(definition)

**Definition:**
The specification of a sequence of values in terms of earlier values in the sequence and base values.

**Also known as** recurrence equations.

**See also**
*Master theorem*.

*Note:
Fibonacci numbers may be described by the recurrence relation F(n) = F(n-1) + F(n-2), where F(1)=1 and F(2)=1. Execution times are often computed by setting up, then solving, a unary recurrence relation, such as T(n) = 2T(n/4) + 2. *

* From Algorithms and Theory of Computation Handbook, page 1-26, Copyright © 1999 by CRC Press LLC. Appearing in the Dictionary of Computer Science, Engineering and Technology, Copyright © 2000 CRC Press LLC.*

Author: CRC-A

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If you have suggestions, corrections, or comments, please get in touch with Paul Black.

Entry modified 17 December 2004.

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Cite this as:

Algorithms and Theory of Computation Handbook, CRC Press LLC, 1999, "recurrence relation", in
*Dictionary of Algorithms and Data Structures* [online], Vreda Pieterse and Paul E. Black, eds. 17 December 2004. (accessed TODAY)
Available from: https://www.nist.gov/dads/HTML/recurrence.html