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A086970 Fix 1, then exchange the subsequent odd numbers in pairs.

%I A086970 #39 Sep 08 2022 08:45:11
%S A086970 1,5,3,9,7,13,11,17,15,21,19,25,23,29,27,33,31,37,35,41,39,45,43,49,
%T A086970 47,53,51,57,55,61,59,65,63,69,67,73,71,77,75,81,79,85,83,89,87,93,91,
%U A086970 97,95,101,99,105,103,109,107,113,111,117,115,121,119
%N A086970 Fix 1, then exchange the subsequent odd numbers in pairs.
%C A086970 Partial sums are A086955.
%H A086970 Vincenzo Librandi, <a href="/A086970/b086970.txt">Table of n, a(n) for n = 0..2000</a>
%H A086970 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,-1).
%F A086970 G.f.: (1+4*x-3*x^2+2*x^3)/((1+x)*(1-x)^2).
%F A086970 a(n) = n + abs(2 - (n + 1)*(-1)^n). - _Lechoslaw Ratajczak_, Dec 09 2016
%F A086970 a(n) = 2*A065190(n+1)-1 and a(n) = 2*A014681(n)+1. - _Michel Marcus_, Dec 10 2016
%F A086970 From _Guenther Schrack_, Jun 09 2017: (Start)
%F A086970 a(n) = 2*n + 1 - 2*(-1)^n for n > 0.
%F A086970 a(n) = 2*n + 1 - 2*cos(n*Pi) for n > 0.
%F A086970 a(n) = 4*n - a(n-1) for n > 1.
%F A086970 Linear recurrence: a(n) = a(n-1) + a(n-2) - a(n-3) for n > 3.
%F A086970 First differences: 2 - 4*(-1)^n for n > 1; -(-1)^n*A010696(n) for n > 1.
%F A086970 a(n) = A065164(n+1) + n for n > 0.
%F A086970 a(A014681(n)) = A005408(n) for n >= 0.
%F A086970 a(A005408(A014681(n)) for n >= 0.
%F A086970 a(n) = A005408(A103889(n)) for n >= 0.
%F A086970 A103889(a(n)) = 2*A065190(n+1) for n >= 0.
%F A086970 a(2*n-1) = A004766(n) for n > 0.
%F A086970 a(2*n+2) = A004767(n) for n >= 0. (End)
%t A086970 Join[{1}, LinearRecurrence[{1, 1, -1}, {5, 3, 9}, 60]] (* _Vincenzo Librandi_, Jun 21 2017 *)
%o A086970 (Magma) [1] cat [2*n+1-2*(-1)^n: n in [1..70]]; // _Vincenzo Librandi_, Jun 21 2017
%o A086970 (PARI) Vec((1+4*x-3*x^2+2*x^3)/((1+x)*(1-x)^2) + O(x^100)) \\ _Michel Marcus_, Jun 21 2017
%Y A086970 Cf. A004442, A014681, A065190.
%K A086970 easy,nonn
%O A086970 0,2
%A A086970 _Paul Barry_, Jul 26 2003