%I #35 Aug 29 2024 00:56:50

%S 3,3,9,9,15,15,21,21,27,27,33,33,39,39,45,45,51,51,57,57,63,63,69,69,

%T 75,75,81,81,87,87,93,93,99,99,105,105,111,111,117,117,123,123,129,

%U 129,135,135,141,141,147,147,153,153,159,159,165,165,171,171,177,177,183,183

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

%H Vincenzo Librandi, <a href="/A168329/b168329.txt">Table of n, a(n) for n = 1..10000</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) - 6 for n>1, a(1)=3.

%F G.f.: 3*x*(1 + x^2)/((1+x)*(1-x)^2). - _Bruno Berselli_, Nov 06 2011

%F a(n) = -a(-n+1) = 3*A109613(n-1) = A198392(n-1) - A198392(-n). - _Bruno Berselli_, Nov 06 2011 - Sep 17 2013

%F E.g.f.: (3/2)*(-1 + 2*exp(x) + (2*x - 1)*exp(2*x))*exp(-x). - _G. C. Greubel_, Jul 18 2016

%t LinearRecurrence[{1,1,-1},{3,3,9},80 ] (* _Vincenzo Librandi_, Nov 15 2011 *)

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

%o (Magma) [(3/2)*(2*n-(-1)^n-1): n in [1..70]]; // _Vincenzo Librandi_, Nov 15 2011

%Y Cf. A016945, A109613, A198392.

%K nonn,easy,less

%O 1,1

%A _Vincenzo Librandi_, Nov 23 2009

%E New definition by _Bruno Berselli_, Sep 17 2013