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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. 1
24, 168, 1368, 11304, 93528, 773928, 6404184, 52994088, 438521688, 3628730664, 30027445848, 248474628648, 2056106982744, 17014115072808, 140790393758808, 1165028853392424, 9640517317978968, 79774482741456168, 660127240765231704 (list; graph; refs; listen; history; text; internal format)
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

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Last modified August 13 20:49 EDT 2022. Contains 356107 sequences. (Running on oeis4.)