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

1,2

Links

Table of n, a(n) for n=1..69.

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

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)

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);

Crossrefs

Sequence in context: A356472 A245653 A209748 * A026212 A026188 A057033

Adjacent sequences: A065169 A065170 A065171 * A065173 A065174 A065175

Keyword

nonn

Author

Antti Karttunen, Oct 19 2001

Status

approved