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%I #3 Apr 21 2012 12:16:21
%S 188,1702,15334,138130,1242978,11177174,100431854,901725738,
%T 8089235074,72498715894,649077462926,5804421919322,51840849262274,
%U 462375098375406,4118031964300046,36620792527293818
%N Number of (n+1)X(n+1) -10..10 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)
%e Some solutions for n=3
%e ..6..2..5..2..-10..9-10..3....9.-6..2.-5....9.-2..4.-2...-8..1.-3.-1
%e ..2-10..3-10....9.-8..9.-2...-6..3..1..2...-2.-5..3.-5....1..6.-4..8
%e ..5..3..4..3..-10..9-10..3....2..1.-5..2....4..3.-1..3...-3.-4..2.-6
%e ..2-10..3-10....3.-2..3..4...-5..2..2..1...-2.-5..3.-5...-1..8.-6.10
%K nonn
%O 1,1
%A _R. H. Hardin_ Apr 21 2012
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