A041056 Numerators of continued fraction convergents to sqrt(34).

5, 6, 29, 35, 379, 414, 2035, 2449, 26525, 28974, 142421, 171395, 1856371, 2027766, 9967435, 11995201, 129919445, 141914646, 697578029, 839492675, 9092504779, 9931997454, 48820494595, 58752492049

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