A041623 Denominators of continued fraction convergents to sqrt(330).

1, 6, 217, 1308, 47305, 285138, 10312273, 62158776, 2248028209, 13550328030, 490059837289, 2953909351764, 106830796500793, 643938688356522, 23288623577335585, 140375680152370032, 5076813109062656737, 30601254334528310454, 1106721969152081833081

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,218,0,-1).

Formula

G.f.: -(x^2-6*x-1) / (x^4-218*x^2+1). - Colin Barker, Nov 20 2013

a(n) = 218*a(n-2) - a(n-4) for n>3. - Vincenzo Librandi, Dec 22 2013

Mathematica

Denominator[Convergents[Sqrt[330], 30]] (* Vincenzo Librandi, Dec 22 2013 *)
LinearRecurrence[{0, 218, 0, -1}, {1, 6, 217, 1308}, 20] (* Harvey P. Dale, Sep 23 2018 *)

Prog

(Magma) I:=[1, 6, 217, 1308]; [n le 4 select I[n] else 218*Self(n-2)-Self(n-4): n in [1..40]]; // Vincenzo Librandi, Dec 22 2013

Crossrefs

Cf. A041622, A040311.

Sequence in context: A194503 A229869 A234610 * A292692 A015477 A331477

Adjacent sequences: A041620 A041621 A041622 * A041624 A041625 A041626

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 20 2013

Status

approved