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%I #20 Jun 17 2017 03:09:36
%S 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,
%T 31,24,33,26,35,28,37,30,39,32,41,34,43,36,45,38,47,40,49,42,51,44,53,
%U 46,55,48,57,50,59,52,61,54,63,56,65,58,67,60,69,62,71,64,73,66,75,68
%N Permutation t->t-2 of Z, folded to N.
%C This permutation consists of just two cycles, both infinite.
%H Vincenzo Librandi, <a href="/A065169/b065169.txt">Table of n, a(n) for n = 1..1000</a>
%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>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,-1).
%F Let f: Z -> N be given by f(z) = 2z if z>0 else 2|z|+1, with inverse g(z) = z/2 if z even else (1-z)/2. Then a(n) = f(g(n)-2).
%F G.f.: x*(x^6-x^5+4*x^4-4*x^3-x^2-2*x+5) / ((x-1)^2*(x+1)). - _Colin Barker_, Feb 18 2013
%F a(n) = -4*(-1)^n+n for n>4. a(n) = a(n-1)+a(n-2)-a(n-3) for n>7. - _Colin Barker_, Mar 07 2014
%t 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 *)
%o (PARI) Vec(x*(x^6-x^5+4*x^4-4*x^3-x^2-2*x+5)/((x-1)^2*(x+1)) + O(x^100)) \\ _Colin Barker_, Mar 07 2014
%Y Inverse permutation to A065165.
%K nonn,easy
%O 1,1
%A _Antti Karttunen_, Oct 19 2001
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