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A223211 3 X 3 X 3 triangular graph coloring a rectangular array: number of n X 1 0..5 arrays where 0..5 label nodes of a graph with edges 0,1 0,2 1,2 1,3 1,4 2,4 3,4 2,5 4,5 and every array movement to a horizontal or vertical neighbor moves along an edge of this graph.

%I A223211 #10 Aug 17 2018 09:22:20
%S A223211 6,18,60,192,624,2016,6528,21120,68352,221184,715776,2316288,7495680,
%T A223211 24256512,78495744,254017536,822018048,2660106240,8608284672,
%U A223211 27856994304,90147127296,291722231808,944032972800,3054954872832,9886041636864
%N A223211 3 X 3 X 3 triangular graph coloring a rectangular array: number of n X 1 0..5 arrays where 0..5 label nodes of a graph with edges 0,1 0,2 1,2 1,3 1,4 2,4 3,4 2,5 4,5 and every array movement to a horizontal or vertical neighbor moves along an edge of this graph.
%C A223211 Column 1 of A223218.
%H A223211 R. H. Hardin, <a href="/A223211/b223211.txt">Table of n, a(n) for n = 1..210</a>
%F A223211 Empirical: a(n) = 2*a(n-1) + 4*a(n-2) = 6*A063782(n-1).
%F A223211 Conjectures from _Colin Barker_, Aug 17 2018: (Start)
%F A223211 G.f.: 6*x*(1 + x) / (1 - 2*x - 4*x^2).
%F A223211 a(n) = (3*((1-sqrt(5))^n*(-3+sqrt(5)) + (1+sqrt(5))^n*(3+sqrt(5)))) / (4*sqrt(5)).
%F A223211 (End)
%e A223211 Some solutions for n=3:
%e A223211 ..4....4....0....2....1....4....2....3....2....2....0....5....1....3....4....5
%e A223211 ..2....1....1....5....2....2....1....1....0....1....1....4....3....4....3....2
%e A223211 ..0....4....4....2....0....4....2....0....2....0....0....2....1....1....1....1
%Y A223211 Cf. A223218.
%K A223211 nonn
%O A223211 1,1
%A A223211 _R. H. Hardin_, Mar 18 2013