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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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9
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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
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OFFSET
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0,2
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COMMENTS
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Also number of partitions of 4*n+k into powers of 4 where k=1,2,3. - Michael Somos, Mar 15 2020
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REFERENCES
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R. K. Guy, personal communication.
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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Seiichi Manyama, Table of n, a(n) for n = 0..1000
C. Banderier, H.-K. Hwang, V. Ravelomanana and V. Zacharovas, Analysis of an exhaustive search algorithm in random graphs and the n^{c logn}-asymptotics, preprint 2012; SIAM J. Discrete Math., 28(1), 342-371, 2014. - N. J. A. Sloane, Dec 23 2012
R. K. Guy, Letters to N. J. A. Sloane and J. W. Moon, 1988
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.
M. Latapy, Partitions of an integer into powers, DMTCS Proceedings AA (DM-CCG), 2001, 215-228. [Cached copy, with permission]
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.
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FORMULA
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a(n) = a(n-1) + a(floor(n/4)).
G.f.: T(x)=(1-x)^(-1)/(Product_{k>=0} 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
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Fold[Append[#1, Total[Take[Flatten[Transpose[Table[#1, {4}]]], #2]]] &, {1}, Range[2, 20]] (* Birkas Gyorgy, Apr 18 2011 *)
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CROSSREFS
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Column k=4 of A292477.
Cf. A000041, A000123, A005704, A005706.
Sequence in context: A130519 A001972 A328325 * A139542 A347656 A238616
Adjacent sequences: A005702 A005703 A005704 * 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
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EXTENSIONS
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Formula and more terms from Henry Bottomley, Apr 30 2001
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STATUS
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approved
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