A118999
Number of real n X n symmetric (+1,-1) matrices with negative permanent.
Original entry on oeis.org
1, 0, 32, 240, 11904, 533568, 134217728, 22741568512, 16885168208896
Offset: 1
A118994
Number of real n X n symmetric (+1,-1) matrices with positive determinant.
Original entry on oeis.org
1, 0, 16, 432, 8448, 282240, 81949952, 32715189248, 12792558313472, 9318420858593280
Offset: 1
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F:= proc(n) local Q,q,X,x,t,A,ii,L,v;
Q:= [[1,1],seq(seq([i,j],i=2..j),j=2..n)];
q:= nops(Q);
X:= [seq(x[q[1],q[2]],q=Q)];
t:= 0:
A:= Matrix(n,n,shape=symmetric,symbol=x);
A[2..n,1]:= Vector(n-1,1);
for ii from 0 to 2^q-1 do
L:= map(s -> 2*s-1, convert(2^q+ii,base,2)[1..q]);
v:= LinearAlgebra:-Determinant(subs(zip(`=`,X,L),A));
if v > 0 then t:= t+1 fi
od;
2^(n-1)*t;
end proc:
seq(F(n),n=1..7); # Robert Israel, Apr 14 2016
A118992
Number of real n X n invertible symmetric (+1,-1) matrices.
Original entry on oeis.org
2, 4, 32, 512, 16896, 1190144, 163899904, 46195853312, 25585116626944, 28281621931343872
Offset: 1
A118996
Number of real n X n symmetric (0,1) matrices with negative determinant.
Original entry on oeis.org
0, 3, 27, 190, 4410, 753592, 127793708, 21893984392, 9100020369720, 16451259308386616
Offset: 1
A118990
Number of symmetric singular n X n (+1,-1) matrices over the reals.
Original entry on oeis.org
0, 4, 32, 512, 15872, 907008, 104535552, 22523623424, 9599255461888, 7747175087620096
Offset: 1
Showing 1-5 of 5 results.