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A223212 3X3X3 triangular graph coloring a rectangular array: number of nX2 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 A223212 #8 Jul 23 2025 03:52:08
%S A223212 18,126,918,6642,48114,348462,2523798,18278946,132387858,958837662,
%T A223212 6944516694,50296639122,364280484978,2638352661966,19108640336598,
%U A223212 138397015977282,1002359858893074,7259732297153982,52579632512961558
%N A223212 3X3X3 triangular graph coloring a rectangular array: number of nX2 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 A223212 Column 2 of A223218
%H A223212 R. H. Hardin, <a href="/A223212/b223212.txt">Table of n, a(n) for n = 1..210</a>
%F A223212 Empirical: a(n) = 6*a(n-1) +9*a(n-2).
%F A223212 Empirical g.f.: -18*x*(1+x)/(-1+6*x+9*x^2) . a(n) = 18*(A189801(n)+A189801(n-1)). - _R. J. Mathar_, May 21 2018
%e A223212 Some solutions for n=3
%e A223212 ..0..1....1..4....0..1....0..2....4..1....4..1....4..2....2..4....0..2....5..2
%e A223212 ..2..4....2..1....1..0....1..4....1..2....2..4....2..4....4..1....2..0....2..5
%e A223212 ..0..2....1..2....4..1....3..1....4..1....4..2....0..2....1..2....0..1....0..2
%K A223212 nonn
%O A223212 1,1
%A A223212 _R. H. Hardin_ Mar 18 2013