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

1,3

Comments

Column 1 of A183729.

Links

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

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

Example

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...

Crossrefs

Cf. A183729.

Sequence in context: A243248 A046023 A369421 * A180797 A137207 A206765

Adjacent sequences: A183718 A183719 A183720 * A183722 A183723 A183724

Keyword

nonn

Author

R. H. Hardin, Jan 06 2011

Status

approved