A168384 - OEIS

%I #30 Mar 19 2024 09:33:34

%S 6,6,14,14,22,22,30,30,38,38,46,46,54,54,62,62,70,70,78,78,86,86,94,

%T 94,102,102,110,110,118,118,126,126,134,134,142,142,150,150,158,158,

%U 166,166,174,174,182,182,190,190,198,198,206,206,214,214,222,222,230,230

%N a(n) = 4*n - 2*(-1)^n.

%H Vincenzo Librandi, <a href="/A168384/b168384.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) = 8*n - a(n-1) - 4, with n>1, a(1)=6.

%F From _Vincenzo Librandi_, Sep 18 2013: (Start)

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

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

%F a(n) = 6 + 8*floor((n-1)/2). (End)

%F E.g.f.: 2*(-1 + exp(x) + 2*x*exp(2*x))*exp(-x). - _G. C. Greubel_, Jul 19 2016

%t CoefficientList[Series[(6 + 2 x^2)/((1 + x) (x - 1)^2), {x, 0, 70}], x] (* _Vincenzo Librandi_, Sep 18 2013 *)

%t LinearRecurrence[{1,1,-1},{6,6,14},70] (* _Harvey P. Dale_, Mar 14 2023 *)

%o (Magma) [4*n -2*(-1)^n: n in [1..70]]; // _Vincenzo Librandi_, Sep 18 2013

%o (Magma) [6+8*Floor((n-1)/2): n in [1..70]]; // _Vincenzo Librandi_, Sep 18 2013

%Y Cf. A296910.

%K nonn,easy

%O 1,1

%A _Vincenzo Librandi_, Nov 24 2009

%E Definition rewritten by _Vincenzo Librandi_, Sep 18 2013