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

Author

N. J. A. Sloane

Keywords

• nonn
• cofr
• frac
• easy

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).

Crossrefs

Cf. A010489, A041057.

Programs

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 *)

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]