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

1,4

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

Links

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

Example

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...

Crossrefs

Sequence in context: A215416 A264970 A287205 * A238718 A303782 A375462

Adjacent sequences: A183726 A183727 A183728 * A183730 A183731 A183732

Keyword

nonn,tabl

Author

R. H. Hardin, Jan 06 2011

Status

approved