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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
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.
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
KEYWORD
nonn,more
AUTHOR
N. J. A. Sloane, Jul 13 2003
EXTENSIONS
a(6)-a(9) from Max Alekseyev, Jan 16 2006
STATUS
approved