cp's OEIS Frontend

A065170 Permutation t->t-3 of Z, folded to N.

%I A065170 #29 Aug 08 2023 03:21:49
%S A065170 7,5,9,3,11,1,13,2,15,4,17,6,19,8,21,10,23,12,25,14,27,16,29,18,31,20,
%T A065170 33,22,35,24,37,26,39,28,41,30,43,32,45,34,47,36,49,38,51,40,53,42,55,
%U A065170 44,57,46,59,48,61,50,63,52,65,54,67,56,69,58,71,60,73,62,75,64,77,66
%N A065170 Permutation t->t-3 of Z, folded to N.
%C A065170 This permutation consists of just three cycles, which are infinite.
%H A065170 Vincenzo Librandi, <a href="/A065170/b065170.txt">Table of n, a(n) for n = 1..1000</a>
%H A065170 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 A065170 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,-1).
%H A065170 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>.
%F A065170 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 A065170 G.f.: x*(x^8-x^7+4*x^6-4*x^5+4*x^4-4*x^3-3*x^2-2*x+7) / ((x-1)^2*(x+1)). - _Colin Barker_, Feb 18 2013
%F A065170 a(n) = -6*(-1)^n+n for n>6. a(n) = a(n-1)+a(n-2)-a(n-3) for n>9. - _Colin Barker_, Mar 07 2014
%F A065170 Sum_{n>=1} (-1)^n/a(n) = 46/15 - log(2). - _Amiram Eldar_, Aug 08 2023
%t A065170 CoefficientList[Series[(x^8 - x^7 + 4 x^6 - 4 x^5 + 4 x^4 - 4 x^3 - 3 x^2 - 2 x + 7)/((x - 1)^2 (x + 1)), {x, 0, 100}], x] (* _Vincenzo Librandi_, Mar 08 2014 *)
%t A065170 LinearRecurrence[{1,1,-1},{7,5,9,3,11,1,13,2,15},80] (* _Harvey P. Dale_, Oct 19 2018 *)
%o A065170 (PARI) Vec(x*(x^8-x^7+4*x^6-4*x^5+4*x^4-4*x^3-3*x^2-2*x+7)/((x-1)^2*(x+1))  + O(x^100)) \\ _Colin Barker_, Mar 07 2014
%Y A065170 Inverse permutation to A065166.
%K A065170 nonn,easy
%O A065170 1,1
%A A065170 _Antti Karttunen_, Oct 19 2001