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A008641
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Number of partitions of n into at most 12 parts.
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3
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1, 1, 2, 3, 5, 7, 11, 15, 22, 30, 42, 56, 77, 100, 133, 172, 224, 285, 366, 460, 582, 725, 905, 1116, 1380, 1686, 2063, 2503, 3036, 3655, 4401, 5262, 6290, 7476, 8877, 10489, 12384, 14552, 17084, 19978, 23334, 27156, 31570, 36578, 42333, 48849, 56297
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| With a different offset, number of partitions of n in which the greatest part is 12.
For n>11: also number of partitions of n into parts <= 12: a(n)=A026820(n,12). [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Jan 21 2010]
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REFERENCES
| A. Cayley, Collected Mathematical Papers. Vols. 1-13, Cambridge Univ. Press, London, 1889-1897, Vol. 10, p. 415.
H. Gupta et al., Tables of Partitions. Royal Society Mathematical Tables, Vol. 4, Cambridge Univ. Press, 1958, p. 2.
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LINKS
| T. D. Noe, Table of n, a(n) for n=0..1000
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 361
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MAPLE
| 1/(1-x)/(1-x^2)/(1-x^3)/(1-x^4)/(1-x^5)/(1-x^6)/(1-x^7)/(1-x^8)/(1-x^9)/(1-x^10)/(1-x^11)/(1-x^12)
with(combstruct):ZL13:=[S, {S=Set(Cycle(Z, card<13))}, unlabeled]:seq(count(ZL13, size=n), n=0..46); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Sep 24 2007
B:=[S, {S = Set(Sequence(Z, 1 <= card), card <=12)}, unlabelled]: seq(combstruct[count](B, size=n), n=0..46); # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 21 2009]
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MATHEMATICA
| CoefficientList[ Series[ 1/ Product[ 1 - x^n, {n, 1, 12} ], {x, 0, 60} ], x ]
Table[ Length[ Select[ Partitions[n], First[ # ] == 12 & ]], {n, 1, 60} ]
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CROSSREFS
| a(n)=A008284(n+12, 12), n >= 0.
Cf. A026810, A026811, A026812, A026813, A026814, A026815, A026816.
Sequence in context: A036011 A104501 A008635 * A194439 A046054 A092885
Adjacent sequences: A008638 A008639 A008640 * A008642 A008643 A008644
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KEYWORD
| nonn,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| More terms from Robert G. Wilson v (rgwv(AT)rgwv.com), Dec 11 2000
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