A207590 Number of 3 X n 0..1 arrays avoiding 0 0 0 and 0 0 1 horizontally and 0 0 1 and 1 1 1 vertically.

6, 36, 60, 144, 324, 756, 1728, 3996, 9180, 21168, 48708, 112212, 258336, 594972, 1369980, 3154896, 7264836, 16729524, 38524032, 88712604, 204284700, 470422512, 1083276612, 2494544148, 5744373984, 13228006428, 30461128380, 70145147664

Offset

1,1

Comments

Row 3 of A207589.

Links

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

Formula

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

Conjectures from Colin Barker, Mar 05 2018: (Start)

G.f.: 6*x*(1 + 5*x + x^2 - 4*x^3) / (1 - x - 3*x^2).

a(n) = (2^(1-n)*((1-sqrt(13))^n*(-35+13*sqrt(13)) + (1+sqrt(13))^n*(35+13*sqrt(13)))) / (9*sqrt(13)) for n>2.

(End)

Example

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

Crossrefs

Cf. A207589.

Sequence in context: A207694 A208496 A207584 * A226119 A036148 A134639

Adjacent sequences: A207587 A207588 A207589 * A207591 A207592 A207593

Keyword

nonn

Author

R. H. Hardin, Feb 19 2012

Status

approved