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A223418 3-level binary fanout graph coloring a rectangular array: number of n X 3 0..6 arrays where 0..6 label nodes of a graph with edges 0,1 1,3 1,4 0,2 2,5 2,6 and every array movement to a horizontal or vertical neighbor moves along an edge of this graph.

%I A223418 #7 Aug 20 2018 08:49:37
%S A223418 26,136,868,4720,29912,163168,1033328,5638336,35704800,194827648,
%T A223418 1233740224,6732071680,42630619008,232619832832,1473057249024,
%U A223418 8037939530752,50899980869120,277742748522496,1758796582951936
%N A223418 3-level binary fanout graph coloring a rectangular array: number of n X 3 0..6 arrays where 0..6 label nodes of a graph with edges 0,1 1,3 1,4 0,2 2,5 2,6 and every array movement to a horizontal or vertical neighbor moves along an edge of this graph.
%C A223418 Column 3 of A223423.
%H A223418 R. H. Hardin, <a href="/A223418/b223418.txt">Table of n, a(n) for n = 1..210</a>
%F A223418 Empirical: a(n) = 38*a(n-2) - 120*a(n-4) + 32*a(n-6).
%F A223418 Empirical g.f.: 2*x*(13 + 68*x - 60*x^2 - 224*x^3 + 24*x^4 + 64*x^5) / (1 - 38*x^2 + 120*x^4 - 32*x^6). - _Colin Barker_, Aug 20 2018
%e A223418 Some solutions for n=3.
%e A223418 ..0..1..0....4..1..4....0..1..4....5..2..6....0..2..0....6..2..0....1..0..1
%e A223418 ..1..3..1....1..4..1....2..0..1....2..6..2....2..0..1....2..6..2....0..1..0
%e A223418 ..4..1..0....4..1..3....0..1..0....0..2..0....0..1..3....6..2..5....1..3..1
%Y A223418 Cf. A223423.
%K A223418 nonn
%O A223418 1,1
%A A223418 _R. H. Hardin_, Mar 20 2013