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

1,1

Comments

Column 2 of A268639.

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

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

(End)

Example

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

Crossrefs

Cf. A268639.

Sequence in context: A127520 A175115 A301812 * A324065 A151883 A009134

Adjacent sequences: A268630 A268631 A268632 * A268634 A268635 A268636

Keyword

nonn

Author

R. H. Hardin, Feb 09 2016

Status

approved