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%I #8 Jul 17 2018 08:37:53
%S 15,19,25,35,51,77,119,187,297,475,763,1229,1983,3203,5177,8371,13539,
%T 21901,35431,57323,92745,150059,242795,392845,635631,1028467,1664089,
%U 2692547,4356627,7049165,11405783,18454939,29860713,48315643,78176347
%N Number of (n+1) X (n+1) -5..5 symmetric matrices with every 2 X 2 subblock having sum zero and one or 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="/A211329/b211329.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 2*a(n-1) - a(n-3).
%F Empirical g.f.: x*(15 - 11*x - 13*x^2) / ((1 - x)*(1 - x - x^2)). - _Colin Barker_, Jul 17 2018
%e Some solutions for n=3:
%e .-1..1.-1.-1....4.-4..4.-4....1..1..1.-1....1.-1..1..1...-2..2.-2..2
%e ..1.-1..1..1...-4..4.-4..4....1.-3..1.-1...-1..1.-1.-1....2.-2..2.-2
%e .-1..1.-1.-1....4.-4..4.-4....1..1..1.-1....1.-1..1..1...-2..2.-2..2
%e .-1..1.-1..3...-4..4.-4..4...-1.-1.-1..1....1.-1..1.-3....2.-2..2.-2
%K nonn
%O 1,1
%A _R. H. Hardin_, Apr 07 2012