A223291 4-loop graph coloring a rectangular array: number of n X 2 0..8 arrays where 0..8 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 0,7 7,8 8,0 and every array movement to a horizontal or vertical neighbor moves along an edge of this graph.

24, 168, 1368, 11304, 93528, 773928, 6404184, 52994088, 438521688, 3628730664, 30027445848, 248474628648, 2056106982744, 17014115072808, 140790393758808, 1165028853392424, 9640517317978968, 79774482741456168, 660127240765231704

Offset

1,1

Comments

Column 2 of A223297.

Links

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

Formula

Empirical: a(n) = 9*a(n-1) - 6*a(n-2).

Conjectures from Colin Barker, Aug 19 2018: (Start)

G.f.: 24*x*(1 - 2*x) / (1 - 9*x + 6*x^2).

a(n) = (2^(2-n)*((9-sqrt(57))^n*(3+sqrt(57)) + (-3+sqrt(57))*(9+sqrt(57))^n)) / sqrt(57).

(End)

Example

Some solutions for n=3:
..2..0....0..3....6..0....4..0....3..0....0..3....0..1....4..0....8..0....0..2
..0..1....3..0....0..3....0..4....0..5....6..0....8..0....0..6....0..3....2..0
..7..0....0..6....8..0....4..3....1..0....0..6....7..8....3..0....8..0....0..6

Crossrefs

Cf. A223297.

Sequence in context: A244908 A087887 A288486 * A221069 A272125 A166756

Adjacent sequences: A223288 A223289 A223290 * A223292 A223293 A223294

Keyword

nonn

Author

R. H. Hardin, Mar 19 2013

Status

approved