A041315 Denominators of continued fraction convergents to sqrt(171).

1, 13, 339, 4420, 115259, 1502787, 39187721, 510943160, 13323709881, 173719171613, 4530022171819, 59064007405260, 1540194214708579, 20081588798616787, 523661502978745041, 6827681127522302320, 178043370818558605361, 2321391501768784172013

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,340,0,-1).

Formula

G.f.: -(x^2-13*x-1) / (x^4-340*x^2+1). - Colin Barker, Nov 15 2013

a(n) = 340*a(n-2) - a(n-4). - Vincenzo Librandi, Dec 15 2013

Mathematica

Denominator[Convergents[Sqrt[171], 30]] (* Vincenzo Librandi, Dec 15 2013 *)
LinearRecurrence[{0, 340, 0, -1}, {1, 13, 339, 4420}, 20] (* Harvey P. Dale, Aug 05 2014 *)

Prog

(Magma) I:=[1, 13, 339, 4420]; [n le 4 select I[n] else 340*Self(n-2)-Self(n-4): n in [1..40]]; // Vincenzo Librandi, Dec 15 2013

Crossrefs

Cf. A041314, A040157.

Sequence in context: A097308 A204195 A238652 * A041312 A372183 A096717

Adjacent sequences: A041312 A041313 A041314 * A041316 A041317 A041318

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 15 2013

Status

approved