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A042208 Numerators of continued fraction convergents to sqrt(630). 2

%I

%S 25,251,12575,126001,6312625,63252251,3168925175,31752504001,

%T 1590794125225,15939693756251,798575481937775,8001694513134001,

%U 400883301138637825,4016834705899512251,201242618596114250375

%N Numerators of continued fraction convergents to sqrt(630).

%H Vincenzo Librandi, <a href="/A042208/b042208.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 (0,502,0,-1).

%F G.f.: (25 +251*x +25*x^2 -x^3)/(x^4 -502*x^2 +1). - _Vincenzo Librandi_, Nov 19 2013

%F a(n) = 502*a(n-2) - a(n-4). - _Vincenzo Librandi_, Nov 19 2013

%t Numerator[Convergents[Sqrt[630], 30]] (* or *) CoefficientList[Series[(25 + 251 x + 25 x^2 - x^3)/(x^4 - 502 x^2 + 1), {x, 0, 20}], x] (* _Vincenzo Librandi_, Nov 19 2013 *)

%t LinearRecurrence[{0,502,0,-1},{25,251,12575,126001},20] (* _Harvey P. Dale_, Apr 01 2018 *)

%o (MAGMA) I:=[25,251,12575,126001]; [n le 4 select I[n] else 502*Self(n-2)-Self(n-4): n in [1..30]]; // _Vincenzo Librandi_, Nov 19 2013

%Y Cf. A042209.

%K nonn,cofr,frac,easy

%O 0,1

%A _N. J. A. Sloane_.

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Last modified August 12 23:52 EDT 2022. Contains 356077 sequences. (Running on oeis4.)