A296957 Number of n X 2 0..1 arrays with each 1 adjacent to 2, 3 or 5 king-move neighboring 1s.

1, 6, 16, 31, 96, 301, 801, 2261, 6746, 19456, 55751, 162436, 472621, 1368341, 3971361, 11541726, 33504416, 97254351, 282443176, 820183901, 2381405001, 6915014781, 20080097266, 58307232656, 169309052471, 491636470476

Offset

1,2

Links

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

Formula

Empirical: a(n) = 4*a(n-1) - 5*a(n-2) + 11*a(n-3) - 18*a(n-4) + 4*a(n-5).

Empirical g.f.: x*(1 + 2*x - 3*x^2 - 14*x^3 + 4*x^4) / (1 - 4*x + 5*x^2 - 11*x^3 + 18*x^4 - 4*x^5). - Colin Barker, Feb 25 2019

Example

Some solutions for n=5:
..1..1. .1..1. .1..1. .1..0. .1..1. .0..0. .1..1. .0..0. .1..1. .0..0
..0..1. .0..1. .1..0. .1..1. .1..1. .0..0. .1..1. .0..0. .0..1. .1..1
..0..0. .0..1. .0..0. .0..0. .1..1. .0..0. .0..0. .0..0. .0..0. .1..1
..1..1. .1..1. .1..1. .1..1. .0..0. .1..1. .1..1. .0..0. .1..1. .0..0
..1..0. .0..1. .0..1. .1..1. .0..0. .1..1. .0..1. .0..0. .1..1. .0..0

Crossrefs

Column 2 of A296963.

Sequence in context: A276917 A097118 A369548 * A341276 A301698 A301713

Adjacent sequences: A296954 A296955 A296956 * A296958 A296959 A296960

Keyword

nonn

Author

R. H. Hardin, Dec 22 2017

Status

approved