

A041145


Denominators of continued fraction convergents to sqrt(82).


5



1, 18, 325, 5868, 105949, 1912950, 34539049, 623615832, 11259624025, 203296848282, 3670602893101, 66274148924100, 1196605283526901, 21605169252408318, 390089651826876625, 7043218902136187568
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OFFSET

0,2


COMMENTS

For n >=2, a(n) equals the permanent of the (n1)X(n1) tridiagonal matrix with 18's along the main diagonal, and 1's along the superdiagonal and the subdiagonal.  John M. Campbell, Jul 08 2011
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


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 (18,1).


FORMULA

a(n) = F(n,18), the nth Fibonacci polynomial evaluated at x=18.  T. D. Noe, Jan 19 2006
a(n) = 18*a(n1)+a(n2) for n>1, a(0)=1, a(1)=18. G.f.: 1/(118*xx^2).  Philippe Deléham, Nov 21 2008


MATHEMATICA

a=0; lst={}; s=0; Do[a=s(a1); AppendTo[lst, a]; s+=a*18, {n, 3*4!}]; lst (* Vladimir Joseph Stephan Orlovsky, Oct 27 2009 *)
Denominator[Convergents[Sqrt[82], 30]] (* Vincenzo Librandi, Dec 11 2013 *)


CROSSREFS

Cf. A041144, A040072, A020839, A010533.
Cf. similar sequences listed in A243399.
Sequence in context: A001027 A285875 A223311 * A041614 A222812 A166787
Adjacent sequences: A041142 A041143 A041144 * A041146 A041147 A041148


KEYWORD

nonn,frac,easy


AUTHOR

N. J. A. Sloane.


STATUS

approved



