A221764 Number of n X 3 arrays of occupancy after each element moves to some horizontal or vertical neighbor, without 2-loops or left turns.

0, 3, 16, 92, 536, 3125, 18216, 106174, 618832, 3606823, 21022112, 122525856, 714133032, 4162272345, 24259501048, 141394733954, 824108902688, 4803258682187, 27995443190448, 163169400460516, 951020959572664

Offset

1,2

Comments

Column 3 of A221768.

Links

R. H. Hardin, Table of n, a(n) for n = 1..71

Formula

Empirical: a(n) = 8*a(n-1) - 14*a(n-2) + 8*a(n-3) - a(n-4).

Conjectures from Colin Barker, Aug 10 2018: (Start)

G.f.: x^2*(3 - 8*x + 6*x^2) / ((1 - x)^2*(1 - 6*x + x^2)).

a(n) = (40+sqrt(2)*((81-56*sqrt(2))*(3+2*sqrt(2))^n - (3-2*sqrt(2))^n*(81+56*sqrt(2))) - 8*(1+n)) / 32.

(End)

Example

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

Crossrefs

Cf. A221768.

Sequence in context: A067679 A099952 A305852 * A371742 A213229 A323968

Adjacent sequences: A221761 A221762 A221763 * A221765 A221766 A221767

Keyword

nonn

Author

R. H. Hardin, Jan 25 2013

Status

approved