A183325 Number of n X 4 binary arrays with each 1 adjacent to exactly two other 1s.

1, 4, 10, 27, 72, 179, 447, 1139, 2912, 7434, 18949, 48256, 122905, 313153, 797993, 2033404, 5181138, 13201355, 33636776, 85706587, 218381247, 556436971, 1417803304, 3612566114, 9204828661, 23453934912, 59760710321, 152270499073

Offset

1,2

Comments

Column 4 of A183328.

Links

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

Formula

Empirical: a(n) = 3*a(n-1) - 2*a(n-2) + 2*a(n-3) + 2*a(n-5) - 5*a(n-7) - 3*a(n-8).

Empirical g.f.: x*(1 + x)^2*(1 - x + x^2 + 2*x^3 - 2*x^4 - 3*x^5) / (1 - 3*x + 2*x^2 - 2*x^3 - 2*x^5 + 5*x^7 + 3*x^8). - Colin Barker, Mar 27 2018

Example

Some solutions for 8 X 4:
..1..1..1..1....1..1..1..1....0..0..0..0....1..1..1..0....0..1..1..0
..1..0..0..1....1..0..0..1....0..0..0..0....1..0..1..1....0..1..1..0
..1..1..0..1....1..0..1..1....0..0..1..1....1..0..0..1....0..0..0..0
..0..1..0..1....1..0..1..0....0..0..1..1....1..0..0..1....0..1..1..1
..0..1..0..1....1..0..1..1....0..0..0..0....1..0..0..1....0..1..0..1
..0..1..1..1....1..0..0..1....0..0..1..1....1..0..0..1....1..1..0..1
..0..0..0..0....1..0..0..1....0..0..1..1....1..1..1..1....1..0..0..1
..0..0..0..0....1..1..1..1....0..0..0..0....0..0..0..0....1..1..1..1

Crossrefs

Cf. A183328.

Sequence in context: A122744 A192879 A077923 * A052982 A108672 A000495

Adjacent sequences: A183322 A183323 A183324 * A183326 A183327 A183328

Keyword

nonn

Author

R. H. Hardin, Jan 03 2011

Status

approved