Auto increment/sequence on multiple columns?

Is it possible to have a sequence across two columns. For example

table1
+---+---+
| a | b |
+---+---+
| 1 | 1 |
| 1 | 2 |
| 1 | 3 |
| 2 | 1 |
| 2 | 2 |
| 2 | 3 |
| 3 | 1 |
| 3 | 2 |
| 3 | 3 |
+---+---+

Would I have to create a new sequence for every unique 'a' column?
That seems pretty tedious. -Nick