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

Author

R. H. Hardin, Feb 21 2016

Keywords

• nonn

Examples

			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
		

Links

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

Crossrefs

Column 2 of A269276.

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)