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Search: id:A000711
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| A000711 |
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Number of partitions of n, with three kinds of 1,2,3 and 4 and two kinds of 5,6,7,...
(Formerly M2787 N1122)
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+0
1
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| 1, 3, 9, 22, 51, 107, 217, 416, 775, 1393, 2446, 4185, 7028, 11569, 18749, 29908, 47083, 73157, 112396, 170783, 256972, 383003, 565961, 829410, 1206282, 1741592, 2497425, 3557957, 5037936, 7091711, 9927583, 13823626
(list; graph; listen)
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OFFSET
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0,2
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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).
H. Gupta et al., Tables of Partitions. Royal Society Mathematical Tables, Vol. 4, Cambridge Univ. Press, 1958, p. 122.
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LINKS
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N. J. A. Sloane, Transforms
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FORMULA
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EULER transform of 3, 3, 3, 3, 2, 2, 2, 2...
G.f.: 1/[(1-x)(1-x^2)(1-x^3)(1-x^4)product((1-x^k)^2, k=1..infinity)].
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EXAMPLE
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a(2)=9 because we have 2, 2', 2", 1+1, 1'+1', 1"+1", 1+1', 1+1", 1'+1".
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MAPLE
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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, 3, 2)): seq (a(n), n=0..31); [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Sep 08 2008]
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CROSSREFS
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Sequence in context: A000715 A034505 A143099 this_sequence A121589 A000716 A001628
Adjacent sequences: A000708 A000709 A000710 this_sequence A000712 A000713 A000714
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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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EXTENSIONS
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Extended with formula from Christian G. Bower (bowerc(AT)usa.net), Apr 15 1998.
Edited by Emeric Deutsch (deutsch(AT)duke.poly.edu), Mar 22 2005
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