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%I #8 Jul 15 2018 12:04:01
%S 12,26,54,106,208,398,766,1458,2792,5324,10206,19550,37616,72446,
%T 140048,271194,526792,1025268,2000636,3911284,7663264,15040266,
%U 29571962,58231566,114837690,226761020,448318274,887305854,1757921506,3485905204
%N Number of (n+1) X (n+1) -2..2 symmetric matrices with every 2 X 2 subblock having sum zero and two or three 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="/A211115/b211115.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 5*a(n-1) - 4*a(n-2) - 16*a(n-3) + 27*a(n-4) + 8*a(n-5) - 35*a(n-6) + 10*a(n-7) + 10*a(n-8) - 4*a(n-9).
%F Empirical g.f.: 2*x*(6 - 17*x - 14*x^2 + 66*x^3 - 7*x^4 - 76*x^5 + 29*x^6 + 22*x^7 - 10*x^8) / ((1 - x)*(1 - 2*x)*(1 - x - x^2)*(1 - 2*x^2)*(1 - x - 2*x^2 + x^3)). - _Colin Barker_, Jul 15 2018
%e Some solutions for n=3:
%e ..0.-1..0.-1...-2..0.-1..0....1.-1..0.-1....2..0..0.-2....2..0..1..0
%e .-1..2.-1..2....0..2.-1..2...-1..1..0..1....0.-2..2..0....0.-2..1.-2
%e ..0.-1..0.-1...-1.-1..0.-1....0..0.-1..0....0..2.-2..0....1..1..0..1
%e .-1..2.-1..2....0..2.-1..2...-1..1..0..1...-2..0..0..2....0.-2..1.-2
%K nonn
%O 1,1
%A _R. H. Hardin_, Apr 02 2012
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