Where I work, there is a keypad for the staff lounge (it looks a little different than pic related, there are six buttons that can be pressed directionally left or right to indicate a number 0 through 9, the last is star).

I was thinking today about how simple the code is. Could someone good at math figure out how many combinations fit this set of clues?
>There are five digits in the combination
>There are only three unique numbers (e.g.: it can't be 11234 which has four different numbers)
>Where a number is not used for the first time, it immediately follows a number of the same value (e.g.: if 1 is used a second time, it must follow a 1)
>The numbers in the combination are ascending in order, except for the final digit

How many possibilities match this description?