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Search: id:A068639
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| A068639 |
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a(0) = 0, a(n) = a(n-1) + (-1)^p(n) for n >= 1, where p(n) = highest power of 2 dividing n. |
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3
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| 0, 1, 0, 1, 2, 3, 2, 3, 2, 3, 2, 3, 4, 5, 4, 5, 6, 7, 6, 7, 8, 9, 8, 9, 8, 9, 8, 9, 10, 11, 10, 11, 10, 11, 10, 11, 12, 13, 12, 13, 12, 13, 12, 13, 14, 15, 14, 15, 16, 17, 16, 17, 18, 19, 18, 19, 18, 19, 18, 19, 20, 21, 20, 21, 22, 23, 22, 23, 24, 25, 24, 25, 24, 25, 24, 25, 26, 27, 26
(list; graph; listen)
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OFFSET
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0,5
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REFERENCES
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J.-P. Allouche and J. Shallit, The ring of k-regular sequences, II, Theoret. Computer Sci., 307 (2003), 3-29.
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LINKS
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J.-P. Allouche, J. Shallit, The Ring of k-regular Sequences, II
R. Stephan, Some divide-and-conquer sequences ...
R. Stephan, Table of generating functions
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FORMULA
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a(n)=(n+2*A065359(n))/3; a(n) is asymptotic to n/3. - Benoit Cloitre (benoit7848c(AT)orange.fr), Oct 04 2003
a(0)=0, a(2n) = -a(n) + n, a(2n+1) = -a(n) + n + 1. a(n) = (1/2) * (A050292(n) + A065639(n)). G.f. 1/2 * 1/(1-x) * sum(k>=0, (-1)^k*t/(1-t^2), t=x^2^k). - Ralf Stephan (ralf(AT)ark.in-berlin.de), Oct 17 2003
a(0)=0 then a(n)=ceiling(n/2)-a(n-ceiling(n/2)) - Benoit Cloitre (benoit7848c(AT)orange.fr), May 03 2004
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PROGRAM
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(PARI) a(n)=if(n<1, 0, ceil(n/2)-a(n-ceil(n/2)))
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CROSSREFS
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Cf. A087733.
Sequence in context: A010693 A139713 A023524 this_sequence A074070 A065067 A086411
Adjacent sequences: A068636 A068637 A068638 this_sequence A068640 A068641 A068642
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KEYWORD
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nonn,easy
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AUTHOR
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njas, Oct 01 2003
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EXTENSIONS
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More terms from John W. Layman (layman(AT)math.vt.edu) and Robert G. Wilson v (rgwv(AT)rgwv.com), Oct 02 2003
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