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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 (list; graph; refs; listen; history; text; internal format)
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.: (1-x+x^2)/(1-x) + (1+x)*Sum(k>=1, 2^(k-1)*x^2^k/(1-x^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

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Last modified August 1 22:36 EDT 2021. Contains 346408 sequences. (Running on oeis4.)