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A042218 Numerators of continued fraction convergents to sqrt(635). 2

%I

%S 25,126,6325,31751,1593875,8001126,401650175,2016252001,101214250225,

%T 508087503126,25505589406525,128036034535751,6427307316194075,

%U 32264572615506126,1619655938091500375

%N Numerators of continued fraction convergents to sqrt(635).

%H Vincenzo Librandi, <a href="/A042218/b042218.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 (0,252,0,-1).

%F G.f.: (25 +126*x +25*x^2 -x^3)/(x^4 -252*x^2 +1). - _Vincenzo Librandi_, Nov 19 2013

%F a(n) = 252*a(n-2) - a(n-4). - _Vincenzo Librandi_, Nov 19 2013

%t Numerator[Convergents[Sqrt[635], 30]] (* _Harvey P. Dale_, Dec 15 2012 *)

%t CoefficientList[Series[(25 + 126 x + 25 x^2 - x^3)/(x^4 - 252 x^2 + 1), {x, 0, 30}], x](* _Vincenzo Librandi_, Nov 19 2013 *)

%o (Magma) I:=[25,126,6325,31751]; [n le 4 select I[n] else 252*Self(n-2)-Self(n-4): n in [1..30]]; // _Vincenzo Librandi_, Nov 19 2013

%Y Cf. A042219.

%K nonn,cofr,frac,easy

%O 0,1

%A _N. J. A. Sloane_.

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Last modified January 28 10:39 EST 2023. Contains 359859 sequences. (Running on oeis4.)