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A085657 Number of n X n symmetric positive definite matrices with 2's on the main diagonal and 1's and 0's elsewhere. 6
1, 2, 8, 61, 819, 17417, 506609, 15582436 (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 A085656. - Max Alekseyev, Dec 13 2005

LINKS

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

Index entries for sequences related to binary matrices

EXAMPLE

The singular matrix

2 0 1 1

0 2 1 1

1 1 2 0

1 1 0 2

is one of the three 4 X 4 matrices which are not positive definite.

PROG

(PARI) { a(n) = M=matrix(n, n, i, j, 2*(i==j)); r=0; b(1); r } { b(k) = if(k>n, r++; return); forvec(x=vector(k-1, i, [0, 1]), for(i=1, k-1, M[k, i]=M[i, k]=x[i]); if( matdet(vecextract(M, 2^k-1, 2^k-1), 1)>0, b(k+1) ) ) } (Max Alekseyev)

CROSSREFS

Cf. A085659, A080858, A083029.

Cf. A085656, A114601.

Sequence in context: A188324 A208356 A188489 * A005215 A058862 A191482

Adjacent sequences:  A085654 A085655 A085656 * A085658 A085659 A085660

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Jul 12 2003

EXTENSIONS

More terms from Max Alekseyev, Dec 13 2005

STATUS

approved

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Last modified January 18 03:13 EST 2019. Contains 319260 sequences. (Running on oeis4.)