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A041145 Denominators of continued fraction convergents to sqrt(82). 7


%S 1,18,325,5868,105949,1912950,34539049,623615832,11259624025,

%T 203296848282,3670602893101,66274148924100,1196605283526901,

%U 21605169252408318,390089651826876625,7043218902136187568

%N Denominators of continued fraction convergents to sqrt(82).

%C For n >=2, a(n) equals the permanent of the (n-1)X(n-1) tridiagonal matrix with 18's along the main diagonal, and 1's along the superdiagonal and the subdiagonal. - _John M. Campbell_, Jul 08 2011

%C a(n) equals the number of words of length n on alphabet {0,1,...,18} avoiding runs of zeros of odd lengths. - _Milan Janjic_, Jan 28 2015

%H Vincenzo Librandi, <a href="/A041145/b041145.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 (18,1).

%F a(n) = F(n,18), the n-th Fibonacci polynomial evaluated at x=18. - _T. D. Noe_, Jan 19 2006

%F a(n) = 18*a(n-1)+a(n-2) for n>1, a(0)=1, a(1)=18. G.f.: 1/(1-18*x-x^2). - _Philippe Deléham_, Nov 21 2008

%t a=0;lst={};s=0;Do[a=s-(a-1);AppendTo[lst,a];s+=a*18,{n,3*4!}];lst (* _Vladimir Joseph Stephan Orlovsky_, Oct 27 2009 *)

%t Denominator[Convergents[Sqrt[82], 30]] (* _Vincenzo Librandi_, Dec 11 2013 *)

%Y Cf. A041144, A040072, A020839, A010533.

%Y Cf. similar sequences listed in A243399.

%K nonn,frac,easy

%O 0,2

%A _N. J. A. Sloane_.

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Last modified November 21 09:14 EST 2019. Contains 329362 sequences. (Running on oeis4.)