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

LINKS

Table of n, a(n) for n=1..9.

Index entries for sequences related to binary matrices

EXAMPLE

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.

CROSSREFS

Cf. A084552, A085659, A080858, A083029.

Sequence in context: A152401 A325138 A009345 * A144164 A003091 A119501

Adjacent sequences:  A084550 A084551 A084552 * A084554 A084555 A084556

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Jul 13 2003

EXTENSIONS

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

STATUS

approved

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Last modified October 18 20:24 EDT 2019. Contains 328197 sequences. (Running on oeis4.)