1,1

Corresponds to simple periodic asynchronic site swap pattern ...333333... (performing a three-ball cascade forever).

This permutation consists of just three infinite cycles.

Table of n, a(n) for n=1..72.

Joe Buhler and R. L. Graham, Juggling Drops and Descents, Amer. Math. Monthly, 101, (no. 6) 1994, 507 - 519.

Index entries for sequences that are permutations of the natural numbers

Let f: Z -> N be given by f(z) = 2z if z>0 else 2|z|+1, with inverse g(z) = z/2 if z even else (1-z)/2. Then a(n) = f(g(n)+3).

Empirical g.f.: x*(3*x^7-3*x^6+4*x^5-4*x^4+4*x^3-10*x^2+2*x+6) / ((x-1)^2*(x+1)). [Colin Barker, Feb 18 2013]

Row 3 of A065167. Inverse permutation: A065170.

Sequence in context: A171784 A200133 A021150 * A006255 A110760 A050710

Adjacent sequences: A065163 A065164 A065165 * A065167 A065168 A065169

nonn

Antti Karttunen, Oct 19 2001

approved