A223242 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.

60, 642, 11538, 144582, 2663082, 33590454, 616998282, 7808992566, 142965076362, 1815370659126, 33127391927562, 422008111094454, 7676351980853898, 98098336800910134, 1778822826035815434, 22802798712088642998

Offset

1,1

Comments

Column 3 of A223247.

Links

R. H. Hardin, Table of n, a(n) for n = 1..210

Formula

Empirical: a(n) = 2*a(n-1) + 231*a(n-2) - 430*a(n-3) - 286*a(n-4) + 180*a(n-5).

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

Example

Some solutions for n=3:
..4..0..3....5..6..0....3..0..2....1..0..6....4..0..2....5..0..3....3..0..6
..0..1..0....6..5..6....0..5..0....0..1..0....0..6..0....0..4..0....0..4..0
..3..0..5....5..0..5....5..6..5....6..0..1....2..0..5....1..0..6....3..0..1

Crossrefs

Cf. A223247.

Sequence in context: A283786 A099344 A324068 * A244837 A268624 A088945

Adjacent sequences: A223239 A223240 A223241 * A223243 A223244 A223245

Keyword

nonn

Author

R. H. Hardin, Mar 18 2013

Status

approved