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Search: id:A000098
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| A000098 |
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Number of partitions of n if there are two kinds of 1, two kinds of 2 and two kinds of 3.
(Formerly M1373 N0533)
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+0
9
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| 1, 2, 5, 10, 19, 33, 57, 92, 147, 227, 345, 512, 752, 1083, 1545, 2174, 3031, 4179, 5719, 7752, 10438, 13946, 18519, 24428, 32051, 41805, 54265, 70079, 90102, 115318, 147005, 186626, 236064, 297492, 373645, 467707
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Also number of partitions of 2*n+1 with exactly 3 odd parts (offset 1). - Vladeta Jovovic (vladeta(AT)eunet.rs), Jan 12 2005
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
H. Gupta et al., Tables of Partitions. Royal Society Mathematical Tables, Vol. 4, Cambridge Univ. Press, 1958, p. 90.
J. Riordan, Combinatorial Identities, Wiley, 1968, p. 199.
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LINKS
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T. D. Noe, Table of n, a(n) for n=0..1000
N. J. A. Sloane, Transforms
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FORMULA
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Euler transform of 2 2 2 1 1 1 1...
G.f.=1/[(1-x)(1-x^2)(1-x^3)*product((1-x^k), k=1..infinity)].
a(n)=sum(A000097(n-3*j), j=0..floor(n/3)), n>=0.
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EXAMPLE
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a(3)=10 because we have 3, 3', 2+1, 2+1', 2'+1, 2'+1', 1+1+1, 1+1+1', 1+1'+1' and 1'+1'+1'.
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CROSSREFS
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Cf. A000070, A008951, A000097, A000710.
Fourth column of Riordan triangle A008951 and of triangle A103923.
Sequence in context: A018739 A011893 A132210 this_sequence A024827 A104161 A065613
Adjacent sequences: A000095 A000096 A000097 this_sequence A000099 A000100 A000101
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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Edited by Emeric Deutsch (deutsch(AT)duke.poly.edu), Mar 23 2005
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