OFFSET
1,1
COMMENTS
Appears to agree with the first 11-section of A186042 except for the first term of both sequences (verified up to a(10000)). - Klaus Brockhaus, Mar 10 2011
LINKS
Klaus Brockhaus, Table of n, a(n) for n = 1..10000
William A. Stein, Dimensions of the spaces S_k(Gamma_0(N)).
William A. Stein, The modular forms database
FORMULA
From Klaus Brockhaus, Mar 10 2011: (Start)
G.f. (conjectured): x*(x^3 + 12*x^2 + 15*x + 2) / ((x - 1)^2*(x + 1)).
Recurrences (conjectured):
a(n) = a(n-1) + a(n-2) - a(n-3) for n > 4;
a(n) = a(n-2) + 30 for n > 3. (End)
Closed formula (conjectured): a(n) = (30*n+(-1)^n-27)/2 for n > 1. - Bruno Berselli, Mar 10 2011
Recurrence (conjectured): a(n) = 2*a(n-1) -a(n-2) +2*(-1)^n, n > 3. - Vincenzo Librandi, Mar 24 2011
Conjecture: a(n) = A007775(4*n - 3), n > 1. - Bill McEachen, May 15 2022
EXAMPLE
G.f. = 2*x + 17*x^2 + 31*x^3 + 47*x^4 + 61*x^5 + 77*x^6 + 91*x^7 + 107*x^8 + 121*x^9 + ...
PROG
(Magma) [ Dimension(CuspForms(Gamma0(50), 2*n)): n in [1..55] ]; // Klaus Brockhaus, Mar 10 2011
(Sage) def a(n) : return( len( CuspForms( Gamma0( 50), 2*n, prec=1) . basis())); # Michael Somos, May 29 2013
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Jul 08 2001
STATUS
approved