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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 two or four distinct values for every i,j,k<=n.
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%I #8 Jul 20 2018 05:20:21

%S 48,74,120,210,376,700,1312,2508,4800,9288,17968,35000,68144,133312,

%T 260688,511616,1003728,1974896,3884688,7659696,15100048,29828560,

%U 58914064,116565456,230605584,456911760,905224720,1795793552,3562275344

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

%H R. H. Hardin, <a href="/A211721/b211721.txt">Table of n, a(n) for n = 1..64</a>

%F Empirical: a(n) = 3*a(n-1) + 4*a(n-2) - 18*a(n-3) + 2*a(n-4) + 30*a(n-5) - 16*a(n-6) - 12*a(n-7) + 8*a(n-8).

%F Empirical g.f.: 2*x*(24 - 35*x - 147*x^2 + 209*x^3 + 251*x^4 - 348*x^5 - 102*x^6 + 140*x^7) / ((1 - x)*(1 - 2*x)*(1 - 2*x^2)*(1 - 4*x^2 + 2*x^4)). - _Colin Barker_, Jul 20 2018

%e Some solutions for n=5:

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

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

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

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

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

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

%K nonn

%O 1,1

%A _R. H. Hardin_, Apr 20 2012