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A097062 Interleave 2*n+1 and 2*n-1.

%I A097062 #45 Jan 23 2023 16:52:55
%S A097062 1,-1,3,1,5,3,7,5,9,7,11,9,13,11,15,13,17,15,19,17,21,19,23,21,25,23,
%T A097062 27,25,29,27,31,29,33,31,35,33,37,35,39,37,41,39,43,41,45,43,47,45,49,
%U A097062 47,51,49,53,51,55,53,57,55,59,57,61,59,63,61,65,63,67,65,69,67,71,69,73,71,75,73,77,75,79,77,81,79,83,81,85,83,87,85
%N A097062 Interleave 2*n+1 and 2*n-1.
%C A097062 Partial sums are A097063, whose pairwise sums are A002061.
%C A097062 Binomial transform is A097064.
%H A097062 Reinhard Zumkeller, <a href="/A097062/b097062.txt">Table of n, a(n) for n = 0..1000</a>
%H A097062 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,-1).
%F A097062 G.f.: (1-2*x+3*x^2)/((1-x^2)*(1-x)).
%F A097062 a(n) = (2*n-1)/2 + 3*(-1)^n/2.
%F A097062 a(n) = 2*(n-1) - a(n-1), with a(0)=1. - _Vincenzo Librandi_, Nov 16 2010
%F A097062 a(n) = n - 2 + 3*((n-1) mod 2). - _Lechoslaw Ratajczak_, May 21 2021
%F A097062 a(n) = a(n-1)+a(n-2)-a(n-3). - _Wesley Ivan Hurt_, May 21 2021
%t A097062 LinearRecurrence[{1, 1, -1}, {1, -1, 3}, 100] (* _Amiram Eldar_, May 21 2021 *)
%t A097062 With[{nn=91},Riffle[Range[1,nn,2],Range[-1,nn-2,2]]] (* _Harvey P. Dale_, Jan 23 2023 *)
%o A097062 (Haskell)
%o A097062 import Data.List (transpose)
%o A097062 a097062 n = a097062_list !! n
%o A097062 a097062_list = concat $ transpose [a005408_list, (-1) : a005408_list]
%o A097062 -- _Reinhard Zumkeller_, Apr 16 2015
%o A097062 (PARI) a(n)=(2*n-1)/2+3*(-1)^n/2 \\ _Charles R Greathouse IV_, Oct 07 2015
%o A097062 (PARI) Vec((1-2*x+3*x^2)/((1-x^2)*(1-x)) + O(x^100)) \\ _Altug Alkan_, Nov 13 2015
%o A097062 (Magma) [(2*n-1)/2 + 3*(-1)^n/2 : n in [0..100]]; // _Wesley Ivan Hurt_, May 22 2021
%Y A097062 Cf. A005408, A097063, A097064.
%K A097062 sign,easy
%O A097062 0,3
%A A097062 _Paul Barry_, Jul 22 2004