Recursive Sequence Calculator

Use our free recursive sequence calculator to generate terms from a linear recurrence aₙ = c₁aₙ₋₁ + c₂aₙ₋₂ + ... with custom initial values and coefficients.

Math

Mode

Order (k)

Initial Terms (comma-sep)

Coefficients (comma-sep)

How Many Terms

Position (for nth term)

Formula

A linear recurrence defines each term as a weighted sum of previous terms. For order k, the recurrence aₙ = c₁aₙ₋₁ + c₂aₙ₋₂ + ... + cₖaₙ₋ₖ requires k initial terms and k coefficients.

aₙ = c₁·aₙ₋₁ + c₂·aₙ₋₂ + ... + cₖ·aₙ₋ₖ

Percentage: The percentage value you want to apply

Number: The original number or value

Result: The calculated result

How It Works

1Select the order (1, 2, or 3).
2Enter initial terms (comma-separated, e.g., '0, 1' for Fibonacci).
3Enter coefficients (comma-separated, e.g., '1, 1' for Fibonacci).
4Enter how many terms to generate or position to find.
5Click Calculate.

Examples

Fibonacci (order 2)

1.aₙ = aₙ₋₁ + aₙ₋₂
2.0, 1, 1, 2, 3, 5, 8, 13, 21, 34

Result: 34

Pell (order 2)

1.aₙ = 2aₙ₋₁ + aₙ₋₂
2.0, 1, 2, 5, 12, 29, 70, 169

Result: 169

Tribonacci (order 3)

1.aₙ = aₙ₋₁ + aₙ₋₂ + aₙ₋₃
2.0, 0, 1, 1, 2, 4, 7, 13, 24, 44

Result: 44

Frequently Asked Questions

Each term depends on previous terms via a formula.

How many previous terms are used (k).

You need exactly k initial terms and k coefficients.

Yes, any real numbers.

Only linear recurrences are supported.

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CalculateMe Team

Last updated: 2026-07-14

Frequently Asked Questions

Each term depends on previous terms via a formula.

How many previous terms are used (k).

You need exactly k initial terms and k coefficients.

Yes, any real numbers.

Only linear recurrences are supported.

Recursive Sequence Calculator

Formula

How It Works

Examples

Fibonacci (order 2)

Pell (order 2)

Tribonacci (order 3)

Frequently Asked Questions

What is a recurrence?

What is the order?

What if order doesn't match inputs?

Can coefficients be negative?

What about non-linear recurrences?

Related Calculators

Recursive Sequence Calculator

Formula

How It Works

Examples

Fibonacci (order 2)

Pell (order 2)

Tribonacci (order 3)

Frequently Asked Questions

What is a recurrence?

What is the order?

What if order doesn't match inputs?

Can coefficients be negative?

What about non-linear recurrences?

Related Calculators