OFFSET
0,2
COMMENTS
Dimension of the space of weight 2n+4 cusp forms for Gamma_0(7).
LINKS
Harvey P. Dale, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (1,0,1,-1).
FORMULA
G.f.: (1 + 2*x + x^3) / (1 - x - x^3 + x^4).
a(-n) = - A168056(n - 1).
a(n) = - A168053(n + 2).
a(n+3) = a(n) + 4.
a(n) = (12*n+9+4*sqrt(3)*sin(2*n*Pi/3))/9. - Wesley Ivan Hurt, Sep 29 2017
EXAMPLE
G.f. = 1 + 3*x + 3*x^2 + 5*x^3 + 7*x^4 + 7*x^5 + 9*x^6 + 11*x^7 + 11*x^8 + ...
MATHEMATICA
Table[2Floor[(2n+1)/3]+1, {n, 0, 70}] (* or *) LinearRecurrence[{1, 0, 1, -1}, {1, 3, 3, 5}, 70] (* Harvey P. Dale, Sep 17 2024 *)
PROG
(PARI) {a(n) = (2*n + 1) \ 3 * 2 + 1};
(Sage) def a(n) : return( len( CuspForms( Gamma0( 7), 2*n + 4, prec=1). basis()));
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Michael Somos, May 29 2013
STATUS
approved