Tribonacci: T(0)=T(1)=0, T(2)=1, T(n)=T(n-1)+T(n-2)+T(n-3). First terms: 0,0,1,1,2,4,7,13,24,44,81... Ratio T(n+1)/T(n) → tribonacci constant τ ≈ 1.83929, the real root of x³=x²+x+1. Generalization of the golden ratio.
How to Use
Enter n:
- T(n): The n-th term
- Sequence: All terms
- Ratios: Convergence to τ
Tribonacci Constant
τ ≈ 1.83929 is the unique real root of x³−x²−x−1=0. Analogous to the golden ratio φ for Fibonacci. τ = (1 + ∛(19+3√33) + ∛(19−3√33))/3.
Properties
- T(n) ~ c·τⁿ for constant c
- Tribonacci word: 3-symbol analog of Fibonacci word
- Rauzy fractal: beautiful 2D tiling from tribonacci
Step-by-Step Instructions
- 1Enter n.
- 2View T(n).
- 3See sequence.
- 4Check ratios.
- 5Compare to τ.