A221891 Number of 2 X n arrays of occupancy after each element moves to some horizontal, diagonal or antidiagonal neighbor, without 2-loops or left turns.

0, 0, 8, 37, 169, 811, 3878, 18502, 88302, 421463, 2011587, 9601013, 45824300, 218713020, 1043886804, 4982326441, 23779950797, 113498396063, 541712050514, 2585516235106, 12340309202426, 58898578606299, 281114719650631

Offset

1,3

Comments

Row 2 of A221890.

Links

R. H. Hardin, Table of n, a(n) for n = 1..162

Formula

Empirical: a(n) = 5*a(n-1) -2*a(n-2) +5*a(n-3) -3*a(n-4).

Empirical g.f.: x^3*(8 - 3*x) / (1 - 5*x + 2*x^2 - 5*x^3 + 3*x^4). - Colin Barker, Feb 12 2018

Example

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

Crossrefs

Sequence in context: A111645 A272739 A220917 * A221063 A221633 A201452

Adjacent sequences: A221888 A221889 A221890 * A221892 A221893 A221894

Keyword

nonn

Author

R. H. Hardin, Jan 30 2013

Status

approved