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A042150 Numerators of continued fraction convergents to sqrt(600). 2

%I

%S 24,49,2376,4801,232824,470449,22814376,46099201,2235576024,

%T 4517251249,219063635976,442644523201,21466000749624,43374646022449,

%U 2103449009827176,4250272665676801,206116536962313624,416483346590304049

%N Numerators of continued fraction convergents to sqrt(600).

%H Vincenzo Librandi, <a href="/A042150/b042150.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 (0,98,0,-1).

%F G.f.: (1 + x)*(24 + 25*x - x^2)/((1 - 10*x + x^2)*(1 + 10*x + x^2)). - _Vincenzo Librandi_, Nov 18 2013

%F a(n) = 98*a(n-2) - a(n-4). - _Vincenzo Librandi_, Nov 18 2013

%t Numerator[Convergents[Sqrt[600], 30]] (* or *) CoefficientList[Series[(24 + 49 x + 24 x^2 - x^3)/(1 - 98 x^2 + x^4), {x, 0, 30}], x] (* _Vincenzo Librandi_, Nov 18 2013 *)

%o (MAGMA) I:=[24,49,2376,4801]; [n le 4 select I[n] else 98*Self(n-2)-Self(n-4): n in [1..30]]; // _Vincenzo Librandi_, Nov 18 2013

%Y Cf. A042151.

%K nonn,cofr,frac,easy,less

%O 0,1

%A _N. J. A. Sloane_.

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Last modified August 8 12:30 EDT 2022. Contains 356009 sequences. (Running on oeis4.)