A recurrence relation is a way of expressing an element of a sequence a_n in terms of "previous" elements a_i, where i < n.

Contents of this section: Recurrence Relations Linear Recurrence Relation Fibonacci Numbers Golden Ratio Recurrence Cycle Successive Powers Sums of Powers of 2

Here's what you'll find in this section:

Linear Recurrence Relation -- one in which a_n+1 is a constant times a_n plus another constant -- a method for finding a closed form.

Fibonacci Numbers -- whose successive ratios approach the Golden Ratio

Golden Ratio -- (sqrt(5)+1)/2, a special number that comes up in a variety of geometrical contexts

Recurrence Cycle -- recurrence relations whose elements repeat in a cycle

Recurrence Relation of Successive Powers of Polynomial Root -- what a mouthful!  The gist of this topic is that the successive powers of a root of a polynomial form a sequence that has an simple recurrence relation.

Internet references

Mathworld - Recurrence Relation

Related pages in this website

Generating Function

Formal Power Series

The webmaster and author of this Math Help site is Graeme McRae.