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A041145 Denominators of continued fraction convergents to sqrt(82). 4
1, 18, 325, 5868, 105949, 1912950, 34539049, 623615832, 11259624025, 203296848282, 3670602893101, 66274148924100, 1196605283526901, 21605169252408318, 390089651826876625, 7043218902136187568 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

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

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 n-th Fibonacci polynomial evaluated at x=18. - T. D. Noe, Jan 19 2006

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

MATHEMATICA

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 *)

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

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Last modified November 23 13:09 EST 2017. Contains 295127 sequences.