A083905 - OEIS

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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 (list; graph; refs; listen; history; internal format)

	OFFSET	`1,10`
	COMMENTS	`For all n, a(3*A006288(n)) = 0 as proved in Russian forum dxdy.ru - see link.`
	LINKS	`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).`
	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)), n):print1(t", "))`
	CROSSREFS	`Cf. A065359, A023416.` `a(n) = A030300(n) - A065359(n).` `Sequence in context: A143240 A153659 A016102 * A179319 A045706 A045634` `Adjacent sequences: A083902 A083903 A083904 * A083906 A083907 A083908`
	KEYWORD	`sign,easy`
	AUTHOR	`Ralf Stephan (ralf(AT)ark.in-berlin.de), Jun 18 2003`

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Last modified February 17 09:41 EST 2012. Contains 206009 sequences.