A041784 Numerators of continued fraction convergents to sqrt(413).

20, 61, 569, 630, 3089, 3719, 36560, 113399, 4572520, 13830959, 129051151, 142882110, 700579591, 843461701, 8291734900, 25718666401, 1037038390940, 3136833839221, 29268542943929, 32405376783150, 158890050076529, 191295426859679, 1880548891813640

Offset

0,1

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, 0, 0, 226798, 0, 0, 0, 0, 0, 0, 0, -1).

Formula

G.f.: -(x^15 -20*x^14 +61*x^13 -569*x^12 +630*x^11 -3089*x^10 +3719*x^9 -36560*x^8 -113399*x^7 -36560*x^6 -3719*x^5 -3089*x^4 -630*x^3 -569*x^2 -61*x -20) / (x^16 -226798*x^8 +1). - Colin Barker, Nov 24 2013

Mathematica

Numerator[Convergents[Sqrt[413], 50]] (* Harvey P. Dale, Oct 30 2011 *)

Crossrefs

Cf. A041785, A040392.

Sequence in context: A359444 A041780 A041782 * A276962 A105092 A112144

Adjacent sequences: A041781 A041782 A041783 * A041785 A041786 A041787

Keyword

nonn,cofr,frac,easy,less

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 24 2013

Status

approved