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%I #27 Mar 04 2024 01:12:41
%S 3,12,12,21,21,30,30,39,39,48,48,57,57,66,66,75,75,84,84,93,93,102,
%T 102,111,111,120,120,129,129,138,138,147,147,156,156,165,165,174,174,
%U 183,183,192,192,201,201,210,210,219,219,228,228,237,237,246,246,255,255
%N a(n) = 3 + 9*floor(n/2).
%H Vincenzo Librandi, <a href="/A168410/b168410.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) - 3, with n>1, a(1)=3.
%F G.f.: 3*x*(1 + 3*x - x^2) / ( (1+x)*(x-1)^2 ). - _R. J. Mathar_, Jul 10 2011
%F a(n) = 3*A168233(n). - _R. J. Mathar_, Jul 10 2011
%F a(n) = a(n-1) +a(n-2) -a(n-3). - _Vincenzo Librandi_, Sep 19 2013
%F E.g.f.: (3/4)*(3 - 4*exp(x) + (6*x + 1)*exp(2*x))*exp(-x). - _G. C. Greubel_, Jul 21 2016
%t Table[3 + 9 Floor[n/2], {n, 70}] (* or *) CoefficientList[Series[3 (1 + 3 x - x^2)/((1 + x) (x - 1)^2), {x, 0, 70}], x] (* _Vincenzo Librandi_, Sep 19 2013 *)
%o (Magma) [3+9*Floor(n/2): n in [1..70]]; // _Vincenzo Librandi_, Sep 19 2013
%Y Cf. A017197, A168233.
%K nonn,easy,less
%O 1,1
%A _Vincenzo Librandi_, Nov 25 2009
%E New definition by _Vincenzo Librandi_, Sep 19 2013
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