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%I #31 May 02 2017 22:17:15
%S 2,4,1,8,6,12,3,16,10,20,5,24,14,28,7,32,18,36,9,40,22,44,11,48,26,52,
%T 13,56,30,60,15,64,34,68,17,72,38,76,19,80,42,84,21,88,46,92,23,96,50,
%U 100,25,104,54,108,27,112,58,116,29,120,62,124,31,128,66,132,33,136,70
%N A057115 conjugated with A059893, inverse of A065259.
%C This permutation of N induces also such permutation of Z, that p(i)-i >= 0 for all i.
%H Colin Barker, <a href="/A065260/b065260.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_08">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,2,0,0,0,-1).
%F a(n) = A059893(A057115(A059893(n))).
%F a(2*k+2) = 4*k+4, a(4*k+1) = 4*k+2, a(4*k+3) = 2*k+1. - _Ralf Stephan_, Jun 10 2005
%F G.f.: x*(x^6+4*x^5+2*x^4+8*x^3+x^2+4*x+2) / ((x-1)^2*(x+1)^2*(x^2+1)^2). - _Colin Barker_, Feb 18 2013
%F a(n) = 2*a(n-4) - a(n-8) for n>8. - _Colin Barker_, Oct 29 2016
%F 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 G.f. = 2*x + 4*x^2 + x^3 + 8*x^4 + 6*x^5 + 12*x^6 + 3*x^7 + 16*x^8 + ...
%o (PARI) Vec(x*(2+4*x+x^2+8*x^3+2*x^4+4*x^5+x^6)/((1-x)^2*(1+x)^2*(1+x^2)^2) + O(x^100)) \\ _Colin Barker_, Oct 29 2016
%o (PARI) {a(n) = if( n%2==0, n*2, n%4==1, n+1, n\2)}; /* _Michael Somos_, Nov 06 2016 */
%Y Cf. also A065171. The siteswap sequence (deltas) is A065261.
%K nonn,easy
%O 1,1
%A _Antti Karttunen_, Oct 28 2001
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