cp's OEIS Frontend

A118994 Number of real n X n symmetric (+1,-1) matrices with positive determinant.

%I A118994 #15 Jun 17 2025 22:08:15
%S A118994 1,0,16,432,8448,282240,81949952,32715189248,12792558313472,
%T A118994 9318420858593280
%N A118994 Number of real n X n symmetric (+1,-1) matrices with positive determinant.
%F A118994 a(n) = A118992(n) - A118997(n). For odd n, a(n) = A118997(n) = A118992(n)/2. - _Max Alekseyev_, Jun 12 2025
%p A118994 F:= proc(n) local Q,q,X,x,t,A,ii,L,v;
%p A118994   Q:= [[1,1],seq(seq([i,j],i=2..j),j=2..n)];
%p A118994   q:= nops(Q);
%p A118994   X:= [seq(x[q[1],q[2]],q=Q)];
%p A118994   t:= 0:
%p A118994   A:= Matrix(n,n,shape=symmetric,symbol=x);
%p A118994   A[2..n,1]:= Vector(n-1,1);
%p A118994   for ii from 0 to 2^q-1 do
%p A118994     L:= map(s -> 2*s-1, convert(2^q+ii,base,2)[1..q]);
%p A118994     v:= LinearAlgebra:-Determinant(subs(zip(`=`,X,L),A));
%p A118994     if v > 0 then t:= t+1 fi
%p A118994   od;
%p A118994   2^(n-1)*t;
%p A118994 end proc:
%p A118994 seq(F(n),n=1..7); # _Robert Israel_, Apr 14 2016
%Y A118994 Cf. A086900, A118992, A118995, A118997, A119003.
%K A118994 nonn,hard,more
%O A118994 1,3
%A A118994 _Giovanni Resta_, May 08 2006
%E A118994 a(8) from _Robert Israel_, Apr 17 2016
%E A118994 a(9)-a(10) from _Max Alekseyev_, Jun 17 2025