OFFSET
0,1
COMMENTS
Apart from initial term(s), dimension of the space of weight 2n cusp forms for Gamma_0( 28 ).
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..10000
Tanya Khovanova, Recursive Sequences
William A. Stein, Dimensions of the spaces S_k(Gamma_0(N))
William A. Stein, The modular forms database
Index entries for linear recurrences with constant coefficients, signature (2,-1).
FORMULA
From Reinhard Zumkeller, Oct 30 2008: (Start)
a(n) = 8*n + 9.
For n > 0: a(n) = A017077(n-1). (End)
a(n) = 2*a(n-1) - a(n-2); a(0)=9, a(1)=17. - Harvey P. Dale, May 10 2015
G.f.: (9 - x) / (1 - x)^2. - Colin Barker, Jul 04 2019
E.g.f.: exp(x)*(9 + 8*x). - Stefano Spezia, May 13 2021
MATHEMATICA
Rest[FromDigits[#, 2]&/@(Join[#, {0, 0, 1}]&/@Tuples[{0, 1}, 7])] (* or *) LinearRecurrence[{2, -1}, {9, 17}, 100] (* Harvey P. Dale, May 10 2015 *)
PROG
(Magma) [8*n + 9: n in [0..60]]; // Vincenzo Librandi, Jul 11 2011
(PARI) a(n) = 8*n+9 \\ Charles R Greathouse IV, Sep 24 2012
(PARI) Vec((9 - x) / (1 - x)^2 + O(x^50)) \\ Colin Barker, Jul 04 2019
(Python)
def a(n): return 8*n + 9
print([a(n) for n in range(61)]) # Michael S. Branicky, Sep 17 2021
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved