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Search: id:A005704
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| A005704 |
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Number of partitions of 3n into powers of 3.
(Formerly M0639)
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+0
12
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| 1, 2, 3, 5, 7, 9, 12, 15, 18, 23, 28, 33, 40, 47, 54, 63, 72, 81, 93, 105, 117, 132, 147, 162, 180, 198, 216, 239, 262, 285, 313, 341, 369, 402, 435, 468, 508, 548, 588, 635, 682, 729, 783, 837, 891, 954, 1017, 1080, 1152, 1224, 1296, 1377, 1458, 1539, 1632
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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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]
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REFERENCES
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G. E. Andrews, Congruence properties of the m-ary partition function, J. Number Theory 3 (1971), 104-110.
R. K. Guy, personal communication.
O. J. Rodseth, Some arithmetical properties of m-ary partitions, Proc. Camb. Phil. Soc. 68 (1970), 447-453.
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.
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.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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M. D. Hirschhorn and J. A. Sellers, A different view of m-ary partitions, Australasian J. Combin., 30 (2004), 193-196.
M. D. Hirschhorn and J. A. Sellers, A different view of m-ary partitions
M. Latapy, Partitions of an integer into powers, DMTCS Proceedings AA (DM-CCG), 2001, 215-228.
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FORMULA
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a(n) = a(n-1)+a([n/3]).
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
a(n) mod 3 = binomial(2n, n) mod 3. - Benoit Cloitre (benoit7848c(AT)orange.fr), Jan 04 2004
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CROSSREFS
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Cf. A000041, A000123, A005705, A005706, A018819.
Cf. A006996.
Sequence in context: A117930 A090632 A022786 this_sequence A022782 A025692 A137285
Adjacent sequences: A005701 A005702 A005703 this_sequence A005705 A005706 A005707
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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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Formula and more terms from Henry Bottomley (se16(AT)btinternet.com), Apr 30 2001
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