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%I #8 Jul 16 2018 05:22:38
%S 64,130,246,456,840,1538,2830,5214,9672,18020,33790,63702,120752,
%T 230126,440512,847370,1635656,3170660,6162524,12020244,23492880,
%U 46050762,90403706,177902814,350479066,691826684,1366757298,2704492222,5354853154
%N Number of (n+1) X (n+1) -6..6 symmetric matrices with every 2 X 2 subblock having sum zero and 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="/A211254/b211254.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 5*a(n-1) - 36*a(n-3) + 41*a(n-4) + 82*a(n-5) - 151*a(n-6) - 54*a(n-7) + 204*a(n-8) - 28*a(n-9) - 110*a(n-10) + 36*a(n-11) + 20*a(n-12) - 8*a(n-13).
%F Empirical g.f.: 2*x*(32 - 95*x - 202*x^2 + 765*x^3 + 308*x^4 - 2192*x^5 + 237*x^6 + 2761*x^7 - 876*x^8 - 1493*x^9 + 604*x^10 + 284*x^11 - 124*x^12) / ((1 - x)*(1 - 2*x)*(1 - x - x^2)*(1 - 2*x^2)*(1 - x - 2*x^2 + x^3)*(1 - 4*x^2 + 2*x^4)). - _Colin Barker_, Jul 16 2018
%e Some solutions for n=3:
%e .-3..4.-3..4....6.-1..6.-1...-5..1.-5..3....6..0..6.-3....4..1..1..1
%e ..4.-5..4.-5...-1.-4.-1.-4....1..3..1..1....0.-6..0.-3....1.-6..4.-6
%e .-3..4.-3..4....6.-1..6.-1...-5..1.-5..3....6..0..6.-3....1..4.-2..4
%e ..4.-5..4.-5...-1.-4.-1.-4....3..1..3.-1...-3.-3.-3..0....1.-6..4.-6
%K nonn
%O 1,1
%A _R. H. Hardin_, Apr 06 2012