A268899 Number of n X 3 0..2 arrays with some element plus some horizontally or antidiagonally adjacent neighbor totalling two exactly once.

12, 168, 1584, 12960, 98496, 715392, 5038848, 34712064, 235146240, 1572120576, 10400182272, 68205846528, 444063596544, 2873352683520, 18493942726656, 118486616113152, 756057455198208, 4807171282305024, 30467987000524800

Offset

1,1

Links

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

Formula

Empirical: a(n) = 12*a(n-1) - 36*a(n-2).

Conjectures from Colin Barker, Jan 16 2019: (Start)

G.f.: 12*x*(1 + 2*x) / (1 - 6*x)^2.

a(n) = 2^(n+1) * 3^(n-1) * (4*n-1).

(End)

Example

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

Crossrefs

Column 3 of A268904.

Sequence in context: A324414 A099745 A360352 * A366710 A182606 A079679

Adjacent sequences: A268896 A268897 A268898 * A268900 A268901 A268902

Keyword

nonn

Author

R. H. Hardin, Feb 15 2016

Status

approved