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%I #24 Jan 29 2024 04:10:25
%S 1,2,4,4,6,8,8,10,12,12,14,16,16,18,20,20,22,24,24,26,28,28,30,32,32,
%T 34,36,36,38,40,40,42,44,44,46,48,48,50,52,52,54,56,56,58,60,60,62,64,
%U 64,66
%N Dimension of the space of weight 2n cuspidal newforms for Gamma_0( 15 ).
%H Paolo Xausa, <a href="/A063200/b063200.txt">Table of n, a(n) for n = 1..10000</a>
%H G. Martin, <a href="http://dx.doi.org/10.1016/j.jnt.2004.10.009">Dimensions of the spaces of cusp forms and newforms on Gamma_0(N) and Gamma_1(N)</a>, J. Numb. Theory 112 (2005) 298-331, Theorem 1.
%H William A. Stein, <a href="http://wstein.org/Tables/dimskg0new.gp">Dimensions of the spaces S_k^{new}(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_04">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,1,-1).
%F G.f.: x +2*x^2*(1+x) / ( (1+x+x^2)*(x-1)^2 ). - _R. J. Mathar_, Jul 15 2015
%F Sum_{n>=1} (-1)^(n+1)/a(n) = 1- Pi/8. - _Amiram Eldar_, Jan 12 2024
%t LinearRecurrence[{1, 0, 1, -1}, {1, 2, 4, 4, 6}, 100] (* _Paolo Xausa_, Jan 29 2024 *)
%o (Python)
%o def A063200(n): return n-1+sum(divmod(n-1,3)) if n > 1 else 1 # _Chai Wah Wu_, Jan 29 2023
%K nonn
%O 1,2
%A _N. J. A. Sloane_, Jul 10 2001
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