A268622 Number of n X 2 0..2 arrays with some element plus some horizontally or vertically adjacent neighbor totalling two no more than once.

9, 42, 174, 666, 2430, 8586, 29646, 100602, 336798, 1115370, 3661038, 11927898, 38618046, 124357194, 398580750, 1272269754, 4046391774, 12827922858, 40550011182, 127848761370, 402142467582, 1262215953162, 3954013510734

Offset: 1

Author

R. H. Hardin, Feb 09 2016

Keywords

• nonn

Comments

Column 2 of A268628.

Examples

			Some solutions for n=8:
..1..0. .0..1. .2..1. .1..2. .2..2. .0..1. .0..0. .0..0. .1..0. .1..0
..2..2. .1..0. .1..0. .2..1. .2..2. .1..0. .0..1. .0..1. .2..2. .0..0
..2..1. .2..1. .2..1. .1..2. .1..2. .2..1. .0..0. .0..0. .1..2. .1..2
..2..2. .2..2. .1..0. .2..2. .2..2. .2..2. .1..0. .0..0. .0..1. .2..1
..2..1. .1..2. .2..1. .2..2. .2..1. .2..1. .0..1. .0..0. .1..0. .1..2
..2..2. .2..2. .1..2. .2..1. .2..2. .2..0. .0..0. .1..0. .2..1. .2..2
..1..2. .1..2. .1..2. .1..2. .0..1. .1..0. .1..0. .2..2. .2..2. .1..2
..2..2. .0..0. .0..1. .2..1. .1..2. .0..0. .0..1. .1..2. .1..2. .0..1
		

Links

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

Crossrefs

Cf. A268628.

Formula

Empirical: a(n) = 6*a(n-1) - 9*a(n-2) for n>3.

Conjectures from Colin Barker, Mar 21 2018: (Start)

G.f.: 3*x*(3 - x)*(1 - x) / (1 - 3*x)^2.

a(n) = 2*3^(n-2)*(5+8*n) for n>1.

(End)