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
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
Programs
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Magma
[8*n + 9: n in [0..60]]; // Vincenzo Librandi, Jul 11 2011
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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
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PARI
Vec((9 - x) / (1 - x)^2 + O(x^50)) \\ Colin Barker, Jul 04 2019
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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
Comments