Search: id:A005704
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%I A005704 M0639
%S A005704 1,2,3,5,7,9,12,15,18,23,28,33,40,47,54,63,72,81,93,105,117,132,147,
%T A005704 162,180,198,216,239,262,285,313,341,369,402,435,468,508,548,588,635,
%U A005704 682,729,783,837,891,954,1017,1080,1152,1224,1296,1377,1458,1539,1632
%N A005704 Number of partitions of 3n into powers of 3.
%C A005704 Infinite convolution product of [1,2,3,3,3,3,3,3,3,3] aerated A000244-1 
               times. i.e. [1,2,3,3,3,3,3,3,3,3] * [1,0,0,2,0,0,3,0,0,3] * [1,0,
               0,0,0,0,0,0,0,2] * ... [From Mats Granvik, Gary W. Adamson (mats.granvik(AT)abo.fi), 
               Aug 07 2009]
%D A005704 G. E. Andrews, Congruence properties of the m-ary partition function, 
               J. Number Theory 3 (1971), 104-110.
%D A005704 R. K. Guy, personal communication.
%D A005704 O. J. Rodseth, Some arithmetical properties of m-ary partitions, Proc. 
               Camb. Phil. Soc. 68 (1970), 447-453.
%D A005704 O. J. Rodseth and J. A. Sellers, On m-ary partition function congruences: 
               A fresh look at a past problem, J. Number Theory 87 (2001), 270-281.
%D A005704 O. J. Rodseth and J. A. Sellers, On a Restricted m-Non-Squashing Partition 
               Function, Journal of Integer Sequences, Vol. 8 (2005), Article 05.5.4.
%D A005704 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%H A005704 M. D. Hirschhorn and J. A. Sellers, A different view of m-ary partitions, 
               <a href="http://www.lacim.uqam.ca/~plouffe/OEIS/archive_in_pdf/mike-m-ary.pdf">
               Australasian J. Combin.</a>, 30 (2004), 193-196.
%H A005704 M. D. Hirschhorn and J. A. Sellers, <a href="http://www.math.psu.edu/
               sellersj/mike-m-ary.pdf">A different view of m-ary partitions</a>
%H A005704 M. Latapy, <a href="http://www.dmtcs.org/proceedings/">Partitions of 
               an integer into powers</a>, DMTCS Proceedings AA (DM-CCG), 2001, 
               215-228.
%F A005704 a(n) = a(n-1)+a([n/3]).
%F A005704 Coefficient of x^(3n) in prod(k>=0, 1/(1-x^(3^k))). Also, coefficient 
               of x^n in prod(k>=0, 1/(1-x^(3^k)))/(1-x). - Benoit Cloitre (benoit7848c(AT)orange.fr), 
               Nov 28 2002
%F A005704 a(n) mod 3 = binomial(2n, n) mod 3. - Benoit Cloitre (benoit7848c(AT)orange.fr), 
               Jan 04 2004
%Y A005704 Cf. A000041, A000123, A005705, A005706, A018819.
%Y A005704 Cf. A006996.
%Y A005704 Sequence in context: A117930 A090632 A022786 this_sequence A022782 A025692 
               A137285
%Y A005704 Adjacent sequences: A005701 A005702 A005703 this_sequence A005705 A005706 
               A005707
%K A005704 nonn
%O A005704 0,2
%A A005704 N. J. A. Sloane (njas(AT)research.att.com).
%E A005704 Formula and more terms from Henry Bottomley (se16(AT)btinternet.com), 
               Apr 30 2001

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