A041176 Numerators of continued fraction convergents to sqrt(98).

9, 10, 89, 99, 1871, 1970, 17631, 19601, 370449, 390050, 3490849, 3880899, 73347031, 77227930, 691170471, 768398401, 14522341689, 15290740090, 136848262409, 152139002499, 2875350307391, 3027489309890

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 (0,0,0,198,0,0,0,-1).

Crossrefs

Cf. A010549, A041177.

Programs

Mathematica

Numerator[Convergents[Sqrt[98], 30]] (* Vincenzo Librandi, Oct 30 2013 *)

Formula

G.f.: (9 + 10*x + 89*x^2 + 99*x^3 + 89*x^4 - 10*x^5 + 9*x^6 - x^7) / ((1 + 14*x^2 - x^4)*(1 - 14*x^2 - x^4)). [Bruno Berselli, Oct 30 2013]