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4-loop graph coloring a rectangular array: number of n X 3 0..8 arrays where 0..8 label nodes of a graph with edges 0,1 1,2 2,0 0,3 3,4 4,0 0,5 5,6 6,0 0,7 7,8 8,0 and every array movement to a horizontal or vertical neighbor moves along an edge of this graph.
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%I #8 Aug 19 2018 07:36:26

%S 96,1368,42168,709320,22346136,377262504,11864385048,200704309992,

%T 6299392974744,106774437227112,3344677464047256,56803388487510120,

%U 1775872406337823128,30218825031419575656,942912161643830193816

%N 4-loop graph coloring a rectangular array: number of n X 3 0..8 arrays where 0..8 label nodes of a graph with edges 0,1 1,2 2,0 0,3 3,4 4,0 0,5 5,6 6,0 0,7 7,8 8,0 and every array movement to a horizontal or vertical neighbor moves along an edge of this graph.

%C Column 3 of A223297.

%H R. H. Hardin, <a href="/A223292/b223292.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 2*a(n-1) + 531*a(n-2) - 1022*a(n-3) - 750*a(n-4) + 448*a(n-5).

%F Empirical g.f.: 24*x*(4 + 49*x - 481*x^2 - 138*x^3 + 266*x^4) / (1 - 2*x - 531*x^2 + 1022*x^3 + 750*x^4 - 448*x^5). - _Colin Barker_, Aug 19 2018

%e Some solutions for n=3:

%e ..7..0..5....2..0..5....2..0..7....8..0..4....7..0..5....4..0..3....3..0..2

%e ..0..5..0....0..5..6....0..8..0....0..8..0....8..7..0....0..2..0....0..1..0

%e ..3..0..8....6..0..5....1..0..3....2..0..4....0..8..7....7..0..3....6..0..1

%Y Cf. A223297.

%K nonn

%O 1,1

%A _R. H. Hardin_, Mar 19 2013