A221401 Number of 2 X n 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, 1, 6, 56, 324, 2196, 13328, 83680, 512752, 3161248, 19384848, 118981520, 729388016, 4471790032, 27407876144, 167983235088, 1029494729904, 6309251897744, 38665450224432, 236955187985936, 1452135101851056

Offset

1,3

Comments

Row 2 of A221400.

Links

R. H. Hardin, Table of n, a(n) for n = 1..69

Formula

Empirical: a(n) = 7*a(n-1) + 6*a(n-2) - 74*a(n-3) + 8*a(n-4) + 132*a(n-5) - 72*a(n-6) - 24*a(n-7) + 16*a(n-8).

Empirical g.f.: x^2*(1 - 2*x)*(1 + x + 10*x^2 - 10*x^3 + 8*x^4 - 8*x^5) / ((1 - 4*x + 2*x^2)*(1 + 2*x - 2*x^2)*(1 - 5*x - 8*x^2 + 6*x^3 + 4*x^4)). - Colin Barker, Aug 05 2018

Example

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

Crossrefs

Cf. A221400.

Sequence in context: A053127 A068495 A166766 * A364471 A097126 A210325

Adjacent sequences: A221398 A221399 A221400 * A221402 A221403 A221404

Keyword

nonn

Author

R. H. Hardin, Jan 15 2013

Status

approved