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A063209 Dimension of the space of weight 2n cuspidal newforms for Gamma_0( 41 ). 1
3, 10, 16, 24, 30, 36, 44, 50, 56, 64, 70, 76, 84, 90, 96, 104, 110, 116, 124, 130, 136, 144, 150, 156, 164, 170, 176, 184, 190, 196, 204, 210, 216, 224, 230, 236, 244, 250, 256, 264, 270, 276, 284, 290, 296, 304, 310, 316, 324, 330 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Robert Israel, 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 (1,0,1,-1).

FORMULA

G.f.: (-1)*x*(x^4 - 5*x^3 - 6*x^2 - 7*x - 3) / ( (1+x+x^2)*(x-1)^2 ). - R. J. Mathar, Jul 15 2015

For n > 1, a(n) = (20 n - 8 - 2 (n-1 mod 3))/3. - Robert Israel, Jan 05 2017

MAPLE

f:= gfun:-rectoproc({a(n+4)-a(n+3)-a(n+1)+a(n)=0, a(1)=3, a(2)=10, a(3)=16, a(4)=24, a(5)=30}, a(n), remember):

map(f, [$1..100]); # Robert Israel, Jan 05 2017

MATHEMATICA

Join[{3}, LinearRecurrence[{1, 0, 1, -1}, {10, 16, 24, 30}, 50]] (* G. C. Greubel, Jan 05 2017 *)

PROG

(PARI) Vec(((-1)*x*(x^4 - 5*x^3 - 6*x^2 - 7*x - 3))/((x - 1)^2*(x^2 + x + 1)) + O(x^50)) \\ G. C. Greubel, Jan 05 2017

CROSSREFS

Sequence in context: A093516 A246302 A278041 * A063109 A083684 A141497

Adjacent sequences:  A063206 A063207 A063208 * A063210 A063211 A063212

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Jul 10 2001

STATUS

approved

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Last modified February 28 22:24 EST 2020. Contains 332335 sequences. (Running on oeis4.)