A042111 Denominators of continued fraction convergents to sqrt(580).

1, 12, 577, 6936, 333505, 4008996, 192765313, 2317192752, 111418017409, 1339333401660, 64399421297089, 774132388966728, 37222754091700033, 447447181489367124, 21514687465581321985, 258623696768465230944, 12435452132351912407297, 149484049284991414118508

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Index entries for linear recurrences with constant coefficients, signature (0,578,0,-1).

Formula

G.f.: -(x^2-12*x-1) / ((x^2-24*x-1)*(x^2+24*x-1)). - Colin Barker, Dec 02 2013

a(n) = 578*a(n-2) - a(n-4) for n>3. - Vincenzo Librandi, Jan 15 2014

Mathematica

Denominator[Convergents[Sqrt[580], 30]] (* Vincenzo Librandi, Jan 15 2014 *)

Prog

(Magma) I:=[1, 12, 577, 6936]; [n le 4 select I[n] else 578*Self(n-2)-Self(n-4): n in [1..30]]; // Vincenzo Librandi, Jan 15 2014

Crossrefs

Cf. A042110, A040555.

Sequence in context: A283490 A159722 A307948 * A159644 A217390 A219103

Adjacent sequences: A042108 A042109 A042110 * A042112 A042113 A042114

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Dec 02 2013

Status

approved