A042327 Denominators of continued fraction convergents to sqrt(690).

1, 3, 4, 11, 15, 56, 2927, 8837, 11764, 32365, 44129, 164752, 8611233, 25998451, 34609684, 95217819, 129827503, 484700328, 25334244559, 76487434005, 101821678564, 280130791133, 381952469697, 1425988200224, 74533338881345, 225026004844259

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,2942,0,0,0,0,0,-1).

Formula

G.f.: -(x^10-3*x^9+4*x^8-11*x^7+15*x^6-56*x^5-15*x^4-11*x^3-4*x^2-3*x-1) / (x^12-2942*x^6+1). - Colin Barker, Dec 07 2013

Maple

convert(sqrt(690), confrac, 30, cvgts): denom(cvgts); # Wesley Ivan Hurt, Dec 07 2013

Mathematica

Denominator/@Convergents[Sqrt[690], 30]  (* Harvey P. Dale, Apr 21 2011 *)
CoefficientList[Series[-(x^10 - 3 x^9 + 4 x^8 - 11 x^7 + 15 x^6 - 56 x^5 - 15 x^4 - 11 x^3 - 4 x^2 - 3 x - 1)/(x^12 - 2942 x^6 + 1), {x, 0, 30}], x] (* Vincenzo Librandi, Jan 20 2014 *)

Crossrefs

Cf. A042326, A040663.

Sequence in context: A002530 A042709 A231067 * A046114 A116654 A041020

Adjacent sequences: A042324 A042325 A042326 * A042328 A042329 A042330

Keyword

nonn,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Dec 07 2013

Status

approved