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Search: id:A065173
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| A065173 |
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Site swap sequence that rises infinitely after t=0. The associated delta sequence p(t)-t for the permutation of Z: A065171. |
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+0
3
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| 0, 1, 2, 2, 1, 3, 6, 4, 2, 5, 10, 6, 3, 7, 14, 8, 4, 9, 18, 10, 5, 11, 22, 12, 6, 13, 26, 14, 7, 15, 30, 16, 8, 17, 34, 18, 9, 19, 38, 20, 10, 21, 42, 22, 11, 23, 46, 24, 12, 25, 50, 26, 13, 27, 54, 28, 14, 29, 58, 30, 15, 31, 62, 32, 16, 33, 66, 34, 17, 35, 70, 36, 18, 37, 74, 38
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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Here the site swap pattern ..., 5, 18, 4, 14, 3, 10, 2, 6, 1, 2, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, ... 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, t=3, t=-3, etc. successively.
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LINKS
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Joe Buhler and Ron Graham, Juggling Drops and Descents, Amer. Math. Monthly, 101, (no. 6) 1994, 507 - 519.
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FORMULA
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a(2n+2) = n+1, a(4n+1) = n, a(4n+3) = 4n+2. - Ralf Stephan, Jun 10 2005
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MAPLE
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[seq((InfRisingSS(N2Z(n))-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
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The other bisection gives A000027.
Sequence in context: A046726 A082137 A091187 this_sequence A098474 A056860 A107111
Adjacent sequences: A065170 A065171 A065172 this_sequence A065174 A065175 A065176
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KEYWORD
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nonn
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AUTHOR
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Antti Karttunen Oct 19 2001
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