A221652 Number of n X 2 arrays of occupancy after each element moves to some horizontal, diagonal or antidiagonal neighbor, without move-in move-out left turns.

1, 4, 12, 40, 136, 460, 1556, 5264, 17808, 60244, 203804, 689464, 2332440, 7890588, 26693668, 90304032, 305496352, 1033486756, 3496260652, 11827765064, 40013042600, 135363153516, 457930268212, 1549167000752, 5240794423984

Offset

1,2

Comments

Column 2 of A221655.

Links

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

Formula

Empirical: a(n) = 3*a(n-1) + a(n-2) + a(n-3) for n>4.

Empirical g.f.: x*(1 - x)*(1 + x)^2 / (1 - 3*x - x^2 - x^3). - Colin Barker, Mar 14 2018

Example

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

Crossrefs

Cf. A221655.

Sequence in context: A289653 A081875 A102433 * A259806 A100320 A064649

Adjacent sequences: A221649 A221650 A221651 * A221653 A221654 A221655

Keyword

nonn

Author

R. H. Hardin, Jan 21 2013

Status

approved