A041343 Denominators of continued fraction convergents to sqrt(185).

1, 1, 2, 3, 5, 133, 138, 271, 409, 680, 18089, 18769, 36858, 55627, 92485, 2460237, 2552722, 5012959, 7565681, 12578640, 334610321, 347188961, 681799282, 1028988243, 1710787525, 45509463893, 47220251418, 92729715311, 139949966729, 232679682040

Offset

0,3

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,136,0,0,0,0,1).

Formula

G.f.: -(x^4-3*x^3+4*x^2-2*x+1)*(x^4+2*x^3+4*x^2+3*x+1) / (x^10+136*x^5-1). - Colin Barker, Nov 15 2013

a(n) = 136*a(n-5) + a(n-10). - Vincenzo Librandi, Dec 16 2013

Mathematica

Denominator[Convergents[Sqrt[185], 30]] (* Vincenzo Librandi, Dec 16 2013 *)
LinearRecurrence[{0, 0, 0, 0, 136, 0, 0, 0, 0, 1}, {1, 1, 2, 3, 5, 133, 138, 271, 409, 680}, 30] (* Harvey P. Dale, Aug 15 2016 *)

Prog

(Magma) I:=[1, 1, 2, 3, 5, 133, 138, 271, 409, 680]; [n le 10 select I[n] else 136*Self(n-5)+Self(n-10): n in [1..40]]; // Vincenzo Librandi, Dec 16 2013

Crossrefs

Cf. A041342, A010227.

Sequence in context: A230372 A234900 A117702 * A229349 A160600 A325505

Adjacent sequences: A041340 A041341 A041342 * A041344 A041345 A041346

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 15 2013

Status

approved