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 A060973 a(2*n+1) = a(n+1)+a(n), a(2*n) = 2*a(n), with a(1)=0 and a(2)=1. 4
 0, 1, 1, 2, 2, 2, 3, 4, 4, 4, 4, 4, 5, 6, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 10, 11, 12, 13, 14, 15, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 REFERENCES Hsien-Kuei Hwang, S Janson, TH Tsai, Exact and asymptotic solutions of the recurrence f(n) = f(floor(n/2)) + f(ceiling(n/2)) + g(n): theory and applications, Preprint, 2016; http://140.109.74.92/hk/wp-content/files/2016/12/aat-hhrr-1.pdf. Also Exact and Asymptotic Solutions of a Divide-and-Conquer Recurrence Dividing at Half: Theory and Applications, ACM Transactions on Algorithms, 13:4 (2017), #47; DOI: 10.1145/3127585 LINKS R. J. Mathar, Table of n, a(n) for n = 1..1000 R. Stephan, Some divide-and-conquer sequences ... R. Stephan, Table of generating functions FORMULA a(n) = n-A006165(n) = A006165(n)-A053646(n) = (n-A053646(n))/2 [for n>1 ]. If n = 2*2^m+k with 0< = k< = 2^m, then a(n) = 2^m; if n = 3*2^m+k with 0< = k< = 2^m, then a(n) = 2^m+k. G.f. -x/(1-x) + x/(1-x)^2 * (1 + sum(k>=0, t^2(t-1), t=x^2^k)). - Ralf Stephan, Sep 12 2003 EXAMPLE a(6)=2*a(3)=2*1=2. a(7)=a(3)+a(4)=1+2=3. MAPLE A060973 := proc(n)     option remember;     if n <= 2 then         return n-1;     fi;     if n mod 2 = 0 then         2*procname(n/2)     else         procname((n-1)/2)+procname((n+1)/2);     fi; end proc: CROSSREFS Sequence in context: A228482 A091822 A173022 * A097915 A255072 A029131 Adjacent sequences:  A060970 A060971 A060972 * A060974 A060975 A060976 KEYWORD nonn AUTHOR Henry Bottomley, May 09 2001 STATUS approved

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Last modified November 17 05:59 EST 2018. Contains 317275 sequences. (Running on oeis4.)