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%I #8 Jul 16 2018 09:12:44
%S 15,29,55,107,209,409,805,1583,3127,6175,12233,24241,48141,95655,
%T 190343,378967,755249,1505841,3004341,5996175,11972503,23911631,
%U 47770041,95451441,190761021,381287447,762198439,1523777639,3046559585,6091487857
%N Number of (n+1) X (n+1) -3..3 symmetric matrices with every 2 X 2 subblock having sum zero and one or three distinct values.
%C Symmetry and 2 X 2 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="/A211324/b211324.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 3*a(n-1) + 2*a(n-2) - 11*a(n-3) + a(n-4) + 12*a(n-5) - 2*a(n-6) - 4*a(n-7).
%F Empirical g.f.: x*(15 - 16*x - 62*x^2 + 49*x^3 + 82*x^4 - 36*x^5 - 36*x^6) / ((1 - x)*(1 + x)*(1 - 2*x)*(1 - x - x^2)*(1 - 2*x^2)). - _Colin Barker_, Jul 16 2018
%e Some solutions for n=3:
%e .-1..0.-1..0....2..0..2.-1....0..0..1..0....0..0..0.-1...-2..0.-2..1
%e ..0..1..0..1....0.-2..0.-1....0..0.-1..0....0..0..0..1....0..2..0..1
%e .-1..0.-1..0....2..0..2.-1....1.-1..2.-1....0..0..0.-1...-2..0.-2..1
%e ..0..1..0..1...-1.-1.-1..0....0..0.-1..0...-1..1.-1..2....1..1..1..0
%K nonn
%O 1,1
%A _R. H. Hardin_, Apr 07 2012
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