A041247 Denominators of continued fraction convergents to sqrt(135).

1, 1, 2, 3, 5, 8, 13, 21, 475, 496, 971, 1467, 2438, 3905, 6343, 10248, 231799, 242047, 473846, 715893, 1189739, 1905632, 3095371, 5001003, 113117437, 118118440, 231235877, 349354317, 580590194, 929944511, 1510534705, 2440479216, 55201077457, 57641556673

Offset

0,3

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,488,0,0,0,0,0,0,0,-1).

Formula

G.f.: -(x^2-x-1)*(x^4+3*x^2+1)*(x^8+7*x^4+1) / (x^16-488*x^8+1). - Colin Barker, Nov 14 2013

a(n) = 488*a(n-8) - a(n-16). - Vincenzo Librandi, Dec 13 2013

Mathematica

Denominator[Convergents[Sqrt[135], 30]]  (* Vincenzo Librandi, Dec 13 2013 *)
LinearRecurrence[{0, 0, 0, 0, 0, 0, 0, 488, 0, 0, 0, 0, 0, 0, 0, -1}, {1, 1, 2, 3, 5, 8, 13, 21, 475, 496, 971, 1467, 2438, 3905, 6343, 10248}, 40] (* Harvey P. Dale, Aug 01 2019 *)

Prog

(Magma) I:=[1, 1, 2, 3, 5, 8, 13, 21, 475, 496, 971, 1467, 2438, 3905, 6343, 10248]; [n le 16 select I[n] else 488*Self(n-8)-Self(n-16): n in [1..40]]; // Vincenzo Librandi, Dec 13 2013

Crossrefs

Cf. A041246, A010194.

Sequence in context: A067517 A042339 A137574 * A117770 A053412 A198202

Adjacent sequences: A041244 A041245 A041246 * A041248 A041249 A041250

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 14 2013

Status

approved