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%I #9 May 02 2017 22:17:15
%S 6,8,4,10,2,12,1,14,3,16,5,18,7,20,9,22,11,24,13,26,15,28,17,30,19,32,
%T 21,34,23,36,25,38,27,40,29,42,31,44,33,46,35,48,37,50,39,52,41,54,43,
%U 56,45,58,47,60,49,62,51,64,53,66,55,68,57,70,59,72,61,74,63,76,65,78
%N Permutation t->t+3 of Z, folded to N.
%C Corresponds to simple periodic asynchronic site swap pattern ...333333... (performing a three-ball cascade forever).
%C This permutation consists of just three infinite cycles.
%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 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)+3).
%F Empirical g.f.: x*(3*x^7-3*x^6+4*x^5-4*x^4+4*x^3-10*x^2+2*x+6) / ((x-1)^2*(x+1)). [_Colin Barker_, Feb 18 2013]
%Y Row 3 of A065167. Inverse permutation: A065170.
%K nonn
%O 1,1
%A _Antti Karttunen_, Oct 19 2001
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