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Numerators of continued fraction convergents to sqrt(730).
3

%I #30 Dec 26 2023 07:04:01

%S 27,1459,78813,4257361,229976307,12422977939,671070785013,

%T 36250245368641,1958184320691627,105778203562716499,

%U 5713981176707382573,308660761745761375441,16673395115447821656387,900671996995928130820339,48652961232895566885954693

%N Numerators of continued fraction convergents to sqrt(730).

%H Vincenzo Librandi, <a href="/A042404/b042404.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 (54, 1).

%F a(n)=54*a(n-1)+a(n-2), n>1; a(0)=27, a(1)=1459. G.f.: (27+x)/(1-54*x-x^2). - _Philippe Deléham_, Nov 23 2008

%t Numerator[Convergents[Sqrt[730], 30]] (* _Vincenzo Librandi_, Nov 23 2013 *)

%t LinearRecurrence[{54,1},{27,1459},20] (* _Harvey P. Dale_, Nov 29 2020 *)

%Y Cf. A042405, A040702.

%K nonn,cofr,frac,easy

%O 0,1

%A _N. J. A. Sloane_

%E a(14) from _Colin Barker_, Dec 11 2013