Sequences

Crystal ball sequence for hyperbolic tessellation 3^7 (from triangle group (2,3,7)).

Number of points in interior of n-th crystal ball in E_8 lattice.

Number of ways of making change for n cents using coins of 1, 2, 4, 10 cents.

Primes in ternary.

Number of ways of making change for n cents using coins of 1, 2, 4, 12, 24, 48, 96, 120 cents (based on English coinage of 1939).

Expansion of 1/(1-x)^2/(1-x^2)/(1-x^6)/(1-x^12)/(1-x^24)/(1-x^48)/(1-x^60).

Maximal number of unattacked squares with n queens on n X n board (answers for n >= 17 only probable).

Solution to f(2) = 1, f(n) = sqrt(n) f(sqrt(n)) + n at values n = 2^2^i.

Number of letters in n (in Irish Gaelic).

Blocks of increasing length using 1,2,3,...,9,10; omit leading 0's.

Sum of digits of 2^n.

Number of n-bead necklaces with beads of 2 colors and primitive period n, when turning over is allowed.

Number of unlabeled mappings (or mapping patterns) from n points to themselves; number of unlabeled endofunctions.

Number of functional digraphs (digraphs of functions on n nodes where every node has outdegree 1 and loops of length 1 are forbidden).

Number of relational systems on n nodes. Also number of directed 3-multigraphs with loops on n nodes.

Relational systems on n nodes.

Relational systems on n nodes.

Number of relations with 4 arguments on n nodes.

Degrees of irreducible representations of Baby Monster group B.

Degrees of irreducible representations of Monster group M.

Weight distribution of binary Golay code of length 24.

Weight distribution of binary [ 48,24,12 ] quadratic residue code.

Weight distribution of ternary [ 24,12,9 ] quadratic residue code (also of Pless symmetry code).

Number of n-node rooted trees of height at most 3.

Number of n-node trees of height at most 4.

Number of n-node trees of height at most 5.

Coordination sequence for 4-dimensional I-centered tetragonal orthogonal lattice.

The binary "look and say" sequence.

Describe the previous term (in base 3)!.

To get the 6th term, for example, note that 5th term has three (10 in ternary!) 1's, one (1) 0, etc., giving 10 1 1 0 1 2 2 1 1 2.

Smallest multiplicative generator for quadratic residues mod prime(n).

To get the 3rd term, for example, note that 2nd term has three (11 in binary!) 1's and one (1) 0, giving 11 1 1 0.

a(n) = 9*binomial(2n,n-4)/(n+5).

High temperature series for spin-1/2 Ising free energy on 3-dimensional simple cubic lattice.

Number of n-step self-avoiding walks on diamond.

Number of (2n+1)-step self-avoiding walks on diamond lattice ending at point with x = 1.

Number of 2n-step self-avoiding walks on diamond lattice ending at point with x = 0.

Number of 2n-step self-avoiding walks on diamond lattice ending at point with x = 2.

Number of (2n+1)-step self-avoiding walks on diamond lattice ending at point with x = 3.

a(n) is the number of partitions of n into at most 3 parts; also partitions of n+3 in which the greatest part is 3; also number of unlabeled multigraphs with 3 nodes and n edges.

Number of partitions of n into at most 4 parts.

Number of partitions of n into at most 5 parts.

Number of partitions of n into at most 6 parts.

Number of combinatorial configurations of type (n_3).

Triangle of values of 2-d recurrence.

a(n) = binomial(n, floor(n/2)).

High temperature series for partition function for spin-1/2 Ising model on b.c.c. lattice.

High temperature series for partition function for spin-1/2 Ising model on f.c.c. lattice.

High temperature series for spin-1/2 Ising specific heat on 3-dimensional simple cubic lattice, divided by 3.

Number of 2n-step polygons on cubic lattice.