Mysql query with count subquery, inner join and group

I'm definitely a noob with SQL, I've been busting my head to write a complex query with the following table structure in Postgresql:

CREATE TABLE reports
(
  reportid character varying(20) NOT NULL,
  userid integer NOT NULL,
  reporttype character varying(40) NOT NULL,
)

CREATE TABLE users
(
  userid serial NOT NULL,
  username character varying(20) NOT NULL,
)

The objective of the query is to fetch the amount of report types per user and display it in one column. There are three different types of reports.

A simple query with group-by will solve the problem but display it in different rows:

select count(*) as Amount,
       u.username,
       r.reporttype
from reports r,
     users u
where r.userid=u.userid
group by u.username,r.reporttype
order by u.username

---

SELECT
  username,
  (
  SELECT
    COUNT(*)
  FROM reports
  WHERE users.userid = reports.userid && reports.reporttype = 'Type1'
  ) As Type1,
  (
  SELECT
    COUNT(*)
  FROM reports
  WHERE users.userid = reports.userid && reports.reporttype = 'Type2'
  ) As Type2,
  (
  SELECT
    COUNT(*)
  FROM reports
  WHERE users.userid = reports.userid && reports.reporttype = 'Type3'
  ) As Type3
FROM
  users
WHERE
  EXISTS(
    SELECT
      NULL
    FROM
      reports
    WHERE
       users.userid = reports.userid
  )