Sequences

The coding-theoretic function A(n,12,10).

The coding-theoretic function A(n,14,9).

The coding-theoretic function A(n,14,10).

The coding-theoretic function A(n,14,11).

The coding-theoretic function A(n,4).

The coding-theoretic function A(n,6).

The coding-theoretic function A(n,8).

a(0) = 1; for n > 0, a(n) = (prime(n)-1)*a(n-1).

Molien series for 3-dimensional representation of Z2 X (double cover of A6), u.g.g.r. # 27 of Shephard and Todd.

Theta series of b.c.c. lattice with respect to short edge.

Numbers represented by hexagonal close-packing.

Theta series of hexagonal close-packing with respect to edge within layer.

Theta series of hexagonal close-packing with respect to octahedral hole.

Theta series of hexagonal close-packing with respect to tetrahedral hole.

Theta series of hexagonal close-packing with respect to triangle between tetrahedra.

Theta series of simple cubic lattice; also number of ways of writing a nonnegative integer n as a sum of 3 squares (zero being allowed).

Theta series of cubic lattice with respect to edge.

Theta series of cubic lattice with respect to square.

Theta series of cubic lattice with respect to deep hole.

Theta series of D_4 lattice with respect to deep hole.

Theta series of D_4 lattice with respect to edge.

Theta series of planar hexagonal lattice (A2) with respect to edge.

Theta series of planar hexagonal lattice (A2) with respect to deep hole.

Theta series of square lattice with respect to deep hole.

Theta series of f.c.c. lattice with respect to edge.

Theta series of f.c.c. lattice with respect to triangle.

Theta series of f.c.c. lattice with respect to tetrahedral hole.

Theta series of f.c.c. lattice with respect to octahedral hole.

Theta series of hexagonal close-packing with respect to edge between layers.

Theta series of hexagonal close-packing with respect to triangle between octahedra.

Theta series of hexagonal close-packing with respect to center of triangle between two layers.

Centered pentagonal numbers: (5n^2+5n+2)/2; crystal ball sequence for 3.3.3.4.4. planar net.

Truncated square numbers: 7*n^2 + 4*n + 1.

Number of points on surface of tetrahedron; coordination sequence for sodalite net (equals 2*n^2+2 for n > 0).

Centered tetrahedral numbers.

Weighted count of partitions with distinct parts.

Weighted count of partitions with odd parts.

a(n) = 6*n^2 + 2 for n > 0, a(0)=1.

Centered cube numbers: n^3 + (n+1)^3.

Number of points on surface of octahedron; also coordination sequence for cubic lattice: a(0) = 1; for n > 0, a(n) = 4n^2 + 2.

Octahedral numbers: a(n) = n*(2*n^2 + 1)/3.

Number of points on surface of cuboctahedron (or icosahedron): a(0) = 1; for n > 0, a(n) = 10n^2 + 2. Also coordination sequence for f.c.c. or A_3 or D_3 lattice.

Centered icosahedral (or cuboctahedral) numbers, also crystal ball sequence for f.c.c. lattice.

Number of points on surface of dodecahedron: a(n) = 30*n^2 + 2 for n > 0.

Centered dodecahedral numbers.

Number of points on surface of truncated tetrahedron: a(n) = 14*n^2 + 2 for n > 0, a(0)=1.

Truncated tetrahedral numbers: a(n) = (1/6)*(n+1)*(23*n^2 + 19*n + 6).

a(n) = floor(tau*a(n-2)) + a(n-1) with a(0)=1 and a(1)=3.

a(n) = floor( phi*a(n-1) ) + floor( phi*a(n-2) ), where phi is the golden ratio.

a(n) = floor(tau*a(n-1)) + floor(tau*a(n-2)) with a(0)=0 and a(1)=2.