A183729 T(n,k) = 1/12 the number of (n+1) X (k+1) 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, 1, 12, 2, 12, 87, 29, 29, 87, 537, 388, 124, 388, 537, 3070, 4170, 1790, 1790, 4170, 3070, 16731, 41423, 30939, 14886, 30939, 41423, 16731, 88331, 388998, 525895, 272215, 272215, 525895, 388998, 88331, 455804, 3528126, 8439116, 7319684

Offset: 1

Author

R. H. Hardin, Jan 06 2011

Keywords

• nonn
• tabl

Comments

Adjacent blocks have the same sense when one uses a gap in a shared side as a fall and the other uses it as an increase.

Table starts

.......0.........1..........12............87.............537..............3070

.......1.........2..........29...........388............4170.............41423

......12........29.........124..........1790...........30939............525895

......87.......388........1790.........14886..........272215...........7319684

.....537......4170.......30939........272215.........3723606.........112949014

....3070.....41423......525895.......7319684.......112949014........2740758406

...16731....388998.....8439116.....200260149......4858574535......134020420595

...88331...3528126...130610844....5355252106....221403152762.....9546147995730

..455804..31206553..1967828529..139489865583...9949950285008...729082624201394

.2311983.270945278.29070445544.3561214845505.439077020908186.55559473375122011

Examples

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

Links

• R. H. Hardin, Table of n, a(n) for n = 1..160