The definition of recurrence relation
A recurrence relation for the sequence {an} is an equation that, for
every n greater or equal to a certain positive integer c, expresses
an in terms of one or more of the previous terms of the sequence.
We say that ac is the first term where the recurrence relation takes
A sequence is called a solution of a recurrence relation if its terms
(except those preceding ac) satisfy the recurrence relation.
The initial conditions for a sequence specify the terms that precede ac.
A recurrence relation together with initial conditions is nothing but a
recursive definition, so it uniquely defines the sequence {an}.
The number of bacteria in a colony doubles every hour. Let an denote
the number of bacteria after n hours from now. Then, for every
n?1, we can define an by an = 2an-1. This is a recurrence relation.