login
Denominators of continued fraction convergents to sqrt(149).
2

%I #20 Sep 08 2022 08:44:54

%S 1,4,5,29,92,305,1617,1922,9305,225242,910273,1135515,6587848,

%T 20899059,69285025,367324184,436609209,2113761020,51166873689,

%U 206781255776,257948129465,1496521903101,4747513838768,15739063419405,83442830935793,99181894355198

%N Denominators of continued fraction convergents to sqrt(149).

%H Vincenzo Librandi, <a href="/A041273/b041273.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 (0,0,0,0,0,0,0,0,227164,0,0,0,0,0,0,0,0,1).

%F G.f.: -(x^16 -4*x^15 +5*x^14 -29*x^13 +92*x^12 -305*x^11 +1617*x^10 -1922*x^9 +9305*x^8 +1922*x^7 +1617*x^6 +305*x^5 +92*x^4 +29*x^3 +5*x^2 +4*x +1) / ((x^6 +61*x^3 -1)*(x^12 -61*x^9 +3722*x^6 +61*x^3 +1)). - _Colin Barker_, Nov 14 2013

%F a(n) = 227164*a(n-9) + a(n-18). - _Vincenzo Librandi_, Dec 14 2013

%p convert(sqrt(149), confrac, 30, cvgts): denom(cvgts); # _Wesley Ivan Hurt_, Dec 22 2013

%t Denominator[Convergents[Sqrt[149], 30]] (* _Vincenzo Librandi_, Dec 14 2013 *)

%o (Magma) I:=[1,4,5,29,92,305,1617,1922,9305,225242, 910273,1135515,6587848,20899059,69285025,367324184, 436609209,2113761020]; [n le 18 select I[n] else 227164*Self(n-9)+Self(n-18): n in [1..40]]; // _Vincenzo Librandi_, Dec 14 2013

%Y Cf. A041272, A010202.

%K nonn,frac,easy

%O 0,2

%A _N. J. A. Sloane_.

%E More terms from _Colin Barker_, Nov 14 2013