A269270 Number of n X 2 0..3 arrays with some element plus some horizontally or antidiagonally adjacent neighbor totalling three exactly once.

4, 108, 1620, 20412, 236196, 2598156, 27634932, 286978140, 2927177028, 29443957164, 292889889684, 2887057484028, 28242953648100, 274521509459532, 2653707924775476, 25530500379736476, 244598664928443012

Offset

1,1

Links

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

Formula

Empirical: a(n) = 18*a(n-1) - 81*a(n-2).

Conjectures from Colin Barker, Jan 20 2019: (Start)

G.f.: 4*x*(1 + 9*x) / (1 - 9*x)^2.

a(n) = 9^(n-1) * (8*n-4).

(End)

Example

Some solutions for n=4:
  2 3   2 2   3 3   2 2   3 0   2 2   0 0   1 1   1 3   3 1
  2 0   2 2   3 1   0 0   0 0   3 1   2 1   0 2   1 1   1 1
  3 1   0 0   0 0   1 2   1 0   0 3   0 1   0 2   2 0   3 0
  1 0   3 3   3 2   0 0   1 3   1 0   0 0   1 0   1 1   2 2

Crossrefs

Column 2 of A269276.

Sequence in context: A220531 A322085 A128865 * A302113 A357510 A336028

Adjacent sequences: A269267 A269268 A269269 * A269271 A269272 A269273

Keyword

nonn

Author

R. H. Hardin, Feb 21 2016

Status

approved