Tribonacci Number
The tribonacci numbers are a generalization of the Fibonacci Numbers defined by 
,
, 
, and the Recurrence Relation
 | (1) |
. The represent the 
case of the Fibonacci n-Step Number. Thefirst few terms are 1, 1, 2, 4, 7, 13, 24, 44, 81, 149, ... (Sloane's A000073). The ratio of adjacent terms tends to1.83929, which is the Real Root of 
. The Tribonacci numbers can also becomputed using the Generating Function | |
 | (2) |
is also given by | (3) |
where 
denotes the Nint function (Plouffe). The first part of a Numerator is related to theReal root of 
, but determination of the Denominator requires an application of theLLL Algorithm. The numbers increase asymptotically to
 | (4) |
 |  |  | |
|  | (5) |
(Plouffe).See also Fibonacci n-Step Number, Fibonacci Number, Tetranacci Number
References
Plouffe, S. ``Tribonacci Constant.''http://www.lacim.uqam.ca/piDATA/tribo.txt. Sloane, N. J. A. SequenceA000073/M1074in ``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.
- Triangle Squaring
- Triangle Tiling
- Triangle Transformation Principle
- Triangular Cupola
- Triangular Dipyramid
- Triangular Graph
- Triangular Hebesphenorotunda
- Triangular Matrix
- Triangular Number
- Triangular Orthobicupola
- Triangular Pyramid
- Triangular Square Number
- Triangular Symmetry Group
- Triangulation
- Triaugmented Dodecahedron
- Triaugmented Hexagonal Prism
- Triaugmented Triangular Prism
- Triaugmented Truncated Dodecahedron
- Triaxial Ellipsoid
- Tribar
- Tribonacci Number
- Tribox
- Trichotomy Law
- Tricolorable
- Tricomi Function