A221121 Number of n X 3 arrays of occupancy after each element stays put or moves to some horizontal or antidiagonal neighbor.

8, 200, 4872, 118472, 2880520, 70036168, 1702839048, 41402332360, 1006644240392, 24475254623432, 595084206353160, 14468703925621448, 351787849605678088, 8553267228797150920, 207961646114893122312, 5056318842606537992392

Offset: 1

Author

R. H. Hardin, Jan 02 2013

Keywords

• nonn

Comments

Column 3 of A221125.

Examples

			Some solutions for n=3.
..2..1..0....2..1..0....1..1..1....1..1..0....1..0..1....0..1..1....1..2..0
..0..4..0....2..1..0....0..2..0....2..1..0....1..2..0....1..2..0....1..1..0
..1..0..1....2..0..1....3..0..1....3..1..0....2..1..1....1..1..2....1..3..0
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..124

Crossrefs

Cf. A221125.

Formula

Empirical: a(n) = 26*a(n-1) - 41*a(n-2).

Conjectures from Colin Barker, Aug 03 2018: (Start)

G.f.: 8*x*(1 - x) / (1 - 26*x + 41*x^2).

a(n) = ((13-8*sqrt(2))^n*(4-7*sqrt(2)) + (4+7*sqrt(2))*(13+8*sqrt(2))^n) / 41.

(End)