A183336 Number of n X 4 binary arrays with each 1 adjacent to exactly one 1 vertically and one 1 horizontally.

1, 4, 7, 12, 26, 51, 97, 193, 380, 741, 1456, 2860, 5605, 10997, 21581, 42332, 83047, 162936, 319650, 627099, 1230289, 2413641, 4735192, 9289761, 18225136, 35754992, 70146009, 137616081, 269982313, 529665276, 1039124759, 2038608652, 3999447882

Offset

1,2

Comments

Equivalent to all 1s connected only in 2 X 2 blocks.

Column 4 of A183342.

Links

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

Formula

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

Empirical g.f.: x*(1 + x)^2*(1 + x - x^2) / (1 - x - x^2 - 2*x^3 + x^5). - Colin Barker, Mar 27 2018

Example

Some solutions for 5 X 4:
..0..0..0..0....0..0..0..0....1..1..0..0....0..0..0..0....0..1..1..0
..0..0..0..0....0..0..0..0....1..1..0..0....0..1..1..0....0..1..1..0
..0..0..1..1....0..0..0..0....0..0..0..0....0..1..1..0....0..0..0..0
..0..0..1..1....0..0..1..1....0..1..1..0....0..0..0..0....1..1..0..0
..0..0..0..0....0..0..1..1....0..1..1..0....0..0..0..0....1..1..0..0

Crossrefs

Cf. A183342.

Sequence in context: A299900 A215329 A208724 * A102953 A111157 A255340

Adjacent sequences: A183333 A183334 A183335 * A183337 A183338 A183339

Keyword

nonn

Author

R. H. Hardin, Jan 04 2011

Status

approved