A297909 Number of n X 2 0..1 arrays with every element equal to 0, 2, 3 or 4 king-move adjacent elements, with upper left element zero.

1, 5, 12, 37, 104, 301, 864, 2485, 7144, 20541, 59056, 169797, 488184, 1403597, 4035520, 11602645, 33359112, 95911773, 275758800, 792842341, 2279524632, 6553929197, 18843397088, 54177212405, 155766517544, 447848955517

Offset

1,2

Comments

Column 2 of A297915.

Links

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

Formula

Empirical: a(n) = 5*a(n-2) + 8*a(n-3) + 4*a(n-4).

Empirical g.f.: x*(1 + 5*x + 7*x^2 + 4*x^3) / ((1 + x)*(1 - x - 4*x^2 - 4*x^3)). - Colin Barker, Feb 21 2018

Example

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

Crossrefs

Cf. A297915.

Sequence in context: A077918 A300534 A359189 * A220705 A034752 A095310

Adjacent sequences: A297906 A297907 A297908 * A297910 A297911 A297912

Keyword

nonn

Author

R. H. Hardin, Jan 08 2018

Status

approved