A296821 Number of n X 2 0..1 arrays with each 1 adjacent to 2, 3 or 4 king-move neighboring 1s.

1, 6, 21, 56, 178, 609, 1997, 6511, 21494, 71021, 234110, 771936, 2546839, 8401997, 27715289, 91426922, 301604833, 994943072, 3282138566, 10827217153, 35717165621, 117824839843, 388684058778, 1282202639897, 4229768507606

Offset

1,2

Links

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

Formula

Empirical: a(n) = 3*a(n-1) + 5*a(n-3) - 2*a(n-4) - 10*a(n-5) - 8*a(n-6).

Empirical g.f.: x*(1 + 3*x + 3*x^2 - 12*x^3 - 18*x^4 - 8*x^5) / (1 - 3*x - 5*x^3 + 2*x^4 + 10*x^5 + 8*x^6). - Colin Barker, Feb 25 2019

Example

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

Crossrefs

Column 2 of A296827.

Sequence in context: A256571 A247904 A074745 * A056414 A056341 A144899

Adjacent sequences: A296818 A296819 A296820 * A296822 A296823 A296824

Keyword

nonn

Author

R. H. Hardin, Dec 21 2017

Status

approved