Matthew’s genealogy has several gaps. One of them occurs in his list of kings of Judah (vv. 8-9). He lists these:

Joram
Uzziah (Greek, OZIAS)
Jotham
Ahaz
Hezekiah

2 Kings, by contrasts, lists the following:

Jehoram (Joram, married Athaliah)
Ahaziah
(Athaliah)
Joash
Amaziah
Azariah (Uzziah)
Jotham
Ahaz
Hezekiah

One problem is the identity of OZIAS – is it Uzziah (as the NASB translates) or Ahaziah? It makes sense that it is a name for Uzziah, and in that case Matthew skips three generations. What accounts for the gaps? Davies and Allison suggest that Matthew is representing the curse placed on the house of Ahab (2 Kings 21:21), extending it to three generations. The houses of David and Ahab intermingled in the marriage of Jehoram and Athaliah, and as a result the curse pronounced against Ahab extends to the house of David.

That makes sense, and in fact replicates to some degree the way the writer of Kings tells the story. Athaliah is the key factor. The writer of Kings doesn’t include either a beginning or ending to the reign of Athaliah. It is as if she never sat on the throne at all. Matthew picks up this hint and extends it to several generations.

In Ahaziah, son of Joram and Athaliah, the house of David is combined with the house of Ahab, and those who descend from that union are excluded to the fourth generation. Only with Uzziah does the Davidic line really pick up again. Perhaps there is some application here of Deuteronomy 23:7-8: Edomites and Egyptians, the law says, are excluded from the assembly of the Lord until the third generation.