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%I #34 Aug 21 2022 04:39:45
%S 2,2,6,6,10,10,14,14,18,18,22,22,26,26,30,30,34,34,38,38,42,42,46,46,
%T 50,50,54,54,58,58,62,62,66,66,70,70,74,74,78,78,82,82,86,86,90,90,94,
%U 94,98,98,102,102,106,106,110,110,114,114,118,118,122,122,126,126,130,130
%N a(n) = 2*n - (-1)^n - 1.
%H Vincenzo Librandi, <a href="/A168276/b168276.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,-1).
%F a(n) = 4*n - a(n-1) - 4, with n>1, a(1)=2.
%F from _R. J. Mathar_, Nov 25 2009: (Start)
%F a(n) = 2*n - (-1)^n - 1.
%F a(n) = 2*A109613(n-1).
%F G.f.: 2*x*(1 + x^2)/((1+x)*(1-x)^2). (End)
%F a(n) = a(n-1) + a(n-2) - a(n-3). - _Vincenzo Librandi_, Sep 16 2013
%F a(n) = A168277(n) + 1. - _Vincenzo Librandi_, Sep 17 2013
%F E.g.f.: (-1 + 2*exp(x) + (2*x -1)*exp(2*x))*exp(-x). - _G. C. Greubel_, Jul 16 2016
%F Sum_{n>=1} 1/a(n)^2 = Pi^2/16. - _Amiram Eldar_, Aug 21 2022
%t CoefficientList[Series[2 (1 + x^2) / ((1 + x) (1 - x)^2), {x, 0, 80}], x] (* _Vincenzo Librandi_, Sep 16 2013 *)
%t Table[2 n - 1 - (-1)^n, {n, 70}] (* _Bruno Berselli_, Sep 17 2013 *)
%t LinearRecurrence[{1,1,-1},{2,2,6},70] (* _Harvey P. Dale_, Oct 22 2014 *)
%o (Magma) [2*n-1-(-1)^n: n in [1..70]]; // _Vincenzo Librandi_, Sep 16 2013
%Y Cf. A039722, A168277.
%Y Cf. A063210. - _R. J. Mathar_, Nov 25 2009
%K nonn,easy
%O 1,1
%A _Vincenzo Librandi_, Nov 22 2009
%E Previous definition replaced with closed-form expression by _Bruno Berselli_, Sep 17 2013
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