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Denominators of continued fraction convergents to sqrt(335).
2

%I #19 Sep 08 2022 08:44:54

%S 1,3,10,33,1198,3627,12079,39864,1447183,4381413,14591422,48155679,

%T 1748195866,5292743277,17626425697,58172020368,2111819158945,

%U 6393629497203,21292707650554,70271752448865,2551075795809694,7723499139877947,25721573215443535

%N Denominators of continued fraction convergents to sqrt(335).

%H Vincenzo Librandi, <a href="/A041633/b041633.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, 1208, 0, 0, 0, -1).

%F G.f.: -(x^2-3*x-1)*(x^4+11*x^2+1) / (x^8-1208*x^4+1). - _Colin Barker_, Nov 20 2013

%F a(n) = 1208*a(n-4) - a(n-8) for n>7. - _Vincenzo Librandi_, Dec 22 2013

%t Denominator[Convergents[Sqrt[335], 30]] (* _Vincenzo Librandi_, Dec 22 2013 *)

%t LinearRecurrence[{0,0,0,1208,0,0,0,-1},{1,3,10,33,1198,3627,12079,39864},30] (* _Harvey P. Dale_, Aug 11 2019 *)

%o (Magma) I:=[1,3,10,33,1198,3627,12079,39864]; [n le 8 select I[n] else 1208*Self(n-4)-Self(n-8): n in [1..40]]; // _Vincenzo Librandi_, Dec 22 2013

%Y Cf. A041632, A040316.

%K nonn,frac,easy

%O 0,2

%A _N. J. A. Sloane_.

%E More terms from _Colin Barker_, Nov 20 2013