Search: id:A003108
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%I A003108 M0209
%S A003108 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,
%T A003108 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,
%U A003108 15,17,17,17,18,18,18,19,19,21,21,21,22,22,22,23,23,25,26,26,27,27,27,
               28
%N A003108 Number of partitions of n into cubes.
%C A003108 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.
%D A003108 F. Iacobescu, Smarandache Partition Type and Other Sequences, Bull. Pure 
               Appl. Sciencea, Vol. 16E, No. 2 (1997), pp. 237-240.
%D A003108 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A003108 F. Smarandache, Sequences of Numbers Involved in Unsolved Problems, Hexis, 
               Phoenix, 2006.
%H A003108 T. D. Noe, <a href="b003108.txt">Table of n, a(n) for n=0..1000</a>
%H A003108 S. Plouffe, <a href="http://www.lacim.uqam.ca/%7Eplouffe/articles/MasterThesis.pdf">
               Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures</
               a>, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 
               1992.
%H A003108 S. Plouffe, <a href="http://www.lacim.uqam.ca/%7Eplouffe/articles/FonctionsGeneratrices.pdf">
               1031 Generating Functions and Conjectures</a>, Universit\'{e} du 
               Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
%H A003108 F. Smarandache, <a href="http://www.gallup.unm.edu/~smarandache/Sequences-book.pdf">
               Sequences of Numbers Involved in Unsolved Problems</a>.
%H A003108 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               CubicNumber.html">Link to a section of The World of Mathematics.</
               a>
%H A003108 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               Partition.html">Link to a section of The World of Mathematics.</a>
%H A003108 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               SmarandacheSequences.html">Link to a section of The World of Mathematics.</
               a>
%F A003108 G.f.=1/product(1-x^(j^3), j=1..infinity). - Emeric Deutsch (deutsch(AT)duke.poly.edu), 
               Mar 30 2006
%e A003108 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].
%p A003108 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
%Y A003108 Cf. A131799.
%Y A003108 Sequence in context: A110656 A104407 A054897 this_sequence A111898 A072746 
               A105390
%Y A003108 Adjacent sequences: A003105 A003106 A003107 this_sequence A003109 A003110 
               A003111
%K A003108 nonn
%O A003108 0,9
%A A003108 N. J. A. Sloane (njas(AT)research.att.com), Herman P. Robinson

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