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An alternative way to describe a sequence is to list a few terms
and to give a rule for computing the rest of the sequence.
Our example (1) above can be described by
the starting value and the rule
for integers .
Starting from , the rule implies that
and so on; each term in the sequence can be computed recursively
in terms of the terms previously computed.
A rule such as this giving the next term in terms of earlier terms
is also called a recurrence relation (or simply recurrence).