A084553 Number of n X n symmetric positive semi-definite matrices with 2's on the main diagonal and -1's and 0's elsewhere.

1, 2, 8, 45, 338, 3178, 34346, 396659, 4694705

Offset: 1

Author

N. J. A. Sloane, Jul 13 2003

Keywords

• nonn
• more

Comments

Of course the total number of symmetric matrices of this type (not necessarily positive definite) is 2^C(n,2).

This gives the number of different values of A + A' where A runs through the matrices counted in A127503.

Examples

			The 5 X 5 matrix
2 -1 -1 -1 -1
-1 2 -1 -1 -1
-1 -1 2 -1 -1
-1 -1 -1 2 -1
-1 -1 -1 -1 2
with eigenvalues -2, 3, 3, 3, 3 is an example of one which is not positive semi-definite.
		

Links

• Index entries for sequences related to binary matrices

Crossrefs

Cf. A084552, A085658, A080858, A083029.

Extensions

a(6)-a(9) from Max Alekseyev, Jan 16 2006