A189644 Number of n X 3 array permutations with each element moving zero or one space horizontally, diagonally or antidiagonally.

3, 33, 263, 2161, 17655, 144353, 1180167, 9648721, 78885143, 644942273, 5272862503, 43109407281, 352450114615, 2881530764193, 23558566731847, 192608065601041, 1574708145738583, 12874360876413313, 105257071556189543

Offset: 1

Author

R. H. Hardin, Apr 24 2011

Keywords

• nonn

Comments

Column 3 of A189650.

Examples

			Some solutions for 4 X 3:
..0..1..2....1..0..2....1..0..4....4..0..2....0..2..1....0..3..4....1..0..2
..7..5..4....3..8..5....3..2..5....3..5..1....3..4..5....1..2..7....3..6..5
..6..3.10....6..9..4...10..6..7...10..6..8....7..9..8....6..5.10....7..8..4
..9..8.11....7.11.10....9..8.11....9.11..7...10..6.11....9..8.11....9.10.11
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..200

Crossrefs

Cf. A189650.

Formula

Empirical: a(n) = 9*a(n-1) - 6*a(n-2) - 8*a(n-3) + 16*a(n-4).

Empirical g.f.: x*(3 + 6*x - 16*x^2 + 16*x^3) / (1 - 9*x + 6*x^2 + 8*x^3 - 16*x^4). - Colin Barker, May 02 2018