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A002569
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Max_{ 0<=k<=n } { Number of partitions of n into exactly k parts }.
(Formerly M0283 N0101)
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5
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1, 1, 1, 1, 2, 2, 3, 4, 5, 7, 9, 11, 15, 18, 23, 30, 37, 47, 58, 71, 90, 110, 136, 164, 201, 248, 300, 364, 436, 525, 638, 764, 919, 1090, 1297, 1549, 1845, 2194, 2592, 3060, 3590, 4242, 5013, 5888, 6912, 8070, 9418, 11004, 12866, 15021, 17475, 20298, 23501, 27169
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,5
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REFERENCES
| F. C. Auluck, S. Chowla and H. Gupta, On the maximum value of the number of partitions into k parts, J. Indian Math. Soc., 6 (1942), 105-112.
T. S. Motzkin, Sorting numbers for cylinders and other classification numbers, in Combinatorics, Proc. Symp. Pure Math. 19, AMS, 1971, pp. 167-176 (p. 172, gives a(9) incorrectly as 6).
T. S. Motzkin, Sorting numbers ...: for a link to this paper see A000262.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| Robert G. Wilson v, (rgwv@rgwv.com), Table of n, a(n) for n = 1..97 . [From Robert G. Wilson v (rgwv(AT)rgwv.com), Jul 20 2010]
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MATHEMATICA
| f[n_] := Block[{k = 1, mx = 0}, While[k < n + 1, a = Length@ IntegerPartitions[n, {k}]; If[a > mx, mx = a]; k++ ]; mx]; Array[f, 53] [From Robert G. Wilson v (rgwv(AT)rgwv.com), Jul 20 2010]
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CROSSREFS
| Cf. A046155.
Cf. A026819, A046155. [From Robert G. Wilson v (rgwv(AT)rgwv.com), Jul 20 2010]
Sequence in context: A122130 A003073 A123946 * A129528 A052336 A061287
Adjacent sequences: A002566 A002567 A002568 * A002570 A002571 A002572
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| More terms from Dave Wilson.
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