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

Author

R. H. Hardin, Jan 03 2011

Keywords

• nonn

Comments

Column 4 of A183328.

Examples

			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
		

Links

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

Crossrefs

Cf. A183328.

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