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%I #4 Apr 07 2012 19:42:31
%S 60,332,1846,10332,58164,329130,1870664,10670876,61044918,349974788,
%T 2009495068,11549465226,66414142512,381959562756,2196335839046,
%U 12624063953180,72516570941316,416247502883594,2387248114517560
%N Number of (n+1)X(n+1) -5..5 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="/A211336/b211336.txt">Table of n, a(n) for n = 1..74</a>
%F Empirical: a(n) = 32*a(n-1) -429*a(n-2) +3078*a(n-3) -12340*a(n-4) +24890*a(n-5) -10895*a(n-6) -35870*a(n-7) +19131*a(n-8) +40338*a(n-9) +18694*a(n-10) +3532*a(n-11) +240*a(n-12)
%e Some solutions for n=3
%e .-3..1.-1..2....5.-3..0.-4....5.-2..4.-5....2..0.-1.-2....2.-1.-1..1
%e ..1..1.-1..0...-3..1..2..2...-2.-1.-1..2....0.-2..3..0...-1..0..2.-2
%e .-1.-1..1..0....0..2.-5..1....4.-1..3.-4...-1..3.-4..1...-1..2.-4..4
%e ..2..0..0.-1...-4..2..1..3...-5..2.-4..5...-2..0..1..2....1.-2..4.-4
%K nonn
%O 1,1
%A _R. H. Hardin_ Apr 07 2012
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