A207846 Number of 3 X n 0..1 arrays avoiding 0 0 0 and 0 0 1 horizontally and 0 0 0 and 1 1 1 vertically.

6, 36, 72, 180, 432, 1044, 2520, 6084, 14688, 35460, 85608, 206676, 498960, 1204596, 2908152, 7020900, 16949952, 40920804, 98791560, 238503924, 575799408, 1390102740, 3356004888, 8102112516, 19560229920, 47222572356, 114005374632

Offset

1,1

Comments

Row 3 of A207845.

Links

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

Formula

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

Conjectures from Colin Barker, Jun 25 2018: (Start)

G.f.: 6*x*(1 + 4*x - x^2) / (1 - 2*x - x^2).

a(n) = 9*(sqrt(2)*((1-sqrt(2))^n*(1+sqrt(2)) + (-1+sqrt(2))*(1+sqrt(2))^n)) for n>2.

(End)

Example

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

Crossrefs

Cf. A207845.

Sequence in context: A171506 A207683 A207509 * A207840 A043116 A044108

Adjacent sequences: A207843 A207844 A207845 * A207847 A207848 A207849

Keyword

nonn

Author

R. H. Hardin, Feb 21 2012

Status

approved