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%I #4 Apr 20 2012 06:18:28
%S 230,516,1030,1908,3528,6312,11390,20316,36520,65646,118702,216006,
%T 394802,728492,1348550,2522796,4730304,8960110,16997998,32539860,
%U 62348810,120381720,232534604,451979570,878630354,1716513328,3353186654
%N Number of (n+1)X(n+1) -11..11 symmetric matrices with every 2X2 subblock having sum zero and 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="/A211711/b211711.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 6*a(n-1) +3*a(n-2) -83*a(n-3) +92*a(n-4) +443*a(n-5) -868*a(n-6) -1073*a(n-7) +3394*a(n-8) +748*a(n-9) -7085*a(n-10) +1842*a(n-11) +8231*a(n-12) -4528*a(n-13) -5075*a(n-14) +3936*a(n-15) +1424*a(n-16) -1511*a(n-17) -121*a(n-18) +244*a(n-19) -6*a(n-20) -12*a(n-21)
%e Some solutions for n=3
%e ..1..2.-5..2...-8..2.-8..3...11.-7..3.-5....7.-8..7.-8....5..1..1..1
%e ..2.-5..8.-5....2..4..2..3...-7..3..1..1...-8..9.-8..9....1.-7..5.-7
%e .-5..8-11..8...-8..2.-8..3....3..1.-5..3....7.-8..7.-8....1..5.-3..5
%e ..2.-5..8.-5....3..3..3..2...-5..1..3.-1...-8..9.-8..9....1.-7..5.-7
%K nonn
%O 1,1
%A _R. H. Hardin_ Apr 20 2012
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