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%I #7 Jul 18 2018 08:22:28
%S 29,65,139,287,593,1189,2397,4755,9475,18743,37193,73609,145989,
%T 289407,574531,1141067,2268401,4512781,8983437,17896131,35666275,
%U 71126615,141881945,283168249,565251477,1128785439,2254414051,4503880043
%N Number of (n+1) X (n+1) -4..4 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="/A211492/b211492.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 3*a(n-1) + 5*a(n-2) - 20*a(n-3) - 5*a(n-4) + 45*a(n-5) - 5*a(n-6) - 40*a(n-7) + 6*a(n-8) + 12*a(n-9).
%F Empirical g.f.: x*(29 - 22*x - 201*x^2 + 125*x^3 + 482*x^4 - 225*x^5 - 480*x^6 + 144*x^7 + 176*x^8) / ((1 - x)*(1 + x)*(1 - 2*x)*(1 - x - x^2)*(1 - 2*x^2)*(1 - 3*x^2)). - _Colin Barker_, Jul 18 2018
%e Some solutions for n=3:
%e .-1..2.-1..2...-4..2..0..2....2.-1..2.-3....0..2..0..0...-2..3.-2..3
%e ..2.-3..2.-3....2..0.-2..0...-1..0.-1..2....2.-4..2.-2....3.-4..3.-4
%e .-1..2.-1..2....0.-2..4.-2....2.-1..2.-3....0..2..0..0...-2..3.-2..3
%e ..2.-3..2.-3....2..0.-2..0...-3..2.-3..4....0.-2..0..0....3.-4..3.-4
%K nonn
%O 1,1
%A _R. H. Hardin_, Apr 13 2012
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