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%I #8 Jul 19 2018 14:31:47
%S 34,46,64,94,142,220,346,550,880,1414,2278,3676,5938,9598,15520,25102,
%T 40606,65692,106282,171958,278224,450166,728374,1178524,1906882,
%U 3085390,4992256,8077630,13069870,21147484,34217338,55364806,89582128,144946918
%N Number of (n+1) X (n+1) -11..11 symmetric matrices with every 2 X 2 subblock having sum zero and two 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="/A211710/b211710.txt">Table of n, a(n) for n = 1..165</a>
%F Empirical: a(n) = 2*a(n-1) - a(n-3).
%F Empirical g.f.: 2*x*(17 - 11*x - 14*x^2) / ((1 - x)*(1 - x - x^2)). - _Colin Barker_, Jul 19 2018
%e Some solutions for n=3:
%e .-3.-3.-3..3....2.-2..2.-2...-6..2.-2..2....1.-1..1..1....1.-1.-1.-1
%e .-3..9.-3..3...-2..2.-2..2....2..2.-2..2...-1..1.-1.-1...-1..1..1..1
%e .-3.-3.-3..3....2.-2..2.-2...-2.-2..2.-2....1.-1..1..1...-1..1.-3..1
%e ..3..3..3.-3...-2..2.-2..2....2..2.-2..2....1.-1..1.-3...-1..1..1..1
%K nonn
%O 1,1
%A _R. H. Hardin_, Apr 20 2012
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