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Definition

A recursive sequence {f(n)}_n, also known as a recurrence sequence, is a sequence of numbers f(n) indexed by an integer n and generated by solving a recurrence equation. The terms of a recursive sequences can be denoted symbolically in a number of different notations, such as f_n, f(n), or f[n], where f is a symbol representing the sequence. The idea of sequences in which later terms are deduced from earlier ones, which is implicit in the principle of mathematical induction, dates to antiquity.