

A068639


a(0) = 0, a(n) = a(n1) + (1)^p(n) for n >= 1, where p(n) = highest power of 2 dividing n.


2



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
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OFFSET

0,5


REFERENCES

J.P. Allouche and J. Shallit, The ring of kregular sequences, II, Theoret. Computer Sci., 307 (2003), 329.


LINKS

Table of n, a(n) for n=0..78.
J.P. Allouche, J. Shallit, The Ring of kregular Sequences, II
R. Stephan, Some divideandconquer sequences ...
R. Stephan, Table of generating functions


FORMULA

a(n)=(n+2*A065359(n))/3; a(n) is asymptotic to n/3.  Benoit Cloitre, 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/(1x) * sum(k>=0, (1)^k*t/(1t^2), t=x^2^k).  Ralf Stephan, Oct 17 2003
a(0)=0 then a(n)=ceiling(n/2)a(nceiling(n/2))  Benoit Cloitre, May 03 2004


PROG

(PARI) a(n)=if(n<1, 0, ceil(n/2)a(nceil(n/2)))


CROSSREFS

Cf. A087733.
Sequence in context: A171465 A178620 A023524 * A074070 A304097 A251101
Adjacent sequences: A068636 A068637 A068638 * A068640 A068641 A068642


KEYWORD

nonn,easy


AUTHOR

N. J. A. Sloane, Oct 01 2003


EXTENSIONS

More terms from John W. Layman and Robert G. Wilson v, Oct 02 2003


STATUS

approved



