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%I #11 Jul 22 2018 06:42:16
%S 1,18,902,60320,4242606,300785428,21350933122,1515863103360,
%T 107625695720486,7641417965382188,542540604803692842,
%U 38520382162939430200,2734947125009349378766,194181245781510954496548
%N Number of 0..5 colorings of an n X 3 array circular in the 3 direction with new values 0..5 introduced in row major order.
%C Column 2 of A214166.
%H R. H. Hardin, <a href="/A214160/b214160.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 84*a(n-1) - 945*a(n-2) + 1562*a(n-3).
%F Conjectures from _Colin Barker_, Jul 22 2018: (Start)
%F G.f.: x*(1 - 66*x + 335*x^2) / ((1 - 2*x)*(1 - 11*x)*(1 - 71*x)).
%F a(n) = (781*2^n + 213*11^n + 11*71^n)/4686.
%F (End)
%e Some solutions for n=4:
%e ..0..1..2....0..1..2....0..1..2....0..1..2....0..1..2....0..1..2....0..1..2
%e ..1..0..3....1..2..3....2..0..1....1..0..3....2..3..0....2..0..1....2..3..0
%e ..2..3..0....3..4..5....0..2..3....2..3..4....3..2..4....0..1..2....3..4..1
%e ..4..2..3....4..0..1....1..0..4....3..2..5....5..0..2....1..2..3....0..3..4
%Y Cf. A214166.
%K nonn
%O 1,2
%A _R. H. Hardin_, Jul 05 2012
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