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Numerators of continued fraction convergents to sqrt(434).
2

%I #18 Sep 08 2022 08:44:54

%S 20,21,104,125,5104,5229,26020,31249,1275980,1307229,6504896,7812125,

%T 318989896,326802021,1626197980,1953000001,79746198020,81699198021,

%U 406542990104,488242188125,19936230515104,20424472703229

%N Numerators of continued fraction convergents to sqrt(434).

%H Vincenzo Librandi, <a href="/A041826/b041826.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 (0,0,0,250,0,0,0,-1).

%F G.f.: (20 + 21*x + 104*x^2 + 125*x^3 + 104*x^4 - 21*x^5 + 20*x^6 - x^7)/(1 - 250*x^4 + x^8). - _Vincenzo Librandi_, Nov 09 2013

%F a(n) = 250*a(n-4) - a(n-8). - _Vincenzo Librandi_, Nov 09 2013

%t Numerator[Convergents[Sqrt[434], 30]] (* or *) CoefficientList[Series[(20 + 21 x + 104 x^2 + 125 x^3 + 104 x^4 - 21 x^5 + 20 x^6 - x^7)/(1 - 250 x^4 + x^8), {x, 0, 30}], x] (* _Vincenzo Librandi_, Nov 09 2013 *)

%o (Magma) I:=[20,21,104,125,5104,5229,26020,31249]; [n le 8 select I[n] else 250*Self(n-4)-Self(n-8): n in [1..40]]; // _Vincenzo Librandi_, Nov 09 2013

%Y Cf. A041827.

%K nonn,cofr,frac,easy,less

%O 0,1

%A _N. J. A. Sloane_