A295247 Number of n X 2 0..1 arrays with each 1 horizontally or vertically adjacent to 0, 1 or 3 1s.

4, 11, 35, 106, 327, 1003, 3082, 9465, 29073, 89296, 274273, 842425, 2587500, 7947475, 24410579, 74976810, 230290407, 707334323, 2172569202, 6673021201, 20496107521, 62953557440, 193361124321, 593906459281, 1824176827764

Offset

1,1

Comments

Column 2 of A295253.

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) + a(n-3) - a(n-5).

Empirical g.f.: x*(4 + 3*x + x^2 - x^3 - x^4) / ((1 + x)*(1 - 3*x - x^3 + x^4)). - Colin Barker, Feb 26 2018

Example

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

Crossrefs

Cf. A295253.

Sequence in context: A119716 A000626 A036364 * A052550 A197626 A349185

Adjacent sequences: A295244 A295245 A295246 * A295248 A295249 A295250

Keyword

nonn

Author

R. H. Hardin, Nov 18 2017

Status

approved