A041629 Denominators of continued fraction convergents to sqrt(333).

1, 4, 145, 584, 21169, 85260, 3090529, 12447376, 451196065, 1817231636, 65871534961, 265303371480, 9616792908241, 38732475004444, 1403985893068225, 5654676047277344, 204972323595052609, 825543970427487780, 29924555258984612689, 120523765006365938536

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, 146, 0, -1).

Formula

G.f.: -(x^2-4*x-1) / ((x^2-12*x-1)*(x^2+12*x-1)). - Colin Barker, Nov 20 2013

a(n) = 146*a(n-2) - a(n-4) for n>3. - Vincenzo Librandi, Dec 22 2013

Mathematica

Denominator[Convergents[Sqrt[333], 30]] (* Vincenzo Librandi, Dec 22 2013 *)
LinearRecurrence[{0, 146, 0, -1}, {1, 4, 145, 584}, 20] (* Harvey P. Dale, Jul 18 2024 *)

Prog

(Magma) I:=[1, 4, 145, 584]; [n le 4 select I[n] else 146*Self(n-2)-Self(n-4): n in [1..40]]; // Vincenzo Librandi, Dec 22 2013

Crossrefs

Cf. A041628, A040314.

Sequence in context: A239350 A343697 A030450 * A278845 A159197 A246961

Adjacent sequences: A041626 A041627 A041628 * A041630 A041631 A041632

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 20 2013

Status

approved