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A065165 Permutation t->t+2 of Z, folded to N. 3
4, 6, 2, 8, 1, 10, 3, 12, 5, 14, 7, 16, 9, 18, 11, 20, 13, 22, 15, 24, 17, 26, 19, 28, 21, 30, 23, 32, 25, 34, 27, 36, 29, 38, 31, 40, 33, 42, 35, 44, 37, 46, 39, 48, 41, 50, 43, 52, 45, 54, 47, 56, 49, 58, 51, 60, 53, 62, 55, 64, 57, 66, 59, 68, 61, 70, 63, 72, 65, 74, 67, 76 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Corresponds to simple periodic asynchronic site swap pattern ...222222... (holding a ball in each hand forever).

This permutation consists of just two infinite cycles.

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

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

Index entries for linear recurrences with constant coefficients, signature (1,1,-1).

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)+2).

G.f.: x*(3*x^5-3*x^4+4*x^3-8*x^2+2*x+4) / ((x-1)^2*(x+1)). - Colin Barker, Feb 18 2013

a(n) = 4*(-1)^n+n for n>3. a(n) = a(n-1)+a(n-2)-a(n-3) for n>6. - Colin Barker, Mar 07 2014

MATHEMATICA

CoefficientList[Series[(3 x^5 - 3 x^4 + 4 x^3 - 8 x^2 + 2 x + 4)/((x - 1)^2 (x + 1)), {x, 0, 100}], x] (* Vincenzo Librandi, Mar 08 2014 *)

LinearRecurrence[{1, 1, -1}, {4, 6, 2, 8, 1, 10}, 80] (* Harvey P. Dale, May 09 2018 *)

PROG

(PARI) Vec(x*(3*x^5-3*x^4+4*x^3-8*x^2+2*x+4)/((x-1)^2*(x+1))  + O(x^100)) \\ Colin Barker, Mar 07 2014

CROSSREFS

Row 2 of A065167. Inverse permutation: A065169.

Sequence in context: A137662 A153124 A066252 * A088516 A114538 A181096

Adjacent sequences:  A065162 A065163 A065164 * A065166 A065167 A065168

KEYWORD

nonn,easy

AUTHOR

Antti Karttunen, Oct 19 2001

STATUS

approved

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Last modified January 21 11:54 EST 2019. Contains 319356 sequences. (Running on oeis4.)