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%I #15 Jun 13 2015 00:49:22
%S 10,101,2030,20401,410050,4120901,82828070,832401601,16730860090,
%T 168141002501,3379550910110,33963650103601,682652552982130,
%U 6860489179924901,137892436151480150,1385784850694726401
%N Numerators of continued fraction convergents to sqrt(102).
%H Vincenzo Librandi and Bruno Berselli, <a href="/A041182/b041182.txt">Table of n, a(n) for n = 0..100</a> (first 66 terms from Vincenzo Librandi).
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,202,0,-1).
%F G.f.: (10 + 101*x + 10*x^2 - x^3)/(1 - 202*x^2 + x^4). [_Bruno Berselli_, Oct 30 2013]
%F a(n) = 202*a(n-2)-a(n-4). [_Bruno Berselli_, Oct 30 2013]
%t Numerator[Convergents[Sqrt[102], 30]] (* _Vincenzo Librandi_, Oct 30 2013 *)
%t RecurrenceTable[{a[0] == 10, a[1] == 101, a[2] == 2030, a[3] == 20401, a[n] == 202 a[n - 2] - a[n - 4]}, a, {n, 0, 15}] (* _Bruno Berselli_, Oct 30 2013 *)
%Y Cf. A041183.
%K nonn,cofr,frac,easy
%O 0,1
%A _N. J. A. Sloane_.
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