A268633 Number of n X 2 0..2 arrays with some element plus some horizontally or vertically adjacent neighbor totalling two exactly once.

3, 24, 120, 504, 1944, 7128, 25272, 87480, 297432, 997272, 3306744, 10865016, 35429400, 114791256, 369882936, 1186176312, 3788111448, 12053081880, 38225488248, 120875192568, 381221761176, 1199453833944, 3765727153080

Offset: 1

Author

R. H. Hardin, Feb 09 2016

Keywords

• nonn

Comments

Column 2 of A268639.

Examples

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

Links

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

Crossrefs

Cf. A268639.

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*(1 + x)^2 / (1 - 3*x)^2.

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

(End)