A223241 3-loop graph coloring a rectangular array: number of n X 2 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.

18, 102, 642, 4086, 26034, 165894, 1057122, 6736278, 42925458, 273533094, 1743029826, 11107076406, 70777415538, 451013603142, 2873985559842, 18313844506326, 116700969304914, 743651407109094, 4738755972544002

Offset

1,1

Comments

Column 2 of A223247.

Links

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

Formula

Empirical: a(n) = 7*a(n-1) - 4*a(n-2).

Empirical g.f.: 6*x*(3 - 4*x) / (1 - 7*x + 4*x^2). - Colin Barker, Aug 17 2018

Example

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

Crossrefs

Cf. A223247.

Sequence in context: A373316 A020881 A285043 * A197339 A304763 A322648

Adjacent sequences: A223238 A223239 A223240 * A223242 A223243 A223244

Keyword

nonn

Author

R. H. Hardin, Mar 18 2013

Status

approved