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A223347 3 X 3 X 3 triangular graph without horizontal edges coloring a rectangular array: number of n X 3 0..5 arrays where 0..5 label nodes of a graph with edges 0,1 0,2 1,3 1,4 2,4 2,5 and every array movement to a horizontal or vertical neighbor moves along an edge of this graph.

%I A223347 #8 Aug 19 2018 13:25:06
%S A223347 28,236,2280,20836,202264,1851020,17970056,164457412,1596586328,
%T A223347 14611562156,141852049992,1298194798372,12603142057880,
%U A223347 115340831992268,1119752515193608,10247697449986948,99486754138704856,910478112673392620
%N A223347 3 X 3 X 3 triangular graph without horizontal edges coloring a rectangular array: number of n X 3 0..5 arrays where 0..5 label nodes of a graph with edges 0,1 0,2 1,3 1,4 2,4 2,5 and every array movement to a horizontal or vertical neighbor moves along an edge of this graph.
%C A223347 Column 3 of A223352.
%H A223347 R. H. Hardin, <a href="/A223347/b223347.txt">Table of n, a(n) for n = 1..210</a>
%F A223347 Empirical: a(n) = 91*a(n-2) - 192*a(n-4) + 64*a(n-6).
%F A223347 Empirical g.f.: 4*x*(7 + 59*x - 67*x^2 - 160*x^3 + 40*x^4 + 64*x^5) / (1 - 91*x^2 + 192*x^4 - 64*x^6). - _Colin Barker_, Aug 19 2018
%e A223347 Some solutions for n=3:
%e A223347 ..1..4..1....1..4..2....2..0..2....0..2..4....5..2..0....4..1..0....4..2..5
%e A223347 ..0..2..4....0..2..0....4..1..0....1..4..1....2..5..2....1..4..1....2..5..2
%e A223347 ..1..0..1....2..4..1....2..4..1....0..1..3....0..2..4....4..1..0....4..2..5
%Y A223347 Cf. A223352.
%K A223347 nonn
%O A223347 1,1
%A A223347 _R. H. Hardin_, Mar 19 2013