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A041545 Denominators of continued fraction convergents to sqrt(290). 2
1, 34, 1157, 39372, 1339805, 45592742, 1551493033, 52796355864, 1796627592409, 61138134497770, 2080493200516589, 70797906952061796, 2409209329570617653, 81983915112353061998, 2789862323149574725585, 94937302902197893731888 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

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 (34,1).

FORMULA

a(n) = F(n, 34), the n-th Fibonacci polynomial evaluated at x=34. - T. D. Noe, Jan 19 2006

a(n) = 34*a(n-1)+a(n-2) for n>1; a(0)=1, a(1)=34. G.f.: 1/(1-34*x-x^2). [Philippe Deléham, Nov 23 2008]

a(n) = (1/2)*((17+sqrt(290))^n + (17-sqrt(290))^n) + (17/580)*sqrt(290)*((17+sqrt(290))^n - (17-sqrt(290))^n). [Paolo P. Lava, Dec 12 2008]

MATHEMATICA

a=0; lst={}; s=0; Do[a=s-(a-1); AppendTo[lst, a]; s+=a*34, {n, 3*4!}]; lst (* Vladimir Joseph Stephan Orlovsky, Oct 27 2009 *)

Denominator[Convergents[Sqrt[290], 30]] (* Vincenzo Librandi, Dec 20 2013 *)

CROSSREFS

Cf. A041544, A040272.

Sequence in context: A264134 A264019 A009978 * A189434 A167258 A251924

Adjacent sequences:  A041542 A041543 A041544 * A041546 A041547 A041548

KEYWORD

nonn,frac,easy

AUTHOR

N. J. A. Sloane.

EXTENSIONS

More terms from Colin Barker, Nov 18 2013

STATUS

approved

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Last modified June 25 09:38 EDT 2017. Contains 288709 sequences.