A042191 Denominators of continued fraction convergents to sqrt(620).

1, 1, 9, 10, 489, 499, 4481, 4980, 243521, 248501, 2231529, 2480030, 121272969, 123752999, 1111296961, 1235049960, 60393695041, 61628745001, 553423655049, 615052400050, 30075938857449, 30690991257499, 275603868917441, 306294860174940, 14977757157314561

Offset

0,3

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, 498, 0, 0, 0, -1).

Formula

G.f.: -(x^2 - x - 1)*(x^4 + 10*x^2 + 1) / (x^8 - 498*x^4 + 1). - Colin Barker, Dec 03 2013

a(n) = 498*a(n-4) - a(n-8). - Wesley Ivan Hurt, Apr 16 2023

Mathematica

Denominator[Convergents[Sqrt[620], 30]] (* Vincenzo Librandi, Jan 16 2014 *)
LinearRecurrence[{0, 0, 0, 498, 0, 0, 0, -1}, {1, 1, 9, 10, 489, 499, 4481, 4980}, 30] (* Harvey P. Dale, Feb 20 2021 *)

Crossrefs

Cf. A042190, A040595.

Sequence in context: A041415 A103869 A041753 * A042729 A156292 A119205

Adjacent sequences: A042188 A042189 A042190 * A042192 A042193 A042194

Keyword

nonn,frac,easy

Author

N. J. A. Sloane

Extensions

More terms from Colin Barker, Dec 03 2013

Status

approved