A041178 Numerators of continued fraction convergents to sqrt(99).

9, 10, 189, 199, 3771, 3970, 75231, 79201, 1500849, 1580050, 29941749, 31521799, 597334131, 628855930, 11916740871, 12545596801, 237737483289, 250283080090, 4742832924909, 4993116004999, 94618921014891, 99612037019890, 1887635587372911, 1987247624392801

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• cofr
• frac
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200
• Index entries for linear recurrences with constant coefficients, signature (0,20,0,-1).

Crossrefs

Cf. A010550, A041179.

Programs

Mathematica

Numerator[Convergents[Sqrt[99], 30]] (* Vincenzo Librandi, Oct 30 2013 *)
LinearRecurrence[{0,20,0,-1},{9,10,189,199},40] (* Harvey P. Dale, Jan 23 2019 *)

Formula

G.f.: -(x^3-9*x^2-10*x-9) / (x^4-20*x^2+1). - Colin Barker, Nov 05 2013

Extensions

More terms from Colin Barker, Nov 05 2013