

A065169


Permutation t>t2 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
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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 2z+1, with inverse g(z) = z/2 if z even else (1z)/2. Then a(n) = f(g(n)2).
G.f.: x*(x^6x^5+4*x^44*x^3x^22*x+5) / ((x1)^2*(x+1)).  Colin Barker, Feb 18 2013
a(n) = 4*(1)^n+n for n>4. a(n) = a(n1)+a(n2)a(n3) 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^6x^5+4*x^44*x^3x^22*x+5)/((x1)^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



