A231280 Number of n X 3 0..3 arrays x(i,j) with each element horizontally or antidiagonally next to at least one element with value (x(i,j)+1) mod 4, and upper left element zero.

0, 2, 8, 66, 400, 2722, 17688, 117026, 768800, 5064642, 33328168, 219411586, 1444225200, 9506897762, 62579419448, 411934939746, 2711589889600, 17849253534082, 117494042259528, 773413479117506, 5091052634882000

Offset

1,2

Links

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

Formula

Empirical: a(n) = 4*a(n-1) + 17*a(n-2).

Conjectures from Colin Barker, Sep 28 2018: (Start)

G.f.: 2*x^2 / (1 - 4*x - 17*x^2).

a(n) = ((2-sqrt(21))^n*(2+sqrt(21)) + (-2+sqrt(21))*(2+sqrt(21))^n)/(17*sqrt(21)).

(End)

Example

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

Crossrefs

Column 3 of A231285.

Sequence in context: A011836 A309251 A100623 * A086594 A132219 A226730

Adjacent sequences: A231277 A231278 A231279 * A231281 A231282 A231283

Keyword

nonn

Author

R. H. Hardin, Nov 06 2013

Status

approved