A297426 Number of n X 3 0..1 arrays with every 1 horizontally, diagonally or antidiagonally adjacent to 2 neighboring 1s.

1, 7, 14, 22, 68, 163, 320, 782, 1889, 4109, 9474, 22365, 50630, 115709, 268817, 616265, 1410697, 3253586, 7480630, 17161490, 39477589, 90787636, 208528864, 479338273, 1102090695, 2532624372, 5820869563, 13380882748, 30754476169

Offset

1,2

Links

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

Formula

Empirical: a(n) = a(n-1) + 7*a(n-3) + a(n-5) - 4*a(n-6).

Empirical g.f.: x*(1 + 6*x + 7*x^2 + x^3 - 3*x^4 - 4*x^5) / (1 - x - 7*x^3 - x^5 + 4*x^6). - Colin Barker, Feb 28 2019

Example

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

Crossrefs

Column 3 of A297431.

Sequence in context: A190367 A246172 A366112 * A036556 A013644 A178894

Adjacent sequences: A297423 A297424 A297425 * A297427 A297428 A297429

Keyword

nonn

Author

R. H. Hardin, Dec 30 2017

Status

approved