Sequences

Triangular star numbers.

Star numbers (A003154) that are squares.

Star-hex numbers.

A card-arranging problem: values of n such that there exists a permutation p_1, ..., p_n of 1, ..., n such that i + p_i is a cube for every i.

Smallest junction number with n generators.

Maximal number of 4-tree rows in n-tree orchard problem.

Kobon triangles: maximal number of nonoverlapping triangles that can be formed from n lines drawn in the plane.

Number of ways to quarter an n X n chessboard, with the central square removed for odd n.

a(n) is Gray-coded into n.

Number of directed Hamiltonian cycles (or Gray codes) on n-cube with a marked starting node.

Number of Hamiltonian paths on n-cube which are strictly not cycles.

Maximal length of rook tour on an n X n board.

Numbers with mirror symmetry about middle.

Numbers k such that k, k+1 and k+2 all have the same number of distinct prime divisors.

Number of polyaboloes (or polytans): number of different shapes that can be formed with n congruent isosceles right triangles, identifying mirror images.

Minimal number of knights needed to cover an n X n board.

Sequence A006075 gives minimal number of knights needed to cover an n X n board. This sequence gives number of inequivalent solutions using A006075(n) knights.

(n+1)^2*a(n+1) = (9n^2+9n+3)*a(n) - 27*n^2*a(n-1), with a(0) = 1 and a(1) = 3.

Number of triangulated (n+2)-gons rooted at an exterior edge.

Number of asymmetric planted projective plane trees with n+1 nodes; bracelets (reversible necklaces) with n black beads and n-1 white beads.

Number of rooted projective plane trees with n nodes.

Number of line-rooted projective plane trees with n nodes.

Number of labeled projective plane trees (or "flat" trees) with n nodes.

Continued fraction for e/2.

Continued fraction for e/3.

Continued fraction for e/4.

Unitary harmonic numbers (those for which the unitary harmonic mean is an integer).

Unitary harmonic means H(n) of the unitary harmonic numbers (A006086).

a(n) = (2^n + 2) a(n-1) (kissing number of Barnes-Wall lattice in dimension 2^n).

Coefficients of elliptic function cn.

Expansion of bracket function.

a(n) = n^n - n + 1.

Numbers beginning with letter 't' when spelled out in English.

a(n) = prime(n) - 1.

Products of 2 successive primes.

Gaussian binomial coefficient [n, 2] for q = 2.

Gaussian binomial coefficient [n, 3] for q = 2.

Gaussian binomial coefficient [n, 4] for q = 2.

Gaussian binomial coefficient [ 2n,n ] for q=2.

Gaussian binomial coefficient [ n, n/2 ] for q=2.

Gaussian binomial coefficient [n, 2] for q = 3.

Gaussian binomial coefficient [ n,3 ] for q=3.

Gaussian binomial coefficient [ n,4 ] for q=3.

Gaussian binomial coefficient [ 2n,n ] for q=3.

Gaussian binomial coefficient [ n,n/2 ] for q=3.

Gaussian binomial coefficient [ n,2 ] for q=4.

Gaussian binomial coefficient [ n,3 ] for q = 4.

Gaussian binomial coefficient [ n,4 ] for q = 4.

Gaussian binomial coefficient [ 2n,n ] for q=4.

Gaussian binomial coefficient [ n,n/2 ] for q=4.