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