%I A005599 M0468
%S A005599 1,2,3,4,5,6,7,6,7,8,9,10,11,12,11,12,13,14,15,16,17,18,19,18,19,20,21,
%T A005599 20,19,18,19,18,19,20,21,22,23,24,25,24,25,26,27,28,29,30,29,30,31,32,
               33,34,35,36,35
%N A005599 Running sum of every third term in the {+1,-1}-version of Thue-Morse 
               sequence A010060.
%C A005599 The generating function -(2*z**4+z**3+z+1)*(z**3-z**2-1)/(z**6+z**5+z**4+z**3+z**2+z+1)/
               (z-1)**2 proposed in the Plouffe thesis is wrong.
%D A005599 J. Coquet, A summation formula related to the binary digits, Inventiones 
               math., 73 (1983), 107-115.
%D A005599 D. J. Newman, On the number of binary digits in a multiple of three, 
               Proc. Amer. Math. Soc., 21 (1969), 719-721.
%D A005599 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%H A005599 P. Flajolet et al., <a href="http://algo.inria.fr/flajolet/Publications/
               FlGrKiPrTi94.pdf">Mellin Transforms And Asymptotics: Digital Sums</
               a>, Theoret. Computer Sci. 23 (1994), 291-314.
%H A005599 P. J. Grabner, H.-K. Hwang, <a href="http://algo.stat.sinica.edu.tw/">
               Digital sums and divide-and-conquer recurrences: Fourier expansions 
               and absolute convergence</a>
%H A005599 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 A005599 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.
%Y A005599 Sequence in context: A017872 A161209 A000026 this_sequence A071934 A161658 
               A066853
%Y A005599 Adjacent sequences: A005596 A005597 A005598 this_sequence A005600 A005601 
               A005602
%K A005599 nonn,easy,nice
%O A005599 1,2
%A A005599 M. R. Schroeder.