[seqfan] Re: seq needed of (0,+-1) matrices

[N. J. A. Sloane]

well, I get a(4) = 125 using Maple, agreeing with Max.

Here's my Maple code:
with(combinat);
A:=Matrix(4,4):
for i from 1 to 4 do A[i,i]:=0; od:
n:=0;
for a from -1 to 1 do A[1,2]:=a; A[2,1]:=-a;
for b from -1 to 1 do A[1,3]:=b; A[3,1]:=-b;
for c from -1 to 1 do A[1,4]:=c; A[4,1]:=-c;
for d from -1 to 1 do A[2,3]:=d; A[3,2]:=-d;
for e from -1 to 1 do A[2,4]:=e; A[4,2]:=-e;
for f from -1 to 1 do A[3,4]:=f; A[4,3]:=-f;
perms:=permute(4);
nsw:=+1;
for i from 1 to 24 do
p:=perms[i];
w:=p[1]; x:=p[2]; y:=p[3]; z:=p[4];
star:=A[w,x]*A[y,z]+A[w,y]*A[x,z]+A[w,z]*A[x,y]-A[w,x]*A[w,y]*A[w,z]*A[x,y]*A[x,z]*A[y,z];
if star <> 0 then nsw:=-1; break; fi;
od:
if nsw = 1 then n:=n+1; fi;
od: od: od: od: od: od:
n;

Neil