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Search: id:A005705
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| A005705 |
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Number of partitions of 4n into powers of 4.
(Formerly M0552)
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+0
6
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| 1, 2, 3, 4, 6, 8, 10, 12, 15, 18, 21, 24, 28, 32, 36, 40, 46, 52, 58, 64, 72, 80, 88, 96, 106, 116, 126, 136, 148, 160, 172, 184, 199, 214, 229, 244, 262, 280, 298, 316, 337, 358, 379, 400, 424, 448, 472, 496, 524, 552, 580, 608, 640, 672, 704, 736, 772, 808, 844
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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The g.f. (1+z)*(z**2+1)*(z**4+1)**2/(z-1)/(2*z**8-1) 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. 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.
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/4]).
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CROSSREFS
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Cf. A000041, A000123, A005704, A005706.
Sequence in context: A019293 A130519 A001972 this_sequence A139542 A093717 A002093
Adjacent sequences: A005702 A005703 A005704 this_sequence A005706 A005707 A005708
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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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