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.
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, -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, 2, 3, 1, 4, 3, 5, 2, 5, 3, 4, 1, 5, 4, 7, 3, 8, 5, 7, 2, 7, 5, 8, 3, 7
Offset: 0
Links
- Bruno Berselli, Table of n, a(n) for n = 0..10000
- Jean-Paul Allouche, On the Stern sequence and its twisted version, arXiv preprint arXiv:1202.4171 [math.NT], 2012.
- Roland Bacher, Twisting the Stern sequence, arXiv:1005.5627v1 [math.CO], 2010.
- Peter Bundschuh & Keijo Väänänen, Algebraic independence of the generating functions of Stern's sequence and of its twist, Journal de théorie des nombres de Bordeaux, 25 no. 1 (2013), p. 43-57, doi: 10.5802/jtnb.824.
- Michael Coons, On Some Conjectures concerning Stern's Sequence and its Twist, arXiv:1008.0193v3 [math.NT], 2010.
Programs
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Mathematica
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 *) -
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 */