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%I #4 Apr 15 2012 11:12:36
%S 181,521,1239,2865,6321,14009,30379,66865,145437,322009,708509,
%T 1586445,3542267,8034795,18210199,41826241,96089585,223154883,
%U 518575357,1215390177,2850562247,6729628421,15897536413,37742249421,89649505903
%N Number of (n+1)X(n+1) -9..9 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="/A211553/b211553.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 7*a(n-1) +14*a(n-2) -200*a(n-3) +78*a(n-4) +2555*a(n-5) -3384*a(n-6) -19202*a(n-7) +37730*a(n-8) +93668*a(n-9) -243670*a(n-10) -306260*a(n-11) +1060307*a(n-12) +654137*a(n-13) -3306120*a(n-14) -762798*a(n-15) +7617393*a(n-16) -164785*a(n-17) -13171236*a(n-18) +2551794*a(n-19) +17194836*a(n-20) -5381852*a(n-21) -16929450*a(n-22) +6682460*a(n-23) +12476338*a(n-24) -5590892*a(n-25) -6783218*a(n-26) +3249146*a(n-27) +2657689*a(n-28) -1305530*a(n-29) -723096*a(n-30) +352500*a(n-31) +128470*a(n-32) -60348*a(n-33) -13280*a(n-34) +5840*a(n-35) +600*a(n-36) -240*a(n-37)
%e Some solutions for n=3
%e .-9..3.-8..4....7.-5..1.-3....4..1..4..1....1..1..1..3....0.-2.-2.-2
%e ..3..3..2..2...-5..3..1..1....1.-6..1.-6....1.-3..1.-5...-2..4..0..4
%e .-8..2.-7..3....1..1.-5..3....4..1..4..1....1..1..1..3...-2..0.-4..0
%e ..4..2..3..1...-3..1..3.-1....1.-6..1.-6....3.-5..3.-7...-2..4..0..4
%K nonn
%O 1,1
%A _R. H. Hardin_ Apr 15 2012
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