A065170 Permutation t->t-3 of Z, folded to N.

7, 5, 9, 3, 11, 1, 13, 2, 15, 4, 17, 6, 19, 8, 21, 10, 23, 12, 25, 14, 27, 16, 29, 18, 31, 20, 33, 22, 35, 24, 37, 26, 39, 28, 41, 30, 43, 32, 45, 34, 47, 36, 49, 38, 51, 40, 53, 42, 55, 44, 57, 46, 59, 48, 61, 50, 63, 52, 65, 54, 67, 56, 69, 58, 71, 60, 73, 62, 75, 64, 77, 66

Offset

1,1

Comments

This permutation consists of just three cycles, which are 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 linear recurrences with constant coefficients, signature (1,1,-1).

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).

G.f.: x*(x^8-x^7+4*x^6-4*x^5+4*x^4-4*x^3-3*x^2-2*x+7) / ((x-1)^2*(x+1)). - Colin Barker, Feb 18 2013

a(n) = -6*(-1)^n+n for n>6. a(n) = a(n-1)+a(n-2)-a(n-3) for n>9. - Colin Barker, Mar 07 2014

Sum_{n>=1} (-1)^n/a(n) = 46/15 - log(2). - Amiram Eldar, Aug 08 2023

Mathematica

CoefficientList[Series[(x^8 - x^7 + 4 x^6 - 4 x^5 + 4 x^4 - 4 x^3 - 3 x^2 - 2 x + 7)/((x - 1)^2 (x + 1)), {x, 0, 100}], x] (* Vincenzo Librandi, Mar 08 2014 *)
LinearRecurrence[{1, 1, -1}, {7, 5, 9, 3, 11, 1, 13, 2, 15}, 80] (* Harvey P. Dale, Oct 19 2018 *)

Prog

(PARI) Vec(x*(x^8-x^7+4*x^6-4*x^5+4*x^4-4*x^3-3*x^2-2*x+7)/((x-1)^2*(x+1))  + O(x^100)) \\ Colin Barker, Mar 07 2014

Crossrefs

Inverse permutation to A065166.

Sequence in context: A339529 A195493 A195399 * A346589 A113816 A358186

Adjacent sequences: A065167 A065168 A065169 * A065171 A065172 A065173

Keyword

nonn,easy

Author

Antti Karttunen, Oct 19 2001

Status

approved