A208309 Number of n X 3 0..1 arrays with new values 0..1 introduced in row major order and no element equal to more than one of its immediate leftward or upward neighbors.

4, 18, 78, 336, 1446, 6222, 26772, 115194, 495654, 2132688, 9176478, 39484326, 169892196, 731008002, 3145363422, 13533793104, 58232875254, 250562996958, 1078116359028, 4638892804266, 19960114944246, 85883896308432

Offset

1,1

Comments

Column 3 of A208314.

Links

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

Formula

Empirical: a(n) = 5*a(n-1) - 3*a(n-2).

Conjectures from Colin Barker, Jun 30 2018: (Start)

G.f.: 2*x*(2 - x) / (1 - 5*x + 3*x^2).

a(n) = (2^(-n)*((5-sqrt(13))^n*(-7+sqrt(13)) + (5+sqrt(13))^n*(7+sqrt(13)))) / (3*sqrt(13)).

(End)

Example

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

Crossrefs

Cf. A208314.

Sequence in context: A219436 A219137 A240342 * A112619 A196810 A177755

Adjacent sequences: A208306 A208307 A208308 * A208310 A208311 A208312

Keyword

nonn

Author

R. H. Hardin, Feb 25 2012

Status

approved