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%I #12 Apr 25 2024 09:31:52
%S 8,14,24,44,80,152,288,560,1088,2144,4224,8384,16640,33152,66048,
%T 131840,263168,525824,1050624,2100224,4198400,8394752,16785408,
%U 33566720,67125248,134242304,268468224,536920064,1073807360,2147581952,4295098368
%N Number of -1..1 arrays x(i) of n+1 elements i=1..n+1 with set{t,u,v in 0,1}((x[i+t]+x[j+u]+x[k+v])*(-1)^(t+u+v)) having two or four distinct values for every i,j,k<=n.
%H R. H. Hardin, <a href="/A211525/b211525.txt">Table of n, a(n) for n = 1..79</a>
%F Empirical: a(n) = 2*a(n-1) + 2*a(n-2) - 4*a(n-3).
%F From _Colin Barker_, Mar 09 2018: (Start)
%F G.f.: 2*x*(4 - x - 10*x^2) / ((1 - 2*x)*(1 - 2*x^2)).
%F a(n) = 3*2^(n/2) + 2^(n+1) for n even.
%F a(n) = 2^(n+1) + 2^((n+3)/2) for n odd.
%F (End)
%e Some solutions for n=5:
%e .-1....1....1...-1....1....0....1...-1...-1...-1....1...-1...-1....0....0...-1
%e ..1....0....1...-1....0...-1....1....0....1...-1....1...-1....1....1...-1....0
%e .-1...-1...-1....1...-1....0....1...-1....1....1....1....1...-1....0....0...-1
%e ..1....0...-1...-1....0....1...-1....0...-1....1...-1...-1....1...-1....1....0
%e .-1...-1...-1...-1....1....0....1...-1...-1...-1...-1....1....1....0....0....1
%e ..1....0....1....1....0...-1...-1....0....1...-1....1....1....1...-1....1....0
%K nonn
%O 1,1
%A _R. H. Hardin_, Apr 14 2012