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A065176
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Site swap sequence associated with the permutation A065174 of Z.
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2
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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, 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, 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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| 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.
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).
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LINKS
| Joe Buhler and Ron Graham, Juggling Drops and Descents, Amer. Math. Monthly, 101, (no. 6) 1994, 507 - 519.
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FORMULA
| 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
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MAPLE
| [seq(TZ2(abs(N2Z(n))), n=1..120)];
N2Z := n -> ((-1)^n)*floor(n/2); Z2N := z -> 2*abs(z)+`if`((z < 1), 1, 0);
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CROSSREFS
| Bisection of this gives 2*A006519 or 2^A001511.
Sequence in context: A165207 A130501 A049116 * A060267 A048244 A056673
Adjacent sequences: A065173 A065174 A065175 * A065177 A065178 A065179
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KEYWORD
| nonn
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AUTHOR
| Antti Karttunen Oct 19 2001
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