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Search: id:A005706
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| A005706 |
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Number of partitions of 5n into powers of 5.
(Formerly M0519)
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+0
6
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| 1, 2, 3, 4, 5, 7, 9, 11, 13, 15, 18, 21, 24, 27, 30, 34, 38, 42, 46, 50, 55, 60, 65, 70, 75, 82, 89, 96, 103, 110, 119, 128, 137, 146, 155, 166, 177, 188, 199, 210, 223, 236, 249, 262, 275, 290, 305, 320, 335, 350, 368, 386, 404, 422, 440, 461, 482, 503, 524, 545
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Euler transform of [2,0,0,0,1,0,0,0,0,...] with 1's at 5^n. - Michael Somos Mar 16 2004
Partial sums of number of partitions of n into powers of 5. - Michael Somos Mar 16 2004
The g.f. -1/(z**4+z**3+z**2+z+1)/(z-1)**3 conjectured by S. Plouffe in his 1992 dissertation is wrong.
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REFERENCES
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R. K. Guy, personal communication.
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. Latapy, Partitions of an integer into powers, DMTCS Proceedings AA (DM-CCG), 2001, 215-228.
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
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.
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FORMULA
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a(n) = a(n-1)+a([n/5]).
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PROGRAM
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(PARI) a(n)=if(n<1, n==0, a(n-1)+a(n\5))
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CROSSREFS
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Cf. A000041, A000123, A005704, A005705.
Sequence in context: A135785 A008732 A130520 this_sequence A064175 A000028 A026416
Adjacent sequences: A005703 A005704 A005705 this_sequence A005707 A005708 A005709
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KEYWORD
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nonn,easy
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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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