cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A065169 Permutation t->t-2 of Z, folded to N.

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%I A065169 #20 Jun 17 2017 03:09:36
%S A065169 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 A065169 31,24,33,26,35,28,37,30,39,32,41,34,43,36,45,38,47,40,49,42,51,44,53,
%U A065169 46,55,48,57,50,59,52,61,54,63,56,65,58,67,60,69,62,71,64,73,66,75,68
%N A065169 Permutation t->t-2 of Z, folded to N.
%C A065169 This permutation consists of just two cycles, both infinite.
%H A065169 Vincenzo Librandi, <a href="/A065169/b065169.txt">Table of n, a(n) for n = 1..1000</a>
%H A065169 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 A065169 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%H A065169 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,-1).
%F A065169 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 A065169 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 A065169 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 A065169 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 A065169 (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 A065169 Inverse permutation to A065165.
%K A065169 nonn,easy
%O A065169 1,1
%A A065169 _Antti Karttunen_, Oct 19 2001