A223240 3-loop graph coloring a rectangular array: number of n X 1 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.

7, 18, 60, 168, 528, 1536, 4704, 13920, 42144, 125664, 378528, 1132512, 3403680, 10198752, 30620832, 91813344, 275538336, 826418400, 2479648416, 7438158816, 22316049312, 66945002208, 200841298080, 602511311328, 1807559099808

Offset

1,1

Comments

Column 1 of A223247.

Links

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

Formula

Empirical: a(n) = a(n-1) + 6*a(n-2).

Conjectures from Colin Barker, Aug 17 2018: (Start)

G.f.: x*(7 + 11*x) / ((1 + 2*x)*(1 - 3*x)).

a(n) = (64*3^n - 9*(-2)^n) / 30.

(End)

Example

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

Crossrefs

Cf. A223247.

Sequence in context: A220031 A197092 A288743 * A304142 A019534 A024830

Adjacent sequences: A223237 A223238 A223239 * A223241 A223242 A223243

Keyword

nonn

Author

R. H. Hardin, Mar 18 2013

Status

approved