This site is supported by donations to The OEIS Foundation.

The October issue of the Notices of the Amer. Math. Soc. has an article about the OEIS.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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 EXTENSIONS Additional term from Colin Barker, Nov 08 2013 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

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