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A041852 Numerators of continued fraction convergents to sqrt(448). 2

%I

%S 21,127,5355,32257,1360149,8193151,345472491,2081028097,87748652565,

%T 528572943487,22287812279019,134255446617601,5661016570218261,

%U 34100354867927167,1437875921023159275

%N Numerators of continued fraction convergents to sqrt(448).

%H Vincenzo Librandi, <a href="/A041852/b041852.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 (0,254,0,-1).

%F G.f.: (21 + 127*x + 21*x^2 - x^3)/(1 - 254*x^2 + x^4). - _Vincenzo Librandi_, Nov 10 2013

%F a(n) = 254*a(n-2) - a(n-4). - _Vincenzo Librandi_, Nov 10 2013

%t Numerator[Convergents[Sqrt[448], 30]] (* or *) CoefficientList[Series[(21 + 127 x + 21 x^2 - x^3)/(1 - 254 x^2 + x^4), {x, 0, 25}], x] (* _Vincenzo Librandi_, Nov 10 2013 *)

%o (Magma) I:=[21,127,5355,32257]; [n le 4 select I[n] else 254*Self(n-2)-Self(n-4): n in [1..20]]; // _Vincenzo Librandi_, Nov 10 2013

%Y Cf. A041853.

%K nonn,cofr,frac,easy,less

%O 0,1

%A _N. J. A. Sloane_.

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Last modified February 5 20:57 EST 2023. Contains 360087 sequences. (Running on oeis4.)