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).
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
KEYWORD
nonn,easy
AUTHOR
Antti Karttunen, Oct 19 2001
STATUS
approved