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 A041181 Denominators of continued fraction convergents to sqrt(101). 5

%I

%S 1,20,401,8040,161201,3232060,64802401,1299280080,26050404001,

%T 522307360100,10472197606001,209966259480120,4209797387208401,

%U 84405914003648140,1692328077460171201,33930967463207072160,680311677341601614401

%N Denominators of continued fraction convergents to sqrt(101).

%C Generalized Pell numbers (A000129). Antidiagonals of A038207. - _Mark Dols_, Aug 31 2009

%C a(n) equals the number of words of length n on alphabet {0,1,...,20} avoiding runs of zeros of odd lengths. - _Milan Janjic_, Jan 28 2015

%H Vincenzo Librandi, <a href="/A041181/b041181.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 (20,1).

%F a(n) = F(n, 20), the n-th Fibonacci polynomial evaluated at x=20. - _T. D. Noe_, Jan 19 2006

%F a(n) = 20*a(n-1)+a(n-2) for n>1, a(0)=1, a(1)=20. G.f.: 1/(1-20*x-x^2). - _Philippe DelĂ©ham_, Nov 21 2008

%F a(n) = (5/101)*sqrt(101)*((10+sqrt(101))^n-(10-sqrt(101))^n)+(1/2)*((10 +sqrt(101))^n+(10-sqrt(101))^n). - _Paolo P. Lava_, Dec 03 2009

%t a=0;lst={};s=0;Do[a=s-(a-1);AppendTo[lst,a];s+=a*20,{n,3*4!}];lst (* _Vladimir Joseph Stephan Orlovsky_, Oct 27 2009 *)

%t Denominator[Convergents[Sqrt[101], 30]] (* _Vincenzo Librandi_, Dec 12 2013 *)

%o (MAGMA) I:=[1, 20]; [n le 2 select I[n] else 20*Self(n-1)+Self(n-2): n in [1..30]]; // _Vincenzo Librandi_, Dec 12 2013

%Y Cf. A041180, A040090.

%Y Cf. similar sequences listed in A243399.

%K nonn,frac,easy,less

%O 0,2

%A _N. J. A. Sloane_

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Last modified October 15 11:03 EDT 2018. Contains 316224 sequences. (Running on oeis4.)