A119005 Number of n X n real symmetric (+1,-1)-matrices having maximal determinant (=A119003(n)).
1, 4, 16, 48, 416, 3840, 161280, 215040, 15482880, 774144000
Offset: 1
Extensions
a(8)-a(10) from Max Alekseyev, Jun 17 2025
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.
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
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