A221853 Number of 2 X n arrays of occupancy after each element stays put or moves to some horizontal, diagonal or antidiagonal neighbor, without consecutive moves in the same direction.

1, 31, 302, 3437, 37155, 406612, 4434129, 48397883, 528123314, 5763315281, 62892896491, 686329748776, 7489683895265, 81732408497079, 891918279715066, 9733204380907645, 106215187016111667, 1159090627331995148

Offset

1,2

Comments

Row 2 of A221852.

Links

R. H. Hardin, Table of n, a(n) for n = 1..37

Formula

Empirical: a(n) = 13*a(n-1) - 14*a(n-2) - 113*a(n-3) + 189*a(n-4) - 10*a(n-5) - 42*a(n-6) + 18*a(n-7) - 2*a(n-8).

Empirical g.f.: x*(1 + 18*x - 87*x^2 + 58*x^3 + 16*x^4 - 8*x^5 - 2*x^6) / (1 - 13*x + 14*x^2 + 113*x^3 - 189*x^4 + 10*x^5 + 42*x^6 - 18*x^7 + 2*x^8). - Colin Barker, Aug 11 2018

Example

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

Crossrefs

Cf. A221852.

Sequence in context: A369173 A001298 A027841 * A000500 A141912 A147297

Adjacent sequences: A221850 A221851 A221852 * A221854 A221855 A221856

Keyword

nonn

Author

R. H. Hardin, Jan 27 2013

Status

approved