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Denominators of continued fraction convergents to sqrt(458).
2

%I #14 Sep 08 2022 08:44:55

%S 1,2,5,212,429,1070,45369,91808,228985,9709178,19647341,49003860,

%T 2077809461,4204622782,10487055025,444660933832,899808922689,

%U 2244278779210,95159517649509,192563314078228,480286145805965,20364581437928758,41209449021663481

%N Denominators of continued fraction convergents to sqrt(458).

%H Vincenzo Librandi, <a href="/A041873/b041873.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 (0,0,214,0,0,1).

%F G.f.: -(x^4 -2*x^3 +5*x^2 +2*x +1) / (x^6 +214*x^3 -1). - _Colin Barker_, Nov 26 2013

%F a(n) = 214*a(n-3) + a(n-6) for n>5. - _Vincenzo Librandi_, Dec 26 2013

%t Denominator[Convergents[Sqrt[458], 30]] (* _Vincenzo Librandi_, Dec 26 2013 *)

%o (Magma) I:=[1,2,5,212,429,1070]; [n le 6 select I[n] else 214*Self(n-3)+Self(n-6): n in [1..40]]; // _Vincenzo Librandi_, Dec 26 2013

%Y Cf. A041872, A040436.

%K nonn,frac,easy

%O 0,2

%A _N. J. A. Sloane_.

%E More terms from _Colin Barker_, Nov 26 2013