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%I #4 Apr 20 2012 06:19:16
%S 231,537,1099,2099,3997,7379,13747,25335,47093,87513,163699,307721,
%T 581223,1105495,2109715,4055319,7812709,15150193,29420803,57448799,
%U 112272663,220389539,432816337,852950837,1681246791,3322791067
%N Number of (n+1)X(n+1) -11..11 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="/A211712/b211712.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 5*a(n-1) +9*a(n-2) -80*a(n-3) +9*a(n-4) +535*a(n-5) -425*a(n-6) -1941*a(n-7) +2321*a(n-8) +4142*a(n-9) -6337*a(n-10) -5243*a(n-11) +10073*a(n-12) +3703*a(n-13) -9603*a(n-14) -1139*a(n-15) +5360*a(n-16) -87*a(n-17) -1632*a(n-18) +123*a(n-19) +238*a(n-20) -18*a(n-21) -12*a(n-22)
%e Some solutions for n=3
%e ..3..0..3..0....5.-1.-3.-1...-1..3..1..0....1..3..2..3...10.-6.10.-2
%e ..0.-3..0.-3...-1.-3..7.-3....3.-5..1.-2....3.-7..2.-7...-6..2.-6.-2
%e ..3..0..3..0...-3..7-11..7....1..1..3.-2....2..2..3..2...10.-6.10.-2
%e ..0.-3..0.-3...-1.-3..7.-3....0.-2.-2..1....3.-7..2.-7...-2.-2.-2.-6
%K nonn
%O 1,1
%A _R. H. Hardin_ Apr 20 2012
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