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 A127502 #7 Jul 21 2025 14:27:14
%S A127502 1,3,19,201,3001,55291,1115003,21837649,373215601,8282131891
%N A127502 Number of n X n positive definite matrices with 1's on the main diagonal and -1's and 0's elsewhere.
%C A127502 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 A127502 M need not be symmetric. For the number of different values of M + M' see A084552.
%e A127502 For n = 2 the three matrices are {{{1, 0}, {0, 1}}, {{1, 0}, {-1, 1}}, {{1, -1}, {0, 1}}}.
%o A127502 (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,[ -1,0]), 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 A127502 Cf. A085656, A085657, A085658, A086215, A038379, A080858, A083029, A127503.
%K A127502 nonn,nice
%O A127502 1,2
%A A127502 _Max Alekseyev_, Jan 16 2007