Lattice Number Generator

I had the idea today of a "lattice" number generator.
The concept of it is this:

1) User inputs how many rows they want
2) User inputs how long they want their number to be.
3) Program selects first number randomly
4) The next number will either be plus or minus the previous.
5) Program continues until the length has been reached.

My issue is I'm not sure how to go about making the number, wether it become one long number, or single ones.
Secondly, I'm unsure about how I would go about setting up the variables for each number, if the amount of numbers can change.
I thought of a way to do it with arrays where it creates as many slots as the first number, and fills them in with it's factorials, but I've never touched arrays before.
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