A221082 Number of n X 3 arrays of occupancy after each element moves to some horizontal or antidiagonal neighbor.

2, 24, 270, 3024, 33858, 379080, 4244238, 47519136, 532031490, 5956705656, 66692184462, 746695862640, 8360120691522, 93601185534504, 1047973140190350, 11733267012473664, 131367445887970818, 1470809947543386840

Offset

1,1

Comments

Column 3 of A221087.

Links

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

Formula

Empirical: a(n) = 12*a(n-1) - 9*a(n-2).

Conjectures from Colin Barker, Aug 03 2018: (Start)

G.f.: 2*x / (1 - 12*x + 9*x^2).

a(n) = ((-(6-3*sqrt(3))^n + (3*(2+sqrt(3)))^n))/(3*sqrt(3)).

(End)

Example

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

Crossrefs

Cf. A221087.

Sequence in context: A173228 A061190 A300399 * A002006 A230129 A355951

Adjacent sequences: A221079 A221080 A221081 * A221083 A221084 A221085

Keyword

nonn

Author

R. H. Hardin, Jan 01 2013

Status

approved