What syntax does the formula use?

Reference previous terms as a(n-1), a(n-2), etc. Use standard math operators: +, -, *, /, ^ for exponentiation, and parentheses for grouping. Example: 2*a(n-1) + a(n-2) - 3.

How many initial terms do I need to provide?

You need at least as many initial terms as the maximum look-back in your formula. If your formula uses a(n-2), provide at least 2 initial terms.

What are common recurrence examples?

Fibonacci: initial = 1,1 → a(n-1)+a(n-2). Arithmetic (+3 each step): initial = 1 → a(n-1)+3. Geometric (×2): initial = 1 → 2*a(n-1). Tribonacci: initial = 0,0,1 → a(n-1)+a(n-2)+a(n-3).

Can I use exponentiation in the formula?

Yes. Use ^ or ** for powers. For example, a(n-1)^2 squares the previous term.

What happens if my sequence diverges to very large numbers?

JavaScript numbers are IEEE 754 double-precision floats, so values up to about 10^308 are representable. Beyond that, terms will display as Infinity. Use fewer terms or a gentler recurrence to stay in range.

Is the formula evaluated securely?

The formula is evaluated using a sandboxed math parser — it only recognises numbers, basic operators, parentheses, and a(n-k) references. No arbitrary code execution is possible.

Recursive Sequence Calculator

Name: Recursive Sequence Calculator
Availability: InStock
Author: Nham Vu

Enter initial terms and a recurrence relation to generate as many sequence terms as you need.

Define the Sequence

Quick Presets

Initial Terms

Comma-separated. Provide as many as your formula looks back.

Recurrence Formula

Use a(n-1), a(n-2), … and operators +, -, *, /, ^

Number of Terms: 15

3100

Term Table

n	a(n)

Define a recurrence and click Generate Sequence

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Summary

Enter initial terms and a recurrence relation to generate as many sequence terms as you need.

How it works

Enter one or more initial terms separated by commas (e.g. "1, 1" for Fibonacci).
Type the recurrence formula referencing a(n-1), a(n-2), etc. (e.g. "a(n-1) + a(n-2)").
Set how many terms to generate (up to 100).
Click Generate — each term is computed from the formula and appended to the sequence.
Copy the result or view the full table with index and value columns.

Use cases

Generate Fibonacci, Lucas, or Padovan numbers for number-theory study.
Explore diverging vs. converging sequences by changing the recurrence multiplier.
Compute arithmetic and geometric progressions without a spreadsheet.
Verify hand-computed recursive homework answers quickly.
Test custom difference equations for discrete dynamical-systems coursework.
Produce lookup tables for programming challenges (e.g. dynamic programming seeds).

Frequently Asked Questions

Last updated: 2026-06-13 · Reviewed by Nham Vu