Tribonacci Number Calculator

How it is calculated

The tool uses the recurrence T(n) = T(n−1) + T(n−2) + T(n−3) with the starting values T(0) = 0, T(1) = 0, T(2) = 1. It computes terms one by one with a loop, so there is no rounding error for the sizes it allows.

The index n must be a whole number from 0 to 60; decimals are cut off and anything outside that range gives no result. Beware that sources start the sequence differently (0, 0, 1 or 0, 1, 1 or 1, 1, 2). This tool starts with 0, 0, 1, so its n may be offset from a book or table using another convention. The result is shown as a whole number with thousands separators.

Common mistakes

• Comparing with a table that starts at 1, 1, 2 or 0, 1, 1. The same number can then appear at a different index, so check the starting values before comparing.
• Counting from 1 instead of 0. The first term is n = 0, so "the tenth term" is n = 9.
• Expecting the ratio of terms to approach the golden ratio. For Tribonacci it approaches about 1.839, the tribonacci constant.
• Entering a very large n. The tool stops at 60 because larger values lose exactness in floating-point arithmetic.