A296399 Number of n X 2 0..1 arrays with each 1 horizontally, vertically or antidiagonally adjacent to 2 or 3 neighboring 1s.

1, 4, 8, 17, 46, 114, 289, 757, 1964, 5118, 13391, 35008, 91589, 239740, 627506, 1642656, 4300361, 11258087, 29473546, 77162161, 202011991, 528872756, 1384604934, 3624939359, 9490209947, 24845686106, 65046840605, 170294825972

Offset

1,2

Links

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

Formula

Empirical: a(n) = 3*a(n-1) - a(n-2) + 2*a(n-3) - 6*a(n-4) + 3*a(n-5) - 2*a(n-6) - a(n-7) - 2*a(n-8) + a(n-9).

Empirical g.f.: x*(1 + x - 3*x^2 - 5*x^3 + x^4 - 2*x^5 - 3*x^6 - x^7 + x^8) / ((1 - 3*x + x^2)*(1 - 2*x^3 - x^5 - x^6 - x^7)). - Colin Barker, Feb 23 2019

Example

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

Crossrefs

Column 2 of A296405.

Sequence in context: A084814 A098125 A335274 * A119471 A145779 A252790

Adjacent sequences: A296396 A296397 A296398 * A296400 A296401 A296402

Keyword

nonn

Author

R. H. Hardin, Dec 11 2017

Status

approved