A183345 Number of n X 3 binary arrays with each 1 adjacent to exactly one 0 vertically and one 0 horizontally.

1, 9, 16, 25, 64, 144, 289, 625, 1369, 2916, 6241, 13456, 28900, 62001, 133225, 286225, 614656, 1320201, 2835856, 6091024, 13082689, 28100601, 60357361, 129640996, 278455969, 598095936, 1284648964, 2759295841, 5926690225, 12729931929

Offset

1,2

Comments

Column 3 of A183352.

Links

R. H. Hardin, Table of n, a(n) for n = 1..200

Formula

Empirical: a(n) = a(n-1) + a(n-2) + 3*a(n-3) + a(n-4) - a(n-5) - a(n-6).

Empirical g.f.: x*(1 + 8*x + 6*x^2 - 3*x^3 - 5*x^4 - x^5) / ((1 + x^2 - x^3)*(1 - x - 2*x^2 - x^3)). - Colin Barker, Mar 28 2018

Example

Some solutions for 5 X 3:
..0..0..0....1..0..1....1..0..0....0..0..0....0..0..1....0..0..0....0..0..1
..1..0..1....0..0..0....0..0..1....0..0..1....1..0..0....1..0..0....1..0..0
..1..0..1....0..0..0....0..0..1....1..0..1....1..0..0....1..0..0....1..0..1
..0..0..0....0..0..0....0..0..0....1..0..0....0..0..0....0..0..0....0..0..1
..1..0..0....1..0..1....0..0..1....0..0..0....0..0..0....1..0..0....1..0..0

Crossrefs

Cf. A183352.

Sequence in context: A075393 A336449 A161183 * A303873 A257496 A351435

Adjacent sequences: A183342 A183343 A183344 * A183346 A183347 A183348

Keyword

nonn

Author

R. H. Hardin, Jan 04 2011

Status

approved