The tribonacci numbers are a generalization of the Fibonacci Numbers defined by ,
, , and the Recurrence Relation

(1) |

(2) |

(3) |

where denotes the Nint function (Plouffe). The first part of a Numerator is related to the
Real root of , but determination of the Denominator requires an application of the
LLL Algorithm. The numbers increase asymptotically to

(4) |

(5) |

(Plouffe).

**References**

Plouffe, S. ``Tribonacci Constant.'' http://www.lacim.uqam.ca/piDATA/tribo.txt.

Sloane, N. J. A. Sequence
A000073/M1074
in ``An On-Line Version of the Encyclopedia of Integer Sequences.''
http://www.research.att.com/~njas/sequences/eisonline.html and Sloane, N. J. A. and Plouffe, S.
*The Encyclopedia of Integer Sequences.* San Diego: Academic Press, 1995.

© 1996-9

1999-05-26