Recurrence relation

Pattern defining an infinite sequence of numbers

In mathematics, a recurrence relation is an equation according to which the n {\displaystyle n} th term of a sequence is equal to some combination of the previous terms. Often, only k {\displaystyle k} previous terms of the sequence appear in the equation, for a parameter k {\displaystyle k} that is independent of n {\displaystyle n} ; this number k {\displaystyle k} is called the order of the relation. If the values of the first k {\displaystyle k} numbers in the sequence have been given, the rest of the sequence can be calculated by repeatedly applying the equation.

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