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%I #4 Apr 06 2012 11:00:30
%S 85,231,547,1283,2901,6595,14775,33409,75157,170723,387687,888293,
%T 2039449,4718583,10949039,25566565,59877913,140930679,332585711,
%U 787830185,1870341077,4452666039,10618825855,25375634725,60720707925
%N Number of (n+1)X(n+1) -6..6 symmetric matrices with every 2X2 subblock having sum zero and one, two 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="/A211257/b211257.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 6*a(n-1) +6*a(n-2) -97*a(n-3) +62*a(n-4) +668*a(n-5) -852*a(n-6) -2556*a(n-7) +4359*a(n-8) +5935*a(n-9) -12593*a(n-10) -8545*a(n-11) +22727*a(n-12) +7400*a(n-13) -26431*a(n-14) -3396*a(n-15) +19783*a(n-16) +389*a(n-17) -9298*a(n-18) +302*a(n-19) +2606*a(n-20) -118*a(n-21) -392*a(n-22) +12*a(n-23) +24*a(n-24)
%e Some solutions for n=3
%e ..3.-2..1.-2...-4..2.-2..1....4..0..0..0...-2..1.-1..2....3.-1..2.-1
%e .-2..1..0..1....2..0..0..1....0.-4..4.-4....1..0..0.-1...-1.-1..0.-1
%e ..1..0.-1..0...-2..0..0.-1....0..4.-4..4...-1..0..0..1....2..0..1..0
%e .-2..1..0..1....1..1.-1..2....0.-4..4.-4....2.-1..1.-2...-1.-1..0.-1
%K nonn
%O 1,1
%A _R. H. Hardin_ Apr 06 2012
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