This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A063289 #53 Feb 17 2025 12:30:05
%S A063289 -1,2,7,11,16,20,25,29,34,38,43,47,52,56,61,65,70,74,79,83,88,92,97,
%T A063289 101,106,110,115,119,124,128,133,137,142,146,151,155,160,164,169,173,
%U A063289 178,182,187,191,196,200,205,209,214,218,223,227,232,236
%N A063289 Dimension of the space of weight n cuspidal newforms for Gamma_1( 16 ).
%C A063289 It appears that for n > 2 a(n) = floor((9n-22)/2). - _Gary Detlefs_, Mar 02 2010
%H A063289 William A. Stein, <a href="http://wstein.org/Tables/dimskg1new.gp">Dimensions of the spaces S_k^{new}(Gamma_1(N))</a>.
%H A063289 William A. Stein, <a href="http://wstein.org/Tables/">The modular forms database</a>.
%H A063289 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1, 1, -1).
%F A063289 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 A063289 From _M. F. Hasler_, Mar 05 2012: (Start)
%F A063289 G.f.: x^2*(-1 + 3*x + 6*x^2 + x^3)/(1 - x - x^2 + x^3).
%F A063289 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 A063289 Sum_{n>=3} (-1)^(n+1)/a(n) = cot(2*Pi/9)*Pi/9. - _Amiram Eldar_, Jan 12 2024
%F A063289 From _Amiram Eldar_, Nov 22 2024: (Start)
%F A063289 Product_{n>=3} (1 - (-1)^n/a(n)) = 2*sin(Pi/18) + 1 (= A130880 + 1).
%F A063289 Product_{n>=3} (1 + (-1)^n/a(n)) = (1/2) * sec(Pi/9) (= A332438 - 3). (End)
%t A063289 Join[{-1}, Table[9*n/2 + (-1)^n/4 - 45/4, {n, 3, 60}]] (* _Amiram Eldar_, Jan 12 2024 *)
%Y A063289 Cf. A063232, A063233, A017185 (bisection), A130880, A332438.
%K A063289 sign,easy
%O A063289 2,2
%A A063289 _N. J. A. Sloane_, Jul 14 2001