A370059 Number of traceless symmetric binary matrices with 2n 1's and all row sums >= 2.

1, 0, 0, 1, 3, 18, 156, 1555, 17907, 234031, 3414375, 54984258, 968680368, 18532158756, 382616109012, 8479409847277, 200776196593073, 5058600736907013, 135130222251100358, 3814891312969572209, 113492694557655580989, 3548800852807887882157, 116359373033373284971070

Offset: 0

Author

Andrew Howroyd, Feb 08 2024

Keywords

• nonn

Examples

			The a(3) = 1 matrix is:
  [0 1 1]
  [1 0 1]
  [1 1 0]
The a(4) = 3 matrices are:
  [0 0 1 1]  [0 1 0 1]  [0 1 1 0]
  [0 0 1 1]  [1 0 1 0]  [1 0 0 1]
  [1 1 0 0]  [0 1 0 1]  [1 0 0 1]
  [1 1 0 0]  [1 0 1 0]  [0 1 1 0]
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..200

Crossrefs

Row sums of A369931.

Cf. A001205 (row sums of matrices exactly 2).

Programs

PARI

G(n)={my(A=x/exp(x*y + O(x*x^n))); exp(y*x^2/2 - x + O(x*x^n)) * sum(k=0, n, (1 + y + O(y*y^n))^binomial(k, 2)*A^k/k!)}
seq(n)={Vec(subst(Pol(serlaplace(G(n))), x, 1))}