Sequences

Expansion of eta(q^10)^12/(eta(q^2)^4*eta(q^5)^8) in powers of q.

Describe previous term from the right (method A - initial term is 1).

Number of 3-edge-colored trivalent graphs with 2n labeled nodes.

Number of 3-edge-colored connected trivalent graphs with 2n labeled nodes.

Number of trivalent bipartite labeled graphs with 2n labeled nodes.

Describe the previous term! (method A - initial term is 3).

Squares with digits 1, 4, 9.

Number of ways of arranging 2n+1 nonattacking semi-queens on a (2n+1) X (2n+1) toroidal board.

Number of golygons of length 8n.

a(n) = A000905(n) + 1.

Somos-4 sequence: a(0)=a(1)=a(2)=a(3)=1; for n >= 4, a(n) = (a(n-1) * a(n-3) + a(n-2)^2) / a(n-4).

Somos-5 sequence: a(n) = (a(n-1) * a(n-4) + a(n-2) * a(n-3)) / a(n-5), with a(0) = a(1) = a(2) = a(3) = a(4) = 1.

Somos-6 sequence: a(n) = (a(n-1) * a(n-5) + a(n-2) * a(n-4) + a(n-3)^2) / a(n-6), a(0) = ... = a(5) = 1.

Somos-7 sequence: a(n) = (a(n-1) * a(n-6) + a(n-2) * a(n-5) + a(n-3) * a(n-4)) / a(n-7), a(0) = ... = a(6) = 1.

Number of fixed n-celled self-avoiding polygons on square lattice.

Number of n-celled polygons with perimeter 2n+2 on square lattice.

Number of n-celled polygons with perimeter 2n on square lattice.

Bond percolation series for square lattice.

Series for first parallel moment of square lattice.

Series for second parallel moment of square lattice (eventually changes sign).

Series for second perpendicular moment of square lattice (eventually changes sign).

Site percolation series for square lattice.

Series for first parallel moment of square lattice.

Series for second parallel moment of square lattice (eventually changes sign).

Series for second perpendicular moment of square lattice.

Bond percolation series for hexagonal net.

Series for first parallel moment of hexagonal lattice.

Series for second parallel moment of hexagonal lattice.

Series for second perpendicular moment of hexagonal lattice.

Site percolation series for hexagonal lattice.

Series for first parallel moment of hexagonal lattice.

Series for second parallel moment of hexagonal lattice.

Series for second perpendicular moment of hexagonal lattice.

Number of convex polygons of length 2n on honeycomb, or EG-convex polyominoes.

Number of n-step self-avoiding walks on a Manhattan lattice.

Number of indefinitely growing n-step self-avoiding walks on Manhattan lattice.

Number of axially symmetric polyominoes with n cells.

Number of rotationally symmetric polyominoes with n cells (that is, polyominoes with exactly the symmetry group C_2 generated by a 180-degree rotation).

Number of diagonally symmetric polyominoes with n cells.

Number of asymmetric polyominoes with n cells.

Coefficients of Legendre polynomials.

Describe the previous term! (method A - initial term is 2).

Decimal expansion of Catalan's constant 1 - 1/9 + 1/25 - 1/49 + 1/81 - ...

Smith (or joke) numbers: composite numbers k such that sum of digits of k = sum of digits of prime factors of k (counted with multiplicity).

The generalized Conway-Guy sequence w^{0}.

The generalized Conway-Guy sequence w^{1}.

The generalized Conway-Guy sequence w^{2}.

The generalized Conway-Guy sequence w^{3}.

Number of strictly 2-dimensional one-sided polyominoes with n cells.

Number of one-sided strictly 3-dimensional polyominoes with n cells.