%I #7 Jul 18 2018 14:02:01
%S 8,22,56,124,270,560,1156,2336,4714,9418,18812,37400,74374,147596,
%T 293042,581384,1154070,2290670,4549186,9036466,17959458,35705544,
%U 71021240,141319688,281322224,560223850,1116045988,2224048908,4433497296
%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, three, four, five or six distinct values for every i,j,k<=n.
%H R. H. Hardin, <a href="/A211530/b211530.txt">Table of n, a(n) for n = 1..58</a>
%F Empirical: a(n) = 4*a(n-1) - 16*a(n-3) + 11*a(n-4) + 19*a(n-5) - 16*a(n-6) - 6*a(n-7) + 4*a(n-8).
%F Empirical g.f.: 2*x*(4 - 5*x - 16*x^2 + 14*x^3 + 19*x^4 - 9*x^5 - 3*x^6 + 2*x^7) / ((1 - 2*x)*(1 - x - x^2)*(1 - 2*x^2)*(1 - x - 2*x^2 + x^3)). - _Colin Barker_, Jul 18 2018
%e Some solutions for n=5:
%e .-1....0....0...-1....1....1....1...-1....0....1....0...-1...-1...-1...-1....0
%e .-1....1...-1...-1...-1....0....0...-1....1....0....1....0....0...-1....1...-1
%e ..0....0...-1....0....1....1...-1...-1....0....1...-1....1....1...-1...-1...-1
%e ..1....1....0....1...-1...-1....0...-1....1....1...-1....0....0....1....0....0
%e ..1...-1....1....0....0....1....1...-1....1....1...-1...-1....1....1...-1....1
%e ..0....1....0....1....1....0....0....1....0....0...-1....0....1....1....0....1
%K nonn
%O 1,1
%A _R. H. Hardin_, Apr 14 2012