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%I #16 Sep 08 2022 08:44:55
%S 30,361,21690,260641,15660150,188182441,11306606610,135867461761,
%T 8163354312270,98096119209001,5893930506852330,70825262201436961,
%U 4255409662593069990,51135741213318276841,3072399882461689680450
%N Numerators of continued fraction convergents to sqrt(905).
%H Vincenzo Librandi, <a href="/A042748/b042748.txt">Table of n, a(n) for n = 0..200</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0, 722, 0, -1).
%F G.f.: (30 +361*x +30*x^2 -x^3)/(1 -722*x^2 +x^4). - _Vincenzo Librandi_, Dec 03 2013
%F a(n) = 722*a(n-2) - a(n-4). - _Vincenzo Librandi_, Dec 03 2013
%t Numerator[Convergents[Sqrt[905], 30]] (* or *) CoefficientList[Series[(30 + 361 x + 30 x^2 - x^3)/(1 - 722 x^2 + x^4), {x, 0, 30}], x] (* _Vincenzo Librandi_, Dec 03 2013 *)
%t LinearRecurrence[{0,722,0,-1},{30,361,21690,260641},20] (* _Harvey P. Dale_, Mar 05 2022 *)
%o (Magma) I:=[30, 361, 21690, 260641]; [n le 4 select I[n] else 722*Self(n-2)-Self(n-4): n in [1..30]]; // _Vincenzo Librandi_, Dec 03 2013
%Y Cf. A042749.
%K nonn,cofr,frac,easy
%O 0,1
%A _N. J. A. Sloane_.
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