%I #28 Dec 26 2023 07:02:24

%S 10,201,4030,80801,1620050,32481801,651256070,13057603201,

%T 261803320090,5249124005001,105244283420110,2110134792407201,

%U 42307940131564130,848268937423689801,17007686688605360150,341002002709530892801

%N Numerators of continued fraction convergents to sqrt(101).

%H Vincenzo Librandi, <a href="/A041180/b041180.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">Index entries for linear recurrences with constant coefficients</a>, signature (20,1).

%F From _Philippe Deléham_, Nov 21 2008: (Start)

%F a(n) = 20*a(n-1) + a(n-2) for n > 1, a(0)=10, a(1)=201.

%F G.f.: (10+x)/(1-20*x-x^2). (End)

%t CoefficientList[Series[(10 + x)/(1 - 20 x - x^2), {x, 0, 30}], x] (* _Vincenzo Librandi_, Oct 30 2013 *)

%t Numerator[Convergents[Sqrt[101], 20]] (* _Bruno Berselli_, Oct 30 2013 *)

%Y Cf. A041181.

%K nonn,cofr,frac,easy

%O 0,1

%A _N. J. A. Sloane_