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%I
%S 40,180,808,3636,16396,74104,335660,1523420,6925768,31527492,
%T 143656108,654965928,2986993420,13622286844,62110476152,283072002980,
%U 1289383564204,5869109209272,26695147549612,121321864635996,550906942638568
%N Number of (n+1)X(n+1) -4..4 symmetric matrices with every 2X2 subblock having sum zero and two, three or four 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="/A211497/b211497.txt">Table of n, a(n) for n = 1..162</a>
%F Empirical: a(n) = 21*a(n-1) -177*a(n-2) +742*a(n-3) -1477*a(n-4) +665*a(n-5) +1725*a(n-6) -952*a(n-7) -1462*a(n-8) -476*a(n-9) -48*a(n-10)
%e Some solutions for n=3
%e ..1..0..2..0....4.-2..1.-2...-2..2.-1..3....4.-2..0.-2...-4..2.-1..0
%e ..0.-1.-1.-1...-2..0..1..0....2.-2..1.-3...-2..0..2..0....2..0.-1..2
%e ..2.-1..3.-1....1..1.-2..1...-1..1..0..2....0..2.-4..2...-1.-1..2.-3
%e ..0.-1.-1.-1...-2..0..1..0....3.-3..2.-4...-2..0..2..0....0..2.-3..4
%K nonn
%O 1,1
%A _R. H. Hardin_ Apr 13 2012
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