A042135 Denominators of continued fraction convergents to sqrt(592).

1, 3, 145, 438, 21169, 63945, 3090529, 9335532, 451196065, 1362923727, 65871534961, 198977528610, 9616792908241, 29049356253333, 1403985893068225, 4241007035458008, 204972323595052609, 619157977820615835, 29924555258984612689, 90392823754774453902

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^2-3*x-1) / ((x^2-12*x-1)*(x^2+12*x-1)). - Colin Barker, Dec 02 2013

a(n) = 146*a(n-2) - a(n-4) for n>3. - Vincenzo Librandi, Jan 15 2014

Mathematica

Denominator[Convergents[Sqrt[592], 30]] (* Vincenzo Librandi, Jan 15 2014 *)
LinearRecurrence[{0, 146, 0, -1}, {1, 3, 145, 438}, 20] (* Harvey P. Dale, Apr 25 2023 *)

Prog

(Magma) I:=[1, 3, 145, 438]; [n le 4 select I[n] else 146*Self(n-2)-Self(n-4): n in [1..30]]; // Vincenzo Librandi, Jan 15 2014

Crossrefs

Cf. A042134, A040567.

Sequence in context: A172145 A100931 A152180 * A326803 A302221 A302667

Adjacent sequences: A042132 A042133 A042134 * A042136 A042137 A042138

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Dec 02 2013

Status

approved