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%I #27 Sep 08 2022 08:45:48
%S 2,2,5,5,8,8,11,11,14,14,17,17,20,20,23,23,26,26,29,29,32,32,35,35,38,
%T 38,41,41,44,44,47,47,50,50,53,53,56,56,59,59,62,62,65,65,68,68,71,71,
%U 74,74,77,77,80,80,83,83,86,86,89,89,92,92,95,95,98,98,101,101,104,104
%N a(n) = (6*n - 3*(-1)^n - 1)/4.
%C Essentially the same as A168199. - _Georg Fischer_, Oct 14 2018
%H Vincenzo Librandi, <a href="/A168236/b168236.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 G.f.: x*(2 + x^2) / ( (1+x)*(x-1)^2 ).
%F a(n+1) = A016789(floor(n/2)).
%F a(n) = a(n-1) +a(n-2) -a(n-3). - _Vincenzo Librandi_, Sep 16 2013
%F E.g.f.: (1/4)*(-3 + 4*exp(x) + (6*x - 1)*exp(2*x))*exp(-x). - _G. C. Greubel_, Jul 16 2016
%t CoefficientList[Series[(2 + x^2) / ((1 + x) (x - 1)^2), {x, 0, 70}], x] (* _Vincenzo Librandi_, Sep 16 2013 *)
%t Table[(6*n - 3*(-1)^n - 1)/4, {n,1,50}] (* or *) LinearRecurrence[ {1,1, -1}, {2, 2, 5}, 50] (* _G. C. Greubel_, Jul 16 2016 *)
%o (Magma) [3*n/2-1/4-3*(-1)^n/4: n in [1..70]]; // _Vincenzo Librandi_, Sep 16 2013
%Y Cf. A016789.
%K nonn,easy,less
%O 1,1
%A _Vincenzo Librandi_, Nov 21 2009
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