A041703 Denominators of continued fraction convergents to sqrt(371).

1, 3, 4, 19, 23, 88, 3367, 10189, 13556, 64413, 77969, 298320, 11414129, 34540707, 45954836, 218360051, 264314887, 1011304712, 38693893943, 117092986541, 155786880484, 740240508477, 896027388961, 3428322675360, 131172289052641, 396945189833283

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,3390,0,0,0,0,0,-1).

Formula

G.f.: -(x^10-3*x^9+4*x^8-19*x^7+23*x^6-88*x^5-23*x^4-19*x^3-4*x^2-3*x-1) / (x^12-3390*x^6+1). - Colin Barker, Nov 22 2013

a(n) = 3390*a(n-6) - a(n-12) for n>11. - Vincenzo Librandi, Dec 23 2013

Mathematica

Denominator[Convergents[Sqrt[371], 30]] (* Vincenzo Librandi, Dec 23 2013 *)

Prog

(Magma) I:=[1, 3, 4, 19, 23, 88, 3367, 10189, 13556, 64413, 77969, 298320]; [n le 12 select I[n] else 3390*Self(n-6)-Self(n-12): n in [1..40]]; // Vincenzo Librandi, Dec 23 2013

Crossrefs

Cf. A041702, A040351.

Sequence in context: A143150 A100340 A042175 * A036253 A212113 A196133

Adjacent sequences: A041700 A041701 A041702 * A041704 A041705 A041706

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 22 2013

Status

approved