A168284 - OEIS

%I #31 Sep 08 2022 08:45:49

%S 0,5,5,10,10,15,15,20,20,25,25,30,30,35,35,40,40,45,45,50,50,55,55,60,

%T 60,65,65,70,70,75,75,80,80,85,85,90,90,95,95,100,100,105,105,110,110,

%U 115,115,120,120,125,125,130,130,135,135,140,140,145,145,150,150,155

%N a(n) = (10*n + 5*(-1)^n - 5)/4.

%C a(n) = A166598(n-1) for n > 1. - _Georg Fischer_, Oct 14 2018

%H Vincenzo Librandi, <a href="/A168284/b168284.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) - 5, with n > 1, a(1)=0.

%F G.f.: 5*x^2/((1+x)*(x-1)^2). - _Vincenzo Librandi_, Sep 16 2013

%F a(n) = 5*A004526(n). - _Bruno Berselli_, Sep 17 2013

%F E.g.f.: (5/4)*(1 + (2*x - 1)*exp(2*x))*exp(-x). - _G. C. Greubel_, Jul 17 2016

%t CoefficientList[Series[5 x/((1 + x) (x - 1)^2), {x, 0, 70}], x] (* _Vincenzo Librandi_, Sep 16 2013 *)

%t Table[5 n/2 + 5 (-1)^n/4 - 5/4, {n, 70}] (* _Bruno Berselli_, Sep 17 2013 *)

%o (Magma) [n le 1 select (n-1) else 5*n-Self(n-1)-5: n in [1..70]]; // _Vincenzo Librandi_, Sep 16 2013

%Y Cf. A004526, A008587.

%K nonn,easy,less

%O 1,2

%A _Vincenzo Librandi_, Nov 22 2009

%E New definition by _Bruno Berselli_, Sep 17 2013