A208403 Number of n X 3 0..3 arrays with new values 0..3 introduced in row major order and no element equal to more than two of its immediate leftward or upward or right-upward antidiagonal neighbors.

5, 182, 10682, 667478, 42012698, 2646531062, 166729574522, 10503950018198, 661748758909658, 41690171165650742, 2626480778916392762, 165468289040095516118, 10424502209304556920218, 656743639184636861807222

Offset

1,1

Comments

Column 3 of A208408.

Links

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

Formula

Empirical: a(n) = 70*a(n-1) - 441*a(n-2) for n>3.

Conjectures from Colin Barker, Jul 02 2018: (Start)

G.f.: x*(5 - 168*x + 147*x^2) / ((1 - 7*x)*(1 - 63*x)).

a(n) = (2/27)*7^(-1+n) * (27+4*9^n) for n>1.

(End)

Example

Some solutions for n=4:
..0..0..0....0..0..0....0..0..0....0..0..0....0..1..1....0..0..0....0..0..0
..1..1..0....0..1..0....0..1..1....0..1..0....1..0..2....0..1..0....0..1..1
..0..1..0....1..2..1....1..0..0....0..1..1....3..0..1....2..1..1....2..0..2
..0..1..0....0..1..3....0..1..1....2..0..2....1..1..1....2..1..1....2..1..0

Crossrefs

Cf. A208408.

Sequence in context: A345338 A256286 A304277 * A280797 A094081 A189645

Adjacent sequences: A208400 A208401 A208402 * A208404 A208405 A208406

Keyword

nonn

Author

R. H. Hardin, Feb 26 2012

Status

approved