A041544 Numerators of continued fraction convergents to sqrt(290).

17, 579, 19703, 670481, 22816057, 776416419, 26420974303, 899089542721, 30595465426817, 1041144914054499, 35429522543279783, 1205644911385567121, 41027356509652561897, 1396135766239572671619, 47509643408655123396943, 1616724011660513768167681

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• cofr
• frac
• easy

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).

Crossrefs

Cf. A041545.

Programs

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 *)

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]

Extensions

Additional term from Colin Barker, Nov 08 2013