Sequences

a(n) = floor((n+2/3)*(5+sqrt(13))/2); v-pile positions in the 3-Wythoff game.

A Beatty sequence: floor(n * (sqrt(5) - 1)).

A Beatty sequence: floor(n * (sqrt(5) + 3)).

Winning positions in the u-pile of the 4-Wythoff game with i=1.

v-pile positions of the 4-Wythoff game with i=1.

u-pile count for the 4-Wythoff game with i=2.

v-pile counts for the 4-Wythoff game with i=2.

u-pile positions for the 4-Wythoff game with i=3.

v-pile positions of the 4-Wythoff game with i=3.

Evil numbers: nonnegative integers with an even number of 1's in their binary expansion.

Functional determinants; partitions of partitions; Euler transform applied twice to all 1's sequence.

Nearest integer to n^2/8.

Expansion of 1/((1-x)^2*(1-x^4)) = 1/( (1+x)*(1+x^2)*(1-x)^3 ).

Expansion of (1+x^3)/((1-x)*(1-x^2)^2*(1-x^3)).

Numbers that are the sum of 3 distinct squares, i.e., numbers of the form x^2 + y^2 + z^2 with 0 <= x < y < z.

Number of partitions of floor(5n/2) into n nonnegative integers each no more than 5.

Number of partitions of floor(5n/2)-1 into n nonnegative integers each no more than 5.

Number of partitions of 3n into n parts from the set {0, 1, ..., 6} (repetitions admissible).

Number of partitions of 3n-1 into n nonnegative integers each no more than 6.

Number of partitions of floor(7n/2) into n nonnegative integers each no more than 7.

Number of partitions of floor(7n/2)-1 into n nonnegative integers each no greater than 7.

Restricted partitions.

Number of partitions of 4n-1 into n nonnegative integers each no greater than 8.

Numbers that are the sum of 2 distinct squares: of form x^2 + y^2 with 0 <= x < y.

Erroneous version of A045535.

Class numbers of quadratic fields.

Let p be the n-th odd prime. Then a(n) is the least prime congruent to 3 modulo 8 such that Legendre(-a(n), q) = -1 for all odd primes q <= p.

Class numbers associated with terms of A001986.

Let p be the n-th odd prime. a(n) is the least prime congruent to 7 modulo 8 such that Legendre(-a(n), q) = -Legendre(-1, q) for all odd primes q <= p.

Class numbers associated with terms of A001988.

Let p be the n-th odd prime. a(n) is the least prime congruent to 5 modulo 8 such that Legendre(-a(n), q) = -Legendre(-2, q) for all odd primes q <= p.

Class numbers associated with terms of A001990.

Let p = n-th odd prime. Then a(n) = least prime congruent to 5 modulo 8 such that Legendre(a(n), q) = -1 for all odd primes q <= p.

Number of two-rowed partitions of length 3.

Expansion of 1/((1-x^2)*(1-x^4)^2*(1-x^6)*(1-x^8)*(1-x^10)) (even powers only).

Numbers that are the sum of 5 distinct squares: of form v^2 + w^2 + x^2 + y^2 + z^2 with 0 <= v < w < x < y < z.

Number of partitions of n into parts 2, 3, 4, 5, 6, 7.

Number of different shapes formed by bending a piece of wire of length n in the plane.

Bending a piece of wire of length n+1; walks of length n+1 on a tetrahedron; also non-branched catafusenes with n+2 condensed hexagons.

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

a(n+1) = a(n)*(a(n)^2 - 3) with a(0) = 7.

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

a(n) = Sum_{k=0..n-1} binomial(n,k+1) * binomial(n+k,k).

a(n) = 2 * Sum_{k=0..n-1} binomial(n-1, k)*binomial(n+k, k).

Davenport-Schinzel numbers of degree 4 on n symbols.

Number of rooted planar cubic maps with 2n vertices.

Almost trivalent maps.

Almost trivalent maps.

Almost trivalent maps.

Almost trivalent maps.