A228501 Number of n X 3 binary arrays with top left value 1 and no two ones adjacent horizontally, vertically, diagonally or antidiagonally.

2, 3, 12, 29, 88, 239, 684, 1909, 5392, 15143, 42644, 119933, 337512, 949535, 2671740, 7517061, 21150272, 59508247, 167433188, 471090573, 1325464216, 3729333775, 10492879052, 29522830997, 83065631600, 233713998087, 657579228980

Offset

1,1

Links

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

Formula

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

Empirical g.f.: x*(2 - x) / (1 - 2*x - 3*x^2 + 2*x^3). - Colin Barker, Sep 11 2018

Example

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

Crossrefs

Column 3 of A228506.

Sequence in context: A215602 A325628 A359221 * A089414 A260631 A374333

Adjacent sequences: A228498 A228499 A228500 * A228502 A228503 A228504

Keyword

nonn

Author

R. H. Hardin, Aug 23 2013

Status

approved