cp's OEIS Frontend

A065171 Permutation of Z, folded to N, corresponding to the site swap pattern ...26120123456... which ascends infinitely after t=0.

%I A065171 #34 May 02 2017 22:17:15
%S A065171 1,4,2,8,3,12,6,16,5,20,10,24,7,28,14,32,9,36,18,40,11,44,22,48,13,52,
%T A065171 26,56,15,60,30,64,17,68,34,72,19,76,38,80,21,84,42,88,23,92,46,96,25,
%U A065171 100,50,104,27,108,54,112,29,116,58,120,31,124,62,128,33,132,66,136,35
%N A065171 Permutation of Z, folded to N, corresponding to the site swap pattern ...26120123456... which ascends infinitely after t=0.
%C A065171 This permutation consists of one fixed point (at 0, mapped here to 1) and an infinite number of infinite cycles.
%H A065171 Colin Barker, <a href="/A065171/b065171.txt">Table of n, a(n) for n = 1..1000</a>
%H A065171 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 A065171 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%H A065171 <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,2,0,0,0,-1).
%F A065171 a(2*k+2) = 4*k+4, a(4*k+1) = 2*k+1, a(4*k+3) = 4*k+2. - _Ralf Stephan_, Jun 10 2005
%F A065171 G.f.: x*(2*x^6+4*x^5+x^4+8*x^3+2*x^2+4*x+1) / ((x-1)^2*(x+1)^2*(x^2+1)^2). - _Colin Barker_, Feb 18 2013
%F A065171 a(n) = 2*a(n-4)-a(n-8) for n>8. - _Colin Barker_, Oct 29 2016
%F A065171 a(n) = (11*n-1+(5*n+1)*(-1)^n+(n-3)*(1-(-1)^n)*(-1)^((2*n+3+(-1)^n)/4))/8. - _Luce ETIENNE_, Oct 20 2016
%e A065171 G.f. = x + 4*x^2 + 2*x^3 + 8*x^4 + 3*x^5 + 12*x^6 + 6*x^7 + 16*x^8 + ...
%p A065171 [seq(Z2N(InfRisingSS(N2Z(n))), n=1..120)]; InfRisingSS := z -> `if`((z < 0),`if`((0 = (z mod 2)),z/2,-z),2*z);
%p A065171 N2Z := n -> ((-1)^n)*floor(n/2); Z2N := z -> 2*abs(z)+`if`((z < 1),1,0);
%o A065171 (PARI) Vec(x*(2*x^6+4*x^5+x^4+8*x^3+2*x^2+4*x+1)/((x-1)^2*(x+1)^2*(x^2+1)^2) + O(x^100)) \\ _Colin Barker_, Oct 29 2016
%o A065171 (PARI) {a(n) = if( n%2, n\2+1, n*2)}; /* _Michael Somos_, Nov 06 2016 */
%Y A065171 Inverse permutation: A065172. A065173 gives the deltas p(t)-t, i.e., the associated site swap sequence. Cf. also A065167, A065174, A065260.
%K A065171 nonn,easy
%O A065171 1,2
%A A065171 _Antti Karttunen_, Oct 19 2001