A041201 Denominators of continued fraction convergents to sqrt(111).

1, 1, 2, 13, 15, 28, 575, 603, 1178, 7671, 8849, 16520, 339249, 355769, 695018, 4525877, 5220895, 9746772, 200156335, 209903107, 410059442, 2670259759, 3080319201, 5750578960, 118091898401, 123842477361

Offset

0,3

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,590,0,0,0,0,0,-1).

Formula

a(n) = 590*a(n-6)-a(n-12). G.f.: -(x^2-2*x-1)*(x^4-x^3+2*x^2+x+1)*(x^4+2*x^3+5*x^2-2*x+1)/(x^12-590*x^6+1). [Colin Barker, Jul 19 2012]

Mathematica

Denominator[Convergents[Sqrt[111], 30]] (* Vincenzo Librandi, Oct 24 2013 *)
LinearRecurrence[{0, 0, 0, 0, 0, 590, 0, 0, 0, 0, 0, -1}, {1, 1, 2, 13, 15, 28, 575, 603, 1178, 7671, 8849, 16520}, 40] (* Harvey P. Dale, Jan 11 2019 *)

Crossrefs

Cf. A041200.

Sequence in context: A179164 A356102 A022116 * A042155 A295336 A042253

Adjacent sequences: A041198 A041199 A041200 * A041202 A041203 A041204

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane.

Status

approved