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

1, 0, 16, 432, 8448, 282240, 81949952, 32715189248

Offset

1,3

Links

Table of n, a(n) for n=1..8.

Maple

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

Crossrefs

Cf. A086900, A118995, A118997.

Sequence in context: A275140 A274731 A111921 * A223686 A000489 A075852

Adjacent sequences: A118991 A118992 A118993 * A118995 A118996 A118997

Keyword

nonn,hard,more

Author

Giovanni Resta, May 08 2006

Extensions

a(8) from Robert Israel, Apr 17 2016

Status

approved