A228791 Number of n X 3 binary arrays with top left element equal to 1 and no two ones adjacent horizontally or nw-se.

2, 8, 36, 156, 672, 2892, 12444, 53544, 230388, 991308, 4265376, 18352956, 78968652, 339784392, 1462016004, 6290726844, 27067586208, 116465750508, 501125993916, 2156232718056, 9277785608532, 39920229888492, 171767792616864

Offset

1,1

Links

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

Formula

Empirical: a(n) = 5*a(n-1) - 3*a(n-2) for n>3.

Conjectures from Colin Barker, Sep 13 2018: (Start)

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

a(n) = -(2^(1-n)*((-11+sqrt(13))*(5+sqrt(13))^n + (5-sqrt(13))^n*(11+sqrt(13)))) / (9*sqrt(13)) for n>1.

(End)

Example

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

Crossrefs

Column 3 of A228796.

Sequence in context: A283847 A123290 A321110 * A088675 A228197 A326244

Adjacent sequences: A228788 A228789 A228790 * A228792 A228793 A228794

Keyword

nonn

Author

R. H. Hardin, Sep 04 2013

Status

approved