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A100529
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a(n) = minimal k such that n has a partition into k parts with the property that every number <= m can be partitioned into a subset of these parts.
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4
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1, 1, 1, 1, 2, 1, 1, 3, 4, 3, 4, 2, 2, 1, 1, 12, 15, 13, 14, 11, 12, 9, 10, 6, 6, 4, 4, 2, 2, 1, 1, 84, 91, 82, 89, 77, 80, 70, 73, 60, 63, 53, 54, 43, 44, 35, 36, 26, 26, 20, 20, 14, 14, 10, 10, 6, 6, 4, 4, 2, 2, 1, 1, 908
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,5
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REFERENCES
| E. O'Shea, M-partitions: optimal partitions of weight for one scale pan, Discrete Math 289 (2004), 81-93.
O. J. Rodseth, Enumeration of M-partitions, Discrete Math., 306 (2006), 694-698.
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FORMULA
| If 2^m + 2^(m-1) - 1 <= n <= 2^(m+1) - 1 for some m, let i = 2^(m+1) - 1 - n. Then a(n) = A000123([i/2]). This determines half the values.
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CROSSREFS
| Cf. A000123 (binary partitions), A002033 (perfect partitions).
Sequence in context: A055068 A015138 A157807 * A124424 A057044 A153899
Adjacent sequences: A100526 A100527 A100528 * A100530 A100531 A100532
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Dec 31 2004
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