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%I #20 Mar 09 2017 10:11:29
%S 1,2,6,8,14,32,56,100,204,388,722,1416,2750,5256,10222,19944,38650,
%T 75272,147142,287120,561018,1098752,2152092,4217620,8276376,16250292,
%U 31921374,62754072,123440514,242921784,478310952,942260548,1856994908,3661288036
%N Number of -1..1 arrays x(0..n-1) of n elements with zero sum and no two neighbors equal.
%C Column 1 of A199704
%H R. H. Hardin, <a href="/A199697/b199697.txt">Table of n, a(n) for n = 1..200</a>
%F G.f.: ((x+1)^2*sqrt((1-x)/(1-x-4*x^3))-2*x-1)/x. - _Stefan Hollos_, Mar 08 2017
%e All solutions for n=5
%e ..0...-1....1...-1....1...-1...-1....0....1...-1....0....1....1....0
%e .-1....1...-1....1....0....1....0...-1...-1....1....1...-1...-1....1
%e ..1....0....0...-1...-1...-1....1....0....1....0....0....1....0...-1
%e .-1...-1....1....1....1....0...-1....1....0....1...-1...-1...-1....1
%e ..1....1...-1....0...-1....1....1....0...-1...-1....0....0....1...-1
%t Rest@ CoefficientList[Series[((x + 1)^2*Sqrt[(1 - x)/(1 - x - 4*x^3)] - 2 x - 1)/x, {x, 0, 34}], x] (* _Michael De Vlieger_, Mar 08 2017 *)
%K nonn
%O 1,2
%A _R. H. Hardin_, Nov 09 2011