A297219 Number of n X 3 0..1 arrays with every 1 horizontally or antidiagonally adjacent to 1 neighboring 1s.

3, 8, 24, 68, 196, 564, 1620, 4660, 13396, 38516, 110740, 318388, 915412, 2631924, 7567124, 21756468, 62552660, 179847028, 517083540, 1486682292, 4274404564, 12289467892, 35333815316, 101589305140, 292082437972, 839774919796

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) + 4*a(n-3).

Empirical g.f.: x*(3 + 5*x + 4*x^2) / (1 - x - 4*x^2 - 4*x^3). - Colin Barker, Feb 26 2019

Example

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

Crossrefs

Column 3 of A297224.

Sequence in context: A176904 A056332 A091588 * A018046 A095125 A078055

Adjacent sequences: A297216 A297217 A297218 * A297220 A297221 A297222

Keyword

nonn

Author

R. H. Hardin, Dec 27 2017

Status

approved