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A041944 Numerators of continued fraction convergents to sqrt(495). 2

%I

%S 22,89,3938,15841,700942,2819609,124763738,501874561,22207244422,

%T 89330852249,3952764743378,15900389825761,703569917076862,

%U 2830180058133209,125231492474938058,503756149957885441

%N Numerators of continued fraction convergents to sqrt(495).

%H Vincenzo Librandi, <a href="/A041944/b041944.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 (0,178,0,-1).

%F G.f.: (22 + 89*x + 22*x^2 - x^3)/(1 - 178*x^2 + x^4). - _Vincenzo Librandi_, Nov 12 2013

%F a(n) = 178*a(n-2) - a(n-4). - _Vincenzo Librandi_, Nov 12 2013

%t Numerator[Convergents[Sqrt[495], 30]] (* or *) CoefficientList[Series[(22 + 89 x + 22 x^2 - x^3)/(1 - 178 x^2 + x^4), {x, 0, 30}], x] (* _Vincenzo Librandi_, Nov 12 2013 *)

%t LinearRecurrence[{0,178,0,-1},{22,89,3938,15841},30] (* _Harvey P. Dale_, Dec 07 2015 *)

%o (MAGMA) I:=[22,89,3938,15841]; [n le 4 select I[n] else 178*Self(n-2)-Self(n-4): n in [1..25]]; // _Vincenzo Librandi_, Nov 12 2013

%Y Cf. A041945.

%K nonn,cofr,frac,easy,less

%O 0,1

%A _N. J. A. Sloane_.

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Last modified September 30 03:03 EDT 2020. Contains 337432 sequences. (Running on oeis4.)