Pascal Triangle c# code space complexity
As I think greybeard was trying to say, unless you are know that memory consumption/allocation costs are a serious concern, then this code is fine from a memory point of view. The space-complexity is the same as the output (quadratic in A), so you can't do better than that.

There a couple of small things to be said:


as GreyBeard says, A is completely meaningless, and should really have a lowerCamelCase name as a parameter (e.g. dimension, size?); generate ought to be GeneratePascalTriangle or something meaningful (public -> UpperCamelCase) (msdn reference)
currenctRowLength should be currentRowLength, and should only be defined inside the for loop (i.e. where it is assigned); I like that this is its own variable.
you are using a while loop over j, when a for could be more readable (simply because people are used to reading for-loops), and doesn't leak j into the outer scope.
List&lt;List&lt;int&gt;&gt; is a pretty horrid type to be returning: much better to have IReadOnlyList&lt;IReadOnlyList&lt;T&gt;&gt; if the return value is meant to be immutable (which is assignable from List&lt;List&lt;T&gt;&gt; or T[][]).
I'd be inclined to initialise previousRow to null, rather than an empty list: it isn't read until i == 2; assigning it to a 'meaningful' value is defensive and only can work to obscure bugs in the rest of the code.


Mindless Performance Musing

If memory usage/allocations/GC hammering is a real concern, then you can improve matters by not using resizing lists. You havn't given us any idea of what the code is actually meant to do, so it's a bit hard to suggest an alternative, but you could either use arrays (which obvious are non-dynamic) or you can preserve the signature by creating lists with a given initial capacity with the .ctor(int) overload. Note that this will give a performance benefit, but change the time-complexity (which is also quadratic in A).

Code

Putting all of that together (and using arrays instead of lists, because mindless performance is fun, and I don't think it harms the readability here much):

/// &lt;summary&gt;
/// Generates a pascal triangle with the given number of rows
/// &lt;/summary&gt;
public static IReadOnlyList&lt;IReadOnlyList&lt;int&gt;&gt; GeneratePascalTriangle(int numberOfRows)
{
    int[][] result = new int[numberOfRows][];

    int[] previousRow = null;
    for (int i = 0; i &lt; numberOfRows; i++)
    {
        int currentRowLength = i + 1;

        int[] row = new int[currentRowLength];
        result[i] = row;

        // start and end
        row[0] = 1;
        row[currentRowLength - 1] = 1;

        // middle
        for (int j = 1; j &lt; currentRowLength - 1; j++)
        {
            row[j] = previousRow[j] + previousRow[j - 1];
        }            

        previousRow = row;
    }

    return result;
}