Need a specific Tribonacci number or the full sequence? This Tribonacci sequence calculator generates any Tribonacci number up to the 100,000th position and shows the full sequence up to the 2,500th term.
Tribonacci Sequence Calculator
Using the Tribonacci calculator
Enter the Position (n) of the Tribonacci number you want. The calculator instantly shows that number and (optionally) the entire sequence from 0 to n.
Indexing starts at 0: the 0th and 1st Tribonacci numbers are both 0, the 2nd is 1, and the sequence grows from there.
What is the Tribonacci sequence?
The Tribonacci sequence extends the Fibonacci idea: instead of summing the previous two numbers, each term is the sum of the previous three:
With starting values:
The first 20 Tribonacci numbers are:
The Tribonacci constant
Just as Fibonacci ratios converge to the golden ratio (φ ≈ 1.618), Tribonacci ratios converge to the Tribonacci constant (τ):
This is the real root of:
The calculator displays the ratio of consecutive terms so you can watch it approach τ as n increases. By around n = 20, it's accurate to several decimal places.
Tribonacci vs Fibonacci growth
Tribonacci numbers grow faster than Fibonacci because each term incorporates three previous values instead of two:
F₂₀ = 6765(20th Fibonacci)T₂₀ = 35890(20th Tribonacci)
By position 20, Tribonacci is already over 5× larger. The growth rate difference reflects the ratio constants: τ ≈ 1.839 vs φ ≈ 1.618.
Example: the 30th Tribonacci number
The 30th Tribonacci number is:
For comparison, F₃₀ = 832,040 – Tribonacci is nearly 20× larger at this point.
Why "Tribonacci"?
The name is a portmanteau of "tri" (three) and "Fibonacci" – coined because it generalizes the Fibonacci rule to three terms. You can extend this further: Tetranacci (4 terms), Pentanacci (5 terms), and so on. These are collectively called n-nacci or higher-order Fibonacci sequences.
