A041577 Denominators of continued fraction convergents to sqrt(306).

1, 2, 69, 140, 4829, 9798, 337961, 685720, 23652441, 47990602, 1655332909, 3358656420, 115849651189, 235057958798, 8107820250321, 16450698459440, 567431567871281, 1151313834202002, 39712101930739349, 80575517695680700, 2779279703583883149

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, 70, 0, -1).

Formula

G.f.: -(x^2-2*x-1) / (x^4-70*x^2+1). - Colin Barker, Nov 19 2013

a(n) = 70*a(n-2) - a(n-4) for n>3. - Vincenzo Librandi, Dec 20 2013

Mathematica

Denominator[Convergents[Sqrt[306], 30]] (* Vincenzo Librandi, Dec 20 2013 *)

Prog

(Magma) I:=[1, 2, 69, 140]; [n le 4 select I[n] else 70*Self(n-2)-Self(n-4): n in [1..40]]; // Vincenzo Librandi, Dec 20 2013

Crossrefs

Cf. A041576, A040288.

Sequence in context: A246744 A362291 A364854 * A180085 A321244 A224506

Adjacent sequences: A041574 A041575 A041576 * A041578 A041579 A041580

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

Additional term from Colin Barker, Nov 19 2013

Status

approved