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 A211526 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, four or five distinct values for every i,j,k<=n. 1

%I

%S 8,18,32,60,104,192,344,648,1208,2328,4472,8760,17144,33912,67064,

%T 133368,265208,528888,1054712,2106360,4206584,8407032,16801784,

%U 33591288,67158008,134291448,268533752,537018360,1073938424,2147778552,4295360504

%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, four or five distinct values for every i,j,k<=n.

%H R. H. Hardin, <a href="/A211526/b211526.txt">Table of n, a(n) for n = 1..69</a>

%F Empirical: a(n) = 3*a(n-1) - 6*a(n-3) + 4*a(n-4).

%F Conjectures from _Colin Barker_, Jul 18 2018: (Start)

%F G.f.: 2*x*(4 - 3*x - 11*x^2 + 6*x^3) / ((1 - x)*(1 - 2*x)*(1 - 2*x^2)).

%F a(n) = 9*2^(n/2) + 2^(n+1) - 8 for n even.

%F a(n) = 2*(2^n + 3*2^((n+1)/2) - 4) for n odd.

%F (End)

%e Some solutions for n=5:

%e .-1...-1...-1....0....0...-1....1....0...-1....1....1....1...-1...-1....1....0

%e ..0....1...-1....1...-1....1....1....1....1...-1....1....1....1...-1...-1....1

%e .-1....0...-1....0....0....1...-1....0....0...-1...-1....1...-1....1....1...-1

%e ..0....1...-1...-1....1...-1...-1....1....1....1...-1....1....0...-1....1....1

%e ..1....0....1....0....0....1....1....0...-1...-1...-1....1...-1....1....1....0

%e ..0....1....1....1...-1....1...-1....1....1...-1....1....1....1...-1....1....1

%K nonn

%O 1,1

%A _R. H. Hardin_, Apr 14 2012

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Last modified December 5 06:52 EST 2021. Contains 349543 sequences. (Running on oeis4.)