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Tribonacci Sequence Calculator

Work out tribonacci sequence instantly with clear inputs, formula shown and shareable results.

About Tribonacci Sequence Calculator

The tribonacci sequence extends Fibonacci by summing the previous three terms instead of two. Consecutive ratios converge to the tribonacci constant ≈ 1.8392868, the real root of x³ = x² + x + 1.

Formula

Tribonacci recurrence

T(n) = T(n−1) + T(n−2) + T(n−3), starting 0, 1, 1

Worked example

With the default values below, Tribonacci Sequence Calculator returns Last term of 274. Change any input above and every figure here is recalculated in your browser.

Inputs used

How many termsaccepts 3–60
12
Third starting value (after 0 and 1)
1

Results

Last term
274
Sequence
0, 1, 1, 2, 4, 7, 13, 24, 44, 81, 149, 274
Sum of all terms
600
Ratio of the last two terms
1.83892617

Step by step

  1. 1Values used
  2. 2Tribonacci recurrence
  3. 3Last term= 274
  4. 4Sequence= 0, 1, 1, 2, 4, 7, 13, 24, 44, 81, 149, 274
  5. 5Sum of all terms= 600
  6. 6Ratio of the last two terms= 1.83892617

Assumptions and limits

  • The result is derived only from the 2 inputs listed above. Anything not among them is not part of the calculation.
  • In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
  • Figures are rounded for display to 8 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

What are the first terms?

0, 1, 1, 2, 4, 7, 13, 24, 44, 81, 149, 274.

What is the tribonacci constant?

About 1.8392868, the analogue of the golden ratio for this three-term recurrence.

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