cp's OEIS Frontend

A213369 The twisted Stern sequence: a(0) = 0, a(1) = 1 and a(2n) = -a(n), a(2n + 1) = -a(n)-a(n + 1) for n>=1.

%I A213369 #69 May 28 2019 11:52:13
%S A213369 0,1,-1,0,1,1,0,-1,-1,-2,-1,-1,0,1,1,2,1,3,2,3,1,2,1,1,0,-1,-1,-2,-1,
%T A213369 -3,-2,-3,-1,-4,-3,-5,-2,-5,-3,-4,-1,-3,-2,-3,-1,-2,-1,-1,0,1,1,2,1,3,
%U A213369 2,3,1,4,3,5,2,5,3,4,1,5,4,7,3,8,5,7,2,7,5,8,3,7
%N A213369 The twisted Stern sequence: a(0) = 0, a(1) = 1 and a(2n) = -a(n), a(2n + 1) = -a(n)-a(n + 1) for n>=1.
%H A213369 Bruno Berselli, <a href="/A213369/b213369.txt">Table of n, a(n) for n = 0..10000</a>
%H A213369 Jean-Paul Allouche, <a href="http://arxiv.org/abs/1202.4171">On the Stern sequence and its twisted version</a>, arXiv preprint arXiv:1202.4171 [math.NT], 2012.
%H A213369 Roland Bacher, <a href="http://arxiv.org/abs/1005.5627">Twisting the Stern sequence</a>, arXiv:1005.5627v1 [math.CO], 2010.
%H A213369 Peter Bundschuh & Keijo Väänänen, <a href="http://dx.doi.org/10.5802/jtnb.824">Algebraic independence of the generating functions of Stern's sequence and of its twist</a>, Journal de théorie des nombres de Bordeaux, 25 no. 1 (2013), p. 43-57, doi: 10.5802/jtnb.824.
%H A213369 Michael Coons, <a href="http://arxiv.org/abs/1008.0193">On Some Conjectures concerning Stern's Sequence and its Twist</a>, arXiv:1008.0193v3 [math.NT], 2010.
%F A213369 a(n) = A287729(n) - A287730(n) for n > 0. - _Michel Marcus_ & _I. V. Serov_, May 28 2019
%t A213369 a[0]=0; a[1]=1; a[n_] := a[n] = If[EvenQ[n], -a[n/2], -a[(n-1)/2]-a[(n+1)/2 ]]; Table[a[n], {n, 0, 77}] (* _Jean-François Alcover_, Oct 02 2018 *)
%o A213369 (Maxima) a[0]:0$ a[1]:1$ a[n]:=-a[floor(n/2)]-(1-(-1)^n)*a[floor((n-1)/2)+1]/2$ makelist(a[n],n,0,77); /* _Bruno Berselli_, Jun 15 2012 */
%Y A213369 Cf. A002487. Absolute values give A020944.
%K A213369 sign,look
%O A213369 0,10
%A A213369 _N. J. A. Sloane_, Jun 13 2012