A233175 - OEIS

%I #7 Oct 10 2018 06:15:03

%S 3,8,80,800,8576,92672,1009664,11018240,120356864,1315045376,

%T 14370209792,157036838912,1716116258816,18754008252416,

%U 204947383648256,2239705722650624,24475955615498240,267478202279002112

%N Number of 2 X n 0..5 arrays with no element x(i,j) adjacent to itself or value 5-x(i,j) horizontally, diagonally or antidiagonally, top left element zero, and 1 appearing before 2 3 and 4, and 2 appearing before 3 in row major order (unlabelled 6-colorings with no clashing color pairs).

%H R. H. Hardin, <a href="/A233175/b233175.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 12*a(n-1) - 128*a(n-3) for n>4.

%F Conjectures from _Colin Barker_, Oct 10 2018: (Start)

%F G.f.: x*(3 - 28*x - 16*x^2 + 224*x^3) / ((1 - 4*x)*(1 - 8*x - 32*x^2)).

%F a(n) = 2^(2*n-3) + (1/32)*sqrt(3)*(-(4-4*sqrt(3))^n + (4*(1+sqrt(3)))^n) for n>1.

%F (End)

%e Some solutions for n=5:

%e ..0..1..5..4..0....0..1..0..2..0....0..1..0..1..0....0..1..2..1..2

%e ..2..1..3..1..3....5..3..5..2..4....2..4..0..2..5....5..1..3..5..3

%Y Row 2 of A233174.

%K nonn

%O 1,1

%A _R. H. Hardin_, Dec 05 2013