A184688 1/3 the number of n X 3 0..2 arrays with no element equal both to the element above and to the element to its left.

9, 192, 4080, 86688, 1841856, 39133824, 831474432, 17666296320, 375354928128, 7975147677696, 169447570059264, 3600244178460672, 76494210805186560, 1625268730858733568, 34532004706009153536, 733699803838461640704

Offset

1,1

Comments

Column 3 of A184694.

Links

R. H. Hardin, Table of n, a(n) for n = 1..200

Formula

Empirical: a(n) = 22*a(n-1) - 16*a(n-2).

Conjectures from Colin Barker, Apr 14 2018: (Start)

G.f.: 3*x*(3 - 2*x) / (1 - 22*x + 16*x^2).

a(n) = ((105-13*sqrt(105))*(11-sqrt(105))^n + (11+sqrt(105))^n*(105+13*sqrt(105))) / 560.

(End)

Example

Some solutions for 5 X 3 with a(1,1)=0:
..0..0..0....0..0..0....0..0..0....0..0..0....0..0..0....0..0..0....0..0..0
..1..2..1....0..2..0....1..2..2....2..1..0....0..2..0....2..2..0....1..2..1
..1..0..2....2..1..2....1..0..0....0..0..2....0..2..0....2..1..2....1..0..2
..1..1..1....1..0..1....1..2..0....2..1..0....1..2..1....2..0..0....1..2..1
..0..0..2....0..2..0....0..1..1....2..2..1....2..0..1....1..1..1....1..1..2

Crossrefs

Cf. A184694.

Sequence in context: A307387 A332119 A261826 * A189178 A297517 A116877

Adjacent sequences: A184685 A184686 A184687 * A184689 A184690 A184691

Keyword

nonn

Author

R. H. Hardin, Jan 20 2011

Status

approved