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Linear Recurrence Sequence Generator

Generate exact Fibonacci, Lucas, Pell or custom integer recurrence sequences with indexed terms and calculation steps.

Worked examplesBrowser processingTXT · CSV · JSON

Explore the example, or adjust the inputs. Save a project to keep your settings.

A useful starting point

Fibonacci starts with 0, 1 and coefficients 1, 1; the first six terms are 0, 1, 1, 2, 3, 5.

Scope and limits

1–8 starting values and matching coefficients, each up to 100 digits. Up to 300 terms and 5,000 digits per result. Integer recurrences only.

Calculations run in your browser. Projects are saved only when you download them. Website advertising and analytics follow the privacy and consent settings. Import large integer CSV columns as text in spreadsheets to preserve their digits.

Using Linear Recurrence Sequence Generator

Generate exact Fibonacci, Lucas, Pell or custom integer recurrence sequences with indexed terms and calculation steps.

Choose a worked example or enter your own values in the labeled controls.
Adjust the available options. Results refresh when you leave a field or choose an option.
Review the result summary, interpretation and calculation table. Check any explicit limits or assumptions.
Copy the text or download TXT, CSV or JSON. Save a project to reopen the same inputs later.

Example

Fibonacci starts with 0, 1 and coefficients 1, 1; the first six terms are 0, 1, 1, 2, 3, 5.

Questions & answers

Which order do coefficients use?

The first coefficient multiplies the most recent previous term, the next multiplies the preceding term. Starting values are entered in normal chronological order.

Does the generator lose digits on large Fibonacci numbers?

No. Supported calculations use exact BigInt integers. A 5,000-digit result limit stops oversized work explicitly.

Can I save and reopen my settings?

Yes. Save project downloads a JSON file for this tool. Open project restores it; undo and redo work during the current session.

Does the table contain every result?

The table is paginated in groups of 50. Downloads contain all listed rows. The partition tool intentionally caps its example listing while reporting the full exact count.