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A041544 Numerators of continued fraction convergents to sqrt(290). 2
17, 579, 19703, 670481, 22816057, 776416419, 26420974303, 899089542721, 30595465426817, 1041144914054499, 35429522543279783, 1205644911385567121, 41027356509652561897, 1396135766239572671619, 47509643408655123396943, 1616724011660513768167681 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

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) = 34*a(n-1)+a(n-2) for n>1, a(0)=17, a(1)=579. G.f.: (17+x)/(1-34*x-x^2). [Philippe Deléham, Nov 23 2008]

a(n) = (17/2)*((17+sqrt(290))^n+(17-sqrt(290))^n)+(1/2)*sqrt(290)*((17+sqrt(290))^n-(17-sqrt(290))^n) = (r^(n+1)+1/(-r)^(n+1))/2, where r=(17+sqrt(290)). [Paolo P. Lava, Nov 28 2008; simplified by Bruno Berselli, Nov 04 2013]

MAPLE

numtheory:-cfrac(sqrt(290), 30, 'convergents'):

map(numer, convergents[1..-2]); # Robert Israel, Jun 22 2015

MATHEMATICA

Numerator[Convergents[Sqrt[290], 30]] (* Vincenzo Librandi, Nov 04 2013 *)

CROSSREFS

Cf. A041545.

Sequence in context: A249862 A056771 A041547 * A202407 A009709 A162490

Adjacent sequences:  A041541 A041542 A041543 * A041545 A041546 A041547

KEYWORD

nonn,cofr,frac,easy

AUTHOR

N. J. A. Sloane.

EXTENSIONS

Additional term from Colin Barker, Nov 08 2013

STATUS

approved

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Last modified September 23 23:21 EDT 2018. Contains 315306 sequences. (Running on oeis4.)