A042307 Denominators of continued fraction convergents to sqrt(680).

1, 13, 677, 8814, 459005, 5975879, 311204713, 4051637148, 210996336409, 2747004010465, 143055204880589, 1862464667458122, 96991217912702933, 1262748297532596251, 65759902689607707985, 856141483262432800056, 44585117032336113310897

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,678,0,-1).

Formula

G.f.: -(x^2-13*x-1) / ((x^2-26*x-1)*(x^2+26*x-1)). - Colin Barker, Dec 07 2013

a(n) = 678*a(n-2) - a(n-4) for n>3. - Vincenzo Librandi, Jan 19 2014

Mathematica

Denominator[Convergents[Sqrt[680], 30]] (* Vincenzo Librandi, Jan 19 2014 *)

Prog

(Magma) I:=[1, 13, 677, 8814]; [n le 4 select I[n] else 678*Self(n-2)-Self(n-4): n in [1..30]]; // Vincenzo Librandi, Jan 19 2014

Crossrefs

Cf. A042306, A040653.

Sequence in context: A092547 A298951 A157027 * A012746 A211094 A290166

Adjacent sequences: A042304 A042305 A042306 * A042308 A042309 A042310

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Dec 07 2013

Status

approved