A005705 Number of partitions of 4*n into powers of 4. (Formerly M0552)

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

0,2

Comments

Also number of partitions of 4*n+k into powers of 4 where k=1,2,3. - Michael Somos, Mar 15 2020

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.

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

Mathematica

Fold[Append[#1, Total[Take[Flatten[Transpose[Table[#1, {4}]]], #2]]] &, {1},  Range[2, 20]] (* Birkas Gyorgy, Apr 18 2011 *)

Crossrefs

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

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

Formula and more terms from Henry Bottomley, Apr 30 2001

Status

approved