A063232 Dimension of the space of weight 2n cuspidal newforms for Gamma_0( 77 ).

5, 16, 24, 36, 44, 56, 64, 76, 84, 96, 104, 116, 124, 136, 144, 156, 164, 176, 184, 196, 204, 216, 224, 236, 244, 256, 264, 276, 284, 296, 304, 316, 324, 336, 344, 356, 364, 376, 384, 396, 404, 416, 424, 436, 444, 456, 464, 476, 484, 496, 504, 516, 524, 536

Offset: 1

Author

N. J. A. Sloane, Jul 10 2001

Keywords

• nonn
• easy

Comments

Also dimension of the space of weight 2n cuspidal newforms for Gamma_0( 93 ).

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..1000
• 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).

Programs

Haskell

a063232 n = a063232_list !! (n-1)
a063232_list = 5 : 16 : 24 : 36 : zipWith3 (((-) .) . (+))
   (drop 3 a063232_list) (drop 2 a063232_list) (tail a063232_list)
-- Reinhard Zumkeller, May 03 2015

Mathematica

Table[5 + 10 (n - 1) + (-1)^n + Mod[Binomial[2 (n - 1), n - 1], 2], {n, 50}] (* Wesley Ivan Hurt, May 25 2014 *)
LinearRecurrence[{1,1,-1},{5,16,24,36},60] (* Harvey P. Dale, Aug 21 2017 *)

PARI

A063232(n)=10*n-3-bittest(n,0)*2-(n>1) \\ M. F. Hasler, Mar 05 2012

Formula

Except for the first term, a(n) = 20*(n-1)-a(n-1), (with a(2)=16). - Vincenzo Librandi, Dec 07 2010

a(n) = -5+(-1)^n+10*n for n>1. a(n)=a(n-1)+a(n-2)-a(n-3) for n>4; G.f.: x*(x^3+3*x^2+11*x+5) / ((x-1)^2*(x+1)). - Colin Barker, Sep 08 2013

Sum_{n>=1} (-1)^(n+1)/a(n) = (sqrt(1+2/sqrt(5))*Pi - 1)/20. - Amiram Eldar, Jan 12 2024