A168286 - OEIS

%I #24 Sep 08 2022 08:45:49

%S 2,8,8,14,14,20,20,26,26,32,32,38,38,44,44,50,50,56,56,62,62,68,68,74,

%T 74,80,80,86,86,92,92,98,98,104,104,110,110,116,116,122,122,128,128,

%U 134,134,140,140,146,146,152,152,158,158,164,164,170,170,176,176,182,182

%N a(n) = (6*n + 3*(-1)^n + 1)/2.

%H Vincenzo Librandi, <a href="/A168286/b168286.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) = 6*n - a(n-1) - 2, with n>1, a(1)=2.

%F From _Vincenzo Librandi_, Sep 17 2013: (Start)

%F a(n) = a(n-1) +a(n-2) -a(n-3).

%F G.f.: 2*x*(1 + 3*x - x^2)/((1+x)*(1-x)^2).

%F a(n) = 2*A168233(n) = A168301(n) + 1. (End)

%F E.g.f.: (1/2)*(3 - 4*exp(x) + (6*x + 1)*exp(2*x))*exp(-x). - _G. C. Greubel_, Jul 17 2016

%t Table[3 n + 3 (-1)^n/2 + 1/2, {n, 70}] (* _Bruno Berselli_, Sep 17 2013 *)

%t CoefficientList[Series[(2 + 6 x - 2 x^2)/((1 + x) (1 - x)^2), {x, 0, 70}], x] (* _Vincenzo Librandi_, Sep 17 2013 *)

%o (Magma) [n le 1 select n+1 else 6*n-Self(n-1)-2: n in [1..70]]; // _Vincenzo Librandi_, Sep 17 2013

%Y Cf. A016933, A168233, A168301.

%K nonn,easy,less

%O 1,1

%A _Vincenzo Librandi_, Nov 22 2009

%E New definition by _Bruno Berselli_, Sep 17 2013