OFFSET
1,1
COMMENTS
Apart from initial term(s), dimension of the space of weight 2n cuspidal newforms for Gamma_0( 17 ).
LINKS
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
a(n) = 2*floor((n-1)/3) + 2*n. - Gary Detlefs, Mar 18 2010
From R. J. Mathar, Dec 05 2011: (Start)
G.f.: 2*x*(1+x)*(1+x^2) / ( (1+x+x^2)*(x-1)^2 ).
a(n) = 2*A042968(n). (End)
a(n) = a(n-1) + a(n-3) - a(n-4) for n>4, with a(1)=2, a(2)=4, a(3)=6, a(4)=10. - Harvey P. Dale, Oct 06 2014
From Wesley Ivan Hurt, Jun 09 2016: (Start)
a(n) = 2*(12*n-6-3*cos(2*n*Pi/3)+sqrt(3)*sin(2*n*Pi/3))/9.
a(3k) = 8k-2, a(3k-1) = 8k-4, a(3k-2) = 8k-6. (End)
Sum_{n>=1} (-1)^(n+1)/a(n) = (2*sqrt(2)-1)*Pi/16. - Amiram Eldar, Dec 19 2021
E.g.f.: 2*(9 + 6*exp(x)*(2*x - 1) - exp(-x/2)*(3*cos(sqrt(3)*x/2) - sqrt(3)*sin(sqrt(3)*x/2)))/9. - Stefano Spezia, Oct 17 2022
MAPLE
A047410:=n->2*(12*n-6-3*cos(2*n*Pi/3)+sqrt(3)*sin(2*n*Pi/3))/9: seq(A047410(n), n=1..100); # Wesley Ivan Hurt, Jun 09 2016
MATHEMATICA
With[{upto=140}, Complement[2*Range[upto/2], 8*Range[upto/8]]] (* or *) LinearRecurrence[{1, 0, 1, -1}, {2, 4, 6, 10}, 60] (* Harvey P. Dale, Oct 06 2014 *)
PROG
(Magma) [n : n in [0..150] | n mod 8 in [2, 4, 6]]; // Wesley Ivan Hurt, Jun 09 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved