Mathematical equivalent of a one-dimensional array as seen in programming Suppose some kind of structure to hold a (finite) number of elements is needed. The order of the elements matters and duplicate elements are allowed. When programming one would use a one-dimensional array for this.
What mathematical structure comes closest to such a one-dimensional array as seen in programming? I've seen both row and column vectors being used for this purpose, but it seems that a sequence would do as well. Is there any reason to choose one over the other or to choose an entirely other structure?

A vector is the wrong object to consider.  While vectors (in $\mathbb{R}^d$) can be represented as ordered lists, calling something a vector implies that it comes from a space with a great deal more structure.  Specifically, vectors can be added together, and can be scaled by field elements (in the case of vectors in $\mathbb{R}^n$, you can multiply a vector by a real number).
A closer analogy would be a sequence (if your array has infinite length, or if you are willing to pad it by zero) or an $n$-tuple (if your arrays are all of the same length $n$).  Either of these objects may be thought of as a function from (a subset of) the natural numbers $\mathbb{N}$ to the appropriate set (e.g. the set of floating point numbers, the set of integers, the set of real numbers, etc).
For example, the array
 float array[5] = {3.14, 0.60309, 2.7183, 2, 1.618}

could be written as a $5$-tuple
$$ (3.14, 0.60309, 2.7183, 2.0, 1.612), $$
which can be thought of as a function $ a : \{0,1,2,3,4\} \to (\text{Set of Floats})$ defined by
$$
\begin{cases}
3.14 & \text{if $x=0$,} \\
0.60309 & \text{if $x=1$,} \\
2.7183 & \text{if $x=2$,} \\
2.0 & \text{if $x=3$, and} \\
1.612 & \text{if $x=4$.}
\end{cases}$$
That is (for example) $a(2) = 2.7182$.
As rschwieb noted in a comment below, this last way of looking at a tuple or array is likely the most relevant for software engineers:  one passes an index to the array, and gets back the value of the array element stored at that index.  This is equivalent to evaluating the function at that index.
