A186454 Number of (n+1) X 2 binary arrays with every 2 X 2 subblock commuting with each of its horizontal and vertical 2 X 2 subblock neighbors.

16, 21, 42, 61, 106, 151, 245, 359, 567, 840, 1301, 1941, 2977, 4465, 6810, 10247, 15577, 23487, 35635, 53800, 81533, 123193, 186569, 282037, 426954, 645623, 977117, 1477831, 2236287, 3382632, 5118213, 7742397, 11714273, 17721097, 26811194

Offset

1,1

Comments

Column 1 of A186462.

Links

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

Formula

Empirical: a(n) = 2*a(n-1) - 2*a(n-3) + 2*a(n-4) - a(n-5) for n>8.

Empirical g.f.: x*(16 - 11*x + 9*x^3 - 6*x^4 - 3*x^5 + 2*x^6 + x^7) / ((1 - x)*(1 - x - x^2 + x^3 - x^4)). - Colin Barker, Feb 28 2018

Example

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

Crossrefs

Cf. A186462.

Sequence in context: A270783 A330591 A302167 * A302638 A302430 A138173

Adjacent sequences: A186451 A186452 A186453 * A186455 A186456 A186457

Keyword

nonn

Author

R. H. Hardin, Feb 22 2011

Status

approved