A041180 Numerators of continued fraction convergents to sqrt(101).

10, 201, 4030, 80801, 1620050, 32481801, 651256070, 13057603201, 261803320090, 5249124005001, 105244283420110, 2110134792407201, 42307940131564130, 848268937423689801, 17007686688605360150, 341002002709530892801

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 (20,1).

Crossrefs

Cf. A041181.

Programs

Mathematica

CoefficientList[Series[(10 + x)/(1 - 20 x - x^2), {x, 0, 30}], x] (* Vincenzo Librandi, Oct 30 2013 *)
Numerator[Convergents[Sqrt[101], 20]] (* Bruno Berselli, Oct 30 2013 *)

Formula

From Philippe Deléham, Nov 21 2008: (Start)

a(n) = 20*a(n-1) + a(n-2) for n > 1, a(0)=10, a(1)=201.

G.f.: (10+x)/(1-20*x-x^2). (End)