

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 semidefinite.


5




OFFSET

1,2


COMMENTS

Necessarily A has all 1's on the main diagonal.
A real matrix M is positive semidefinite 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



