cp's OEIS Frontend

A214181 Number of 0..6 colorings of an n X 3 array circular in the 3 direction with new values 0..6 introduced in row major order.

%I A214181 #9 Jul 22 2018 06:42:13
%S A214181 1,18,1046,108893,13701111,1808609113,241491378451,32332391658753,
%T A214181 4331663509964171,580414863999963833,77774694477831007731,
%U A214181 10421780348518296089713,1396517647955429913843931
%N A214181 Number of 0..6 colorings of an n X 3 array circular in the 3 direction with new values 0..6 introduced in row major order.
%C A214181 Column 2 of A214187.
%H A214181 R. H. Hardin, <a href="/A214181/b214181.txt">Table of n, a(n) for n = 1..210</a>
%F A214181 Empirical: a(n) = 179*a(n-1) - 6468*a(n-2) + 59396*a(n-3) - 94336*a(n-4).
%F A214181 Conjectures from _Colin Barker_, Jul 22 2018: (Start)
%F A214181 G.f.: x*(1 - 161*x + 4292*x^2 - 21313*x^3) / ((1 - 2*x)*(1 - 11*x)*(1 - 32*x)*(1 - 134*x)).
%F A214181 a(n) = (2^(n-4)*(67^(n-1)+9) + 11^(n-1) + 3*2^(5*n-7))/3.
%F A214181 (End)
%e A214181 Some solutions for n=4:
%e A214181 ..0..1..2....0..1..2....0..1..2....0..1..2....0..1..2....0..1..2....0..1..2
%e A214181 ..1..0..3....1..0..3....3..0..1....1..2..3....1..2..3....1..2..3....1..0..3
%e A214181 ..3..4..1....0..3..1....0..1..2....3..0..1....0..1..4....0..1..4....3..4..0
%e A214181 ..4..0..2....1..4..0....1..0..3....4..1..5....4..2..0....1..0..5....0..5..1
%Y A214181 Cf. A214187.
%K A214181 nonn
%O A214181 1,2
%A A214181 _R. H. Hardin_, Jul 07 2012