Sequences

Number of nonseparable rooted toroidal maps with n + 5 edges and n + 1 vertices.

Number of nonseparable tree-rooted planar maps with n + 2 edges and 3 vertices.

Number of nonseparable tree-rooted planar maps with n + 3 edges and 4 vertices.

Number of nonseparable tree-rooted planar maps with n + 4 edges and 5 vertices.

Number of nonseparable toroidal tree-rooted maps with n + 2 edges and n + 1 vertices.

Number of nonseparable toroidal tree-rooted maps with n + 3 edges and n + 1 vertices.

Number of loopless rooted planar maps with 3 faces and n vertices and no isthmuses. Also a(n)=T(4,n-3), array T as in A049600.

Number of loopless rooted planar maps with 4 faces and n vertices and no isthmuses.

Number of loopless rooted planar maps with 5 faces and n vertices and no isthmuses.

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

Number of rooted planar maps with 3 vertices and n faces and no isthmuses.

Number of rooted planar maps with 4 vertices and n faces and no isthmuses.

Number of rooted toroidal maps with 2 faces and n vertices and without separating cycles or isthmuses.

Number of rooted toroidal maps with 3 faces and n vertices and without separating cycles or isthmuses.

Number of rooted toroidal maps with 4 faces and n vertices and without separating cycles or isthmuses.

Number of rooted toroidal maps with 2 vertices and n faces and no isthmuses.

Number of rooted toroidal maps with 3 vertices and n faces and no isthmuses.

Number of rooted toroidal maps with 4 vertices and n faces and no isthmuses.

Number of loopless tree-rooted planar maps with 3 vertices and n faces and no isthmuses.

Number of loopless tree-rooted planar maps with 4 vertices and n faces.

Number of loopless tree-rooted planar maps with 5 vertices and n faces and no isthmuses.

Numbers that have a unique partition into a sum of four nonnegative squares.

Number of tree-rooted planar maps with 3 vertices and n faces and no isthmuses.

Number of tree-rooted planar maps with 4 vertices and n faces and no isthmuses.

Number of tree-rooted toroidal maps with 2 faces and n vertices and without separating loops or isthmuses.

Number of tree-rooted toroidal maps with 3 faces and n vertices and without separating loops or isthmuses.

Number of tree-rooted toroidal maps with 2 faces and n vertices and without isthmuses.

Number of tree-rooted toroidal maps with 3 faces and n vertices and without isthmuses.

Expansion of e.g.f. 1/sqrt(1-8x+x^2).

Number of tree-rooted toroidal maps with 2 faces and n vertices and without separating loops.

Number of tree-rooted toroidal maps with 3 faces and n vertices and without separating loops.

Number of nonseparable toroidal tree-rooted maps with n + 4 edges and n + 1 vertices.

Expansion of 1/sqrt(1 - 10*x + x^2).

Number of achiral planar maps with n edges.

Number of achiral 2-connected planar maps with n edges.

Number of n-edge 3-connected planar maps with a sense-reversing automorphism.

Numbers k such that floor(sqrt(k)) divides k.

Consider a 2-D cellular automaton generated by the Schrandt-Ulam rule of A170896, but confined to a semi-infinite strip of width n, starting with one ON cell at the top left corner; a(n) is the period of the resulting structure.

Number of n-element algebras with 1 binary operator and 1 constant (pointed groupoids).

Row sums of Fibonacci-Pascal triangle in A045995.

Prime-indexed primes: primes with prime subscripts.

Numbers k such that k*(k+1)/2 + 1 is a square.

a(n) = 6*a(n-2) - a(n-4).

Expansion of 1/sqrt(1 - 12x + x^2).

Solution to a Diophantine equation: each term is a triangular number and each term + 1 is a square.

Number of partial orders on {1,2,...,n} that are contained in the usual linear order (i.e., xRy => x<y).

Number of compositions (ordered partitions) of n into squares.

Number of elements in Z[ i ] whose 'smallest algorithm' is <= n.

Number of elements in Z[ omega ] whose 'smallest algorithm' is <= n, where omega^2 = -omega - 1.

Number of elements in Z[ sqrt(-2) ] whose 'smallest algorithm' is <= n.