Questions regarding functions defined recursively, such as the Fibonacci sequence.
A recurrence relation is an equation that recursively defines a sequence or multidimensional array of values: once one or more initial terms are given, each further term of the sequence or array is defined as a function of the preceding terms.
Simple examples include the geometric sequence $a_{n}=r a_{n-1}$, which has the closed-form $a_{n}=r^n a_0$, the aforementioned Fibonacci sequence with initial conditions $f_0=0,f_1=1$ and recurrence $f_{n+2}=f_{n+1}+f_n$, and series: the sequence $S_n =\sum_{k=1}^{n} a_k$ can be written as $S_n= S_{n-1}+a_n$.
The term order is often used to describe the number of prior terms used to calculate the next one; for instance, the Fibonacci sequence is of order 2.
See the Wikipedia page for more information.
