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%I #30 Sep 08 2022 08:44:51
%S 1,39,125,259,441,671,949,1275,1649,2071,2541,3059,3625,4239,4901,
%T 5611,6369,7175,8029,8931,9881,10879,11925,13019,14161,15351,16589,
%U 17875,19209,20591,22021,23499,25025
%N a(n) = (2*n+1)*(12*n+1).
%H Vincenzo Librandi, <a href="/A033576/b033576.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F From _Colin Barker_, Jun 10 2012: (Start)
%F a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).
%F G.f.: (1 + 36*x + 11*x^2)/(1-x)^3. (End)
%F a(n) = A005408(n) * A017533(n). - _Wesley Ivan Hurt_, Feb 02 2014
%F E.g.f.: (1 + 38*x + 24*x^2)*exp(x). - _G. C. Greubel_, Oct 12 2019
%p A033576:=n->(2*n+1)*(12*n+1); seq(A033576(n), n=0..50); # _Wesley Ivan Hurt_, Feb 02 2014
%t Table[(2n+1)(12n+1),{n,0,50}] (* _Harvey P. Dale_, Mar 30 2011 *)
%t CoefficientList[Series[(1+36*x+11*x^2)/(1-x)^3,{x,0,50}],x] (* _Vincenzo Librandi_, Jul 07 2012 *)
%o (Magma) [(2*n+1)*(12*n+1): n in [0..50]]; // _Vincenzo Librandi_, Jul 07 2012
%o (PARI) a(n)=(2*n+1)*(12*n+1) \\ _Charles R Greathouse IV_, Jun 17 2017
%o (Sage) [(2*n+1)*(12*n+1) for n in range(50)] # _G. C. Greubel_, Oct 12 2019
%o (GAP) List([0..50], n-> (2*n+1)*(12*n+1)); # _G. C. Greubel_, Oct 12 2019
%Y Cf. A005408, A017533.
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_
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