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

Author

N. J. A. Sloane, Jul 12 2003

Keywords

• nonn

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

Examples

			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.
		

Links

• Index entries for sequences related to binary matrices

Crossrefs

Cf. A085659, A080858, A083029.

Cf. A085656, A114601.

Programs

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)

Extensions

More terms from Max Alekseyev, Dec 13 2005