A065172 Inverse permutation to A065171.

1, 3, 5, 2, 9, 7, 13, 4, 17, 11, 21, 6, 25, 15, 29, 8, 33, 19, 37, 10, 41, 23, 45, 12, 49, 27, 53, 14, 57, 31, 61, 16, 65, 35, 69, 18, 73, 39, 77, 20, 81, 43, 85, 22, 89, 47, 93, 24, 97, 51, 101, 26, 105, 55, 109, 28, 113, 59, 117, 30, 121, 63, 125, 32, 129, 67, 133, 34, 137

Offset: 1

Author

Antti Karttunen, Oct 19 2001

Keywords

• nonn

Links

• 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

Programs

Maple

[seq(Z2N(InfRisingSSInv(N2Z(n))), n=1..120)]; InfRisingSSInv := z -> `if`((z > 0),`if`((0 = (z mod 2)), z/2,-z),2*z);
N2Z := n -> ((-1)^n)*floor(n/2); Z2N := z -> 2*abs(z)+`if`((z < 1),1,0);

Formula

a(2n+1) = 4n+1, a(4n+2) = 4n+3, a(4n+4) = 2n+2. - Ralf Stephan, Jun 10 2005

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

From Luce ETIENNE, Nov 11 2016: (Start)

a(n) = (11*n-2-(5*n-6)*(-1)^n-(n+2)*((-1)^((2*n+1-(-1)^n)/4)+(-1)^((2*n-1+(-1)^n)/4)))/8.

a(n) = (11*n-2-(5*n-6)*cos(n*Pi)-2*(n+2)*cos(n*Pi/2))/8.

a(n) = (11*n-2-(5*n-6)*(-1)^n-(n+2)*(1+(-1)^n)*i^n)/8 where i = sqrt(-1). (End)