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A041180 Numerators of continued fraction convergents to sqrt(101). 2
10, 201, 4030, 80801, 1620050, 32481801, 651256070, 13057603201, 261803320090, 5249124005001, 105244283420110, 2110134792407201, 42307940131564130, 848268937423689801, 17007686688605360150, 341002002709530892801 (list; graph; refs; listen; history; text; internal format)
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)

a(n) = (1/2)*sqrt(101)*((10+sqrt(101))^n - (10-sqrt(101))^n) + 5*((10+sqrt(101))^n + (10-sqrt(101))^n). - Paolo P. Lava, Nov 28 2008

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 * A027014 A088746 A293970

Adjacent sequences:  A041177 A041178 A041179 * A041181 A041182 A041183

KEYWORD

nonn,cofr,frac,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified September 21 13:20 EDT 2020. Contains 337272 sequences. (Running on oeis4.)