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%I #19 May 02 2017 22:17:15
%S 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,
%T 53,14,57,31,61,16,65,35,69,18,73,39,77,20,81,43,85,22,89,47,93,24,97,
%U 51,101,26,105,55,109,28,113,59,117,30,121,63,125,32,129,67,133,34,137
%N Inverse permutation to A065171.
%H Joe Buhler and R. L. Graham, <a href="http://www.cecm.sfu.ca/organics/papers/buhler/index.html">Juggling Drops and Descents</a>, Amer. Math. Monthly, 101, (no. 6) 1994, 507 - 519.
%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F a(2n+1) = 4n+1, a(4n+2) = 4n+3, a(4n+4) = 2n+2. - _Ralf Stephan_, Jun 10 2005
%F 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
%F From _Luce ETIENNE_, Nov 11 2016: (Start)
%F 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.
%F a(n) = (11*n-2-(5*n-6)*cos(n*Pi)-2*(n+2)*cos(n*Pi/2))/8.
%F a(n) = (11*n-2-(5*n-6)*(-1)^n-(n+2)*(1+(-1)^n)*i^n)/8 where i = sqrt(-1). (End)
%p [seq(Z2N(InfRisingSSInv(N2Z(n))), n=1..120)]; InfRisingSSInv := z -> `if`((z > 0),`if`((0 = (z mod 2)), z/2,-z),2*z);
%p N2Z := n -> ((-1)^n)*floor(n/2); Z2N := z -> 2*abs(z)+`if`((z < 1),1,0);
%K nonn
%O 1,2
%A _Antti Karttunen_, Oct 19 2001
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