A297953 Number of n X 2 0..1 arrays with every element equal to 1, 2, 4 or 5 king-move adjacent elements, with upper left element zero.

1, 3, 7, 13, 23, 49, 99, 189, 383, 777, 1531, 3061, 6167, 12289, 24531, 49197, 98351, 196473, 393259, 786661, 1572551, 3145585, 6292227, 12582429, 25164767, 50333673, 100663387, 201322453, 402657143, 805310689, 1610600499, 3221229069

Offset

1,2

Comments

Column 2 of A297959.

Links

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

Formula

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

Empirical g.f.: (1 + x)*(1 + 2*x^2 - 4*x^3) / ((1 - x)*(1 - 2*x)*(1 + x + 2*x^2)). - Colin Barker, Feb 19 2018

Example

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

Crossrefs

Cf. A297959.

Sequence in context: A349793 A100720 A297852 * A084898 A147380 A146606

Adjacent sequences: A297950 A297951 A297952 * A297954 A297955 A297956

Keyword

nonn

Author

R. H. Hardin, Jan 09 2018

Status

approved