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A041181 Denominators of continued fraction convergents to sqrt(101). 4
1, 20, 401, 8040, 161201, 3232060, 64802401, 1299280080, 26050404001, 522307360100, 10472197606001, 209966259480120, 4209797387208401, 84405914003648140, 1692328077460171201, 33930967463207072160, 680311677341601614401 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Generalized Pell numbers (A000129). Antidiagonals of A038207. - Mark Dols, Aug 31 2009

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

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Tanya Khovanova, Recursive Sequences

Index entries for linear recurrences with constant coefficients, signature (20,1).

FORMULA

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

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 Deléham, Nov 21 2008

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

MATHEMATICA

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 *)

Denominator[Convergents[Sqrt[101], 30]] (* Vincenzo Librandi, Dec 12 2013 *)

PROG

(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

CROSSREFS

Cf. A041180, A040090.

Cf. similar sequences listed in A243399.

Sequence in context: A007545 A055476 A223180 * A041762 A196740 A196898

Adjacent sequences:  A041178 A041179 A041180 * A041182 A041183 A041184

KEYWORD

nonn,frac,easy,less

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified November 20 04:05 EST 2017. Contains 294959 sequences.