It is said that a sequence of three claps followed by one final clap (3-3-3-1) are used because 3+3+3=9 (九 in Japanese) and the addition of an extra clap makes a circle (丸) which signifies 'maruku osamaru' (lit. to be settled amicably).
拍数の「3回・3回・3回・1回」は3回の拍が3回で九になり、もう1回手を打つと九に点が打たれて「丸」になり、「丸く納まる」の意味になるからとも言われている。