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Number of -3..3 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 three, four or five distinct values for every i,j,k<=n.
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%I #8 Jul 20 2018 06:02:26

%S 36,66,104,178,280,476,768,1324,2208,3880,6672,11928,21008,38048,

%T 68144,124512,225456,414288,755312,1392784,2549872,4711856,8647920,

%U 16000432,29410032,54455152,100180464,185574000,341574128,632894192,1165280240

%N Number of -3..3 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 three, four or five distinct values for every i,j,k<=n.

%H R. H. Hardin, <a href="/A211724/b211724.txt">Table of n, a(n) for n = 1..57</a>

%F Empirical: a(n) = a(n-1) + 6*a(n-2) - 6*a(n-3) - 10*a(n-4) + 10*a(n-5) + 4*a(n-6) - 4*a(n-7).

%F Empirical g.f.: 2*x*(18 + 15*x - 89*x^2 - 53*x^3 + 117*x^4 + 26*x^5 - 42*x^6) / ((1 - x)*(1 - 2*x^2)*(1 - 4*x^2 + 2*x^4)). - _Colin Barker_, Jul 20 2018

%e Some solutions for n=5:

%e ..2...-1...-3...-1....2....0....1...-2...-2...-2....0....3....1...-1....1....0

%e .-3....0...-2....0....0....2...-3...-1...-3....0...-2....0....0...-2....3...-1

%e ..2....1...-1...-1...-2....0....1....0...-2...-2....0...-3...-2...-1....1....0

%e ..0....2...-2....3....0...-1....3....1...-1....3....1....0....0....0...-3....2

%e ..2....1...-1...-1....2....0....1....0....0...-2....0...-3...-2...-1....1....0

%e .-3....2...-2....0....0....2...-3...-1....1....0...-2....0....0...-2...-3...-1

%K nonn

%O 1,1

%A _R. H. Hardin_, Apr 20 2012