Sequences

Smallest number containing n syllables in UK English.

Erroneous version of A002439.

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

a(0) = 4; for n > 0, a(n) = a(n-1)^3 - 3*a(n-1)^2 + 3.

For n > 1: a(n) = a(n-1)^3 + 3a(n-1)^2 - 3; a(0) = 1, a(1) = 2.

a(n) = n + Sum_{k=1..n} pi(k), where pi() = A000720.

Number of polygons that can be formed from n points on a circle, no two adjacent.

Doubly triangular numbers: a(n) = n*(n+1)*(n^2+n+2)/8.

Nearest integer to exp n^2.

Liouville's function L(n) = partial sums of A008836.

Number of n X n invertible binary matrices A such that A+I is invertible.

a(n) = nearest integer to n^(3/2).

Numbers m such that 6m-1, 6m+1 are twin primes.

Number of period-n solutions to a certain "universal" equation related to transformations on the unit interval.

Number of precomplete Post functions.

Number of precomplete Post functions.

Number of precomplete Post functions of n variables.

Unitary perfect numbers: numbers k such that usigma(k) - k = k.

Least number of squares that add up to n.

Number of trivalent (or cubic) labeled graphs with 2n nodes.

Number of 3-edge-colored trivalent graphs with 2n nodes.

Number of 3-edge-colored connected trivalent graphs with 2n nodes.

Median Euler numbers.

Number of threshold functions of n variables.

Number of ways of getting a straight flush, 4 of a kind, full house, flush, straight, 3 of a kind, 2 pair, a pair, nothing in a 3-card poker hand.

Solid partitions of n which are restricted to two planes.

Let F(x) = 1 + x + 4x^2 + 10x^3 + ... = g.f. for A000293 (solid partitions) and expand (1-x)(1-x^2)(1-x^3)...*F(x) in powers of x.

Numbers k such that k^2 - k + 41 is prime.

Balancing weights on the integer line.

Number of simple perfect squared rectangles of order n up to symmetry.

Number of polyhedral graphs with n edges.

Number of 3-connected self-dual planar graphs with 2n edges.

Number of strongly asymmetric sequences of length n.

Number of partitions of n into parts 1/2, 3/4, 7/8, 15/16, etc.

Number of non-isentropic binary rooted trees with n nodes.

Number of distinct values taken by 2^2^...^2 (with n 2's and parentheses inserted in all possible ways).

Number of ways of transforming a set of n indistinguishable objects into n singletons via a sequence of n-1 refinements.

Number of ways of getting a straight flush, 4 of a kind, full house, flush, straight, 3 of a kind, 2 pair, a pair, no pair in poker.

Number of maximal collections of pairwise disjoint subsets {X,Y,Z} of {1, 2, ..., n} with X + Y = Z (as in A002849), with the property that n is in one of the subsets.

Number of maximal collections of pairwise disjoint subsets {X,Y,Z} of {1, 2, ..., n}, each satisfying X + Y = Z.

Number of decompositions of 2n into sum of 2 lucky numbers.

Number of unlabeled trivalent (or cubic) connected simple graphs with 2n nodes.

Continued fraction for Euler's constant (or Euler-Mascheroni constant) gamma.

Maximal size of a set of equiangular lines in n dimensions.

Number of unlabeled Euler graphs with n nodes; number of unlabeled two-graphs with n nodes; number of unlabeled switching classes of graphs with n nodes; number of switching classes of unlabeled signed complete graphs on n nodes; number of Seidel matrices of order n.

{m + n: m in A002382, n in A002381}.

Number of polyhedra with n nodes and n faces.

Number of Post functions of n variables.

Ulam numbers: a(1) = 1; a(2) = 2; for n>2, a(n) = least number > a(n-1) which is a unique sum of two distinct earlier terms.

a(1) = 1, a(2) = 3; for n >= 3, a(n) is smallest number that is uniquely of the form a(j) + a(k) with 1 <= j < k < n.