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

Author

N. J. A. Sloane

Keywords

• nonn
• frac
• easy

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).

Crossrefs

Cf. A041246, A010194.

Programs

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

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 *)

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

Extensions

More terms from Colin Barker, Nov 14 2013