|
%I #18 Sep 08 2022 08:44:54
%S 1,1,2,3,5,8,13,21,475,496,971,1467,2438,3905,6343,10248,231799,
%T 242047,473846,715893,1189739,1905632,3095371,5001003,113117437,
%U 118118440,231235877,349354317,580590194,929944511,1510534705,2440479216,55201077457,57641556673
%N Denominators of continued fraction convergents to sqrt(135).
%H Vincenzo Librandi, <a href="/A041247/b041247.txt">Table of n, a(n) for n = 0..200</a>
%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,0,0,488,0,0,0,0,0,0,0,-1).
%F G.f.: -(x^2-x-1)*(x^4+3*x^2+1)*(x^8+7*x^4+1) / (x^16-488*x^8+1). - _Colin Barker_, Nov 14 2013
%F a(n) = 488*a(n-8) - a(n-16). - _Vincenzo Librandi_, Dec 13 2013
%t Denominator[Convergents[Sqrt[135], 30]] (* _Vincenzo Librandi_, Dec 13 2013 *)
%t LinearRecurrence[{0,0,0,0,0,0,0,488,0,0,0,0,0,0,0,-1},{1,1,2,3,5,8,13,21,475,496,971,1467,2438,3905,6343,10248},40] (* _Harvey P. Dale_, Aug 01 2019 *)
%o (Magma) I:=[1,1,2,3,5,8,13,21,475,496,971,1467,2438,3905,6343,10248]; [n le 16 select I[n] else 488*Self(n-8)-Self(n-16): n in [1..40]]; // _Vincenzo Librandi_, Dec 13 2013
%Y Cf. A041246, A010194.
%K nonn,frac,easy
%O 0,3
%A _N. J. A. Sloane_.
%E More terms from _Colin Barker_, Nov 14 2013
|
