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A233251 Number of n X 3 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 A233251 #9 Oct 10 2018 15:54:06
%S A233251 3,104,4672,221696,10620928,509640704,24461443072,1174138781696,
%T A233251 56358577635328,2705211055407104,129850125290831872,
%U A233251 6232805971010256896,299174686264894947328,14360384937966178402304,689298477000386330755072
%N A233251 Number of n X 3 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 A233251 R. H. Hardin, <a href="/A233251/b233251.txt">Table of n, a(n) for n = 1..210</a>
%F A233251 Empirical: a(n) = 56*a(n-1) - 384*a(n-2).
%F A233251 Conjectures from _Colin Barker_, Oct 10 2018: (Start)
%F A233251 G.f.: x*(3 - 64*x) / ((1 - 8*x)*(1 - 48*x)).
%F A233251 a(n) = 8^(n-1) * (6^n+3) / 3.
%F A233251 (End)
%e A233251 Some solutions for n=4:
%e A233251 ..0..1..0....0..1..0....0..1..2....0..1..2....0..1..0....0..1..2....0..1..0
%e A233251 ..5..4..0....0..4..5....2..0..3....2..0..2....2..1..0....2..1..2....5..4..5
%e A233251 ..5..2..5....2..1..3....3..0..4....2..0..2....2..4..5....5..4..0....2..1..2
%e A233251 ..1..3..4....0..4..3....3..0..2....3..4..3....2..4..0....5..2..1....2..0..1
%Y A233251 Column 3 of A233256.
%K A233251 nonn
%O A233251 1,1
%A A233251 _R. H. Hardin_, Dec 06 2013