Search: id:A005706
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%I A005706 M0519
%S A005706 1,2,3,4,5,7,9,11,13,15,18,21,24,27,30,34,38,42,46,50,55,60,65,70,75,
%T A005706 82,89,96,103,110,119,128,137,146,155,166,177,188,199,210,223,236,249,
%U A005706 262,275,290,305,320,335,350,368,386,404,422,440,461,482,503,524,545
%N A005706 Number of partitions of 5n into powers of 5.
%C A005706 Euler transform of [2,0,0,0,1,0,0,0,0,...] with 1's at 5^n. - Michael 
               Somos Mar 16 2004
%C A005706 Partial sums of number of partitions of n into powers of 5. - Michael 
               Somos Mar 16 2004
%C A005706 The g.f. -1/(z**4+z**3+z**2+z+1)/(z-1)**3 conjectured by S. Plouffe in 
               his 1992 dissertation is wrong.
%D A005706 R. K. Guy, personal communication.
%D A005706 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.
%D A005706 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%H A005706 M. Latapy, <a href="http://www.dmtcs.org/proceedings/">Partitions of 
               an integer into powers</a>, DMTCS Proceedings AA (DM-CCG), 2001, 
               215-228.
%H A005706 M. D. Hirschhorn and J. A. Sellers, A different view of m-ary partitions, 
               <a href="http://www.lacim.uqam.ca/~plouffe/OEIS/archive_in_pdf/mike-m-ary.pdf">
               Australasian J. Combin.</a>, 30 (2004), 193-196.
%H A005706 M. D. Hirschhorn and J. A. Sellers, <a href="http://www.math.psu.edu/
               sellersj/mike-m-ary.pdf">A different view of m-ary partitions</a>
%H A005706 S. Plouffe, <a href="http://www.lacim.uqam.ca/%7Eplouffe/articles/MasterThesis.pdf">
               Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures</
               a>, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 
               1992.
%H A005706 S. Plouffe, <a href="http://www.lacim.uqam.ca/%7Eplouffe/articles/FonctionsGeneratrices.pdf">
               1031 Generating Functions and Conjectures</a>, Universit\'{e} du 
               Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
%F A005706 a(n) = a(n-1)+a([n/5]).
%o A005706 (PARI) a(n)=if(n<1,n==0,a(n-1)+a(n\5))
%Y A005706 Cf. A000041, A000123, A005704, A005705.
%Y A005706 Sequence in context: A135785 A008732 A130520 this_sequence A064175 A000028 
               A026416
%Y A005706 Adjacent sequences: A005703 A005704 A005705 this_sequence A005707 A005708 
               A005709
%K A005706 nonn,easy
%O A005706 0,2
%A A005706 N. J. A. Sloane (njas(AT)research.att.com).
%E A005706 Formula and more terms from Henry Bottomley (se16(AT)btinternet.com), 
               Apr 30 2001

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