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A041035 Denominators of continued fraction convergents to sqrt(22). 2
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified October 26 11:59 EDT 2021. Contains 348267 sequences. (Running on oeis4.)