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Number of -2..2 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, three or four distinct values for every i,j,k<=n.
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%I #7 Jul 19 2018 08:23:07

%S 24,44,78,142,256,472,868,1626,3046,5790,11016,21196,40828,79318,

%T 154246,301890,591328,1163856,2292084,4530250,8957830,17760094,

%U 35222584,69994044,139121260,276928662,551322342,1098804034,2190169552,4369076320

%N Number of -2..2 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, three or four distinct values for every i,j,k<=n.

%H R. H. Hardin, <a href="/A211568/b211568.txt">Table of n, a(n) for n = 1..65</a>

%F Empirical: a(n) = 4*a(n-1) + a(n-2) - 21*a(n-3) + 16*a(n-4) + 29*a(n-5) - 34*a(n-6) - 6*a(n-7) + 12*a(n-8).

%F Empirical g.f.: 2*x*(12 - 26*x - 61*x^2 + 145*x^3 + 75*x^4 - 228*x^5 - x^6 + 82*x^7) / ((1 - x)*(1 - 2*x)*(1 - x - x^2)*(1 - 2*x^2)*(1 - 3*x^2)). - _Colin Barker_, Jul 19 2018

%e Some solutions for n=5:

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

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

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

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

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

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

%K nonn

%O 1,1

%A _R. H. Hardin_, Apr 16 2012