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A065172 Inverse permutation to A065171. 1
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 (list; graph; refs; listen; history; text; internal format)
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: A273668 A245653 A209748 * A026188 A026212 A057033

Adjacent sequences:  A065169 A065170 A065171 * A065173 A065174 A065175

KEYWORD

nonn

AUTHOR

Antti Karttunen, Oct 19 2001

STATUS

approved

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Last modified January 18 23:05 EST 2019. Contains 319282 sequences. (Running on oeis4.)