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 A063093 #36 Apr 15 2023 04:18:50
%S A063093 0,5,9,15,19,25,29,35,39,45,49,55,59,65,69,75,79,85,89,95,99,105,109,
%T A063093 115,119,125,129,135,139,145,149,155,159,165,169,175,179,185,189,195,
%U A063093 199,205,209,215,219,225,229,235,239,245
%N A063093 Dimension of the space of weight 2n cusp forms for Gamma_0( 25 ).
%C A063093 If b(n) is the sequence of integers congruent to {0,3} (mod 5) and c(n) is the sequence of integers congruent to {2,4}(mod 5). Then a(n) = b(n) + c(n). Equivalently a(n) = A047218(n+1) + A047211(n). - _Anthony Hernandez_, Aug 16 2016
%H A063093 William A. Stein, <a href="http://wstein.org/Tables/dimskg0n.gp">Dimensions of the spaces S_k(Gamma_0(N))</a>.
%H A063093 William A. Stein, <a href="http://wstein.org/Tables/">The modular forms database</a>.
%H A063093 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,-1).
%F A063093 a(n) = 10*n - a(n-1) - 16 for n>2, with a(1)=0, a(2)=5. - _Vincenzo Librandi_, Aug 07 2010
%F A063093 From _Colin Barker_, Sep 26 2012: (Start)
%F A063093 a(n) = ((-1)^n + 10*n - 11)/2 for n>1.
%F A063093 a(n) = a(n-1) + a(n-2) - a(n-3) for n>3.
%F A063093 G.f.: x^2*(5+4*x+x^2)/((1-x)^2*(1+x)). (End)
%F A063093 Sum_{n>=2} (-1)^n/a(n) = sqrt(5+2*sqrt(5))*Pi/20 - 3*sqrt(5)*log(phi)/20 - log(5)/8, where phi is the golden ratio (A001622). - _Amiram Eldar_, Apr 15 2023
%t A063093 Rest@ CoefficientList[Series[x^2*(5 + 4 x + x^2)/((1 - x)^2*(1 + x)), {x, 0, 50}], x] (* _Michael De Vlieger_, Aug 26 2016 *)
%t A063093 LinearRecurrence[{1,1,-1},{0,5,9,15},50] (* _Harvey P. Dale_, Apr 09 2019 *)
%Y A063093 Cf. A001622, A047211, A047218.
%K A063093 nonn,easy
%O A063093 1,2
%A A063093 _N. J. A. Sloane_, Jul 08 2001