A295937 Number of n X 2 0..1 arrays with each 1 adjacent to 1 or 3 king-move neighboring 1s.

2, 8, 15, 33, 104, 228, 529, 1469, 3442, 8212, 21431, 51717, 125296, 317400, 775809, 1895433, 4734066, 11634128, 28553071, 70839225, 174478216, 429240572, 1061586753, 2617025573, 6446295426, 15919369724, 39257673143, 96762290109

Offset

1,1

Links

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

Formula

Empirical: a(n) = a(n-1) + a(n-2) + 9*a(n-3) - 4*a(n-4) - 4*a(n-5) - 4*a(n-6).

Empirical g.f.: x*(2 + 6*x + 5*x^2 - 8*x^3 - 8*x^4 - 4*x^5) / (1 - x - x^2 - 9*x^3 + 4*x^4 + 4*x^5 + 4*x^6). - Colin Barker, Feb 22 2019

Example

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

Crossrefs

Column 2 of A295943.

Sequence in context: A095298 A297734 A100596 * A305674 A082638 A077388

Adjacent sequences: A295934 A295935 A295936 * A295938 A295939 A295940

Keyword

nonn

Author

R. H. Hardin, Nov 30 2017

Status

approved