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%I #4 Apr 12 2012 06:34:51
%S 144,380,856,1808,3706,7454,14786,29300,57442,113394,221676,437914,
%T 857230,1698058,3335170,6630316,13078566,26101324,51724674,103628922,
%U 206316160,414882652,829705256,1674253282,3362428628,6806756646
%N Number of (n+1)X(n+1) -8..8 symmetric matrices with every 2X2 subblock having sum zero and two or three distinct values
%C Symmetry and 2X2 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="/A211469/b211469.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 3*a(n-1) +20*a(n-2) -64*a(n-3) -172*a(n-4) +598*a(n-5) +826*a(n-6) -3213*a(n-7) -2390*a(n-8) +10954*a(n-9) +4103*a(n-10) -24660*a(n-11) -3463*a(n-12) +36968*a(n-13) -524*a(n-14) -36330*a(n-15) +4151*a(n-16) +22474*a(n-17) -3786*a(n-18) -8144*a(n-19) +1410*a(n-20) +1540*a(n-21) -180*a(n-22) -120*a(n-23)
%e Some solutions for n=3
%e ..1.-2..1..1....5.-5..0.-5....2..1..1..1...-8..6.-4..6....1..1..1.-2
%e .-2..3.-2..0...-5..5..0..5....1.-4..2.-4....6.-4..2.-4....1.-3..1..0
%e ..1.-2..1..1....0..0.-5..0....1..2..0..2...-4..2..0..2....1..1..1.-2
%e ..1..0..1.-3...-5..5..0..5....1.-4..2.-4....6.-4..2.-4...-2..0.-2..3
%K nonn
%O 1,1
%A _R. H. Hardin_ Apr 12 2012
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