A297390 Number of n X 3 0..1 arrays with every 1 horizontally, diagonally or antidiagonally adjacent to 1 neighboring 1.

3, 9, 19, 57, 139, 369, 963, 2489, 6523, 16929, 44147, 114953, 299307, 779697, 2030243, 5287833, 13770971, 35864001, 93402579, 243249193, 633503627, 1649849553, 4296752131, 11190160825, 29142853947, 75897603297, 197662332211

Offset

1,1

Links

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

Formula

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

Empirical g.f.: x*(1 + 2*x)*(3 - 2*x^2) / (1 - x - 4*x^2 - 2*x^3 + 4*x^4). - Colin Barker, Feb 28 2019

Example

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

Crossrefs

Column 3 of A297395.

Sequence in context: A077442 A147455 A146429 * A018316 A146605 A147070

Adjacent sequences: A297387 A297388 A297389 * A297391 A297392 A297393

Keyword

nonn

Author

R. H. Hardin, Dec 29 2017

Status

approved