%I #4 Apr 12 2012 06:36:51

%S 120,856,6040,42492,297572,2076768,14447284,100224428,693541160,

%T 4788481556,32994512924,226924908072,1558056553740,10680681136996,

%U 73109657722272,499746329784652,3411594843779188,23261004734670688

%N Number of (n+1)X(n+1) -8..8 symmetric matrices with every 2X2 subblock having sum zero and three or four distinct values

%C Symmetry and 2X2 block sums zero implies that the diagonal x(i,i) are equal modulo 2 and x(i,j)=(x(i,i)+x(j,j))/2*(-1)^(i-j)

%H R. H. Hardin, <a href="/A211471/b211471.txt">Table of n, a(n) for n = 1..30</a>

%e Some solutions for n=3

%e .-7..4.-3..6....8.-1..6..0....4.-6..4.-5....6..1..2.-4....1..2..2.-4

%e ..4.-1..0.-3...-1.-6..1.-7...-6..8.-6..7....1.-8..5.-3....2.-5..1..1

%e .-3..0..1..2....6..1..4..2....4.-6..4.-5....2..5.-2..0....2..1..3.-5

%e ..6.-3..2.-5....0.-7..2.-8...-5..7.-5..6...-4.-3..0..2...-4..1.-5..7

%K nonn

%O 1,1

%A _R. H. Hardin_ Apr 12 2012