A187721 Number of (n+1) X 2 binary arrays with no 2 X 2 subblock commuting with any of its horizontal and vertical 2 X 2 subblock neighbors.

16, 43, 130, 391, 1173, 3520, 10558, 31672, 95004, 284980, 854840, 2564222, 7691771, 23072626, 69209824, 207605302, 622743418, 1868012800, 5603386130, 16808201791, 50418736274, 151238603566, 453663001075, 1360830592810, 4082016602475

Offset

1,1

Comments

Column 1 of A187729.

Links

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

Formula

Empirical: a(n) = 5*a(n-2) + 10*a(n-3) + 8*a(n-4) - 2*a(n-5) - 10*a(n-6) - 7*a(n-7) + 3*a(n-9) + a(n-10) for n>11.

Empirical g.f.: x*(16 + 43*x + 50*x^2 + 16*x^3 - 35*x^4 - 47*x^5 - 11*x^6 + 16*x^7 + 13*x^8 - 2*x^9 - 2*x^10) / (1 - 5*x^2 - 10*x^3 - 8*x^4 + 2*x^5 + 10*x^6 + 7*x^7 - 3*x^9 - x^10). - Colin Barker, Apr 25 2018

Example

Some solutions for 3 X 2:
..1..0....0..0....1..1....1..1....0..0....0..1....1..0....1..1....0..1....0..1
..1..1....1..1....1..1....0..0....1..1....1..1....1..1....1..0....1..1....0..0
..1..1....1..1....0..1....1..1....0..0....1..1....0..1....1..1....0..0....1..0

Crossrefs

Cf. A187729.

Sequence in context: A187729 A088800 A316636 * A253397 A258554 A253326

Adjacent sequences: A187718 A187719 A187720 * A187722 A187723 A187724

Keyword

nonn

Author

R. H. Hardin, Mar 13 2011

Status

approved