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%I #37 Sep 08 2022 08:44:43
%S 3,15,27,39,51,63,75,87,99,111,123,135,147,159,171,183,195,207,219,
%T 231,243,255,267,279,291,303,315,327,339,351,363,375,387,399,411,423,
%U 435,447,459,471,483,495,507,519,531,543,555,567,579,591,603,615,627,639
%N a(n) = 12*n + 3.
%C Apart from initial term(s), dimension of the space of weight 2n cusp forms for Gamma_0( 44 ).
%H Vincenzo Librandi, <a href="/A017557/b017557.txt">Table of n, a(n) for n = 0..2000</a>
%H Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>.
%H William A. Stein, <a href="http://wstein.org/Tables/dimskg0n.gp">Dimensions of the spaces S_k(Gamma_0(N))</a>.
%H William A. Stein, <a href="http://wstein.org/Tables/">The modular forms database</a>.
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1).
%F a(n) = 2*a(n-1) - a(n-2). - _Vincenzo Librandi_, Jun 07 2011
%F A089911(2*a(n)) = 8. - _Reinhard Zumkeller_, Jul 05 2013
%F From _G. C. Greubel_, Sep 18 2019: (Start)
%F G.f.: 3*(1+3*x)/(1-x)^2.
%F E.g.f.: 3*(1+4*x)*exp(x). (End)
%F Sum_{n>=0} (-1)^n/a(n) = (Pi + 2*log(sqrt(2)+1))/(12*sqrt(2)). - _Amiram Eldar_, Dec 12 2021
%p seq(12*n+3, n=0..60); # _G. C. Greubel_, Sep 18 2019
%t 12*Range[0,60]+3 (* _Vladimir Joseph Stephan Orlovsky_, Feb 19 2011 *)
%o (Magma) [12*n+3: n in [0..60]]; // _Vincenzo Librandi_, Jun 07 2011
%o (Haskell)
%o a017557 = (+ 3) . (* 12) -- _Reinhard Zumkeller_, Jul 05 2013
%o (PARI) a(n)=12*n+3 \\ _Charles R Greathouse IV_, Jul 10 2016
%o (Sage) [12*n+3 for n in (0..60)] # _G. C. Greubel_, Sep 18 2019
%o (GAP) List([0..60], n-> 12*n+3 ); # _G. C. Greubel_, Sep 18 2019
%Y Cf. A008594, A016813, A017533, A017545, A089911.
%K nonn,easy
%O 0,1
%A _N. J. A. Sloane_
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