A063210 Dimension of the space of weight 2n cuspidal newforms for Gamma_0( 42 ).

1, 2, 6, 6, 10, 10, 14, 14, 18, 18, 22, 22, 26, 26, 30, 30, 34, 34, 38, 38, 42, 42, 46, 46, 50, 50, 54, 54, 58, 58, 62, 62, 66, 66, 70, 70, 74, 74, 78, 78, 82, 82, 86, 86, 90, 90, 94, 94, 98, 98

Offset: 1

Author

N. J. A. Sloane, Jul 10 2001

Keywords

• nonn
• easy

Comments

Equals triangle A153860 * [1,2,3,...]. - Gary W. Adamson, Jan 03 2009

Links

• 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 (1,1,-1).

Crossrefs

Cf. A153860. - Gary W. Adamson, Jan 03 2009

Programs

Mathematica

With[{c=Range[6,102,4]},Join[{1,2},Riffle[c,c]]] (* or *) LinearRecurrence[ {1,1,-1},{1,2,6,6,10},50] (* Harvey P. Dale, Jun 22 2019 *)

PARI

Vec(-x*(x^3-3*x^2-x-1)/((x-1)^2*(x+1)) + O(x^100)) \\ Colin Barker, Sep 08 2013

Formula

a(n) = (n^2 - n)/floor(n/2) for n >=2. (Excludes leading 1.) - William A. Tedeschi, Mar 20 2008

Except for the first term, a(n) = 4*(n-1) - a(n-1), (with a(2)=2). - Vincenzo Librandi, Dec 07 2010

From Colin Barker, Sep 08 2013: (Start)

a(n) = a(n-1) + a(n-2) - a(n-3) for n > 4.

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