The formula in my post tells you the number of possible sequences (if I have used it correctly), but it won't *generate* them. Since you couldn't possibly try them out one by one yourself, you'd be reduced in essence to a brute force algorithm - or at least, I suspect that's where we'd end up, which isn't allowed in this forum. I'm sure your case is legitimate but I'm sorry to say that's irrelevant, as the rules make no such distinctions.
What "program" are you using? As a general rule, I think that most software companies do *not* in fact keep track of customers passwords for them ...