A068639 a(0) = 0, a(n) = a(n-1) + (-1)^p(n) for n >= 1, where p(n) = highest power of 2 dividing n.

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

Offset

0,5

Links

Table of n, a(n) for n=0..78.

J.-P. Allouche and J. Shallit, The Ring of k-regular Sequences, II

J.-P. Allouche and J. Shallit, The ring of k-regular sequences, II, Theoret. Computer Sci., 307 (2003), 3-29.

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

Ralf 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

From Ralf Stephan, Oct 17 2003: (Start)

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) where t=x^2^k. (End)

a(0)=0 then a(n) = ceiling(n/2)-a(n-ceiling(n/2)). - Benoit Cloitre, May 03 2004

Prog

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

Crossrefs

Cf. A087733.

Sequence in context: A178620 A342866 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