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

Author

Antti Karttunen, Oct 19 2001

Keywords

• nonn

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

• 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

Crossrefs

Row 3 of A065167. Inverse permutation: A065170.

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]