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

Author

R. H. Hardin, Dec 27 2017

Keywords

• nonn

Examples

			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
		

Links

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

Crossrefs

Column 3 of A297224.

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