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n\k 1 2 3 4 5 6 7 8
1: 1
2: 0 2
3: 0 2 6
4: 0 6 14 22
5: 0 28 56 86 92
6: 0 162 298 428 518 422
7: 0 1076 1868 2562 3096 3144 2074
8: 0 7852 13076 17292 20624 21990 19366 10754
Closed meander: Closed meander split with bottom rotated right
4 top arches to form top of semi-meander with 8 arches
______ ______
/ ____ \ / ____ \
/ / __ \ \ / / __ \ \ __
/ / / \ \ \ / / / \ \ \ / \
/ / / /\ \ \ \ / / / /\ \ \ \ /\ /\ / /\ \
\ \/ / \/ \/ binary representation of semi-meander
\__/ 1 1 1 1 0 0 0 0 1 0 1 0 1 1 0 0
Semi-meander top arches with no covering center arch = cm
START: center |
Reduction of semi-meander: 1 1 1 1 0 0 0 0 1 0 1 0 1 1 0 0 cm(1)
Combine end of first arch 1 1 1 1 0 0 0 0e 1 0 1 0 1s 1 0 0
Oe with beginning of last 1 1 1 0 0 0 1 1 0 1 0 0 1 0
arch 1s. 0e...1s becomes 1 1 1 0 0 0e 1 1 0 1 0 0 1s 0
1...0 in the next line. The 1 1 0 0 1 1 1 0 1 0 0 0
starting 1 and ending 0 1 1 0 0e 1s 1 1 0 1 0 0 0
are removed in the next line 1 0 1 0 1 1 0 1 0 0
reducing number of arches. 1 0e 1 0 1s 1 0 1 0
by one. 1 1 0 0 1 0 1 0 cm(2)
1 1 0 0e 1 0 1s 0
1 0 1 1 0 0
1 0e 1s 1 0 0
1 0 1 0 cm(3)
Example: T(4,3) 4 starting top arches with 3 closed meanders in history.
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