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%I #4 Apr 07 2012 19:41:44
%S 47,203,851,3551,14747,61279,255139,1066031,4472467,18846943,79770595,
%T 339053711,1446716915,6194800095,26609084003,114610153487,
%U 494820389939,2140706570911,9277278747747,40264500902671,174969241485427
%N Number of (n+1)X(n+1) -5..5 symmetric matrices with every 2X2 subblock having sum zero and one, 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="/A211335/b211335.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 13*a(n-1) -40*a(n-2) -130*a(n-3) +771*a(n-4) +305*a(n-5) -5330*a(n-6) +176*a(n-7) +18744*a(n-8) +2324*a(n-9) -31120*a(n-10) -14864*a(n-11) +9312*a(n-12) +3072*a(n-13) -1152*a(n-14)
%e Some solutions for n=3
%e ..5.-2..0.-5....5..0..2.-5...-5..0.-3..0...-4..3.-4..1....2..1..1.-3
%e .-2.-1..3..2....0.-5..3..0....0..5.-2..5....3.-2..3..0....1.-4..2..0
%e ..0..3.-5..0....2..3.-1.-2...-3.-2.-1.-2...-4..3.-4..1....1..2..0.-2
%e .-5..2..0..5...-5..0.-2..5....0..5.-2..5....1..0..1..2...-3..0.-2..4
%K nonn
%O 1,1
%A _R. H. Hardin_ Apr 07 2012