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 A115638 A Jacobsthal-related divide-and-conquer sequence. 2

%I

%S 1,-1,5,-1,-3,-1,21,-1,-3,-1,-11,-1,-3,-1,85,-1,-3,-1,-11,-1,-3,-1,

%T -43,-1,-3,-1,-11,-1,-3,-1,341,-1,-3,-1,-11,-1,-3,-1,-43,-1,-3,-1,-11,

%U -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

%N A Jacobsthal-related divide-and-conquer sequence.

%C Partial sums are A115637.

%H Antti Karttunen, <a href="/A115638/b115638.txt">Table of n, a(n) for n = 0..1024</a>

%H R. Stephan, <a href="https://arxiv.org/abs/math/0307027">Divide-and-conquer generating functions. I. Elementary sequences</a>, arXiv:math/0307027 [math.CO], 2003.

%F 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).

%F a(0) = 1; for n >= 1, a(n) = A115637(n) - A115637(n-1). - _Antti Karttunen_, Nov 02 2018

%o (PARI) A115638(n) = if(!n,1, A115637(n)-A115637(n-1)); \\ (Needs also code from A115637) - _Antti Karttunen_, Nov 02 2018

%Y Cf. A001045, A115637.

%K easy,sign

%O 0,3

%A _Paul Barry_, Jan 27 2006

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Last modified August 1 18:27 EDT 2021. Contains 346402 sequences. (Running on oeis4.)