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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. 6
1, 2, 8, 64, 924, 21737, 749684, 33568376 (list; graph; refs; listen; history; text; internal format)
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

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

Index entries for sequences related to binary matrices

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

Cf. A085658, A080858, A083029.

Sequence in context: A134956 A011803 A007625 * A153541 A153569 A153532

Adjacent sequences:  A085655 A085656 A085657 * A085659 A085660 A085661

KEYWORD

nonn,more

AUTHOR

N. J. A. Sloane, Jul 12 2003

EXTENSIONS

3 more terms from Max Alekseyev, Nov 08 2006

STATUS

approved

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Last modified January 20 16:20 EST 2019. Contains 319335 sequences. (Running on oeis4.)