A042115 Denominators of continued fraction convergents to sqrt(582).

1, 8, 385, 3088, 148609, 1191960, 57362689, 460093472, 22141849345, 177594888232, 8546696484481, 68551166764080, 3299002701160321, 26460572776046648, 1273406495951399425, 10213712540387242048, 491531608434539017729, 3942466580016699383880

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, 386, 0, -1).

Formula

G.f.: -(x^2-8*x-1) / (x^4-386*x^2+1). - Colin Barker, Dec 02 2013

a(n) = 386*a(n-2) - a(n-4) for n>3. - Vincenzo Librandi, Jan 15 2014

Mathematica

Denominator[Convergents[Sqrt[582], 30]] (* Vincenzo Librandi, Jan 15 2014 *)
LinearRecurrence[{0, 386, 0, -1}, {1, 8, 385, 3088}, 20] (* Harvey P. Dale, May 14 2021 *)

Prog

(Magma) I:=[1, 8, 385, 3088]; [n le 4 select I[n] else 386*Self(n-2)-Self(n-4): n in [1..30]]; // Vincenzo Librandi, Jan 15 2014

Crossrefs

Cf. A042114, A040557.

Sequence in context: A153836 A151941 A085806 * A159515 A369770 A220799

Adjacent sequences: A042112 A042113 A042114 * A042116 A042117 A042118

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Dec 02 2013

Status

approved