OFFSET
1,2
COMMENTS
Apart from initial term(s), dimension of the space of weight 2n cuspidal newforms for Gamma_0( 27 ).
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
Equals A097806 * A042965, where A097806 = the pairwise operator and A042965 = numbers not congruent to 2 mod 4. - Gary W. Adamson, Sep 12 2007
From Wesley Ivan Hurt, Jun 09 2016: (Start)
G.f.: x*(1+3*x+3*x^2+x^3)/((x-1)^2*(1+x+x^2)).
a(n) = a(n-1) + a(n-3) - a(n-4) for n>4.
a(n) = (24*n-12+3*cos(2*n*Pi/3)-sqrt(3)*sin(2*n*Pi/3))/9.
a(3k) = 8k-1, a(3k-1) = 8k-4, a(3k-2) = 8k-7. (End)
Sum_{n>=1} (-1)^(n+1)/a(n) = (tan(Pi/16)+cot(Pi/16)-1)*Pi/16 = (2*sqrt(2*(2+sqrt(2)))-1)*Pi/16. - Amiram Eldar, Dec 19 2021
MAPLE
A047537:=n->(24*n-12+3*cos(2*n*Pi/3)-sqrt(3)*sin(2*n*Pi/3))/9: seq(A047537(n), n=1..100); # Wesley Ivan Hurt, Jun 09 2016
MATHEMATICA
Select[Range[200], MemberQ[{1, 4, 7}, Mod[#, 8]]&] (* or *) LinearRecurrence[{1, 0, 1, -1}, {1, 4, 7, 9}, 100] (* Harvey P. Dale, Apr 01 2016 *)
PROG
(Magma) [n : n in [0..150] | n mod 8 in [1, 4, 7]]; // Wesley Ivan Hurt, Jun 09 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved