Aggregates and Views

Is it possible to use an aggregate on a view
that contains an aggregate? I can't seem to get
this to work:

(cut & paste into psql to reproduce)

CREATE TABLE x ( n int );
INSERT INTO x VALUES(5);
INSERT INTO x VALUES(5);
INSERT INTO x VALUES(5);
INSERT INTO x VALUES(10);
INSERT INTO x VALUES(10);
INSERT INTO x VALUES(10);
INSERT INTO x VALUES(15);
INSERT INTO x VALUES(15);
INSERT INTO x VALUES(15);
INSERT INTO x VALUES(15);
INSERT INTO x VALUES(20);
INSERT INTO x VALUES(20);

SELECT count(*) from x; -- Correctly returns 12

CREATE VIEW y AS SELECT n, count(*) AS total FROM x GROUP BY n;
SELECT * FROM y; -- Correctly returns (5,3), (10,3), (15,4),
(20,2)

-- So far so good
-- but if I do this:

SELECT count(*) FROM y; -- Instead of getting 4, I get 3,3,4,2
SELECT sum(total) FROM y; -- Returns nonsense values 0, 9, 12, 8

DROP TABLE x;
DROP VIEW y;

(end cut & paste)

Thanks,
Mark