A295913 Number of n X 3 0..1 arrays with each 1 adjacent to 0 or 3 king-move neighboring 1's.

5, 13, 39, 115, 337, 993, 2919, 8587, 25257, 74289, 218511, 642715, 1890449, 5560465, 16355255, 48106475, 141497817, 416194129, 1224171199, 3600711835, 10590941633, 31151630513, 91627743527, 269508954923, 792719257161, 2331662118065

Offset

1,1

Links

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

Formula

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

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

Example

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

Crossrefs

Column 3 of A295918.

Sequence in context: A360797 A080143 A077919 * A272225 A272585 A026069

Adjacent sequences: A295910 A295911 A295912 * A295914 A295915 A295916

Keyword

nonn

Author

R. H. Hardin, Nov 29 2017

Status

approved