A207106 Number of n X 3 0..1 arrays avoiding 0 0 0 and 0 1 1 horizontally and 0 0 1 and 1 1 0 vertically.

6, 36, 98, 200, 350, 556, 826, 1168, 1590, 2100, 2706, 3416, 4238, 5180, 6250, 7456, 8806, 10308, 11970, 13800, 15806, 17996, 20378, 22960, 25750, 28756, 31986, 35448, 39150, 43100, 47306, 51776, 56518, 61540, 66850, 72456, 78366, 84588, 91130, 98000

Offset

1,1

Comments

Column 3 of A207111.

Links

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

Formula

Empirical: a(n) = (4/3)*n^3 + 8*n^2 - (10/3)*n.

Conjectures from Colin Barker, Feb 20 2018: (Start)

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

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>4.

(End)

Example

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

Crossrefs

Cf. A207111.

Sequence in context: A207559 A207414 A192278 * A207306 A207112 A207392

Adjacent sequences: A207103 A207104 A207105 * A207107 A207108 A207109

Keyword

nonn

Author

R. H. Hardin, Feb 15 2012

Status

approved