A085658 - OEIS

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

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OFFSET

1,2

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

LINKS

EXAMPLE

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]

CROSSREFS

KEYWORD

nonn,more

AUTHOR

EXTENSIONS

3 more terms from Max Alekseyev, Nov 08 2006

STATUS

approved