A042187 Denominators of continued fraction convergents to sqrt(618).

1, 1, 7, 57, 349, 406, 19837, 20243, 141295, 1150603, 7044913, 8195516, 400429681, 408625197, 2852180863, 23226072101, 142208613469, 165434685570, 8083073520829, 8248508206399, 57574122759223, 468841490280183, 2870623064440321, 3339464554720504

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, 0, 0, 20186, 0, 0, 0, 0, 0, -1).

Formula

G.f.: -(x^10 - x^9 + 7*x^8 - 57*x^7 + 349*x^6 - 406*x^5 - 349*x^4 - 57*x^3 - 7*x^2 - x - 1) / (x^12 - 20186*x^6 + 1). - Colin Barker, Dec 03 2013

Mathematica

Denominator[Convergents[Sqrt[618], 30]] (* Vincenzo Librandi, Jan 16 2014 *)
LinearRecurrence[{0, 0, 0, 0, 0, 20186, 0, 0, 0, 0, 0, -1}, {1, 1, 7, 57, 349, 406, 19837, 20243, 141295, 1150603, 7044913, 8195516}, 30] (* Harvey P. Dale, May 25 2023 *)

Crossrefs

Cf. A042186, A040593.

Sequence in context: A180817 A201438 A202510 * A201872 A218587 A218838

Adjacent sequences: A042184 A042185 A042186 * A042188 A042189 A042190

Keyword

nonn,frac,easy

Author

N. J. A. Sloane

Extensions

More terms from Colin Barker, Dec 03 2013

Status

approved