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A065169 Permutation t->t-2 of Z, folded to N. 2
5, 3, 7, 1, 9, 2, 11, 4, 13, 6, 15, 8, 17, 10, 19, 12, 21, 14, 23, 16, 25, 18, 27, 20, 29, 22, 31, 24, 33, 26, 35, 28, 37, 30, 39, 32, 41, 34, 43, 36, 45, 38, 47, 40, 49, 42, 51, 44, 53, 46, 55, 48, 57, 50, 59, 52, 61, 54, 63, 56, 65, 58, 67, 60, 69, 62, 71, 64, 73, 66, 75, 68 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

This permutation consists of just two cycles, both infinite.

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*(x^6-x^5+4*x^4-4*x^3-x^2-2*x+5) / ((x-1)^2*(x+1)). - Colin Barker, Feb 18 2013

a(n) = -4*(-1)^n+n for n>4. a(n) = a(n-1)+a(n-2)-a(n-3) for n>7. - Colin Barker, Mar 07 2014

MATHEMATICA

CoefficientList[Series[(x^6 - x^5 + 4 x^4 - 4 x^3 - x^2 - 2 x + 5)/((x - 1)^2 (x + 1)), {x, 0, 100}], x] (* Vincenzo Librandi, Mar 08 2014 *)

PROG

(PARI) Vec(x*(x^6-x^5+4*x^4-4*x^3-x^2-2*x+5)/((x-1)^2*(x+1))  + O(x^100)) \\ Colin Barker, Mar 07 2014

CROSSREFS

Inverse permutation to A065165.

Sequence in context: A097907 A198749 A066253 * A247617 A099217 A023103

Adjacent sequences:  A065166 A065167 A065168 * A065170 A065171 A065172

KEYWORD

nonn,easy

AUTHOR

Antti Karttunen, Oct 19 2001

STATUS

approved

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Last modified January 18 01:36 EST 2019. Contains 319260 sequences. (Running on oeis4.)