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%I #4 Apr 21 2012 12:14:41
%S 189,435,881,1701,3247,6081,11421,21369,40139,75675,143095,272447,
%T 519721,999049,1922557,3726521,7226935,14102879,27524803,53995609,
%U 105915029,208603523,410770735,811441587,1602540065,3172707173,6279776411
%N Number of (n+1)X(n+1) -10..10 symmetric matrices with every 2X2 subblock having sum zero and one 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="/A211815/b211815.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 5*a(n-1) +8*a(n-2) -75*a(n-3) +16*a(n-4) +465*a(n-5) -403*a(n-6) -1541*a(n-7) +1945*a(n-8) +2941*a(n-9) -4737*a(n-10) -3219*a(n-11) +6630*a(n-12) +1827*a(n-13) -5437*a(n-14) -299*a(n-15) +2516*a(n-16) -186*a(n-17) -591*a(n-18) +94*a(n-19) +54*a(n-20) -12*a(n-21)
%e Some solutions for n=3
%e ..5.-3..5.-1....2.-1..1.-2....4..2..3..2...-5..4.-3..2...-2..3.-2..3
%e .-3..1.-3.-1...-1..0..0..1....2.-8..3.-8....4.-3..2.-1....3.-4..3.-4
%e ..5.-3..5.-1....1..0..0.-1....3..3..2..3...-3..2.-1..0...-2..3.-2..3
%e .-1.-1.-1.-3...-2..1.-1..2....2.-8..3.-8....2.-1..0..1....3.-4..3.-4
%K nonn
%O 1,1
%A _R. H. Hardin_ Apr 21 2012
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