A268898 Number of n X 2 0..2 arrays with some element plus some horizontally or antidiagonally adjacent neighbor totalling two exactly once.

3, 36, 240, 1344, 6912, 33792, 159744, 737280, 3342336, 14942208, 66060288, 289406976, 1258291200, 5435817984, 23353884672, 99857989632, 425201762304, 1803886264320, 7627861917696, 32160715112448, 135239930216448

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 16 2019: (Start)

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

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

(End)

Example

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

Crossrefs

Column 2 of A268904.

Sequence in context: A303152 A188891 A073992 * A127960 A005446 A056307

Adjacent sequences: A268895 A268896 A268897 * A268899 A268900 A268901

Keyword

nonn

Author

R. H. Hardin, Feb 15 2016

Status

approved