MariaDB 10.2

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CREATE TABLE booking(booking_date DATE,nights INT,room_no INT,arrival_time TIME);
INSERT INTO booking(booking_date,nights,room_no,arrival_time)
VALUES
('2016-12-01',2,201,'17:00'),
('2016-12-02',2,301,'20:00'),
('2016-12-03',5,101,'16:00'),
('2016-12-03',4,201,'18:00'),
('2016-12-04',1,301,'15:00'),
('2016-12-05',5,301,'14:00'),
('2016-12-07',4,201,'20:00'),
('2016-12-08',2,101,'18:00'),
('2016-12-10',5,101,'23:00'),
('2016-12-12',1,301,'12:00'),
('2016-12-15',3,101,'19:00');
WITH cte AS (
SELECT room_no, 
       booking_date + INTERVAL nights DAY d_start, 
       DATEDIFF(COALESCE(LEAD(booking_date) OVER (PARTITION BY room_no ORDER BY booking_date), '2100-01-01'), booking_date + INTERVAL nights DAY) d_free
FROM booking
)
SELECT room_no, d_start
FROM cte
WHERE d_free >= 3
ORDER BY 2;


room_no
d_start


201
2016-12-11

301
2016-12-13

101
2016-12-18