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%I #24 Sep 08 2022 08:45:49
%S 6,6,15,15,24,24,33,33,42,42,51,51,60,60,69,69,78,78,87,87,96,96,105,
%T 105,114,114,123,123,132,132,141,141,150,150,159,159,168,168,177,177,
%U 186,186,195,195,204,204,213,213,222,222,231,231,240,240,249,249,258
%N a(n) = (18*n - 9*(-1)^n - 3)/4.
%H Vincenzo Librandi, <a href="/A168414/b168414.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) = 9*n - a(n-1) - 6, n>1.
%F a(n) = 3*A168236(n). - _R. J. Mathar_, Jul 10 2011
%F G.f. 3*x*(2 + x^2) / ( (1+x)*(x-1)^2 ). - _R. J. Mathar_, Jul 10 2011
%F a(n) = 6 + 9*Floor((n-1)/2). - _Vincenzo Librandi_, Sep 19 2013
%F From _G. C. Greubel_, Jul 22 2016: (Start)
%F a(n) = a(n-1) + a(n-2) - a(n-3).
%F E.g.f.: (3/4)*(-3 + 4*exp(x) +(6*x - 1)*exp(2*x))*exp(-x). (End)
%t Table[6 + 9 Floor[(n - 1)/2], {n, 70}] (* or *) CoefficientList[Series[3 (2 + x^2)/((1 + x) (x - 1)^2), {x, 0, 70}], x] (* _Vincenzo Librandi_, Sep 19 2013 *)
%t LinearRecurrence[{1,1,-1},{6,6,15},60] (* _Harvey P. Dale_, May 17 2017 *)
%o (Magma) [6+9*Floor((n-1)/2): n in [1..70]]; // _Vincenzo Librandi_, Set 19 2013
%K nonn,easy
%O 1,1
%A _Vincenzo Librandi_, Nov 25 2009
%E Definition replaced by Lava formula of Nov 2009. - _R. J. Mathar_, Jul 10 2011
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