A230179 Number of n X 3 0..2 arrays x(i,j) with each element horizontally or antidiagonally next to at least one element with value 2-x(i,j).

3, 27, 231, 1971, 16815, 143451, 1223799, 10440387, 89068287, 759853035, 6482404167, 55302225363, 471790411599, 4024904802939, 34336981580055, 292933215008739, 2499051008758431, 21319726218790923, 181881331934084583

Offset

1,1

Links

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

Formula

Empirical: a(n) = 9*a(n-1) - 4*a(n-2).

Conjectures from Colin Barker, Sep 21 2018: (Start)

G.f.: 3*x / (1 - 9*x + 4*x^2).

a(n) = ((-3)*(2^(-n)*((9-sqrt(65))^n - (9+sqrt(65))^n))) / sqrt(65). (End)

Conjectured e.g.f.: 6*exp(9*x/2)*sinh(sqrt(65)*x/2)/sqrt(65). - Stefano Spezia, Feb 23 2025

Example

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

Crossrefs

Column 3 of A230184.

Sequence in context: A087426 A145608 A083713 * A221769 A065100 A035088

Adjacent sequences: A230176 A230177 A230178 * A230180 A230181 A230182

Keyword

nonn

Author

R. H. Hardin, Oct 11 2013

Status

approved