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A005705
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Number of partitions of 4*n into powers of 4.
(Formerly M0552)
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5
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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; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| 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
| 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
| 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
| a(n) = a(n-1)+a(floor(n/4)).
G.f.: T(x)=1/prod(k=0,infinity,1-x^(4^k)), it satisfies T(x)=(1-x^4)/(1-x)^2*T(x^4). [Joerg Arndt, May 12 2010]
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MATHEMATICA
| Fold[Append[#1, Total[Take[Flatten[Transpose[Table[#1, {4}]]], #2]]] &, {1}, Range[2, 20]] (* Gyorgy Birkas, Apr 18, 2011 *)
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CROSSREFS
| Cf. A000041, A000123, A005704, A005706.
Sequence in context: A019293 A130519 A001972 * A139542 A093717 A002093
Adjacent sequences: A005702 A005703 A005704 * A005706 A005707 A005708
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KEYWORD
| nonn,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| Formula and more terms from Henry Bottomley (se16(AT)btinternet.com), Apr 30 2001
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