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%I #41 Sep 08 2022 08:44:33
%S 9,17,25,33,41,49,57,65,73,81,89,97,105,113,121,129,137,145,153,161,
%T 169,177,185,193,201,209,217,225,233,241,249,257,265,273,281,289,297,
%U 305,313,321,329,337,345,353,361,369,377,385,393,401,409,417,425,433,441,449,457,465,473,481,489
%N Binary expansion ends 001.
%C Apart from initial term(s), dimension of the space of weight 2n cusp forms for Gamma_0( 28 ).
%H Vincenzo Librandi, <a href="/A004768/b004768.txt">Table of n, a(n) for n = 0..10000</a>
%H Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>
%H William A. Stein, <a href="http://wstein.org/Tables/dimskg0n.gp">Dimensions of the spaces S_k(Gamma_0(N))</a>
%H William A. Stein, <a href="http://wstein.org/Tables/">The modular forms database</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1).
%F From _Reinhard Zumkeller_, Oct 30 2008: (Start)
%F a(n) = 8*n + 9.
%F For n > 0: a(n) = A017077(n-1). (End)
%F a(n) = 2*a(n-1) - a(n-2); a(0)=9, a(1)=17. - _Harvey P. Dale_, May 10 2015
%F G.f.: (9 - x) / (1 - x)^2. - _Colin Barker_, Jul 04 2019
%F E.g.f.: exp(x)*(9 + 8*x). - _Stefano Spezia_, May 13 2021
%t Rest[FromDigits[#,2]&/@(Join[#,{0,0,1}]&/@Tuples[{0,1},7])] (* or *) LinearRecurrence[{2,-1},{9,17},100] (* _Harvey P. Dale_, May 10 2015 *)
%o (Magma) [8*n + 9: n in [0..60]]; // _Vincenzo Librandi_, Jul 11 2011
%o (PARI) a(n) = 8*n+9 \\ _Charles R Greathouse IV_, Sep 24 2012
%o (PARI) Vec((9 - x) / (1 - x)^2 + O(x^50)) \\ _Colin Barker_, Jul 04 2019
%o (Python)
%o def a(n): return 8*n + 9
%o print([a(n) for n in range(61)]) # _Michael S. Branicky_, Sep 17 2021
%Y Complement of A004774.
%Y Cf. A017077.
%Y Cf. A146302. - _Reinhard Zumkeller_, Oct 30 2008
%K nonn,easy
%O 0,1
%A _N. J. A. Sloane_
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