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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.

%I A183729 #7 Oct 06 2015 22:06:25
%S A183729 0,1,1,12,2,12,87,29,29,87,537,388,124,388,537,3070,4170,1790,1790,
%T A183729 4170,3070,16731,41423,30939,14886,30939,41423,16731,88331,388998,
%U A183729 525895,272215,272215,525895,388998,88331,455804,3528126,8439116,7319684
%N 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.
%C A183729 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 A183729 Table starts
%C A183729 .......0.........1..........12............87.............537..............3070
%C A183729 .......1.........2..........29...........388............4170.............41423
%C A183729 ......12........29.........124..........1790...........30939............525895
%C A183729 ......87.......388........1790.........14886..........272215...........7319684
%C A183729 .....537......4170.......30939........272215.........3723606.........112949014
%C A183729 ....3070.....41423......525895.......7319684.......112949014........2740758406
%C A183729 ...16731....388998.....8439116.....200260149......4858574535......134020420595
%C A183729 ...88331...3528126...130610844....5355252106....221403152762.....9546147995730
%C A183729 ..455804..31206553..1967828529..139489865583...9949950285008...729082624201394
%C A183729 .2311983.270945278.29070445544.3561214845505.439077020908186.55559473375122011
%H A183729 R. H. Hardin, <a href="/A183729/b183729.txt">Table of n, a(n) for n = 1..160</a>
%e A183729 Some solutions with the first block increasing clockwise for 4 X 3:
%e A183729 ..3..4..2....4..0..5....0..1..0....4..5..4....0..2..0....3..4..3....5..2..1
%e A183729 ..1..0..1....2..1..2....5..2..5....3..0..3....4..3..4....2..5..2....4..3..4
%e A183729 ..2..5..2....3..0..3....4..3..4....2..1..2....5..2..5....1..0..1....5..2..5
%e A183729 ..3..4..3....4..5..4....0..2..5....4..0..4....0..1..0....3..5..4....0..1..0
%e A183729 ...
%e A183729 ...R..L.......R..L.......R..L.......R..L.......R..L.......R..L.......R..L...
%e A183729 ...L..R.......L..R.......R..L.......R..L.......L..R.......R..L.......L..R...
%e A183729 ...L..R.......L..R.......L..R.......L..R.......L..R.......L..R.......L..R...
%K A183729 nonn,tabl
%O A183729 1,4
%A A183729 _R. H. Hardin_, Jan 06 2011