A223292 4-loop graph coloring a rectangular array: number of n X 3 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.

96, 1368, 42168, 709320, 22346136, 377262504, 11864385048, 200704309992, 6299392974744, 106774437227112, 3344677464047256, 56803388487510120, 1775872406337823128, 30218825031419575656, 942912161643830193816

Offset

1,1

Comments

Column 3 of A223297.

Links

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

Formula

Empirical: a(n) = 2*a(n-1) + 531*a(n-2) - 1022*a(n-3) - 750*a(n-4) + 448*a(n-5).

Empirical g.f.: 24*x*(4 + 49*x - 481*x^2 - 138*x^3 + 266*x^4) / (1 - 2*x - 531*x^2 + 1022*x^3 + 750*x^4 - 448*x^5). - Colin Barker, Aug 19 2018

Example

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

Crossrefs

Cf. A223297.

Sequence in context: A229533 A282017 A263567 * A168526 A128962 A071765

Adjacent sequences: A223289 A223290 A223291 * A223293 A223294 A223295

Keyword

nonn

Author

R. H. Hardin, Mar 19 2013

Status

approved