Tribonacci Calculator
Calculate the tribonacci sequence, where each term is the sum of the previous three, and find the nth term with the sequence listed.
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Generate the tribonacci sequence, summing the previous three terms.
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Generate the tribonacci sequence
The tribonacci sequence is a generalisation of the famous Fibonacci sequence in which each term is the sum of the three preceding terms rather than two. Starting from zero, zero and one, the sequence continues one, two, four, seven, thirteen, twenty-four, and so on. This calculator generates as many terms as you request and reports the last one. Where Fibonacci grows by roughly the golden ratio each step, tribonacci grows by its own constant, the tribonacci constant.
The sequence is a natural next step for anyone who enjoys Fibonacci numbers and recurrence relations.
Beyond Fibonacci
Summing more previous terms gives a whole family of sequences: two terms give Fibonacci, three give tribonacci, four give tetranacci, and so on. Each grows faster than the last and approaches a limiting ratio closer to two. These sequences appear in combinatorics, tiling problems and computer science, and they are a fun way to explore how a small change to a rule reshapes the pattern of growth.
The starting values used here, zero, zero and one, are the most common convention, though some definitions differ. All calculation happens locally in your browser.
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Frequently Asked Questions
What is the tribonacci sequence?
A sequence where each term is the sum of the previous three, starting from zero, zero and one, generalising the Fibonacci sequence.
How is it different from Fibonacci?
Fibonacci sums the previous two terms, while tribonacci sums the previous three, so it grows faster toward its own limiting ratio.
What is the tribonacci constant?
It is the ratio that consecutive tribonacci terms approach, analogous to the golden ratio for Fibonacci, with a value a little under two.
Can I change the starting values?
This tool uses the common zero, zero, one convention. Other definitions exist, which shift the sequence but keep the same growth behaviour.
Privacy & Security
Everything runs in your browser; nothing is uploaded.
How to Use
Enter how many terms to generate.
Disclaimer: This tool is provided "as is" without warranty of any kind. Results are for educational and utility purposes.