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

Author

N. J. A. Sloane

Keywords

• nonn
• cofr
• frac
• easy

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).

Crossrefs

Cf. A010478, A041034.

Programs

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 *)

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

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)