

A222659


Table a(m,n) read by antidiagonals, m, n >= 1, where a(m,n) is the number of divideandconquer partitions of an m X n rectangle into integer subrectangles.


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1, 2, 2, 4, 8, 4, 8, 34, 34, 8, 16, 148, 320, 148, 16, 32, 650, 3118, 3118, 650, 32, 64, 2864, 30752, 68480, 30752, 2864, 64, 128, 12634, 304618, 1525558, 1525558, 304618, 12634, 128
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OFFSET

1,2


COMMENTS

The divideandconquer partition of an integersided rectangle is one that can be obtained by repeated bisections into adjacent integersided rectangles.
The table is symmetric: a(m,n) = a(n,m).


LINKS



EXAMPLE

Table begins:
1, 2, 4, 8, 16, 32, 64, ...
2, 8, 34, 148, 650, 2864, 12634, ...
4, 34, 320, 3118, 30752, 304618, 3022112, ...
8, 148, 3118, 68480, 1525558, ...
16, 650, 30752, 1525558, ...
32, 2864, 304618, ...
64, 12634, 3022112, ...
Not every partition (cf. A116694) into integer subrectangles is divideandconquer. For example, the following partition of a 3 X 3 rectangle into 5 subrectangles is not divideandconquer:
112
342
355


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KEYWORD



AUTHOR



STATUS

approved



