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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. 10

%I

%S 0,1,1,12,2,12,87,29,29,87,537,388,124,388,537,3070,4170,1790,1790,

%T 4170,3070,16731,41423,30939,14886,30939,41423,16731,88331,388998,

%U 525895,272215,272215,525895,388998,88331,455804,3528126,8439116,7319684

%N 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.

%C 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.

%C Table starts

%C .......0.........1..........12............87.............537..............3070

%C .......1.........2..........29...........388............4170.............41423

%C ......12........29.........124..........1790...........30939............525895

%C ......87.......388........1790.........14886..........272215...........7319684

%C .....537......4170.......30939........272215.........3723606.........112949014

%C ....3070.....41423......525895.......7319684.......112949014........2740758406

%C ...16731....388998.....8439116.....200260149......4858574535......134020420595

%C ...88331...3528126...130610844....5355252106....221403152762.....9546147995730

%C ..455804..31206553..1967828529..139489865583...9949950285008...729082624201394

%C .2311983.270945278.29070445544.3561214845505.439077020908186.55559473375122011

%H R. H. Hardin, <a href="/A183729/b183729.txt">Table of n, a(n) for n = 1..160</a>

%e Some solutions with the first block increasing clockwise for 4 X 3:

%e ..3..4..2....4..0..5....0..1..0....4..5..4....0..2..0....3..4..3....5..2..1

%e ..1..0..1....2..1..2....5..2..5....3..0..3....4..3..4....2..5..2....4..3..4

%e ..2..5..2....3..0..3....4..3..4....2..1..2....5..2..5....1..0..1....5..2..5

%e ..3..4..3....4..5..4....0..2..5....4..0..4....0..1..0....3..5..4....0..1..0

%e ...

%e ...R..L.......R..L.......R..L.......R..L.......R..L.......R..L.......R..L...

%e ...L..R.......L..R.......R..L.......R..L.......L..R.......R..L.......L..R...

%e ...L..R.......L..R.......L..R.......L..R.......L..R.......L..R.......L..R...

%K nonn,tabl

%O 1,4

%A _R. H. Hardin_, Jan 06 2011

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Last modified September 20 01:58 EDT 2019. Contains 327207 sequences. (Running on oeis4.)