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 A222659 Table a(m,n) read by antidiagonals, m, n >= 1, where a(m,n) is the number of divide-and-conquer partitions of an m X n rectangle into integer sub-rectangles. 0
 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 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS The divide-and-conquer partition of an integer-sided rectangle is one that can be obtained by repeated bisections into adjacent integer-sided rectangles. The table is symmetric: a(m,n) = a(n,m). LINKS Table of n, a(n) for n=1..36. 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 sub-rectangles is divide-and-conquer. For example, the following partition of a 3 X 3 rectangle into 5 sub-rectangles is not divide-and-conquer: 112 342 355 CROSSREFS a(1,n) = a(n,1) = A000079(n-1) a(2,n) = a(n,2) = A034999(n) Cf. A116694 (all partitions). Sequence in context: A317517 A300182 A317532 * A116694 A220810 A221024 Adjacent sequences: A222656 A222657 A222658 * A222660 A222661 A222662 KEYWORD tabl,nonn,more AUTHOR Arsenii Abdrafikov, May 29 2013 STATUS approved

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Last modified September 11 15:28 EDT 2024. Contains 375836 sequences. (Running on oeis4.)