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In many places, (1,2,3) (a tuple) and [1,2,3] (a list) can be used interchangeably.
When should I use one or the other, and why?
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(1,2,3) is immutable, so you can't add to it or change one of the items. In contrast, [1,2,3] is mutable, so you can add to it or change the items.
So A[1:] is the slice notation that says, "Take elements 1 to the end" of the list. So in my simple example A[1:] gives you a slice of the list that is [4,5,6]
Difference(if any) between a*3 and (a,a,a). The difference is that a*3 repeats the elements for 3 times in the given order as a whole and encloses them into the given iterable, i.e., tuple. While (a, a, a) is nothing but the enclosing of iterables, i.e., tuples a - as it is - into a new tuple.
From the Python FAQ:
Lists and tuples, while similar in many respects, are generally used in fundamentally different ways. Tuples can be thought of as being similar to Pascal records or C structs; they're small collections of related data which may be of different types which are operated on as a group. For example, a Cartesian coordinate is appropriately represented as a tuple of two or three numbers.
Lists, on the other hand, are more like arrays in other languages. They tend to hold a varying number of objects all of which have the same type and which are operated on one-by-one.
Generally by convention you wouldn't choose a list or a tuple just based on its (im)mutability. You would choose a tuple for small collections of completely different pieces of data in which a full-blown class would be too heavyweight, and a list for collections of any reasonable size where you have a homogeneous set of data.
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The list [1,2,3] is dynamic and flexible but that flexibility comes at a speed cost.
The tuple (1,2,3) is fixed (immutable) and therefore faster.
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