A038379 Number of real {0,1} n X n matrices A such that M = A + A' has 2's on the main diagonal, 0's and 1's elsewhere and is positive semi-definite.

1, 3, 27, 729, 52649, 9058475, 3383769523, 2520512534065

Offset: 1

Author

N. J. A. Sloane, Jul 13 2003

Keywords

• nonn
• more
• nice

Comments

Necessarily A has all 1's on the main diagonal.

A real matrix M is positive semi-definite if its eigenvalues are >= 0.

For n <= 4, a(n) equals the upper bound 3^C(n,2).

For the number of different values of symmetric parts A + A', see A085658. - Max Alekseyev, Nov 11 2006

Links

• Index entries for sequences related to binary matrices

Crossrefs

Cf. A055165, which counts nonsingular {0, 1} matrices, A003024, which counts {0, 1} matrices with positive eigenvalues, A085656 (positive definite matrices).

Cf. A085657, A085658, A080858, A083029.

Formula

a(n) = Sum_{k=0..C(n,2)} 2^k * A083029(n,k).

Extensions

Definition corrected Nov 10 2006

a(6)-a(8) from Max Alekseyev, Nov 11 2006

Edited by Max Alekseyev, Jun 05 2024