cp's OEIS Frontend

A233124 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 vertically, 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 A233124 #7 Mar 19 2018 09:41:50
%S A233124 3,80,2688,96256,3497984,127533056,4653056000,169793814528,
%T A233124 6196127858688,226111237652480,8251342992703488,301111464108752896,
%U A233124 10988286523845115904,400989192448372637696,14633067014086637649920
%N A233124 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 vertically, 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).
%C A233124 Column 3 of A233129.
%H A233124 R. H. Hardin, <a href="/A233124/b233124.txt">Table of n, a(n) for n = 1..210</a>
%F A233124 Empirical: a(n) = 48*a(n-1) - 448*a(n-2) + 1024*a(n-3).
%F A233124 Conjectures from _Colin Barker_, Mar 19 2018: (Start)
%F A233124 G.f.: x*(3 - 64*x + 192*x^2) / ((1 - 8*x)*(1 - 40*x + 128*x^2)).
%F A233124 a(n) = 8^(-1+n) + ((20-4*sqrt(17))^n*(-3+sqrt(17)) + (3+sqrt(17))*(4*(5+sqrt(17)))^n) / (32*sqrt(17)).
%F A233124 (End)
%e A233124 Some solutions for n=4:
%e A233124 ..0..1..0....0..1..5....0..1..5....0..1..2....0..1..2....0..1..5....0..1..2
%e A233124 ..2..5..2....2..0..4....4..5..2....1..2..1....4..3..5....2..5..2....3..0..1
%e A233124 ..0..1..5....5..2..5....0..3..4....3..0..3....2..0..2....0..4..0....1..3..0
%e A233124 ..3..5..4....1..5..4....3..1..2....0..3..5....0..3..5....1..0..1....3..4..2
%Y A233124 Cf. A233129.
%K A233124 nonn
%O A233124 1,1
%A A233124 _R. H. Hardin_, Dec 04 2013