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%I #44 Jan 12 2024 01:22:51
%S -1,2,7,11,16,20,25,29,34,38,43,47,52,56,61,65,70,74,79,83,88,92,97,
%T 101,106,110,115,119,124,128,133,137,142,146,151,155,160,164,169,173,
%U 178,182,187,191,196,200,205,209,214,218,223,227,232,236
%N Dimension of the space of weight n cuspidal newforms for Gamma_1( 16 ).
%C It appears that for n > 2 a(n) = floor((9n-22)/2). - _Gary Detlefs_, Mar 02 2010
%H William A. Stein, <a href="http://wstein.org/Tables/dimskg1new.gp">Dimensions of the spaces S_k^{new}(Gamma_1(N))</a>
%H William A. Stein, <a href="http://wstein.org/Tables/">The modular forms database</a>
%F a(n) = 9*n/2 + (-1)^n/4 - 45/4 for n >= 3, with first differences in A010710. - _R. J. Mathar_, Dec 06 2010
%F From _M. F. Hasler_, Mar 05 2012: (Start)
%F G.f.: x^2*(-1 + 3*x + 6*x^2 + x^3)/(1 - x - x^2 + x^3).
%F a(n+2) = a(n)+9 (n>2), a(2n+1) = a(2n)+4 (n>1), a(2n) = a(2n-1)+5 (n>1). (End)
%F Sum_{n>=3} (-1)^(n+1)/a(n) = cot(2*Pi/9)*Pi/9. - _Amiram Eldar_, Jan 12 2024
%t Join[{-1}, Table[9*n/2 + (-1)^n/4 - 45/4, {n, 3, 60}]] (* _Amiram Eldar_, Jan 12 2024 *)
%Y Cf. A063232, A063233, A017185 (bisection).
%K sign
%O 2,2
%A _N. J. A. Sloane_, Jul 14 2001
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