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%I #6 Oct 01 2021 17:36:34
%S 90,548,3296,19844,119260,716592,4303756,25835124,154970728,928644692,
%T 5557654436,33210094112,198105342332,1179507539876,7008630194584,
%U 41558569591508,245903742193060,1451916609628912,8554514693602716
%N Number of (n+1) X (n+1) -7..7 symmetric matrices with every 2 X 2 subblock having sum zero and three or four distinct values.
%C Symmetry and 2 X 2 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="/A211446/b211446.txt">Table of n, a(n) for n = 1..69</a>
%e Some solutions for n=3
%e ..4.-2..3.-4...-1.-3..0..3...-4.-1.-1.-1....0..2.-1.-2...-5..3..0..6
%e .-2..0.-1..2...-3..7.-4..1...-1..6.-4..6....2.-4..3..0....3.-1.-2.-4
%e ..3.-1..2.-3....0.-4..1..2...-1.-4..2.-4...-1..3.-2.-1....0.-2..5..1
%e .-4..2.-3..4....3..1..2.-5...-1..6.-4..6...-2..0.-1..4....6.-4..1.-7
%K nonn
%O 1,1
%A _R. H. Hardin_ Apr 11 2012
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