A042711 Denominators of continued fraction convergents to sqrt(885).

1, 1, 3, 4, 235, 239, 713, 952, 55929, 56881, 169691, 226572, 13310867, 13537439, 40385745, 53923184, 3167930417, 3221853601, 9611637619, 12833491220, 753954128379, 766787619599, 2287529367577, 3054316987176, 179437914623785, 182492231610961

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, 238, 0, 0, 0, -1).

Formula

G.f.: -(x^2-x-1)*(x^4+4*x^2+1) / (x^8-238*x^4+1). - Colin Barker, Dec 22 2013

a(n) = 238*a(n-4) - a(n-8) for n>7. - Vincenzo Librandi, Dec 22 2013

Mathematica

Denominator[Convergents[Sqrt[885], 30]] (* Vincenzo Librandi, Dec 22 2013 *)
LinearRecurrence[{0, 0, 0, 238, 0, 0, 0, -1}, {1, 1, 3, 4, 235, 239, 713, 952}, 30] (* Harvey P. Dale, Mar 25 2019 *)

Prog

(Magma) I:=[1, 1, 3, 4, 235, 239, 713, 952]; [n le 8 select I[n] else 238*Self(n-4)-Self(n-8): n in [1..40]]; // Vincenzo Librandi, Dec 22 2013

Crossrefs

Cf. A042710, A040855.

Sequence in context: A349885 A042485 A111315 * A195566 A348278 A348280

Adjacent sequences: A042708 A042709 A042710 * A042712 A042713 A042714

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Dec 22 2013

Status

approved