|
%I #20 Sep 08 2022 08:44:54
%S 1,3,7,24,823,2493,5809,19920,683089,2069187,4821463,16533576,
%T 566963047,1717422717,4001808481,13722848160,470578645921,
%U 1425458785923,3321496217767,11389947439224,390579709151383,1183129074893373,2756837858938129,9453642651707760
%N Denominators of continued fraction convergents to sqrt(299).
%H Vincenzo Librandi, <a href="/A041563/b041563.txt">Table of n, a(n) for n = 0..200</a>
%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (0, 0, 0, 830, 0, 0, 0, -1).
%F G.f.: -(x^2-3*x-1)*(x^4+8*x^2+1) / (x^8-830*x^4+1). - _Colin Barker_, Nov 19 2013
%F a(n) = 830*a(n-4) - a(n-8) for n>7. - _Vincenzo Librandi_, Dec 20 2013
%t Denominator[Convergents[Sqrt[299], 30]] (* _Harvey P. Dale_, May 02 2012 *)
%t CoefficientList[Series[(1 + 3 x - x^2) (x^4 + 8 x^2 + 1)/(x^8 - 830 x^4+1), {x, 0, 30}], x] (* _Vincenzo Librandi_, Dec 20 2013 *)
%o (Magma) I:=[1,3,7,24,823,2493,5809,19920]; [n le 8 select I[n] else 830*Self(n-4)-Self(n-8): n in [1..40]]; // _Vincenzo Librandi_, Dec 20 2013
%Y Cf. A041562, A040281.
%K nonn,frac,easy
%O 0,2
%A _N. J. A. Sloane_.
%E More terms from _Colin Barker_, Nov 19 2013
|
