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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 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 May 26 09:37 EDT 2020. Contains 334620 sequences. (Running on oeis4.)