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A041056 Numerators of continued fraction convergents to sqrt(34). 2
5, 6, 29, 35, 379, 414, 2035, 2449, 26525, 28974, 142421, 171395, 1856371, 2027766, 9967435, 11995201, 129919445, 141914646, 697578029, 839492675, 9092504779, 9931997454, 48820494595, 58752492049 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (0,0,0,70,0,0,0,-1).

FORMULA

a(n) = 70*a(n-4)-a(n-8). G.f.: -(x^7-5*x^6+6*x^5-29*x^4-35*x^3-29*x^2-6*x-5)/(x^8-70*x^4+1). [Colin Barker, Jul 16 2012]

MATHEMATICA

Table[Numerator[FromContinuedFraction[ContinuedFraction[Sqrt[34], n]]], {n, 1, 50}] (* Vladimir Joseph Stephan Orlovsky, Mar 18 2011 *)

Numerator[Convergents[Sqrt[34], 30]] (* Harvey P. Dale, Feb 17 2012 *)

CoefficientList[Series[- (x^7 - 5 x^6 + 6 x^5 - 29 x^4 - 35 x^3 - 29 x^2 - 6 x - 5)/(x^8 - 70 x^4 + 1), {x, 0, 30}], x] (* Vincenzo Librandi, Oct 23 2013 *)

CROSSREFS

Cf. A010489, A041057.

Sequence in context: A127040 A041011 A152118 * A042643 A047179 A166023

Adjacent sequences:  A041053 A041054 A041055 * A041057 A041058 A041059

KEYWORD

nonn,cofr,frac,easy

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified October 14 01:36 EDT 2019. Contains 327994 sequences. (Running on oeis4.)