A063197 Dimension of the space of weight 2n cuspidal newforms for Gamma_0( 9 ).

0, 1, 1, 3, 3, 4, 5, 6, 6, 8, 8, 9, 10, 11, 11, 13, 13, 14, 15, 16, 16, 18, 18, 19, 20, 21, 21, 23, 23, 24, 25, 26, 26, 28, 28, 29, 30, 31, 31, 33, 33, 34, 35, 36, 36, 38, 38, 39, 40, 41

Offset

1,4

Links

Michael De Vlieger, Table of n, a(n) for n = 1..10000

William A. Stein, Dimensions of the spaces S_k^{new}(Gamma_0(N))

William A. Stein, The modular forms database

Index entries for linear recurrences with constant coefficients, signature (0,1,1,0,-1).

Formula

From Colin Barker, Sep 27 2012: (Start)

a(n) = a(n-2) + a(n-3) - a(n-5) for n > 5.

G.f.: x^2*(1 + x + 2*x^2 + x^3)/((1 - x)^2*(1 + x)*(1 + x + x^2)).

(End)

a(n) = n-1 - floor((n-1)/2) + floor((n-1)/3). - Ridouane Oudra, Oct 15 2020

Mathematica

Rest@ CoefficientList[Series[x^2*(1 + x + 2*x^2 + x^3)/((1 - x)^2*(1 + x)*(1 + x + x^2)), {x, 0, 69}], x] (* or *)
Array[# - Floor[#/2] + Floor[#/3] &[# - 1] &, 69] (* Michael De Vlieger, Oct 15 2020 *)

Prog

(PARI) concat(0, Vec(x^2*(1 +x +2*x^2 +x^3)/((1 -x)^2*(1 +x)*(1 +x +x^2)) + O(x^80))) \\ Michel Marcus, Oct 15 2020

Crossrefs

Sequence in context: A120180 A339412 A279400 * A327226 A011977 A104803

Adjacent sequences: A063194 A063195 A063196 * A063198 A063199 A063200

Keyword

nonn

Author

N. J. A. Sloane, Jul 10 2001

Status

approved