Search: id:A065176
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%I A065176
%S A065176 0,2,2,4,4,2,2,8,8,2,2,4,4,2,2,16,16,2,2,4,4,2,2,8,8,2,2,4,4,2,2,32,32,
%T A065176 2,2,4,4,2,2,8,8,2,2,4,4,2,2,16,16,2,2,4,4,2,2,8,8,2,2,4,4,2,2,64,64,2,
%U A065176 2,4,4,2,2,8,8,2,2,4,4,2,2,16,16,2,2,4,4,2,2,8,8,2,2,4,4,2,2,32,32,2,2
%N A065176 Site swap sequence associated with the permutation A065174 of Z.
%C A065176 Here the site swap pattern ...,2,16,2,4,2,8,2,4,2,0,2,4,2,8,2,4,2,16,
               2,... that spans over the Z (zero throw is at t=0) has been folded 
               to N by picking values at t=0, t=1, t=-1, t=2, t=-2, etc. successively.
%C A065176 This pattern is shown in the figure 7 of Buhler and Graham paper and 
               uses infinitely many balls, with each ball at step t thrown always 
               to constant "height" 2^A001511[abs(t)] (no balls in hands at step 
               t=0).
%H A065176 Joe Buhler and Ron Graham, <a href="http://www.cecm.sfu.ca/organics/papers/
               buhler/index.html">Juggling Drops and Descents</a>, Amer. Math. Monthly, 
               101, (no. 6) 1994, 507 - 519.
%F A065176 G.f.: (1-x+x^2)/(1-x) + (1+x)*Sum(k>=1, 2^(k-1)*x^2^k/(1-x^2^k)). - Ralf 
               Stephan (ralf(AT)ark.in-berlin.de), Apr 17 2003
%p A065176 [seq(TZ2(abs(N2Z(n))), n=1..120)];
%p A065176 N2Z := n -> ((-1)^n)*floor(n/2); Z2N := z -> 2*abs(z)+`if`((z < 1),1,
               0);
%Y A065176 Bisection of this gives 2*A006519 or 2^A001511.
%Y A065176 Sequence in context: A165207 A130501 A049116 this_sequence A060267 A048244 
               A056673
%Y A065176 Adjacent sequences: A065173 A065174 A065175 this_sequence A065177 A065178 
               A065179
%K A065176 nonn
%O A065176 1,2
%A A065176 Antti Karttunen Oct 19 2001

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