OFFSET
0,1
COMMENTS
Apart from initial term(s), dimension of the space of weight 2n cusp forms for Gamma_0( 44 ).
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..2000
Tanya Khovanova, Recursive Sequences.
William A. Stein, Dimensions of the spaces S_k(Gamma_0(N)).
William A. Stein, The modular forms database.
Index entries for linear recurrences with constant coefficients, signature (2,-1).
FORMULA
a(n) = 2*a(n-1) - a(n-2). - Vincenzo Librandi, Jun 07 2011
A089911(2*a(n)) = 8. - Reinhard Zumkeller, Jul 05 2013
From G. C. Greubel, Sep 18 2019: (Start)
G.f.: 3*(1+3*x)/(1-x)^2.
E.g.f.: 3*(1+4*x)*exp(x). (End)
Sum_{n>=0} (-1)^n/a(n) = (Pi + 2*log(sqrt(2)+1))/(12*sqrt(2)). - Amiram Eldar, Dec 12 2021
MAPLE
seq(12*n+3, n=0..60); # G. C. Greubel, Sep 18 2019
MATHEMATICA
12*Range[0, 60]+3 (* Vladimir Joseph Stephan Orlovsky, Feb 19 2011 *)
PROG
(Magma) [12*n+3: n in [0..60]]; // Vincenzo Librandi, Jun 07 2011
(Haskell)
a017557 = (+ 3) . (* 12) -- Reinhard Zumkeller, Jul 05 2013
(PARI) a(n)=12*n+3 \\ Charles R Greathouse IV, Jul 10 2016
(Sage) [12*n+3 for n in (0..60)] # G. C. Greubel, Sep 18 2019
(GAP) List([0..60], n-> 12*n+3 ); # G. C. Greubel, Sep 18 2019
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved