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Denominators of continued fraction convergents to sqrt(218).
2

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

%S 1,1,4,13,17,489,506,2007,6527,8534,245479,254013,1007518,3276567,

%T 4284085,123230947,127515032,505776043,1644843161,2150619204,

%U 61862180873,64012800077,253900581104,825714543389,1079615124493,31054938029193,32134553153686

%N Denominators of continued fraction convergents to sqrt(218).

%H Vincenzo Librandi, <a href="/A041407/b041407.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 (0,0,0,0,502,0,0,0,0,1).

%F G.f.: -(x^8-x^7+4*x^6-13*x^5+17*x^4+13*x^3+4*x^2+x+1) / (x^10+502*x^5-1). - _Colin Barker_, Nov 17 2013

%F a(n) = 502*a(n-5) + a(n-10) for n>9. - _Vincenzo Librandi_, Dec 17 2013

%t Denominator[Convergents[Sqrt[218], 30]] (* _Vincenzo Librandi_, Dec 17 2013 *)

%t LinearRecurrence[{0,0,0,0,502,0,0,0,0,1},{1,1,4,13,17,489,506,2007,6527,8534},30] (* _Harvey P. Dale_, Jul 26 2014 *)

%o (Magma) I:=[1,1,4,13,17,489,506,2007,6527,8534]; [n le 10 select I[n] else 502*Self(n-5)+Self(n-10): n in [1..40]]; // _Vincenzo Librandi_, Dec 17 2013

%Y Cf. A041406, A040203.

%K nonn,frac,easy

%O 0,3

%A _N. J. A. Sloane_.

%E More terms from _Colin Barker_, Nov 17 2013