Sequences

Number of inequivalent ways of dissecting a regular (n+2)-gon into n triangles by n-1 non-intersecting diagonals under rotations and reflections; also the number of (unlabeled) maximal outerplanar graphs on n+2 vertices.

Number of even sequences with period 2n.

Nearest integer to tan n.

A Beatty sequence: floor(n*(e-1)).

a(n) = a(n-1) + a(n-2) - 2, a(0) = 4, a(1) = 3.

a(n) = floor(n^2/3).

Tribonacci numbers: a(n) = a(n-1) + a(n-2) + a(n-3) with a(0)=a(1)=a(2)=1.

Number of equivalence classes of Boolean functions of n variables under action of AG(n,2).

Fermat numbers: a(n) = 2^(2^n) + 1.

Take sum of squares of digits of previous term, starting with 2.

Take sum of squares of digits of previous term; start with 3.

Number of plane partitions (or planar partitions) of n.

Number of asymmetric trees with n nodes (also called identity trees).

Take sum of squares of digits of previous term; start with 5.

Coefficients of ménage hit polynomials.

Let A(n) = #{(i,j,k): i^2 + j^2 + k^2 <= n}, V(n) = (4/3)Pi*n^(3/2), P(n) = A(n) - V(n); A000092 gives values of n where |P(n)| sets a new record; sequence gives (nearest integer to, I believe) P(A000092(n)).

Number of squares mod n.

a(n) = 2^n - 1. (Sometimes called Mersenne numbers, although that name is usually reserved for A001348.)

Number of n-node unlabeled connected graphs with one cycle of length 3.

Nearest integer to e^n.

Number of hexagonal polyominoes (or hexagonal polyforms, or planar polyhexes) with n cells.

a(n) is the least number m such that the n-th prime is the least quadratic nonresidue modulo m.

a(0)=2; for n>=1, a(n) = smallest prime p such that there is a gap of exactly 2n between p and next prime, or -1 if no such prime exists.

Number of inequivalent Boolean functions of n variables under action of complementing group.

Construct a triangle as in A036262. Sequence is one less than the position of the first number larger than 2 in the n-th row (n-th difference).

Generalized class numbers c_(n,1).

Partitions into non-integral powers (see Comments for precise definition).

Number of n-node rooted trees of height 3.

Maximum m such that there are no two adjacent elements belonging to the same n-th power residue class modulo some prime p in the sequence 1,2,...,m (equivalently, there is no n-th power residue modulo p in the sequence 1/2,2/3,...,(m-1)/m).

Number of mixed Husimi trees with n nodes; or rooted polygonal cacti with bridges.

Number of oriented trees with n nodes.

One-half of number of permutations of [n] with exactly one run of adjacent symbols differing by 1.

Rencontres numbers: number of permutations of [n] with exactly one fixed point.

Crossing number of complete graph with n nodes.

3rd power of rooted tree enumerator; number of linear forests of 3 rooted trees.

Number of trees with n nodes, 2 of which are labeled.

Powers of 3: a(n) = 3^n.

a(n) = 3*(2*n)!/((n+2)!*(n-1)!).

Number of permutations in the symmetric group S_n that have odd order.

a(n) = 2^n - n - 2.

Expansion of e.g.f. exp(x*exp(x)).

Nearest integer to modified Bessel function K_n(5).

Number of symmetric reflexive relations on n nodes: (1/2)*A000666.

Number of trees of diameter 6.

Number of invertible 2 X 2 matrices mod n.

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

Unsigned Stirling numbers of first kind, s(n+1,2): a(n+1) = (n+1)*a(n) + n!.

a(n) = n*a(n-1) + (n-1)*a(n-2), a(0) = 1, a(1) = 1.

Number of simple triangulations of the plane with n nodes.

Number of rooted bicubic maps: a(n) = (8*n-4)*a(n-1)/(n+2) for n >= 2, a(0) = a(1) = 1.