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 A065259 A057114 conjugated with A059893, inverse of A065260. 3

%I

%S 3,1,7,2,11,5,15,4,19,9,23,6,27,13,31,8,35,17,39,10,43,21,47,12,51,25,

%T 55,14,59,29,63,16,67,33,71,18,75,37,79,20,83,41,87,22,91,45,95,24,99,

%U 49,103,26,107,53,111,28,115,57,119,30,123,61,127,32,131,65,135,34,139

%N A057114 conjugated with A059893, inverse of A065260.

%H Colin Barker, <a href="/A065259/b065259.txt">Table of n, a(n) for n = 1..1000</a>

%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(A057114(A059893(n))).

%F a(2*k+1) = 4*k+3, a(4*k+2) = 4*k+1, a(4*k+4) = 2*k+2. - _Ralf Stephan_, Jun 10 2005

%F a(n) = (11*n+2-(5*n+6)*(-1)^n+(n-2)*(1+(-1)^n)*(-1)^((2*n-3-(-1)^n)/4))/8. - _Luce ETIENNE_, Oct 29 2016

%F From _Colin Barker_, Oct 29 2016: (Start)

%F a(n) = 2*a(n-4) - a(n-8) for n>8.

%F G.f.: x*(3 + x + 7*x^2 + 2*x^3 + 5*x^4 + 3*x^5 + x^6)/((1 - x)^2*(1 + x)^2*(1 + x^2)^2). (End)

%e G.f. = 3*x + x^2 + 7*x^3 + 2*x^4 + 11*x^5 + 5*x^6 + 15*x^7 + 4*x^8 + ...

%o (PARI) Vec(x*(3+x+7*x^2+2*x^3+5*x^4+3*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, 2*n+1, n%4, n-1, n/2)}; /* _Michael Somos_, Nov 06 2016 */

%K nonn,easy

%O 1,1

%A _Antti Karttunen_, Oct 28 2001

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Last modified March 20 13:18 EDT 2019. Contains 321345 sequences. (Running on oeis4.)