SQLite foreach类型的行

I have got table for example

+------+--------+--------+---------------------+
| Type | Value1 | Value2 |      DateAdded      |
+------+--------+--------+---------------------+
|    1 | a      | a      | 2014-03-31 20:00:00 |
|    2 | a      | a      | 2014-03-31 20:00:10 |
|    3 | a      | a      | 2014-03-31 20:00:25 |
|    1 | a      | a      | 2014-03-31 20:00:40 |
|    2 | a      | a      | 2014-03-31 20:00:50 |
|    3 | a      | a      | 2014-03-31 20:00:60 |
|    1 | a      | a      | 2014-03-31 20:01:10 |
|    2 | a      | a      | 2014-03-31 20:01:25 |
|    3 | a      | a      | 2014-03-31 20:01:35 |
+------+--------+--------+---------------------+

and many more rows... I want to to recieve in a single query:

• 20 rows WHERE type = 1 ORDER BY DateAdded DESC
• 20 rows WHERE type = 2 ORDER BY DateAdded DESC
• 20 rows WHERE type = 3 ORDER BY DateAdded DESC

and there can be more than three types.

One approach to this type of query is the count(*) in a subquery approach:

select *
from table t
where 20 >= (select count(*)
             from table t2
             where t2.type = t.type and
                   t2.DateAdded >= t.DateAdded
            );

Count the number of rows with the same time that have a larger DateAdded and choose the ones that have up to 20 of them.