A042119 Denominators of continued fraction convergents to sqrt(584).

1, 6, 289, 1740, 83809, 504594, 24304321, 146330520, 7048169281, 42435346206, 2043944787169, 12306104069220, 592736940109729, 3568727744727594, 171891668687034241, 1034918739866933040, 49847991182299820161, 300122865833665854006, 14455745551198260812449

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, 290, 0, -1).

Formula

G.f.: -(x^2-6*x-1) / (x^4-290*x^2+1). - Colin Barker, Dec 02 2013

a(n) = 290*a(n-2) - a(n-4) for n>3. - Vincenzo Librandi, Jan 15 2014

Mathematica

Denominator[Convergents[Sqrt[584], 30]] (* Vincenzo Librandi, Jan 15 2014 *)

Prog

(Magma) I:=[1, 6, 289, 1740]; [n le 4 select I[n] else 290*Self(n-2)-Self(n-4): n in [1..30]]; // Vincenzo Librandi, Jan 15 2014

Crossrefs

Cf. A042118, A040559.

Sequence in context: A340540 A027875 A203422 * A196980 A197165 A264706

Adjacent sequences: A042116 A042117 A042118 * A042120 A042121 A042122

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Dec 02 2013

Status

approved