A207656 Number of n X 3 0..1 arrays avoiding 0 0 0 and 1 1 1 horizontally and 0 0 1 and 1 0 0 vertically.

6, 36, 84, 198, 474, 1140, 2748, 6630, 16002, 38628, 93252, 225126, 543498, 1312116, 3167724, 7647558, 18462834, 44573220, 107609268, 259791750, 627192762, 1514177268, 3655547292, 8825271846, 21306090978, 51437453796, 124180998564

Offset

1,1

Comments

Column 3 of A207661.

Links

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

Formula

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

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

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

a(n) = (3/2)*(2 + (1-2*sqrt(2))*(1-sqrt(2))^n + (1+sqrt(2))^n*(1+2*sqrt(2))) for n>1.

(End)

Example

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

Crossrefs

Cf. A207661.

Sequence in context: A207347 A207769 A207896 * A207341 A152746 A207363

Adjacent sequences: A207653 A207654 A207655 * A207657 A207658 A207659

Keyword

nonn

Author

R. H. Hardin, Feb 19 2012

Status

approved