A083905 G.f.: 1/(1-x) * sum(k>=0, (-1)^k*x^2^(k+1)/(1+x^2^k)).

0, 1, 0, 0, -1, 1, 0, 1, 0, 2, 1, 0, -1, 1, 0, 0, -1, 1, 0, -1, -2, 0, -1, 1, 0, 2, 1, 0, -1, 1, 0, 1, 0, 2, 1, 0, -1, 1, 0, 2, 1, 3, 2, 1, 0, 2, 1, 0, -1, 1, 0, -1, -2, 0, -1, 1, 0, 2, 1, 0, -1, 1, 0, 0, -1, 1, 0, -1, -2, 0, -1, 1, 0, 2, 1, 0, -1, 1, 0, -1, -2, 0, -1, -2, -3, -1

Offset

1,10

Comments

For all n, a(3*A006288(n)) = 0 as proved in Russian forum dxdy.ru - see link.

Links

Table of n, a(n) for n=1..86.

Discussion in Russian forum dxdy.ru

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

R. Stephan, Table of generating functions

R. Stephan, Divide-and-conquer generating functions. I. Elementary sequences

Formula

a(1)=0, a(2n) = -a(n)+1, a(2n+1) = -a(n).

a(n) = A030300(n) - A065359(n).

Prog

(PARI) for(n=1, 100, l=ceil(log(n)/log(2)); t=polcoeff(1/(1-x)*sum(k=0, l, (-1)^k*(x^2^(k+1))/(1+x^2^k)) + O(x^(n+1)), n); print1(t", "))
(PARI) a(n) = sum(i=0, logint(n, 2)-1, if(!bittest(n, i), (-1)^i)); \\ Kevin Ryde, May 24 2021

Crossrefs

Cf. A030300, A065359, A023416, A006288.

Sequence in context: A366851 A357525 A016102 * A179319 A321916 A257265

Adjacent sequences: A083902 A083903 A083904 * A083906 A083907 A083908

Keyword

sign,easy

Author

Ralf Stephan, Jun 18 2003

Status

approved