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Denominators of continued fraction convergents to sqrt(498).
2

%I #18 Sep 08 2022 08:44:55

%S 1,3,19,421,2545,8056,357009,1079083,6831507,151372237,915064929,

%T 2896567024,128364013985,387988608979,2456295667859,54426493301877,

%U 329015255479121,1041472259739240,46153794684005681,139502856311756283,883170932554543379

%N Denominators of continued fraction convergents to sqrt(498).

%H Vincenzo Librandi, <a href="/A041951/b041951.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 (0,0,0,0,0,359554,0,0,0,0,0,-1).

%F G.f.: -(x^10 -3*x^9 +19*x^8 -421*x^7 +2545*x^6 -8056*x^5 -2545*x^4 -421*x^3 -19*x^2 -3*x -1) / (x^12 -359554*x^6 +1). - _Colin Barker_, Nov 27 2013

%F a(n) = 359554*a(n-6) - a(n-12) for n>11. - _Vincenzo Librandi_, Dec 27 2013

%t Denominator[Convergents[Sqrt[498], 30]] (* _Vincenzo Librandi_, Dec 27 2013 *)

%t LinearRecurrence[{0,0,0,0,0,359554,0,0,0,0,0,-1},{1,3,19,421,2545,8056,357009,1079083,6831507,151372237,915064929,2896567024},30] (* _Harvey P. Dale_, Oct 21 2016 *)

%o (Magma) I:=[1,3,19,421,2545,8056,357009,1079083,6831507, 151372237,915064929,2896567024]; [n le 12 select I[n] else 359554*Self(n-6)-Self(n-12): n in [1..40]]; // _Vincenzo Librandi_, Dec 27 2013

%Y Cf. A041950, A040475.

%K nonn,frac,easy

%O 0,2

%A _N. J. A. Sloane_.

%E More terms from _Colin Barker_, Nov 27 2013