Sequences

Number of solid partitions of height n in a cube of side n.

(n+1) * a(n+1) - 2 (68*n^2+68*n+27) * a(n) + 6 * n * (772*n^2+35) * a(n-1) - 2 * (2*n-1)^2 * (68*n^2-68*n+27) * a(n-2) + (2*n-1)^2 * (n-1) * (2*n-3)^2 * a(n-3) = 0.

Number of domino tilings of a certain region.

Number of pairs of length n permutations achievable by double-ended priority queue.

Number of nonintersecting (or self-avoiding) rook paths joining opposite corners of an n X n grid.

Primes p == 1 (mod 8), p = a^2 +64*b^2 such that y^2 = x^3 + p*x has rank 0.

Primes p == 1 (mod 8), p = a^2 + 64*b^2 such that y^2 = x^3 + p*x has rank 2.

Number of pairs of permutations of degree n that avoid (12,21).

From Engel product expansion of 4/7.

Number of chord diagrams with n chords; number of pairings on a necklace.

Values of Ehrhart polynomial of dilation by 2 of Relaxed Boolean Quadric Polytope of order 4.

Values of Ehrhart polynomial of dilation by 2 of Relaxed Boolean Quadric Polytope of order 3.

For any circular arrangement of 0..n-1, let S = sum of squares of every sum of two contiguous numbers; then a(n) = # of distinct values of S.

Numbers that are divisible by exactly 2 different primes; numbers n with omega(n) = A001221(n) = 2.

Numbers not divisible by 2, 3 or 5.

Number of connected posets with n elements of height 1.

Number of overlap-free binary words of length n.

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

Coefficients of asymptotic expansion of Ramanujan false theta series.

Losing initial configurations in 2-hole Tchuka Ruma.

a(n) = (n+1)^(n+1) - n^n for n>0, a(0) = 1.

Number of factors in the infinite word formed by the Kolakoski sequence A000002.

Mixed Van der Waerden numbers w(n, 3; 2).

Van der Waerden numbers W(4,n).

Number of sets of positive integers <= n^2 whose sum is (n^3 + n)/2.

Number of nonintersecting rook paths joining opposite corners of 4 X n board.

Number of nonintersecting rook paths joining opposite corners of 5 X n board.

Number of augmented André 3-signed permutations: E.g.f. (1-sin(3*x))^(-1/3).

From a problem concerning circulant matrices and Gauss sums.

From a problem concerning circulant matrices and Gauss sums.

From a problem concerning circulant matrices and Gauss sums.

From a problem concerning circulant matrices and Gauss sums.

Number of conjugacy classes of compact Cartan subgroups in Sp_{2n}(F), where p>n and the p-adic field F contains all r-th roots of unity for all r <= 2n.

Juxtapose pairs of primes (starting at 1).

Juxtapose pairs of primes.

List of pairs of primes in reverse order, starting at 1.

List of pairs of primes in reverse order.

Expected number of random moves in Tower of Hanoi problem with n disks starting with a randomly chosen position and ending at a position with all disks on the same peg.

Irregular triangle read by rows: Whitney numbers of the second kind a(n,k), n >= 1, k >= 0, for the star poset.

From a problem in AI planning: a(n) = 4+a(n-1)+a(n-2)+a(n-3)+a(n-4)-a(n-5)-a(n-6)-a(n-7), n>7.

Expansion of f(f(x)), where f = x + x^2 + x^4 + x^8 + x^16 + ...

Numbers n such that game of n X n Button Madness need have no solution; this lists only the primitive elements of the set.

Number of connected series-parallel graphs with a longest path of at most n edges and also a largest cut set of at most n edges.

Related to the asymptotic expansion of Sum_{k = 0..n} C(n,k)^4.

a(n) = Fibonacci(6*n + 3)/2.

Integer part of Sum_{i=1..n} binomial(n,i) * (n/i)^i.

A variation on Euclid: a(n)=g(n)-1, where g(0)=0, g(1)=1, g(n+1)=g(n)(g(n-1)+1).

Number of directed column-convex polyominoes of height n: a(k+1)=(k+1)*a(k)+(a(1)+...+a(k)).

Smallest prime with n distinct digits.

Largest prime with n distinct decimal digits.