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Tribonacci sequence and the convergence of its ratios to T
11.331.672T~1.839ratio a(n+1)/a(n)1469nQuotient

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.

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The n-nacci family: growth rates approaching 2 as n increases

Table comparing Fibonacci Tribonacci and Tetranacci sequences and their limiting ratios

FolgeRegelTermeGrenzwert
FibonacciSumme von 21,1,2,3,5,8,13,21...φ≈1,618
TribonacciSumme von 31,1,2,4,7,13,24...T≈1,839
TetranacciSumme von 41,1,2,4,8,15,29...≈1,928
PentanacciSumme von 51,1,2,4,8,16,31...≈1,966
n-nacciSumme von n...→ 2
Je mehr Terme summiert werden, desto näher rückt die Wachstumsrate an 2.
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