A208689 Number of 3 X n 0..1 arrays avoiding 0 0 0 and 0 0 1 horizontally and 0 1 1 and 1 0 1 vertically.

6, 36, 78, 282, 768, 2430, 7086, 21588, 64230, 193554, 579264, 1740054, 5216502, 15655428, 46956702, 140885610, 422631744, 1267935822, 3803741790, 11411331636, 34233822966, 102701747106, 308104791168, 924315101862, 2772944127078

Offset

1,1

Comments

Row 3 of A208688.

Links

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

Formula

Empirical: a(n) = 2*a(n-1) + 4*a(n-2) - 3*a(n-3).

Conjectures from Colin Barker, Mar 07 2018: (Start)

G.f.: 6*x*(1 + 4*x - 3*x^2) / ((1 - 3*x)*(1 + x - x^2)).

a(n) = 2^(-n)*(5*6^(2+n) + (75-27*sqrt(5))*(-1+sqrt(5))^n + 3*(-1-sqrt(5))^n*(25+9*sqrt(5))) / 55.

(End)

Example

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

Crossrefs

Cf. A208688.

Sequence in context: A207730 A208103 A207724 * A207483 A207264 A207270

Adjacent sequences: A208686 A208687 A208688 * A208690 A208691 A208692

Keyword

nonn

Author

R. H. Hardin, Mar 01 2012

Status

approved