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%I #4 Apr 07 2012 19:41:03
%S 46,194,802,3322,13754,57170,238650,1001306,4222530,17893954,76173162,
%T 325583338,1396612370,6009460210,25926690010,112107619226,
%U 485673993154,2107375609954,9156123643082,39825088001994,173378643531634
%N Number of (n+1)X(n+1) -5..5 symmetric matrices with every 2X2 subblock having sum zero and 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="/A211334/b211334.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 8*a(n-1) -114*a(n-3) +81*a(n-4) +646*a(n-5) -276*a(n-6) -1588*a(n-7) -180*a(n-8) +672*a(n-9) -144*a(n-10)
%e Some solutions for n=3
%e .-1.-2.-2..3....1..0..3..2....5..0..3.-4...-5..2.-1..4....2.-1..0.-1
%e .-2..5.-1..0....0.-1.-2.-3....0.-5..2.-1....2..1.-2.-1...-1..0..1..0
%e .-2.-1.-3..4....3.-2..5..0....3..2..1.-2...-1.-2..3..0....0..1.-2..1
%e ..3..0..4.-5....2.-3..0.-5...-4.-1.-2..3....4.-1..0.-3...-1..0..1..0
%K nonn
%O 1,1
%A _R. H. Hardin_ Apr 07 2012
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