|
%I #8 Oct 11 2018 04:42:26
%S 3,10,104,1184,13952,166400,1992704,23896064,286687232,3439984640,
%T 41278767104,495341010944,5944075354112,71328837140480,
%U 855945777250304,10271348253261824,123256174744174592,1479074079750225920
%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 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="/A233257/b233257.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 16*a(n-1) - 48*a(n-2) for n>3.
%F Conjectures from _Colin Barker_, Oct 11 2018: (Start)
%F G.f.: x*(3 - 38*x + 88*x^2) / ((1 - 4*x)*(1 - 12*x)).
%F a(n) = 2^(2*n-3) * (4*3^n+9) / 9 for n>1.
%F (End)
%e Some solutions for n=5:
%e ..0..1..2..5..3....0..1..2..4..3....0..1..5..4..2....0..1..2..1..0
%e ..0..4..2..1..2....5..1..5..4..2....2..4..3..1..2....2..1..5..4..0
%Y Row 2 of A233256.
%K nonn
%O 1,1
%A _R. H. Hardin_, Dec 06 2013
| 