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A042405 Denominators of continued fraction convergents to sqrt(730). 2

%I

%S 1,54,2917,157572,8511805,459795042,24837444073,1341681774984,

%T 72475653293209,3915026959608270,211483931472139789,

%U 11424047326455156876,617110039560050611093,33335366183569188155898,1800726883952296211029585,97272587099607564583753488

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

%H Vincenzo Librandi, <a href="/A042405/b042405.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) = F(n, 54), the n-th Fibonacci polynomial evaluated at x=54. - _T. D. Noe_, Jan 19 2006

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

%F a(n) = (1/2)*((27+sqrt(730))^n+(27-sqrt(730))^n)+(27/1460)*sqrt(730)*((27+sqrt(730))^n-(27 -sqrt(730))^n). [_Paolo P. Lava_, Dec 01 2008]

%t a=0; lst = {}; s = 0; Do[a = s-(a-1); AppendTo[lst, a]; s+ = a*54, {n, 3*4!}]; lst (* _Vladimir Joseph Stephan Orlovsky_, Nov 03 2009 *)

%t Denominator[Convergents[Sqrt[730], 30]] (* _Vincenzo Librandi_, Jan 21 2014 *)

%Y Cf. A042404.

%K nonn,frac,easy

%O 0,2

%A _N. J. A. Sloane_.

%E a(15) from _Colin Barker_, Dec 11 2013

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Last modified August 20 23:06 EDT 2018. Contains 313929 sequences. (Running on oeis4.)