A221397 Number of n X 3 arrays of occupancy after each element moves to some horizontal, diagonal or antidiagonal neighbor, with no 2-loops and with no occupancy greater than 2.

0, 6, 30, 144, 672, 3108, 14328, 65976, 303672, 1397520, 6431136, 29594352, 136184256, 626677152, 2883768672, 13270180608, 61065117312, 281002082880, 1293081432192, 5950345861248, 27381582408576, 126001256419584

Offset

1,2

Comments

Column 3 of A221400.

Links

R. H. Hardin, Table of n, a(n) for n = 1..41

Formula

Empirical: a(n) = 6*a(n-1) - 6*a(n-2) -2*a(n-3).

Empirical g.f.: 6*x^2*(1 - x) / (1 - 6*x + 6*x^2 + 2*x^3). - Colin Barker, Aug 05 2018

Example

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

Crossrefs

Cf. A221400.

Sequence in context: A307321 A026749 A003279 * A082134 A030192 A026376

Adjacent sequences: A221394 A221395 A221396 * A221398 A221399 A221400

Keyword

nonn

Author

R. H. Hardin, Jan 15 2013

Status

approved