A085657 Number of n X n symmetric positive definite matrices with 2's on the main diagonal and 1's and 0's elsewhere.

1, 2, 8, 61, 819, 17417, 506609, 15582436

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: A370913 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