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%I #8 Jul 16 2018 05:22:30
%S 11,15,21,31,47,73,115,183,293,471,759,1225,1979,3199,5173,8367,13535,
%T 21897,35427,57319,92741,150055,242791,392841,635627,1028463,1664085,
%U 2692543,4356623,7049161,11405779,18454935,29860709,48315639,78176343
%N Number of (n+1) X (n+1) -3..3 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="/A211322/b211322.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 16 2018: (Start)
%F G.f.: x*(11 - 7*x - 9*x^2) / ((1 - x)*(1 - x - x^2)).
%F a(n) = 5 + (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 .-1.-1.-1..1...-1..1.-1.-1....0..0..0..0...-3..1.-3..1....3.-3..3.-3
%e .-1..3.-1..1....1.-1..1..1....0..0..0..0....1..1..1..1...-3..3.-3..3
%e .-1.-1.-1..1...-1..1.-1.-1....0..0..0..0...-3..1.-3..1....3.-3..3.-3
%e ..1..1..1.-1...-1..1.-1..3....0..0..0..0....1..1..1..1...-3..3.-3..3
%K nonn
%O 1,1
%A _R. H. Hardin_, Apr 07 2012