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A118994 Number of real n X n symmetric (+1,-1) matrices with positive determinant. 3
1, 0, 16, 432, 8448, 282240, 81949952, 32715189248 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,3
LINKS
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
Sequence in context: A275140 A274731 A111921 * A223686 A000489 A075852
KEYWORD
nonn,hard,more
AUTHOR
Giovanni Resta, May 08 2006
EXTENSIONS
a(8) from Robert Israel, Apr 17 2016
STATUS
approved

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Last modified June 15 10:58 EDT 2024. Contains 373407 sequences. (Running on oeis4.)