Multi row sequence?

Hi,

I just started looking into PostgreSQL (coming from Mysql before), but have
a question:

Is it possible to have a sequence (as a multirow prim key), where sequence
(id) only increase per group of data (grp).

E.g.
+--------+----+---------+
| grp | id | name |
+--------+----+---------+
| fish | 1 | lax |
| mammal | 1 | dog |
| mammal | 2 | cat |
| mammal | 3 | whale |
| bird | 1 | penguin |
| bird | 2 | ostrich |
+--------+----+---------+

Many thanks,

Filip