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A223419 3-level binary fanout graph coloring a rectangular array: number of n X 4 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 A223419 #7 Aug 20 2018 09:13:26
%S A223419 48,464,4720,47872,486016,4934272,50097024,508632832,5164146176,
%T A223419 52431620096,532338988032,5404846559232,54875501465600,
%U A223419 557151943860224,5656773689024512,57433325141737472,583121585796284416
%N A223419 3-level binary fanout graph coloring a rectangular array: number of n X 4 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 A223419 Column 4 of A223423.
%H A223419 R. H. Hardin, <a href="/A223419/b223419.txt">Table of n, a(n) for n = 1..210</a>
%F A223419 Empirical: a(n) = 14*a(n-1) - 36*a(n-2) - 40*a(n-3) + 88*a(n-4) + 32*a(n-5) - 32*a(n-6).
%F A223419 Empirical g.f.: 16*x*(3 - 13*x - 3*x^2 + 26*x^3 + 4*x^4 - 8*x^5) / (1 - 14*x + 36*x^2 + 40*x^3 - 88*x^4 - 32*x^5 + 32*x^6). - _Colin Barker_, Aug 20 2018
%e A223419 Some solutions for n=3:
%e A223419 ..0..2..0..2....5..2..0..1....3..1..0..1....1..3..1..3....3..1..0..2
%e A223419 ..1..0..1..0....2..0..1..0....1..0..1..0....0..1..4..1....1..0..1..0
%e A223419 ..4..1..4..1....6..2..0..2....0..1..0..2....1..0..1..4....3..1..4..1
%Y A223419 Cf. A223423.
%K A223419 nonn
%O A223419 1,1
%A A223419 _R. H. Hardin_, Mar 20 2013