A268965 Number of n X 2 0..2 arrays with some element plus some horizontally or antidiagonally adjacent neighbor totalling two not more than once.

9, 60, 336, 1728, 8448, 39936, 184320, 835584, 3735552, 16515072, 72351744, 314572800, 1358954496, 5838471168, 24964497408, 106300440576, 450971566080, 1906965479424, 8040178778112, 33809982554112, 141836999983104

Offset

1,1

Links

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

Formula

Empirical: a(n) = 8*a(n-1) - 16*a(n-2).

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

G.f.: 3*x*(3 - 4*x) / (1 - 4*x)^2.

a(n) = 4^(n-1) * (6*n+3).

(End)

Example

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

Crossrefs

Column 2 of A268971.

Sequence in context: A268972 A288962 A074431 * A081904 A085373 A241976

Adjacent sequences: A268962 A268963 A268964 * A268966 A268967 A268968

Keyword

nonn

Author

R. H. Hardin, Feb 16 2016

Status

approved