A005705 Number of partitions of 4*n into powers of 4.
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
Offset: 0
References
- R. K. Guy, personal communication.
- N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
Links
- 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.
Programs
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Mathematica
Fold[Append[#1, Total[Take[Flatten[Transpose[Table[#1, {4}]]], #2]]] &, {1}, Range[2, 20]] (* Birkas Gyorgy, Apr 18 2011 *)
Formula
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
Extensions
Formula and more terms from Henry Bottomley, Apr 30 2001
Comments