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A080776 Oscillating sequence which rises to 2^(k-1) in k-th segment (k>=1) then falls back to 0. 1
0, 0, 1, 0, 1, 2, 1, 0, 1, 2, 3, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 7, 6, 5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 31, 30 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,6

COMMENTS

k-th segment has length 2^k (k>=0).

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

Table of n, a(n) for n=0..97.

R. Stephan, Some divide-and-conquer sequences ...

R. Stephan, Table of generating functions

FORMULA

G.f.: -1 + 2/(1-x) + 1/(1-x)^2 * (-1 + sum(k>=0, 2t^2(t-1), t=x^2^k)). a(n) = A005942(n+2) - 3(n+1), n>0. - Ralf Stephan, Sep 13 2003

a(0)=0, a(2n) = a(n) + a(n-1) + (n==1), a(2n+1) = 2a(n). - Ralf Stephan, Oct 20 2003

CROSSREFS

Essentially the same as A053646.

Sequence in context: A004074 A245615 A053646 * A065358 A062329 A022958

Adjacent sequences:  A080773 A080774 A080775 * A080777 A080778 A080779

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Mar 11 2003

STATUS

approved

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Last modified February 19 14:53 EST 2018. Contains 299334 sequences. (Running on oeis4.)