Sequences

Number of n-node unlabeled graphs without endpoints (i.e., no nodes of degree 1).

Number of rooted identity trees with n nodes (rooted trees whose automorphism group is the identity group).

Numbers k where |cos(k)| (or |cosec(k)| or |cot(k)|) decreases monotonically to 0; also numbers k where |tan(k)| (or |sec(k)|, or |sin(k)|) increases.

Number of rooted trees with n nodes and 2-colored non-leaf nodes.

Number of trees with n nodes and 2-colored internal (non-leaf) nodes.

Number of unlabeled rooted nonseparable graphs with n nodes.

a(n) = floor((n^2 + 6n - 3)/4).

Numerators of expansion of (1-x)^(-1/3).

Maximal excess of a Hadamard matrix of order 4n.

a(0) = 1; thereafter a(n) = 3*2^(n-1) + 1.

Expansion of (1 + x - x^5) / (1 - x)^3.

Generalized weak orders on n points.

Generalized weak orders on n points.

Number of generalized weak orders on n points.

Discriminant of n-th cyclotomic polynomial.

Sum of remainders of n mod k, for k = 1, 2, 3, ..., n.

a(n) = n*(7*n^2 - 1)/6.

Number of planar hexagon trees with n hexagons.

a(n) = Sum_{k=1..n} floor(3*n/3^k).

Postage stamp problem: largest m such that there exists an n-subset S of nonnegative integers such that 1,...,m can be expressed as a sum of two distinct elements of S.

Numerators in expansion of (1-x)^{-1/4}.

Modular postage stamp problem: largest m such that there exists an n-subset S of nonnegative integers such that 0,...,m-1 can be expressed as a mod-m sum of two distinct elements of S.

Modular postage stamp problem.

Additive bases: a(n) is the least integer such that there is an n-element set of nonnegative integers, the sums of pairs (of distinct elements) of which are distinct and at most a(n).

Denominators in expansion of (1-x)^{-1/4} are 2^a(n).

Additive bases: a(n) is the least integer k such that in the cyclic group Z_k there is a subset of n elements all pairs (of distinct elements) of which add up to a different sum (in Z_k).

Additive bases: a(n) is the least integer k such that in the cyclic group Z_k there is a subset of n elements all pairs (of not necessarily distinct elements) of which add up to a different sum (in Z_k).

Maximal number of edges in a graceful graph on n nodes.

From a counter moving problem.

Odd primes excluding 5.

Number of nonempty labeled simple graphs on nodes chosen from an n-set.

Norm of a matrix.

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

From the powers that be.

Nonhypotenuse numbers (indices of positive squares that are not the sums of 2 distinct nonzero squares).

Number of degenerate simplices in n-cube.

Alternate Lucas numbers - 2.

Number of n-state Turing machines which halt.

Generalized Catalan numbers: a(n+1) = a(n) + Sum_{k=1..n-1} a(k)*a(n-1-k).

Generalized Catalan numbers: a(n+1) = a(n) + Sum_{k=2..n-1} a(k)*a(n-1-k).

Euler numbers written backwards.

Omit trailing zeros from n.

Sum of digits of n!.

Factorial numbers written backwards.

a(n) = n! with trailing zeros omitted.

Sum of digits of n-th odd number.

Odd numbers written backwards.

Sum of digits of n-th triangular number.

Triangular numbers written backwards.

Sum of digits of n^2.