Search: id:A026465
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%I A026465
%S A026465 1,2,1,1,2,2,2,1,1,2,1,1,2,1,1,2,2,2,1,1,2,2,2,1,1,2,2,2,1,1,2,1,1,2,1,
%T A026465 1,2,2,2,1,1,2,1,1,2,1,1,2,2,2,1,1,2,1,1,2,1,1,2,2,2,1,1,2,2,2,1,1,2,2,
%U A026465 2,1,1,2,1,1,2,1,1,2,2,2,1,1,2,2,2,1,1,2,2,2,1,1,2,1,1,2,1,1,2,2,2,1,1
%N A026465 Length of n-th run of identical symbols in A001285 (Thue-Morse sequence).
%C A026465 Number of representations of n as a sum of Jacobsthal numbers (1 is allowed 
               twice as a part). Partial sums are A003159. With interpolated zeros, 
               g.f. is Product{k>=1, 1+x^A078008(k)}/2. - Paul Barry (pbarry(AT)wit.ie), 
               Dec 09 2004
%C A026465 Can also be generated by counting the consecutive 0's or 1's in A010060 
               or A010059. - Robin D. Saunders (saunders_robin_d(AT)hotmail.com), 
               Sep 06 2006
%D A026465 J.-P. Allouche, Andre Arnold, Jean Berstel, Srecko Brlek, William Jockusch, 
               Simon Plouffe and Bruce E. Sagan, A sequence related to that of Thue-Morse, 
               Discrete Math., 139 (1995), 455-461.
%D A026465 S. Brlek, Enumeration of factors in the Thue-Morse word, Discrete Applied 
               Math., 24 (1989), 83-96.
%F A026465 It appears that the sequence can be calculated by any of the following 
               three methods: (1) Start with 1 and repeatedly replace 1 with 1, 
               2, 1 and 2 with 1, 2, 2, 2, 1; (2) a(1)=1, all terms are either 1 
               or 2 and, for n>0, a(n)=1 if the length of the n-th run of 2's is 
               1; a(n)=2 if the length of the n-th run of consecutive 2's is 3, 
               with each run of 2's separated by a run of two 1's; (3) replace each 
               3 in A080426 with 2. - John W. Layman (layman(AT)math.vt.edu), Feb 
               18 2003
%F A026465 a(1)=1, for n>1 a(n)= A003159(n)-A003159(n-1) - Benoit Cloitre (benoit7848c(AT)orange.fr), 
               May 31 2003
%F A026465 G.f.: Product{k>=1, 1+x^A001045(k)} - Paul Barry (pbarry(AT)wit.ie), 
               Dec 09 2004
%Y A026465 Cf. A101615.
%Y A026465 Sequence in context: A023191 A029256 A109073 this_sequence A051486 A081355 
               A060778
%Y A026465 Adjacent sequences: A026462 A026463 A026464 this_sequence A026466 A026467 
               A026468
%K A026465 nonn
%O A026465 1,2
%A A026465 Clark Kimberling (ck6(AT)evansville.edu)
%E A026465 Corrected and extended by John W. Layman (layman(AT)math.vt.edu), Feb 
               18 2003

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