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A042102 Numerators of continued fraction convergents to sqrt(575). 2

%I #16 Sep 08 2022 08:44:55

%S 23,24,1127,1151,54073,55224,2594377,2649601,124476023,127125624,

%T 5972254727,6099380351,286543750873,292643131224,13748127787177,

%U 14040770918401,659623590033623,673664360952024

%N Numerators of continued fraction convergents to sqrt(575).

%H Vincenzo Librandi, <a href="/A042102/b042102.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 (0,48,0,-1).

%F G.f.: -(x^3 - 23*x^2 - 24*x - 23)/(x^4 - 48*x^2 + 1). - _Vincenzo Librandi_, Nov 16 2013

%F a(n) = 48*a(n-2) - a(n-4). - _Vincenzo Librandi_, Nov 12 2013

%t Numerator[Convergents[Sqrt[575], 20]] (* _Harvey P. Dale_, Aug 10 2011 *)

%t CoefficientList[Series[-(x^3 - 23 x^2 - 24 x - 23)/(x^4 - 48 x^2 + 1), {x, 0, 30}], x] (* _Vincenzo Librandi_, Nov 16 2013 *)

%o (Magma) I:=[23,24,1127,1151]; [n le 4 select I[n] else 48*Self(n-2)-Self(n-4): n in [1..30]]; // _Vincenzo Librandi_, Nov 16 2013

%Y Cf. A042103.

%K nonn,cofr,frac,easy,less

%O 0,1

%A _N. J. A. Sloane_.

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Last modified March 28 09:03 EDT 2024. Contains 371239 sequences. (Running on oeis4.)