A183721 1/12 the number of (n+1) X 2 0..5 arrays with every 2 X 2 subblock strictly increasing clockwise or counterclockwise with one decrease, and at least two adjacent blocks having the same increasing direction.

0, 1, 12, 87, 537, 3070, 16731, 88331, 455804, 2311983, 11571209, 57295330, 281223411, 1370286715, 6635743136, 31964799247, 153273890393, 732031932806, 3483896304443, 16529018119643, 78202676604548, 369073777749215

Offset: 1

Author

R. H. Hardin, Jan 06 2011

Keywords

• nonn

Comments

Column 1 of A183729.

Examples

			All solutions with the first block increasing clockwise for 3 X 2:
..3..4....1..2....4..5....2..3....5..0....0..1
..2..5....0..3....3..0....1..4....4..1....5..2
..1..0....5..4....2..1....0..5....3..2....4..3
...
...R.......R.......R.......R.......R.......R...
...R.......R.......R.......R.......R.......R...
		

Links

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

Crossrefs

Cf. A183729.

Formula

Empirical: a(n) = 8*a(n-1) - 11*a(n-2) - 23*a(n-3) + 6*a(n-4) + 7*a(n-5) - 2*a(n-6).

Empirical g.f.: x^2*(1 + 2*x - x^2)^2 / ((1 + x)*(1 - 5*x + 2*x^2)*(1 - 4*x - 2*x^2 + x^3)). - Colin Barker, Apr 04 2018