OFFSET
0,1
COMMENTS
Apart from initial term(s), dimension of the space of weight 2n cusp forms for Gamma_0( 33 ).
Apart from initial term(s), dimension of the space of weight 2n cuspidal newforms for Gamma_0( 81 ).
First differences of A002939. - Aaron David Fairbanks, May 13 2014
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..5000
Tanya Khovanova, Recursive Sequences.
William A. Stein, Dimensions of the spaces S_k(Gamma_0(N)).
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 (2,-1).
FORMULA
a(n) = 8*n+2; a(n) = 2*a(n-1)-a(n-2). - Vincenzo Librandi, May 28 2011
Sum_{n>=0} (-1)^n/a(n) = (Pi + 2*log(cot(Pi/8)))/(8*sqrt(2)). - Amiram Eldar, Dec 11 2021
From Elmo R. Oliveira, Mar 17 2024: (Start)
G.f.: 2*(1+3*x)/(1-x)^2.
E.g.f.: 2*exp(x)*(1 + 4*x).
MAPLE
MATHEMATICA
Range[2, 1000, 8] (* Vladimir Joseph Stephan Orlovsky, May 27 2011 *)
PROG
(Magma) [8*n+2: n in [0..60]]; // Vincenzo Librandi, May 28 2011
(Haskell)
a017089 = (+ 2) . (* 8)
a017089_list = [2, 10 ..] -- Reinhard Zumkeller, Jun 07 2015
(PARI) a(n) = 8*n+2; \\ Michel Marcus, Sep 17 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Dec 11 1996
STATUS
approved