A042171 Denominators of continued fraction convergents to sqrt(610).

1, 1, 3, 10, 53, 275, 878, 2031, 2909, 141663, 144572, 430807, 1436993, 7615772, 39515853, 126163331, 291842515, 418005846, 20356123123, 20774128969, 61904381061, 206487272152, 1094340741821, 5678190981257, 18128913685592, 41936018352441, 60064932038033

Offset

0,3

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,143694,0,0,0,0,0,0,0,0,1).

Formula

G.f.: -(x^16 - x^15 + 3*x^14 - 10*x^13 + 53*x^12 - 275*x^11 + 878*x^10 - 2031*x^9 + 2909*x^8 + 2031*x^7 + 878*x^6 + 275*x^5 + 53*x^4 + 10*x^3 + 3*x^2 + x + 1) / (x^18 + 143694*x^9 - 1). - Colin Barker, Dec 03 2013

Mathematica

Denominator[Convergents[Sqrt[610], 30]] (* Vincenzo Librandi, Jan 16 2014 *)
LinearRecurrence[{0, 0, 0, 0, 0, 0, 0, 0, 143694, 0, 0, 0, 0, 0, 0, 0, 0, 1}, {1, 1, 3, 10, 53, 275, 878, 2031, 2909, 141663, 144572, 430807, 1436993, 7615772, 39515853, 126163331, 291842515, 418005846}, 30] (* Harvey P. Dale, Apr 21 2016 *)

Crossrefs

Cf. A042170, A040585.

Sequence in context: A290489 A002873 A309910 * A133148 A189815 A143599

Adjacent sequences: A042168 A042169 A042170 * A042172 A042173 A042174

Keyword

nonn,frac,easy

Author

N. J. A. Sloane

Extensions

More terms from Colin Barker, Dec 03 2013

Status

approved