arrays of 1..n on rectangular grid (otherwise zero) with only one local maximum. 2. Number of n-polyominoes labeled 1...n such that each successive labeled cell is the neighbor of a previously labeled cell. 3. Number of connected n-step paths on a rectangular lattice, diagonal or repeated steps not allowed.

Number of hyperplanes spanned by the vertices of an n-cube.

Number of skew hyperplanes spanned by the vertices of an n-cube.

Number of hyperplanes spanned by the vertices of an n-cube that cover exactly n vertices.

Giuga numbers: composite numbers n such that p divides n/p - 1 for every prime divisor p of n.

Number of elements w of the Weyl group D(n) such that the roots sent negative by w span an Abelian subalgebra of the Lie algebra.

Number of antichains in rooted plane trees on n nodes.

Number of maximal antichains in rooted plane trees on n nodes.

Expansion of 1/(1 - 3*x*C(x)), where C(x) = (1 - sqrt(1 - 4*x))/(2*x) = g.f. for the Catalan numbers A000108.

Infima closed sets in rooted plane trees on n nodes.

Subtrees in rooted plane trees on n nodes.

Number of independent sets in rooted plane trees on n nodes.

G.f. is 1 - 1/f(x), where f(x) = 1+x+3*x^2+9*x^3+32*x^4+... is 1/x times g.f. for A063020.

Number of matchings in rooted plane trees on n nodes.

Maximal matchings in rooted plane trees on n nodes.