A223243 - OEIS

A223243

3-loop 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), (1,2), (2,0), (0,3), (3,4), (4,0), (0,5), (5,6), and (6,0), and every array movement to a horizontal or vertical neighbor moves along an edge of this graph.

%I #13 Aug 17 2018 16:10:16

%S 168,4086,144582,5336844,198634758,7399451382,275682413748,

%T 10271315554206,382687513971798,14258133000231516,531228116681596086,

%U 19792445044329718422,737424976053389046756,27474907428586558064526

%N 3-loop 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), (1,2), (2,0), (0,3), (3,4), (4,0), (0,5), (5,6), and (6,0), and every array movement to a horizontal or vertical neighbor moves along an edge of this graph.

%C Column 4 of A223247.

%H R. H. Hardin, <a href="/A223243/b223243.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 40*a(n-1) - 80*a(n-2) - 869*a(n-3) + 1566*a(n-4) + 1650*a(n-5) - 1796*a(n-6) for n>7.

%F Empirical g.f.: 6*x*(28 - 439*x - 903*x^2 + 4406*x^3 + 2534*x^4 - 4256*x^5 + 160*x^6) / (1 - 40*x + 80*x^2 + 869*x^3 - 1566*x^4 - 1650*x^5 + 1796*x^6). - _Colin Barker_, Aug 17 2018

%e Some solutions for n=3:

%e ..0..2..0..3....1..2..0..1....0..1..0..1....0..1..2..0....1..2..0..2

%e ..3..0..2..0....2..0..4..0....4..0..4..0....1..2..0..4....2..0..1..0

%e ..0..6..0..2....0..2..0..1....0..6..0..4....0..1..2..0....0..3..0..3

%Y Cf. A223247.

%K nonn

%O 1,1

%A _R. H. Hardin_, Mar 18 2013