Sequences

Number of n-node trees not determined by their spectra.

Number of n-node forests not determined by their spectra.

Number of n-node bipartite graphs not determined by their spectra.

Zarankiewicz's problem.

A variant of Zarankiewicz's problem: a(n) is the least k such that every n X n {0,1}-matrix with k ones contains an all-ones 2 X 4 submatrix.

A variant of Zarankiewicz's problem: a(n) is the least k such that every n X n {0,1}-matrix with k ones contains an all-ones 3 X 4 submatrix.

Zarankiewicz's problem k_4(n).

Zarankiewicz's problem.

Zarankiewicz's problem.

Zarankiewicz's problem.

A variant of Zarankiewicz's problem: a(n) is the least k such that every n X (n+1) {0,1}-matrix with k ones contains an all-ones 2 X 2 submatrix.

Zarankiewicz's problem k_3(n,n+1).

A variant of Zarankiewicz's problem: a(n) is the least k such that every n X (n+1) {0,1}-matrix with k ones contains an all-ones 3 X 4 submatrix.

Zarankiewicz's problem.

a(n) is the least k such that every n X (n+3) {0,1}-matrix with k ones contains an all-ones 2 X 4 submatrix.

A variant of Zarankiewicz's problem: a(n) is the least k such that every n X (n+2) {0,1}-matrix with k ones contains an all-ones 3 X 4 submatrix.

Zarankiewicz's problem k_4(n,n+1).

Number of nonisomorphic 2-graphs with n nodes with first and second cohomology invariants both 0.

From a partition of the integers.

Self-convolution 4th power of A001764, which enumerates ternary trees.

From generalized Catalan numbers.

From generalized Catalan numbers.

a(n) = 3*binomial(4*n-1, n-1)/(4*n-1).

Expansion of hypergeom([3/2, 7/4, 2, 9/4], [7/3, 8/3, 3], (256/27)*x).

a(n) = 3*binomial(4*n+8, n)/(n+3).

a(n) = 4*binomial(4*n+11, n)/(n+4).

a(n) = (n + 1)*(n + 2)*(n + 4)*(n + 8)*(n + 15)/120.

Expansion of (2 - x)^4/(1 - x)^8.

Restricted postage stamp problem with n denominations and 2 stamps.

Restricted postage stamp problem.

Restricted postage stamp problem.

Class number of forms with discriminant -A003657(n), or equivalently class number of imaginary quadratic field with discriminant -A003657(n).

Class number of quadratic field with discriminant -4n+1.

Class number of quadratic field with discriminant -4n as n runs through A089269: squarefree numbers congruent to 1 or 2 mod 4.

Indices of records in Landau's function A000793.

Self-convolution of Pell numbers (A000129).

Exponential self-convolution of Pell numbers.

Number of graphs with n nodes, n-2 edges and no isolated vertices.

Number of graphs with n nodes, n-1 edges and no isolated vertices.

Number of graphs with n nodes, n edges and no isolated vertices.

Number of graphs with n nodes, n+1 edges and no isolated vertices.

Number of graphs with n nodes, n+2 edges and no isolated vertices.

From the graph reconstruction problem.

From the graph reconstruction problem.

From the graph reconstruction problem.

From the graph reconstruction problem.

Denominators of expansion of sinh x / sin x.

Number of closed meanders with 2 components and 2n bridges.

Closed meanders with 3 components and 2n bridges.

Number of closed meander systems of order n+1 with n components.