A041035 Denominators of continued fraction convergents to sqrt(22).

1, 1, 3, 13, 29, 42, 365, 407, 1179, 5123, 11425, 16548, 143809, 160357, 464523, 2018449, 4501421, 6519870, 56660381, 63180251, 183020883, 795263783, 1773548449, 2568812232, 22324046305, 24892858537

Offset

0,3

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,394,0,0,0,0,0,-1).

Formula

From Colin Barker, Jul 16 2012: (Start)

a(n) = 394*a(n-6) - a(n-12).

G.f.: -(x^10 - x^9 + 3*x^8 - 13*x^7 + 29*x^6 - 42*x^5 - 29*x^4 - 13*x^3 - 3*x^2 - x - 1)/(x^12 - 394*x^6 + 1). (End)

Mathematica

Table[Denominator[FromContinuedFraction[ContinuedFraction[Sqrt[22], n]]], {n, 1, 50}] (* Vladimir Joseph Stephan Orlovsky, Mar 17 2011 *)
LinearRecurrence[{0, 0, 0, 0, 0, 394, 0, 0, 0, 0, 0, -1 }, {1, 1, 3, 13, 29, 42, 365, 407, 1179, 5123, 11425, 16548}, 50] (* Stefano Spezia, Sep 30 2018 *)
CoefficientList[Series[-(x^10 - x^9 + 3*x^8 - 13*x^7 + 29*x^6 - 42*x^5 - 29*x^4 - 13*x^3 - 3*x^2 - x- 1)/(x^12 - 394*x^6 + 1), {x, 0, 50}], x] (* Stefano Spezia, Sep 30 2018 *)

Prog

(PARI) vector(26, i, contfracpnqn(contfrac(sqrt(22), i))[2, 1]) \\ Arkadiusz Wesolowski, Sep 29 2018
(PARI) Vec(-(x^10 - x^9 + 3*x^8 - 13*x^7 + 29*x^6 - 42*x^5 - 29*x^4 - 13*x^3 - 3*x^2 - x - 1)/(x^12 - 394*x^6 + 1) + O(x^50)) \\ Stefano Spezia, Sep 30 2018

Crossrefs

Cf. A010478, A041034.

Sequence in context: A075726 A296776 A074498 * A042269 A049043 A031378

Adjacent sequences: A041032 A041033 A041034 * A041036 A041037 A041038

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane

Status

approved