A297809 Number of n X 2 0..1 arrays with every element equal to 2 or 3 king-move adjacent elements, with upper left element zero.

0, 1, 2, 1, 8, 5, 22, 29, 60, 121, 194, 425, 704, 1421, 2574, 4821, 9156, 16769, 31962, 58977, 111112, 207317, 387366, 726221, 1354508, 2538761, 4741234, 8872857, 16592208, 31023517, 58039870, 108509253, 202982228, 379560465, 709885450

Offset

1,3

Comments

Column 2 of A297814.

Links

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

Formula

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

Empirical g.f.: x^2*(1 + 2*x - 2*x^2) / (1 - 3*x^2 - 2*x^3 + 2*x^4). - Colin Barker, Feb 21 2018

Example

Some solutions for n=7:
..0..0. .0..0. .0..0. .0..0. .0..0. .0..0. .0..0. .0..0. .0..0. .0..0
..1..0. .1..0. .0..0. .0..0. .0..0. .0..1. .0..1. .0..0. .0..1. .1..0
..1..1. .1..1. .1..1. .1..1. .1..1. .1..1. .1..1. .1..1. .1..1. .1..1
..1..0. .1..0. .1..1. .0..1. .0..1. .1..0. .0..1. .1..0. .1..0. .1..0
..0..0. .0..0. .0..0. .0..0. .0..0. .0..0. .0..0. .0..0. .0..0. .0..0
..1..1. .0..1. .0..1. .1..0. .1..1. .1..1. .0..1. .1..1. .0..1. .1..0
..1..1. .1..1. .1..1. .1..1. .1..1. .1..1. .1..1. .1..1. .1..1. .1..1

Crossrefs

Cf. A297814.

Sequence in context: A199468 A337684 A004732 * A160641 A011244 A189966

Adjacent sequences: A297806 A297807 A297808 * A297810 A297811 A297812

Keyword

nonn

Author

R. H. Hardin, Jan 06 2018

Status

approved