sequence , but it is not the same as the sequence denoted by the expression. Defining a sequence by recursion Sequences whose elements are related to the previous elements in a straightforward way are often defined using recursion. This is in contrast to the definition of sequences of elements as functions of their positions. To define a sequence by recursion, one needs a rule, called recurrence relation to construct each element in terms of the ones before it. In addition, enough initial elements must be provided so that all subsequent elements of the sequence can be computed by successive applications of the recurrence relation. The Fibonacci sequence is a simple classical example, defined by the recurrence relation with initial terms and . From this, a simple computation shows that the first ten terms of this sequence are 0, 1, 1, 2, 3, 5, 8, 13, 21, and 34. A complicated example of a sequence defined by a recurrence relation is Recamán's sequence, defined by the recurrence relation with initial term A linear recurrence with constant coefficients is a recurrence relation of the form where are constants. There is a general method for expressing the general term of such a sequence as a function of ; see Linear recurrence. In the case of the Fibonacci sequence, one has and the resulting function of is given by Binet's formula. A holonomic sequence is a sequence defined by a recurrence relation of the form where are polynomials in . For most holonomic sequences, there is no explicit formula for expressing as a function of . Nevertheless, holonomic sequences play an important role in various areas of mathematics. For example, many special functions have a Taylor series whose sequence of coefficients is holonomic. The use of the recurrence relation allows a fast computation of values of such special functions. Not all sequences can be specified by a recurrence relation. An example is the sequence of prime numbers in their natural order (2, 3, 5, 7, 11, 13, 17, ...). Formal definition and basic properties There are many different notions of sequences in mathematics, some of which (e.g., exact sequence) are not covered by the definitions and notations introduced below. Definition In this article, a sequence is formally defined as a function whose domain is an interval of integers. This definition covers several different uses of the word "sequence", including one-sided infinite sequences, bi-infinite sequences,