A085658 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, 64, 924, 21737, 749684, 33568376

Offset: 1

Author

N. J. A. Sloane, Jul 12 2003

Keywords

• nonn
• more

Comments

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

This gives the number of different values of M + M' where M runs through the matrices counted in A038379. - Max Alekseyev, Nov 11 2006

Examples

			The matrix
2 0 0 0 1
0 2 0 1 1
0 0 2 1 1
0 1 1 2 0
1 1 1 0 2
is one of the 100 5 X 5 matrices which are not positive semi-definite.
Its eigenvalues are approximately [2., -0.135779205069857, 4.135779205069857, 1.337846553138044, 2.662153446861956]
		

Links

• Index entries for sequences related to binary matrices

Crossrefs

Cf. A085658, A080858, A083029.

Extensions

3 more terms from Max Alekseyev, Nov 08 2006