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A000716
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Number of partitions of n into parts of 3 kinds.
(Formerly M2788 N1123)
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10
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1, 3, 9, 22, 51, 108, 221, 429, 810, 1479, 2640, 4599, 7868, 13209, 21843, 35581, 57222, 90882, 142769, 221910, 341649, 521196, 788460, 1183221, 1762462, 2606604, 3829437, 5590110, 8111346, 11701998, 16790136
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| A000712: (1, 2, 5, 10, 20, 36,...) = A000716 convolved with A010815. [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Oct 26 2008]
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REFERENCES
| H. Gupta et al., Tables of Partitions. Royal Society Mathematical Tables, Vol. 4, Cambridge Univ. Press, 1958, p. 122.
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
| T. D. Noe, Table of n, a(n) for n=0..500
Index entries for expansions of Product_{k >= 1} (1-x^k)^m
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 391
N. J. A. Sloane, Transforms
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FORMULA
| G.f.: Product_{m>=1} 1/(1-x^m)^3.
EULER transform of 3, 3, 3, 3, 3, 3, 3, 3...
a(0)=1, a(n)=1/n*sum(k=0,n-1, 3*a(k)*sigma_1(n-k)) - Joerg Arndt, Feb 5 2011
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PROG
| (PARI) \ps100 for(n=0, 100, print1((polcoeff(1/eta(x)^3, n, x)), ", "))
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CROSSREFS
| Cf. A000713.
A000712, A010815 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Oct 26 2008]
Sequence in context: A000711 A160526 A121589 * A001628 A099166 A202882
Adjacent sequences: A000713 A000714 A000715 * A000717 A000718 A000719
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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
| Extended with formula from Christian G. Bower (bowerc(AT)usa.net), Apr 15 1998.
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