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A065166 Permutation t->t+3 of Z, folded to N. 7
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 (list; graph; refs; listen; history; text; internal format)
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: A171784 A200133 A021150 * A006255 A110760 A050710

Adjacent sequences:  A065163 A065164 A065165 * A065167 A065168 A065169

KEYWORD

nonn

AUTHOR

Antti Karttunen, Oct 19 2001

STATUS

approved

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Last modified January 22 09:52 EST 2019. Contains 319363 sequences. (Running on oeis4.)