A042089 Denominators of continued fraction convergents to sqrt(568).

1, 1, 5, 6, 281, 287, 1429, 1716, 80365, 82081, 408689, 490770, 22984109, 23474879, 116883625, 140358504, 6573374809, 6713733313, 33428308061, 40142041374, 1879962211265, 1920104252639, 9560379221821, 11480483474460, 537662619046981, 549143102521441

Offset

0,3

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,286,0,0,0,-1).

Formula

G.f.: (1 + x - x^2)*(1 + 6*x^2 + x^4)/(1 - 286*x^4 + x^8). - Colin Barker, Dec 01 2013

a(n) = 286*a(n-4) - a(n-8) for n>7. - Vincenzo Librandi, Jan 14 2014

Mathematica

Denominator[Convergents[Sqrt[568], 30]] (* Vincenzo Librandi, Jan 14 2014 *)
LinearRecurrence[{0, 0, 0, 286, 0, 0, 0, -1}, {1, 1, 5, 6, 281, 287, 1429, 1716}, 40] (* Harvey P. Dale, Sep 15 2019 *)

Prog

(Magma) I:=[1, 1, 5, 6, 281, 287, 1429, 1716]; [n le 8 select I[n] else 286*Self(n-4)-Self(n-8): n in [1..40]]; // Vincenzo Librandi, Jan 14 2014

Crossrefs

Cf. A042088, A040544.

Sequence in context: A041601 A301648 A041827 * A156191 A042387 A007666

Adjacent sequences: A042086 A042087 A042088 * A042090 A042091 A042092

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Dec 01 2013

Status

approved