A223373 3 X 3 square grid graph coloring a rectangular array: number of n X 2 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.

24, 144, 912, 5808, 37008, 235824, 1502736, 9575856, 61020048, 388836912, 2477778192, 15789099696, 100612585104, 641131696944, 4085471538192, 26033773979568, 165894531704208, 1057126626011184, 6736308255261456

Offset

1,1

Comments

Column 2 of A223379.

Links

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

Formula

Empirical: a(n) = 7*a(n-1) - 4*a(n-2).

Empirical g.f.: 24*x*(1 - x) / (1 - 7*x + 4*x^2). - Colin Barker, Mar 16 2018

Example

Some solutions for n=3:
..0..3....6..3....4..5....1..0....3..6....4..3....4..5....3..4....5..4....5..4
..1..4....7..4....7..4....4..3....6..7....5..4....1..2....4..7....4..3....4..3
..0..1....6..7....6..3....3..0....7..8....2..1....4..1....5..4....5..4....3..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: A200194 A182075 A054118 * A001342 A029572 A129923

Adjacent sequences: A223370 A223371 A223372 * A223374 A223375 A223376

Keyword

nonn

Author

R. H. Hardin, Mar 19 2013

Status

approved