A065169 Permutation t->t-2 of Z, folded to N.

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

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: A198749 A338294 A066253 * A247617 A099217 A023103

Adjacent sequences: A065166 A065167 A065168 * A065170 A065171 A065172

Keyword

nonn,easy

Author

Antti Karttunen, Oct 19 2001

Status

approved