OFFSET
2,2
COMMENTS
It appears that for n > 2 a(n) = floor((9n-22)/2). - Gary Detlefs, Mar 02 2010
LINKS
William A. Stein, Dimensions of the spaces S_k^{new}(Gamma_1(N)).
William A. Stein, The modular forms database.
FORMULA
a(n) = 9*n/2 + (-1)^n/4 - 45/4 for n >= 3, with first differences in A010710. - R. J. Mathar, Dec 06 2010
From M. F. Hasler, Mar 05 2012: (Start)
G.f.: x^2*(-1 + 3*x + 6*x^2 + x^3)/(1 - x - x^2 + x^3).
a(n+2) = a(n)+9 (n>2), a(2n+1) = a(2n)+4 (n>1), a(2n) = a(2n-1)+5 (n>1). (End)
Sum_{n>=3} (-1)^(n+1)/a(n) = cot(2*Pi/9)*Pi/9. - Amiram Eldar, Jan 12 2024
From Amiram Eldar, Nov 22 2024: (Start)
Product_{n>=3} (1 - (-1)^n/a(n)) = 2*sin(Pi/18) + 1 (= A130880 + 1).
Product_{n>=3} (1 + (-1)^n/a(n)) = (1/2) * sec(Pi/9) (= A332438 - 3). (End)
MATHEMATICA
Join[{-1}, Table[9*n/2 + (-1)^n/4 - 45/4, {n, 3, 60}]] (* Amiram Eldar, Jan 12 2024 *)
CROSSREFS
KEYWORD
sign,easy,changed
AUTHOR
N. J. A. Sloane, Jul 14 2001
STATUS
approved