A208044 - OEIS

%I #11 Mar 07 2018 02:31:01

%S 2,8,44,244,1356,7540,41932,233204,1296972,7213172,40116428,223109620,

%T 1240835916,6900974452,38380133836,213453141236,1187130917964,

%U 6602291295860,36718991727308,204214611724276,1135750348251468

%N Number of n X 3 0..3 arrays with new values 0..3 introduced in row major order and no element equal to any horizontal, vertical or antidiagonal neighbor (colorings ignoring permutations of colors).

%C Column 3 of A208050.

%H R. H. Hardin, <a href="/A208044/b208044.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 7*a(n-1) - 8*a(n-2) for n>3.

%F Conjectures from _Colin Barker_, Mar 06 2018: (Start)

%F G.f.: 2*x*(1 - x)*(1 - 2*x) / (1 - 7*x + 8*x^2).

%F a(n) = (2^(-5-n)*((7-sqrt(17))^n*(-13+5*sqrt(17)) + (7+sqrt(17))^n*(13+5*sqrt(17)))) / sqrt(17) for n>1.

%F (End)

%e Some solutions for n=4:

%e   0 1 0   0 1 0   0 1 2   0 1 0   0 1 2   0 1 0   0 1 2

%e   2 3 2   2 3 1   2 0 3   2 3 1   2 3 0   2 3 1   2 3 0

%e   1 0 1   1 2 0   3 1 2   0 2 0   0 1 3   0 2 3   0 1 2

%e   2 3 2   3 1 2   0 3 1   1 3 1   2 0 1   3 1 2   2 3 1

%Y Cf. A208050.

%K nonn

%O 1,1

%A _R. H. Hardin_, Feb 22 2012