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

1,1

Comments

Column 2 of A268628.

Links

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

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)

Example

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

Crossrefs

Cf. A268628.

Sequence in context: A268262 A293101 A084899 * A289364 A074443 A221425

Adjacent sequences: A268619 A268620 A268621 * A268623 A268624 A268625

Keyword

nonn

Author

R. H. Hardin, Feb 09 2016

Status

approved