A004768 Binary expansion ends 001.

9, 17, 25, 33, 41, 49, 57, 65, 73, 81, 89, 97, 105, 113, 121, 129, 137, 145, 153, 161, 169, 177, 185, 193, 201, 209, 217, 225, 233, 241, 249, 257, 265, 273, 281, 289, 297, 305, 313, 321, 329, 337, 345, 353, 361, 369, 377, 385, 393, 401, 409, 417, 425, 433, 441, 449, 457, 465, 473, 481, 489

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

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).

Crossrefs

Complement of A004774.

Cf. A017077.

Cf. A146302. - Reinhard Zumkeller, Oct 30 2008

Programs

Magma

[8*n + 9: n in [0..60]]; // Vincenzo Librandi, Jul 11 2011

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 *)

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

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