%I #8 Jul 18 2018 07:47:34
%S 13,17,23,33,49,75,117,185,295,473,761,1227,1981,3201,5175,8369,13537,
%T 21899,35429,57321,92743,150057,242793,392843,635629,1028465,1664087,
%U 2692545,4356625,7049163,11405781,18454937,29860711,48315641,78176345
%N Number of (n+1) X (n+1) -4..4 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="/A211490/b211490.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 2*a(n-1) - a(n-3).
%F Conjectures from _Colin Barker_, Jul 18 2018: (Start)
%F G.f.: x*(13 - 9*x - 11*x^2) / ((1 - x)*(1 - x - x^2)).
%F a(n) = 7 + (2^(1-n)*((1-sqrt(5))^n*(-2+sqrt(5)) + (1+sqrt(5))^n*(2+sqrt(5)))) / sqrt(5).
%F (End)
%e Some solutions for n=3:
%e .-2..2.-2..2....0..0..0..0....1.-1.-1.-1....4.-4..4.-4...-3..1.-1..3
%e ..2.-2..2.-2....0..0..0..0...-1..1..1..1...-4..4.-4..4....1..1.-1.-1
%e .-2..2.-2..2....0..0..0..0...-1..1.-3..1....4.-4..4.-4...-1.-1..1..1
%e ..2.-2..2.-2....0..0..0..0...-1..1..1..1...-4..4.-4..4....3.-1..1.-3
%K nonn
%O 1,1
%A _R. H. Hardin_, Apr 13 2012