A223374 3 X 3 square grid graph coloring a rectangular array: number of n X 3 0..8 arrays where 0..8 label nodes of the square grid graph and every array movement to a horizontal or vertical neighbor moves along an edge of this graph.

68, 912, 13232, 192752, 2812608, 41044048, 598980512, 8741293936, 127567402912, 1861673117136, 27168612726112, 396489050362864, 5786223905786400, 84442089417201488, 1232318612693585248, 17984018624753407088

Offset

1,1

Comments

Column 3 of A223379.

Links

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

Formula

Empirical: a(n) = 221*a(n-2) - 1718*a(n-4) + 1872*a(n-6) for n>7.

Empirical g.f.: 4*x*(17 + 228*x - 449*x^2 - 2200*x^3 + 1290*x^4 + 3168*x^5 - 144*x^6) / (1 - 221*x^2 + 1718*x^4 - 1872*x^6). - Colin Barker, Aug 20 2018

Example

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

Crossrefs

Cf. A223379.

Sequence in context: A039507 A250144 A250338 * A360656 A254645 A281049

Adjacent sequences: A223371 A223372 A223373 * A223375 A223376 A223377

Keyword

nonn

Author

R. H. Hardin, Mar 19 2013

Status

approved