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

1,1

Comments

Column 3 of A221125.

Links

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

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)

Example

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

Crossrefs

Cf. A221125.

Sequence in context: A229265 A323562 A034861 * A264124 A317631 A309904

Adjacent sequences: A221118 A221119 A221120 * A221122 A221123 A221124

Keyword

nonn

Author

R. H. Hardin, Jan 02 2013

Status

approved