Sequences

Fermionic string states.

Solution to Berlekamp's switching game (or lightbulb game) on an n X n board.

Maximal sum of inverse squares of the singular values of symmetric anti-Hadamard matrices of order n.

Maximal sum of inverse squares of the singular values of triangular anti-Hadamard matrices of order n.

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

Closed meandric numbers (or meanders): number of ways a loop can cross a road 2n times.

Meandric numbers: number of ways a river can cross a road n times.

a(n) = (2^n + C(2*n,n))/2.

Conway-Guy sequence: a(n + 1) = 2a(n) - a(n - floor( 1/2 + sqrt(2n) )).

a(n) = 6*a(n-1) - a(n-2).

a(n) = 4*a(n-1) - a(n-2), with a(0) = 0, a(1) = 3.

Upper triangular n X n (0,1)-matrices with no zero rows or columns.

Column of Motzkin triangle.

Column of Motzkin triangle.

Column of Motzkin triangle A026300.

Column of Motzkin triangle.

Permanent of "coprime?" matrix.

Certain subgraphs of a directed graph (inverse binomial transform of A005321).

Certain subgraphs of a directed graph.

a(n) = Product_{i=1..n} (2^i - 1). Also called 2-factorial numbers.

Certain subgraphs of a directed graph.

Certain subgraphs of a directed graph (binomial transform of A005321).

Certain subgraphs of a directed graph.

Number of 2-colored connected labeled graphs with n vertices of the first color and n vertices of the second color.

Number of labeled nonseparable (or 2-connected) bicolored graphs with n nodes of the first color and n nodes of the second color.

Number of labeled nonseparable (or 2-connected) bipartite graphs with 2n nodes and n nodes in each part.

Number of labeled nonseparable (or 2-connected) bipartite graphs with 2n nodes.

Number of ways in which n identical balls can be distributed among 4 boxes in a row such that each pair of adjacent boxes contains at least 4 balls.

Number of ways in which n identical balls can be distributed among 5 boxes in a row such that each pair of adjacent boxes contains at least 4 balls.

Number of ways in which n identical balls can be distributed among 6 boxes in a row such that each pair of adjacent boxes contains at least 4 balls.

Number of ways in which n identical balls can be distributed among 7 boxes in a row such that each pair of adjacent boxes contains at least 4 balls.

Length of n-th term in Look and Say sequences A005150 and A007651.

a(n) = solution to the postage stamp problem with n denominations and 7 stamps.

a(n) = solution to the postage stamp problem with n denominations and 8 stamps.

a(n) = solution to the postage stamp problem with n denominations and 9 stamps.

Number of elements of a free idempotent monoid on n letters.

Van der Waerden numbers W(2,n).

First differences of A005579.

Number of ways to add n ordinals.

Niven (or Harshad, or harshad) numbers: numbers that are divisible by the sum of their digits.

a(1) = a(2) = a(3) = 1, a(n) = a(a(n-1)) + a(n-a(n-1)) for n >= 4.

Base -2 representation for n regarded as base 2, then evaluated.

Base -2 representation of -n reinterpreted as binary.

Number of 2 X 2 matrices with entries mod n and nonzero determinant.

Number of asymmetric planar trees with n nodes.

Number of asymmetric permutation rooted trees with n nodes.

Number of low discrepancy sequences in base 2.

Number of low discrepancy sequences in base 3.

Number of low discrepancy sequences in base 5.

a(n) = n! if n is even, otherwise 0 (from Taylor series for cos x).