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A233252 Number of n X 4 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).

%I A233252 #8 Oct 10 2018 15:53:50
%S A233252 10,1184,166400,23896064,3439984640,495341010944,71328837140480,
%T A233252 10271348253261824,1479074079750225920,212986666384520904704,
%U A233252 30670079941778824232960,4416491511334675712835584
%N A233252 Number of n X 4 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 A233252 R. H. Hardin, <a href="/A233252/b233252.txt">Table of n, a(n) for n = 1..210</a>
%F A233252 Empirical: a(n) = 160*a(n-1) - 2304*a(n-2).
%F A233252 Conjectures from _Colin Barker_, Oct 10 2018: (Start)
%F A233252 G.f.: 2*x*(5 - 208*x) / ((1 - 16*x)*(1 - 144*x)).
%F A233252 a(n) = 2^(4*n-3) * (4*9^n+9) / 9.
%F A233252 (End)
%e A233252 Some solutions for n=2:
%e A233252 ..0..1..2..1....0..1..0..1....0..1..2..4....0..1..0..1....0..1..2..4
%e A233252 ..0..1..3..0....0..2..5..3....3..1..5..4....5..2..5..3....3..4..5..3
%Y A233252 Column 4 of A233256.
%K A233252 nonn
%O A233252 1,1
%A A233252 _R. H. Hardin_, Dec 06 2013