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Denominators of continued fraction convergents to sqrt(57).
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%I #19 May 26 2024 00:55:30

%S 1,1,2,9,11,20,291,311,602,2719,3321,6040,87881,93921,181802,821129,

%T 1002931,1824060,26539771,28363831,54903602,247978239,302881841,

%U 550860080,8014922961,8565783041,16580706002

%N Denominators of continued fraction convergents to sqrt(57).

%H Vincenzo Librandi, <a href="/A041099/b041099.txt">Table of n, a(n) for n = 0..200</a>

%H <a href="/index/Rec#order_12">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,302,0,0,0,0,0,-1).

%F From _Colin Barker_, Jul 18 2012: (Start)

%F a(n) = 302*a(n-6)-a(n-12).

%F G.f.: -(x^4-x^3+2*x^2+x+1)*(x^6-10*x^3-1)/(x^12-302*x^6+1). (End)

%t Denominator[Convergents[Sqrt[57], 30]] (* _Vincenzo Librandi_, Oct 24 2013 *)

%Y Cf. A010510, A041098.

%K nonn,cofr,frac,easy

%O 0,3

%A _N. J. A. Sloane_.