A268966 Number of n X 3 0..2 arrays with some element plus some horizontally or antidiagonally adjacent neighbor totalling two not more than once.

24, 240, 2016, 15552, 114048, 808704, 5598720, 38071296, 255301632, 1693052928, 11125776384, 72559411200, 470184984576, 3030081011712, 19434312695808, 124128835928064, 789910774087680, 5010291195641856, 31686706480545792

Offset: 1

Author

R. H. Hardin, Feb 16 2016

Keywords

• nonn

Examples

			Some solutions for n=4:
..1..0..0. .0..1..2. .0..2..2. .2..2..2. .0..0..0. .1..2..1. .1..2..2
..1..1..2. .2..2..2. .1..2..2. .1..2..2. .0..1..0. .2..1..0. .0..1..0
..2..2..2. .1..2..2. .2..2..2. .1..0..1. .2..0..1. .0..0..1. .0..0..1
..2..2..2. .2..1..0. .2..2..2. .1..0..0. .1..0..1. .1..2..1. .0..0..0
		

Links

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

Crossrefs

Column 3 of A268971.

Formula

Empirical: a(n) = 12*a(n-1) - 36*a(n-2).

Conjectures from Colin Barker, Jan 17 2019: (Start)

G.f.: 24*x*(1 - 2*x) / (1 - 6*x)^2.

a(n) = 2^(n+2) * 3^(n-1) * (2*n+1).

(End)