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A002799
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Number of 4-line partitions of n (i.e. planar partitions of n with at most 4 lines).
(Formerly M2563 N1014)
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2
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1, 3, 6, 13, 23, 45, 78, 141, 239, 409, 674, 1116, 1794, 2882, 4544, 7131, 11031, 16983, 25844, 39124, 58680, 87538, 129578, 190830, 279140, 406334, 588026, 847034, 1213764, 1731780, 2459244, 3478185, 4898285, 6872041, 9603356
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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REFERENCES
| 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.
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
| N. J. A. Sloane, Transforms
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FORMULA
| Euler transform of 1, 2, 3, 4, 4, 4, ...
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MAPLE
| with (numtheory): etr:= proc(p) local b; b:=proc(n) option remember; local d, j; if n=0 then 1 else add (add (d*p(d), d=divisors(j)) *b(n-j), j=1..n)/n fi end end: a:=etr (n-> `if`(n<5, n, 4)): seq (a(n), n=1..35); [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Sep 08 2008]
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CROSSREFS
| Cf. A000219, A000990, A000991, A001452.
Sequence in context: A058397 A174369 A022811 * A162426 A058554 A128517
Adjacent sequences: A002796 A002797 A002798 * A002800 A002801 A002802
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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
| Edited and extended with formula by Christian G. Bower (bowerc(AT)usa.net), Jan 01 2004
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