Tribonacci sequence and the convergence of its ratios to T
Consecutive Tribonacci ratios converge to T ~1.839 (red line). The sequence overshoots and oscillates in. The golden ratio phi ~1.618 emerges the same way from Fibonacci.
The n-nacci family: growth rates approaching 2 as n increases
Table comparing Fibonacci Tribonacci and Tetranacci sequences and their limiting ratios
| Folge | Regel | Terme | Grenzwert |
|---|---|---|---|
| Fibonacci | Summe von 2 | 1,1,2,3,5,8,13,21... | φ≈1,618 |
| Tribonacci | Summe von 3 | 1,1,2,4,7,13,24... | T≈1,839 |
| Tetranacci | Summe von 4 | 1,1,2,4,8,15,29... | ≈1,928 |
| Pentanacci | Summe von 5 | 1,1,2,4,8,16,31... | ≈1,966 |
| n-nacci | Summe von n | ... | → 2 |
| Je mehr Terme summiert werden, desto näher rückt die Wachstumsrate an 2. |
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