Saint Matthew stated that: “all the generations from Abraham to David are fourteen generations; from David until the captivity in Babylon are fourteen generations; and from the captivity in Babylon until the Christ are fourteen generations” (Matt. 1:17). But when we count them, we find them to be 41 only, not 14 × 3, which is 42. Did Matthew count the number of generations incorrectly?  

Patrilineage of Jesus according to Matthew:

Matthew reached the number of generations to be 42 rather than 41 because Jeconiah was counted in two fourteens. Hang on, don’t get ahead of yourself. Saint Ambrose of Milan said that historically, there were two Jeconiah:

 “Again, from Jeconiah to Joseph are computed twelve generations; yet he afterwards calls these also fourteen. But if you look attentively, you will be able to discover the method by which fourteen are reckoned here. Twelve are reckoned, including Joseph, and Christ is the thirteenth, and history declares that there were two Joakim’s, that is, two Jeconiahs, father and son. The Evangelist has not passed over either of these but has named them both. Thus, adding the younger Jeconiah, fourteen generations are computed.” 

This is also supported by Rainer Albertz in Israel, in exile:

Jeconiah (Hebrew: יְכָנְיָה Yəḵonəyā [jəxɔnjaː], meaning “Yah has established”; Greek: Ιεχονιας; Latin: Iechonias, Jechonias), also known as Coniah and as Jehoiachin (Hebrew: יְהוֹיָכִין Yəhōyāḵīn [jəhoːjaːˈxiːn]; Latin: Ioachin, Joachin). 

Listing the generations in fourteens gives a great analogy for the state of Israel. Saint John Chrysostom explained that:  

“Having enumerated the generations from Abraham to Christ, he divides them into three divisions of fourteen generations, because three times at the end of fourteen generations, the state of the people of the Jews was changed. From Abraham to David, they were under Judges; from David to the carrying away into Babylon under Kings; from the carrying away to Christ under the High Priests.”   

 In summary:

The “captivity in Babylon until the Christ” ‎‎(Matt. 1:17c) began with the son of Jehoiakim, Jehoiachin, who only reigned for three months. However, Jesus’ genealogy was through Shealtiel, Jehoiakim’s other son. Matthew’s strategy of counting Jehoiachin in this verse had a deeper purpose – not meant as a genealogy but as an analogy.

Here are links to the other articles in this series:
Who was Jesus’ paternal ‎grandfather – Jacob or Heli?‎ (Jesus’ Genealogy: 1 of 3)
How can Jesus be the descendant of the cursed ‎Jeconiah? ‎(Jesus’ Genealogy: 3 of 3)

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