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A115638 A Jacobsthal-related divide-and-conquer sequence. 2
1, -1, 5, -1, -3, -1, 21, -1, -3, -1, -11, -1, -3, -1, 85, -1, -3, -1, -11, -1, -3, -1, -43, -1, -3, -1, -11, -1, -3, -1, 341, -1, -3, -1, -11, -1, -3, -1, -43, -1, -3, -1, -11, -1, -3, -1, -171, -1, -3, -1, -11, -1, -3, -1, -43, -1, -3, -1, -11, -1, -3, -1, 1365, -1, -3, -1, -11, -1, -3, -1, -43 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Partial sums are A115637.

LINKS

Antti Karttunen, Table of n, a(n) for n = 0..1024

R. Stephan, Divide-and-conquer generating functions. I. Elementary sequences, arXiv:math/0307027 [math.CO], 2003.

FORMULA

G.f.: Sum_{k>=0} 4^k*x^(2^(k+1)-2)/(1+x^(2^k)); the g.f. G(x) satisfies G(x) - 4*x^2*G(x^2) = 1/(1+x).

a(0) = 1; for n >= 1, a(n) = A115637(n) - A115637(n-1). - Antti Karttunen, Nov 02 2018

PROG

(PARI) A115638(n) = if(!n, 1, A115637(n)-A115637(n-1)); \\ (Needs also code from A115637) - Antti Karttunen, Nov 02 2018

CROSSREFS

Cf. A001045, A115637.

Sequence in context: A111740 A155059 A206076 * A055515 A215010 A136744

Adjacent sequences:  A115635 A115636 A115637 * A115639 A115640 A115641

KEYWORD

easy,sign

AUTHOR

Paul Barry, Jan 27 2006

STATUS

approved

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Last modified March 22 01:06 EDT 2019. Contains 321406 sequences. (Running on oeis4.)