The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

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