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

Author

N. J. A. Sloane

Keywords

• nonn
• frac
• easy

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).

Crossrefs

Cf. A041628, A040314.

Programs

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

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 *)

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

Extensions

More terms from Colin Barker, Nov 20 2013