This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A085656 #15 Feb 16 2025 08:32:50
%S A085656 1,3,27,681,43369,6184475,1688686483,665444089745
%N A085656 Number of positive-definite real {0,1} n X n matrices.
%C A085656 A real matrix M is positive-definite if x M x' > 0 for all nonzero real vectors x. Equivalently, all eigenvalues of M + M' are positive.
%C A085656 M need not be symmetric. For the number of different values of M + M' see A085657. - _Max Alekseyev_, Dec 13 2005
%H A085656 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/01-Matrix.html">(0,1)-Matrix</a>
%H A085656 Eric Weisstein's World of Mathematica, <a href="https://mathworld.wolfram.com/PositiveDefiniteMatrix.html">Positive Definite Matrix</a>
%H A085656 <a href="/index/Mat#binmat">Index entries for sequences related to binary matrices</a>
%e A085656 For n = 2 the three matrices are {{{1, 0}, {0, 1}}, {{1, 0}, {1, 1}}, {{1, 1}, {0, 1}}}.
%t A085656 Table[Count[Tuples[{0, 1}, {n, n}], _?PositiveDefiniteMatrixQ], {n, 4}] (* _Eric W. Weisstein_, Jan 03 2021 *)
%o A085656 (PARI) { a(n) = M=matrix(n,n,i,j,2*(i==j)); r=0; b(1); r } { b(k) = local(t); if(k>n, t=0; for(i=1,n, for(j=1,i-1, if(M[i,j]==1,t++); )); r+=2^t; 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) ) ) } (Alekseyev)
%Y A085656 Cf. A055165, which counts nonsingular {0, 1} matrices and A085506, which counts {-1, 0, 1} matrices with positive eigenvalues.
%Y A085656 Cf. A085657, A085658, A086215, A038379 (positive semi-definite matrices), A080858, A083029.
%K A085656 nonn,nice
%O A085656 1,2
%A A085656 _N. J. A. Sloane_, Jul 12 2003
%E A085656 More terms from _Max Alekseyev_, Dec 13 2005