A063215 Dimension of the space of weight 2n cuspidal newforms for Gamma_0( 47 ).

4, 11, 19, 27, 35, 41, 51, 57, 65, 73, 81, 87, 97, 103, 111, 119, 127, 133, 143, 149, 157, 165, 173, 179, 189, 195, 203, 211, 219, 225, 235, 241, 249, 257, 265, 271, 281, 287, 295, 303, 311, 317, 327, 333, 341, 349, 357, 363, 373, 379

Offset

1,1

Links

Table of n, a(n) for n=1..50.

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

a(n) = a(n-2)+a(n-3)-a(n-5) for n>6. G.f.: x*(4+11*x+15*x^2+12*x^3+5*x^4-x^5)/((1 -x)^2*(1 +x)*(1 +x +x^2)). - Colin Barker, Sep 27 2012

Mathematica

a[n_] := a[n] = If[n <= 6, {4, 11, 19, 27, 35, 41}[[n]], a[n-2] + a[n-3] - a[n-5]]; Array[a, 50] (* Jean-François Alcover, Dec 06 2016 after Colin Barker *)

Prog

(PARI) a(n)=if(n>1, ([0, 1, 0, 0, 0; 0, 0, 1, 0, 0; 0, 0, 0, 1, 0; 0, 0, 0, 0, 1; -1, 0, 1, 1, 0]^(n-1)*[5; 11; 19; 27; 35])[1, 1], 4) \\ Charles R Greathouse IV, Nov 27 2016

Crossrefs

Sequence in context: A361434 A360038 A304499 * A278709 A247988 A162996

Adjacent sequences: A063212 A063213 A063214 * A063216 A063217 A063218

Keyword

nonn,easy

Author

N. J. A. Sloane, Jul 10 2001

Status

approved