A208316 Number of n X 2 0..2 arrays with new values 0..2 introduced in row major order and no element equal to more than two of its immediate leftward or upward or left-upward diagonal neighbors.

2, 13, 113, 982, 8534, 74164, 644516, 5601112, 48675992, 423014608, 3676172816, 31947470176, 277636798304, 2412779207488, 20968054449728, 182221110842752, 1583577213440384, 13761944372579584, 119597018261278976

Offset

1,1

Comments

Column 2 of A208322.

Links

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

Formula

Empirical: a(n) = 8*a(n-1) + 6*a(n-2) for n>3.

Conjectures from Colin Barker, Jul 02 2018: (Start)

G.f.: x*(2 - 3*x - 3*x^2) / (1 - 8*x - 6*x^2).

a(n) = ((4-sqrt(22))^n*(-5+sqrt(22)) + (4+sqrt(22))^n*(5+sqrt(22))) / (12*sqrt(22)) for n>1.

(End)

Example

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

Crossrefs

Cf. A208322.

Sequence in context: A166921 A046811 A046813 * A096497 A247153 A088604

Adjacent sequences: A208313 A208314 A208315 * A208317 A208318 A208319

Keyword

nonn

Author

R. H. Hardin, Feb 25 2012

Status

approved