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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. 5
1, 3, 27, 729, 52649, 9058475, 3383769523, 2520512534065 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

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) = the upper bound 3^C(n,2).

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

Number of symmetric parts is given by A085658. - Max Alekseyev, Nov 11 2006

LINKS

Table of n, a(n) for n=1..8.

Index entries for sequences related to binary matrices

FORMULA

Equals Sum_{k=0..C(n,2)} 2^k*T(n,k), where T(n,k) is given by A083029.

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.

Sequence in context: A099084 A085656 A113100 * A047656 A193610 A052269

Adjacent sequences:  A038376 A038377 A038378 * A038380 A038381 A038382

KEYWORD

nonn,more,nice

AUTHOR

N. J. A. Sloane, Jul 13 2003

EXTENSIONS

Definition corrected Nov 10 2006

STATUS

approved

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Last modified October 15 09:22 EDT 2019. Contains 328026 sequences. (Running on oeis4.)