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Search: id:A003108
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| A003108 |
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Number of partitions of n into cubes.
(Formerly M0209)
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+0
7
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| 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 7, 7, 7, 7, 7, 8, 8, 8, 9, 9, 9, 9, 9, 10, 10, 10, 11, 11, 11, 12, 12, 13, 13, 13, 14, 14, 14, 15, 15, 17, 17, 17, 18, 18, 18, 19, 19, 21, 21, 21, 22, 22, 22, 23, 23, 25, 26, 26, 27, 27, 27, 28
(list; graph; listen)
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OFFSET
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0,9
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COMMENT
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The g.f. 1/(z+1)/(z**2+1)/(z**4+1)/(z-1)**2 conjectured by S. Plouffe in his 1992 dissertation is wrong.
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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).
F. Iacobescu, Smarandache Partition Type and Other Sequences, Bull. Pure Appl. Sciencea, Vol. 16E, No. 2 (1997), pp. 237-240.
F. Smarandache, Sequences of Numbers Involved in Unsolved Problems, Hexis, Phoenix, 2006.
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LINKS
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T. D. Noe, Table of n, a(n) for n=0..1000
S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
S. Plouffe, 1031 Generating Functions and Conjectures, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
F. Smarandache, Sequences of Numbers Involved in Unsolved Problems.
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
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FORMULA
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G.f.=1/product(1-x^(j^3), j=1..infinity). - Emeric Deutsch (deutsch(AT)duke.poly.edu), Mar 30 2006
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EXAMPLE
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a(16)=3 because we have [8,8],[8,1,1,1,1,1,1,1,1] and [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1].
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MAPLE
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g:=1/product(1-x^(j^3), j=1..30): gser:=series(g, x=0, 70): seq(coeff(gser, x, n), n=0..65); - Emeric Deutsch (deutsch(AT)duke.poly.edu), Mar 30 2006
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CROSSREFS
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Cf. A131799.
Adjacent sequences: A003105 A003106 A003107 this_sequence A003109 A003110 A003111
Sequence in context: A110656 A104407 A054897 this_sequence A111898 A072746 A105390
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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), Herman P. Robinson
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