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A063233 Dimension of the space of weight 2n cuspidal newforms for Gamma_0( 79 ).

%I A063233 #39 Jan 12 2024 01:24:12
%S A063233 6,19,33,45,59,71,85,97,111,123,137,149,163,175,189,201,215,227,241,
%T A063233 253,267,279,293,305,319,331,345,357,371,383,397,409,423,435,449,461,
%U A063233 475,487,501,513,527,539,553,565,579,591,605,617,631,643
%N A063233 Dimension of the space of weight 2n cuspidal newforms for Gamma_0( 79 ).
%H A063233 William A. Stein, <a href="http://wstein.org/Tables/dimskg0new.gp">Dimensions of the spaces S_k^{new}(Gamma_0(N))</a>.
%H A063233 William A. Stein, <a href="http://wstein.org/Tables/">The modular forms database</a>.
%H A063233 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,-1).
%F A063233 Except for the first term, a(n) = 26*(n-1) - a(n-1) (with a(2)=19). - _Vincenzo Librandi_, Dec 07 2010
%F A063233 From _M. F. Hasler_, Mar 05 2012: (Start)
%F A063233 a(n+2) = a(n) + 26 (n > 1);
%F A063233 a(2n+1) = a(2n) + 14 (n > 0);
%F A063233 a(2n) = a(2n-1) + 12 (n > 1);
%F A063233 a(n) = 13n - { 6 if n = 2k+1, k > 0; 7 otherwise }.
%F A063233 G.f.: x*(6 + 13*x + 8*x^2 - x^3)/(1 - x - x^2 + x^3). (End)
%F A063233 Sum_{n>=1} (-1)^(n+1)/a(n) = 1/42 + tan(3*Pi/13)*Pi/26 . - _Amiram Eldar_, Jan 12 2024
%t A063233 Join[{6}, Table[13*n - (13 + (-1)^n)/2, {n, 2, 50}]] (* _Amiram Eldar_, Jan 12 2024 *)
%K A063233 nonn
%O A063233 1,1
%A A063233 _N. J. A. Sloane_, Jul 10 2001