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%I #4 Apr 11 2012 07:21:05
%S 113,307,723,1659,3681,8171,17905,39605,87221,194399,433363,977621,
%T 2211117,5053989,11592995,26825177,62296037,145661855,341690587,
%U 805669229,1904747123,4520182115,10749370491,25632216197,61218130049
%N Number of (n+1)X(n+1) -7..7 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="/A211445/b211445.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 6*a(n-1) +9*a(n-2) -114*a(n-3) +38*a(n-4) +953*a(n-5) -941*a(n-6) -4622*a(n-7) +6247*a(n-8) +14455*a(n-9) -23114*a(n-10) -30709*a(n-11) +54571*a(n-12) +45628*a(n-13) -86067*a(n-14) -48323*a(n-15) +91676*a(n-16) +37008*a(n-17) -65251*a(n-18) -20648*a(n-19) +30111*a(n-20) +8274*a(n-21) -8512*a(n-22) -2240*a(n-23) +1318*a(n-24) +356*a(n-25) -84*a(n-26) -24*a(n-27)
%e Some solutions for n=3
%e .-7..2.-7..2....7.-4..2.-4....1..0..2..0...-6..0.-6..0...-2..2..0..4
%e ..2..3..2..3...-4..1..1..1....0.-1.-1.-1....0..6..0..6....2.-2..0.-4
%e .-7..2.-7..2....2..1.-3..1....2.-1..3.-1...-6..0.-6..0....0..0..2..2
%e ..2..3..2..3...-4..1..1..1....0.-1.-1.-1....0..6..0..6....4.-4..2.-6
%K nonn
%O 1,1
%A _R. H. Hardin_ Apr 11 2012
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