%I #21 Sep 08 2022 08:45:48
%S 3,3,8,8,13,13,18,18,23,23,28,28,33,33,38,38,43,43,48,48,53,53,58,58,
%T 63,63,68,68,73,73,78,78,83,83,88,88,93,93,98,98,103,103,108,108,113,
%U 113,118,118,123,123,128,128,133,133,138,138,143,143,148,148,153,153,158
%N a(n) = (10*n - 5*(-1)^n - 3)/4.
%H Vincenzo Librandi, <a href="/A168283/b168283.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) = 5*n - a(n-1) - 4, with n>1, a(1)=3.
%F From _R. J. Mathar_, Nov 25 2009: (Start)
%F a(n) = A168209(n-1), n>1.
%F a(n) = (10*n + 5*(-1)^(n+1) - 3)/4.
%F G.f.: x*(3 + 2*x^2)/((1+x)*(x-1)^2). (End)
%F a(n) = a(n-1) +a(n-2) -a(n-3). - _Vincenzo Librandi_, Sep 16 2013
%F E.g.f.: (1/4)*(-5 + 8*exp(x) + (10*x - 3)*exp(2*x))*exp(-x). - _G. C. Greubel_, Jul 17 2016
%t CoefficientList[Series[(3 + 2 x^2) / ((1 + x) (x - 1)^2), {x, 0, 70}], x] (* _Vincenzo Librandi_, Sep 16 2013 *)
%t Table[5 n/2 - 5 (-1)^n/4 - 3/4, {n, 70}] (* _Bruno Berselli_, Sep 17 2013 *)
%o (Magma) [n le 1 select n+2 else 5*n-Self(n-1)-4: n in [1..70] ]; // _Vincenzo Librandi_, Sep 16 2013
%K nonn,easy
%O 1,1
%A _Vincenzo Librandi_, Nov 22 2009
%E Previous definition replaced with the closed form by _Bruno Berselli_, Sep 17 2013