

A065176


Site swap sequence associated with the permutation A065174 of Z.


3



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
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OFFSET

1,2


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).


LINKS

Table of n, a(n) for n=1..99.
Joe Buhler and R. L. Graham, Juggling Drops and Descents, Amer. Math. Monthly, 101, (no. 6) 1994, 507  519.


FORMULA

G.f.: (1x+x^2)/(1x) + (1+x)*Sum(k>=1, 2^(k1)*x^2^k/(1x^2^k)).  Ralf Stephan, Apr 17 2003


MAPLE

[seq(TZ2(abs(N2Z(n))), n=1..120)]; # using TZ2 from A065174
N2Z := n > ((1)^n)*floor(n/2); Z2N := z > 2*abs(z)+`if`((z < 1), 1, 0);


PROG

(PARI) a(n) = if(n==1, 0, 1<<valuation(bitnegimply(n, 1), 2)); \\ Kevin Ryde, Jul 09 2021


CROSSREFS

Bisection of this gives A171977 or 2*A006519 or 2^A001511.
Sequence in context: A165207 A130501 A049116 * A060267 A214516 A238004
Adjacent sequences: A065173 A065174 A065175 * A065177 A065178 A065179


KEYWORD

easy,nonn


AUTHOR

Antti Karttunen, Oct 19 2001


STATUS

approved



