A041347 Denominators of continued fraction convergents to sqrt(187).

1, 1, 3, 40, 83, 123, 3281, 3404, 10089, 134561, 279211, 413772, 11037283, 11451055, 33939393, 452663164, 939265721, 1391928885, 37129416731, 38521345616, 114172107963, 1522758749135, 3159689606233, 4682448355368, 124903346845801, 129585795201169

Offset

0,3

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,3364,0,0,0,0,0,-1).

Formula

G.f.: -(x^10-x^9+3*x^8-40*x^7+83*x^6-123*x^5-83*x^4-40*x^3-3*x^2-x-1) / (x^12-3364*x^6+1). - Colin Barker, Nov 16 2013

a(n) = 3364*a(n-6) - a(n-12) for n>11. - Vincenzo Librandi, Dec 16 2013

Mathematica

Denominator[Convergents[Sqrt[187], 30]] (* Vincenzo Librandi, Dec 16 2013 *)

Prog

(Magma) I:=[1, 1, 3, 40, 83, 123, 3281, 3404, 10089, 134561, 279211, 413772]; [n le 12 select I[n] else 3364*Self(n-6)-Self(n-12): n in [1..40]]; // Vincenzo Librandi, Dec 16 2013

Crossrefs

Cf. A041346, A010229.

Sequence in context: A100306 A101014 A262036 * A326608 A160659 A197247

Adjacent sequences: A041344 A041345 A041346 * A041348 A041349 A041350

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 16 2013

Status

approved