%I #23 Mar 19 2024 09:33:20
%S 2,10,10,18,18,26,26,34,34,42,42,50,50,58,58,66,66,74,74,82,82,90,90,
%T 98,98,106,106,114,114,122,122,130,130,138,138,146,146,154,154,162,
%U 162,170,170,178,178,186,186,194,194,202,202,210,210,218,218,226,226,234,234
%N a(n) = 4*n + 2*(-1)^n.
%H Vincenzo Librandi, <a href="/A168381/b168381.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)=2.
%F G.f.: 2*x*(1 + 4*x - x^2)/((1+x)*(x-1)^2). - _Vincenzo Librandi_, Sep 18 2013
%F a(n) = a(n-1) +a(n-2) -a(n-3). - _Vincenzo Librandi_, Sep 18 2013
%F From _Bruno Berselli_, Sep 18 2013: (Start)
%F a(n) = 2*A163980(n).
%F a(n) = 2 + 8*floor(n/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[(2 + 8 x - 2 x^2)/((1 + x) (x -1)^2), {x, 0, 70}], x] (* _Vincenzo Librandi_, Sep 18 2013 *)
%o (Magma) [4*n +2*(-1)^n: n in [1..70]]; // _Vincenzo Librandi_, Sep 18 2013
%Y Cf. A163980.
%K nonn,easy,less,changed
%O 1,1
%A _Vincenzo Librandi_, Nov 24 2009
%E Definition rewritten by _Vincenzo Librandi_, Sep 18 2013
|