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%I #7 Aug 17 2018 17:02:18
%S 60,642,11538,144582,2663082,33590454,616998282,7808992566,
%T 142965076362,1815370659126,33127391927562,422008111094454,
%U 7676351980853898,98098336800910134,1778822826035815434,22802798712088642998
%N 3-loop 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 1,2 2,0 0,3 3,4 4,0 0,5 5,6 6,0 and every array movement to a horizontal or vertical neighbor moves along an edge of this graph.
%C Column 3 of A223247.
%H R. H. Hardin, <a href="/A223242/b223242.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 2*a(n-1) + 231*a(n-2) - 430*a(n-3) - 286*a(n-4) + 180*a(n-5).
%F Empirical g.f.: 6*x*(10 + 87*x - 601*x^2 - 166*x^3 + 310*x^4) / (1 - 2*x - 231*x^2 + 430*x^3 + 286*x^4 - 180*x^5). - _Colin Barker_, Aug 17 2018
%e Some solutions for n=3:
%e ..4..0..3....5..6..0....3..0..2....1..0..6....4..0..2....5..0..3....3..0..6
%e ..0..1..0....6..5..6....0..5..0....0..1..0....0..6..0....0..4..0....0..4..0
%e ..3..0..5....5..0..5....5..6..5....6..0..1....2..0..5....1..0..6....3..0..1
%Y Cf. A223247.
%K nonn
%O 1,1
%A _R. H. Hardin_, Mar 18 2013
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