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%I #19 Sep 08 2022 08:44:55
%S 21,43,1827,3697,157101,317899,13508859,27335617,1161604773,
%T 2350545163,99884501619,202119548401,8588905534461,17379930617323,
%U 738545991462027,1494471913541377,63506366360199861,128507204633941099
%N Numerators of continued fraction convergents to sqrt(462).
%H Vincenzo Librandi, <a href="/A041880/b041880.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 (0,86,0,-1).
%F G.f.: (21 +43*x +21*x^2 -x^3)/(1 -86*x^2 +x^4). - _Vincenzo Librandi_, Nov 11 2013
%F a(n) = 86*a(n-2) -a(n-4). - _Vincenzo Librandi_, Nov 11 2013
%t Numerator[Convergents[Sqrt[462], 30]] (* or *) CoefficientList[Series[(21 + 43 x + 21 x^2 - x^3)/(1 - 86 x^2 + x^4), {x, 0, 25}], x] (* _Vincenzo Librandi_, Nov 11 2013 *)
%t LinearRecurrence[{0,86,0,-1},{21,43,1827,3697},30] (* _Harvey P. Dale_, Jul 25 2015 *)
%o (Magma) I:=[21,43,1827,3697]; [n le 4 select I[n] else 86*Self(n-2)-Self(n-4): n in [1..20]]; // _Vincenzo Librandi_, Nov 11 2013
%Y Cf. A041881.
%K nonn,cofr,frac,easy,less
%O 0,1
%A _N. J. A. Sloane_.
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