A065166 Permutation t->t+3 of Z, folded to N.

6, 8, 4, 10, 2, 12, 1, 14, 3, 16, 5, 18, 7, 20, 9, 22, 11, 24, 13, 26, 15, 28, 17, 30, 19, 32, 21, 34, 23, 36, 25, 38, 27, 40, 29, 42, 31, 44, 33, 46, 35, 48, 37, 50, 39, 52, 41, 54, 43, 56, 45, 58, 47, 60, 49, 62, 51, 64, 53, 66, 55, 68, 57, 70, 59, 72, 61, 74, 63, 76, 65, 78

Offset

1,1

Comments

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

This permutation consists of just three infinite cycles.

Links

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

Formula

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]

Crossrefs

Row 3 of A065167. Inverse permutation: A065170.

Sequence in context: A200133 A021150 A347407 * A006255 A110760 A050710

Adjacent sequences: A065163 A065164 A065165 * A065167 A065168 A065169

Keyword

nonn

Author

Antti Karttunen, Oct 19 2001

Status

approved