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

0,1

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 (20,1).

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)

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 *)

Crossrefs

Cf. A041181.

Sequence in context: A279833 A041183 A210168 * A367200 A365177 A027014

Adjacent sequences: A041177 A041178 A041179 * A041181 A041182 A041183

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane

Status

approved