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%I #26 Dec 26 2023 07:03:54
%S 29,1683,97643,5664977,328666309,19068310899,1106290698451,
%T 64183928821057,3723774162319757,216043085343366963,
%U 12534222724077603611,727200961081844376401,42190189965471051434869,2447758218958402827598803
%N Numerators of continued fraction convergents to sqrt(842).
%H Vincenzo Librandi, <a href="/A042624/b042624.txt">Table of n, a(n) for n = 0..200</a>
%H Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (58, 1).
%F a(n) = 58*a(n-1)+a(n-2) for n>1; a(0)=29, a(1)=1683. G.f.: (29+x)/(1-58*x-x^2). [_Philippe Deléham_, Nov 23 2008]
%t Numerator[Convergents[Sqrt[842], 20]] (* or *) LinearRecurrence[{58, 1}, {29, 1683}, 20] (* _Harvey P. Dale_, Sep 24 2013 *)
%t CoefficientList[Series[(29 + x)/(1 - 58 x - x^2), {x, 0, 30}], x] (* _Vincenzo Librandi_, Nov 30 2013 *)
%Y Cf. A042625.
%K nonn,cofr,frac,easy
%O 0,1
%A _N. J. A. Sloane_.
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