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

Author

R. H. Hardin, Feb 22 2011

Keywords

• nonn

Comments

Column 1 of A186462.

Examples

			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
		

Links

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

Crossrefs

Cf. A186462.

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