1) A person or thing that comes before another of the same kind;
a forerunner.
2) A substance from which another is formed, especially by metabolic
reaction (OxforddDctionaries.com)

M.E., from L. præcursor "forerunner," from præcursus, p.p. of
præcurrere, from præ- "before," → pre-, +
currere "to run," → current.

A → sequence based on a → rule
that gives the next → term as a → function
of the previous term(s). For example, the sequence 3, 9, 21, 45,... can be represented
by the recurrence relation u_{n}+1 = 2u_{n} + 3, where
u_{1} = 3 and n ≥ 1.

Math.: A definition of a function from
which values of the same function can be calculated in a finite number of
steps. In mathematical logic and computer science, a recursive definition
is used to define an object in terms of itself. An example is the
→ factorial:
n! = n*(n-1)!