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Search: id:A000991
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| A000991 |
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Number of 3-line partitions of n.
(Formerly M2554 N1011)
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+0
4
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| 1, 3, 6, 12, 21, 40, 67, 117, 193, 319, 510, 818, 1274, 1983, 3032, 4610, 6915, 10324, 15235, 22371, 32554, 47119, 67689, 96763, 137404, 194211, 272939, 381872
(list; graph; listen)
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OFFSET
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1,2
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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).
L. Carlitz, Generating functions and partition problems, pp. 144-169 of A. L. Whiteman, ed., Theory of Numbers, Proc. Sympos. Pure Math., 8 (1965). Amer. Math. Soc., see p. 145, eq. (1.8).
M. S. Cheema and B. Gordon, Some remarks on two- and three-line partitions, Duke Math. J., 31 (1964), 267-273.
P. A. MacMahon, The connexion between the sum of the squares of the divisors and the number of partitions of a given number, Messenger Math., 54 (1924), 113-116.
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FORMULA
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G.f.: prod from k =1 to inf ( 1 - x^k )^(-3) / ( 1 - x )^2 ( 1 - x^2 ).
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CROSSREFS
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Cf. A000990.
Sequence in context: A087503 A133627 A092176 this_sequence A095093 A139422 A062483
Adjacent sequences: A000988 A000989 A000990 this_sequence A000992 A000993 A000994
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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