A205329 Number of (n+1) X 3 0..2 arrays with the number of equal 2 X 2 subblock diagonal pairs and equal antidiagonal pairs differing from each horizontal or vertical neighbor, and new values 0..2 introduced in row major order.

72, 594, 4860, 39852, 326592, 2676888, 21939984, 179823888, 1473863040, 12080008224, 99009584064, 811497652416, 6651158427648, 54513908309376, 446804301553920, 3662076158892288, 30014934381324288, 246006977148006912

Offset

1,1

Comments

Column 2 of A205335.

Links

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

Formula

Empirical: a(n) = 6*a(n-1) + 18*a(n-2).

Conjectures from Colin Barker, Jun 11 2018: (Start)

G.f.: 18*x*(4 + 9*x) / (1 - 6*x - 18*x^2). - Colin Barker, Jun 11 2018

a(n) = ((9-5*sqrt(3))*(3-3*sqrt(3))^n + (3*(1+sqrt(3)))^n*(9+5*sqrt(3))) / 2.

(End)

Example

Some solutions for n=4:
..0..0..0....0..1..1....0..0..0....0..0..1....0..1..1....0..0..0....0..1..1
..0..1..2....1..1..1....1..1..0....2..1..2....2..2..1....0..0..1....0..2..1
..0..1..1....0..2..1....0..1..0....1..0..0....1..2..0....2..0..1....2..2..0
..0..0..2....1..0..0....2..2..1....2..2..0....2..1..2....2..0..0....0..0..1
..2..2..1....1..2..0....0..2..0....1..2..1....1..1..2....2..2..2....1..0..1

Crossrefs

Cf. A205335.

Sequence in context: A204484 A235178 A085718 * A380433 A077120 A200451

Adjacent sequences: A205326 A205327 A205328 * A205330 A205331 A205332

Keyword

nonn

Author

R. H. Hardin, Jan 26 2012

Status

approved