A211575 - OEIS

%I #7 Jul 19 2018 09:49:43

%S 24,80,202,476,1082,2470,5562,12796,29044,67738,155328,366934,849090,

%T 2027430,4726368,11383748,26693878,64741904,152513458,371958154,

%U 879391758,2154278468,5107665568,12557355846,29839686200,73574774818

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

%H R. H. Hardin, <a href="/A211575/b211575.txt">Table of n, a(n) for n = 1..37</a>

%F Empirical: a(n) = 6*a(n-1) - 3*a(n-2) - 46*a(n-3) + 88*a(n-4) + 49*a(n-5) - 231*a(n-6) + 82*a(n-7) + 168*a(n-8) - 100*a(n-9) - 36*a(n-10) + 24*a(n-11).

%F Empirical g.f.: 2*x*(12 - 32*x - 103*x^2 + 304*x^3 + 200*x^4 - 759*x^5 - 134*x^6 + 666*x^7 + 52*x^8 - 156*x^9) / ((1 - x)*(1 - 2*x)*(1 - x - x^2)*(1 - 2*x^2)*(1 - 6*x^2)*(1 - 2*x - x^2 + x^3)). - _Colin Barker_, Jul 19 2018

%e Some solutions for n=5:

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

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

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

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

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

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

%K nonn

%O 1,1

%A _R. H. Hardin_, Apr 16 2012