A042267 Denominators of continued fraction convergents to sqrt(659).

1, 1, 3, 76, 155, 231, 11705, 11936, 35577, 901361, 1838299, 2739660, 138821299, 141560959, 421943217, 10690141384, 21802225985, 32492367369, 1646420594435, 1678912961804, 5004246518043, 126785075912879, 258574398343801, 385359474256680

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, 11860, 0, 0, 0, 0, 0, -1).

Formula

G.f.: -(x^10-x^9+3*x^8-76*x^7+155*x^6-231*x^5-155*x^4-76*x^3-3*x^2-x-1) / (x^12-11860*x^6+1). - Colin Barker, Dec 06 2013

Maple

convert(sqrt(659), confrac, 30, cvgts): denom(cvgts); # Wesley Ivan Hurt, Dec 07 2013

Mathematica

Denominator[Convergents[Sqrt[659], 30]] (* Vincenzo Librandi, Jan 19 2014 *)
LinearRecurrence[{0, 0, 0, 0, 0, 11860, 0, 0, 0, 0, 0, -1}, {1, 1, 3, 76, 155, 231, 11705, 11936, 35577, 901361, 1838299, 2739660}, 30] (* Harvey P. Dale, Dec 18 2022 *)

Prog

(Magma) I:=[1, 1, 3, 76, 155, 231, 11705, 11936, 35577, 901361, 1838299, 2739660]; [n le 12 select I[n] else 11860*Self(n-6)-Self(n-12): n in [1..40]]; // Vincenzo Librandi, Jan 19 2014

Crossrefs

Cf. A042266, A040633.

Sequence in context: A089301 A037110 A168385 * A201428 A141103 A300386

Adjacent sequences: A042264 A042265 A042266 * A042268 A042269 A042270

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Dec 06 2013

Status

approved