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A223348 3 X 3 X 3 triangular graph without horizontal edges coloring a rectangular array: number of n X 4 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 A223348 #8 Aug 19 2018 13:09:13
%S A223348 60,1076,20836,405988,7918948,154482340,3013692516,58792282660,
%T A223348 1146943179236,22375024222628,436500886445412,8515433203445028,
%U A223348 166122463695945956,3240783209292085412,63222490059635217508
%N A223348 3 X 3 X 3 triangular graph without horizontal edges coloring a rectangular array: number of n X 4 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 A223348 Column 4 of A223352.
%H A223348 R. H. Hardin, <a href="/A223348/b223348.txt">Table of n, a(n) for n = 1..210</a>
%F A223348 Empirical: a(n) = 23*a(n-1) - 66*a(n-2) - 52*a(n-3) + 208*a(n-4) + 32*a(n-5) - 128*a(n-6).
%F A223348 Empirical g.f.: 4*x*(1 - 4*x)*(15 - 16*x - 52*x^2 + 16*x^3 + 32*x^4) / (1 - 23*x + 66*x^2 + 52*x^3 - 208*x^4 - 32*x^5 + 128*x^6). - _Colin Barker_, Aug 19 2018
%e A223348 Some solutions for n=3:
%e A223348 ..1..4..1..3....2..0..1..0....1..4..2..4....5..2..0..1....4..2..4..2
%e A223348 ..4..2..0..1....4..2..0..1....0..2..4..2....2..0..1..3....1..4..2..4
%e A223348 ..1..0..1..0....1..4..1..3....2..0..2..4....0..1..0..1....4..2..0..2
%Y A223348 Cf. A223352.
%K A223348 nonn
%O A223348 1,1
%A A223348 _R. H. Hardin_, Mar 19 2013