(number after, number throughout the) genealogy (to be reckoned), be reckoned by genealogies

Boyd’s Bible Dictionary:

(birth record). In Hebrew, “book of generations” (Gen. 5; 10; 1 Chron. 1-8; 9:11So all Israel were reckoned by genealogies; and, behold, they were written in the book of the kings of Israel and Judah, who were carried away to Babylon for their transgression. (1 Chronicles 9:1); Matt. 1:1-171The book of the generation of Jesus Christ, the son of David, the son of Abraham. 2Abraham begat Isaac; and Isaac begat Jacob; and Jacob begat Judas and his brethren; 3And Judas begat Phares and Zara of Thamar; and Phares begat Esrom; and Esrom begat Aram; 4And Aram begat Aminadab; and Aminadab begat Naasson; and Naasson begat Salmon; 5And Salmon begat Booz of Rachab; and Booz begat Obed of Ruth; and Obed begat Jesse; 6And Jesse begat David the king; and David the king begat Solomon of her that had been the wife of Urias; 7And Solomon begat Roboam; and Roboam begat Abia; and Abia begat Asa; 8And Asa begat Josaphat; and Josaphat begat Joram; and Joram begat Ozias; 9And Ozias begat Joatham; and Joatham begat Achaz; and Achaz begat Ezekias; 10And Ezekias begat Manasses; and Manasses begat Amon; and Amon begat Josias; 11And Josias begat Jechonias and his brethren, about the time they were carried away to Babylon: 12And after they were brought to Babylon, Jechonias begat Salathiel; and Salathiel begat Zorobabel; 13And Zorobabel begat Abiud; and Abiud begat Eliakim; and Eliakim begat Azor; 14And Azor begat Sadoc; and Sadoc begat Achim; and Achim begat Eliud; 15And Eliud begat Eleazar; and Eleazar begat Matthan; and Matthan begat Jacob; 16And Jacob begat Joseph the husband of Mary, of whom was born Jesus, who is called Christ. 17So all the generations from Abraham to David are fourteen generations; and from David until the carrying away into Babylon are fourteen generations; and from the carrying away into Babylon unto Christ are fourteen generations. (Matthew 1:1‑17); Luke 3:23-3823And Jesus himself began to be about thirty years of age, being (as was supposed) the son of Joseph, which was the son of Heli, 24Which was the son of Matthat, which was the son of Levi, which was the son of Melchi, which was the son of Janna, which was the son of Joseph, 25Which was the son of Mattathias, which was the son of Amos, which was the son of Naum, which was the son of Esli, which was the son of Nagge, 26Which was the son of Maath, which was the son of Mattathias, which was the son of Semei, which was the son of Joseph, which was the son of Juda, 27Which was the son of Joanna, which was the son of Rhesa, which was the son of Zorobabel, which was the son of Salathiel, which was the son of Neri, 28Which was the son of Melchi, which was the son of Addi, which was the son of Cosam, which was the son of Elmodam, which was the son of Er, 29Which was the son of Jose, which was the son of Eliezer, which was the son of Jorim, which was the son of Matthat, which was the son of Levi, 30Which was the son of Simeon, which was the son of Juda, which was the son of Joseph, which was the son of Jonan, which was the son of Eliakim, 31Which was the son of Melea, which was the son of Menan, which was the son of Mattatha, which was the son of Nathan, which was the son of David, 32Which was the son of Jesse, which was the son of Obed, which was the son of Booz, which was the son of Salmon, which was the son of Naasson, 33Which was the son of Aminadab, which was the son of Aram, which was the son of Esrom, which was the son of Phares, which was the son of Juda, 34Which was the son of Jacob, which was the son of Isaac, which was the son of Abraham, which was the son of Thara, which was the son of Nachor, 35Which was the son of Saruch, which was the son of Ragau, which was the son of Phalec, which was the son of Heber, which was the son of Sala, 36Which was the son of Cainan, which was the son of Arphaxad, which was the son of Sem, which was the son of Noe, which was the son of Lamech, 37Which was the son of Mathusala, which was the son of Enoch, which was the son of Jared, which was the son of Maleleel, which was the son of Cainan, 38Which was the son of Enos, which was the son of Seth, which was the son of Adam, which was the son of God. (Luke 3:23‑38)).

Concise Bible Dictionary:

This is given in Matthew 1 and Luke 3. According to the distinctive character of Matthew in which Christ is emphatically the Messiah and Son of David, the genealogy commences with Abraham; whereas in Luke, in which Christ is displayed as the Son of Man, the list is traced up to “Adam who was the son of God.” Both lists are the same from Abraham to David; then they differ until they reach Salathiel and Zorobabel, which names are in both lists; and then they again differ. The list in Luke is much fuller, having from David to Joseph forty-one names, where Matthew has only twenty-six. Names are omitted from Matthew, and this enables the whole to be brought into the three divisions of “fourteen generations.” Ozias is placed as the son of Joram, but on consulting 1 Chronicles 3:11-1211Joram his son, Ahaziah his son, Joash his son, 12Amaziah his son, Azariah his son, Jotham his son, (1 Chronicles 3:11‑12) (where for Ozias is read Azariah, as also in 2 Kings 14:2121And all the people of Judah took Azariah, which was sixteen years old, and made him king instead of his father Amaziah. (2 Kings 14:21)), it will be seen that three kings are omitted, Ahaziah, Joash, and Amaziah. Such omissions are found in the genealogies in the Old Testament In 2 Chronicles 22:99And he sought Ahaziah: and they caught him, (for he was hid in Samaria,) and brought him to Jehu: and when they had slain him, they buried him: Because, said they, he is the son of Jehoshaphat, who sought the Lord with all his heart. So the house of Ahaziah had no power to keep still the kingdom. (2 Chronicles 22:9) Ahaziah is called the son of Jehoshaphat; whereas he was his grandson; and by comparing the generations in 1 Chronicles 6:3-153And the children of Amram; Aaron, and Moses, and Miriam. The sons also of Aaron; Nadab, and Abihu, Eleazar, and Ithamar. 4Eleazar begat Phinehas, Phinehas begat Abishua, 5And Abishua begat Bukki, and Bukki begat Uzzi, 6And Uzzi begat Zerahiah, and Zerahiah begat Meraioth, 7Meraioth begat Amariah, and Amariah begat Ahitub, 8And Ahitub begat Zadok, and Zadok begat Ahimaaz, 9And Ahimaaz begat Azariah, and Azariah begat Johanan, 10And Johanan begat Azariah, (he it is that executed the priest's office in the temple that Solomon built in Jerusalem:) 11And Azariah begat Amariah, and Amariah begat Ahitub, 12And Ahitub begat Zadok, and Zadok begat Shallum, 13And Shallum begat Hilkiah, and Hilkiah begat Azariah, 14And Azariah begat Seraiah, and Seraiah begat Jehozadak, 15And Jehozadak went into captivity, when the Lord carried away Judah and Jerusalem by the hand of Nebuchadnezzar. (1 Chronicles 6:3‑15) with Ezra 7:1-51Now after these things, in the reign of Artaxerxes king of Persia, Ezra the son of Seraiah, the son of Azariah, the son of Hilkiah, 2The son of Shallum, the son of Zadok, the son of Ahitub, 3The son of Amariah, the son of Azariah, the son of Meraioth, 4The son of Zerahiah, the son of Uzzi, the son of Bukki, 5The son of Abishua, the son of Phinehas, the son of Eleazar, the son of Aaron the chief priest: (Ezra 7:1‑5) seven names will be found to be omitted in the latter.
It will be noted that in Matthew the word “begat” is used, whereas in Luke it is more indefinite. Jesus was “supposed” or “accounted” to be the son of Joseph, and “Joseph was of Heli” without the word “begat.” Again, it should be noted that by a Jewish law if a man died childless, his brother was to raise up seed to the deceased by his widow, so that a son born thus might be called the legal son of the deceased, whereas he would be the actual or lineal son of his father, the brother of the deceased. The list in Matthew is clearly the royal line; between David and Salathiel twelve kings are given, all of whom are omitted from Luke. Being the royal line it must also be the legal line.
There is more difficulty as to the genealogy in Luke: is it the lineal line of Joseph or Mary? Women are never quoted as forming a line of succession, yet Christ is spoken of as the “seed” of the woman (Gen. 3:1515And I will put enmity between thee and the woman, and between thy seed and her seed; it shall bruise thy head, and thou shalt bruise his heel. (Genesis 3:15)); “come of woman” (Gal. 4:44But when the fulness of the time was come, God sent forth his Son, made of a woman, made under the law, (Galatians 4:4)); “the seed of Abraham” (Heb. 2:1616For verily he took not on him the nature of angels; but he took on him the seed of Abraham. (Hebrews 2:16)); “the seed of David according to flesh” (Rom. 1:33Concerning his Son Jesus Christ our Lord, which was made of the seed of David according to the flesh; (Romans 1:3); 2 Tim. 2:88Remember that Jesus Christ of the seed of David was raised from the dead according to my gospel: (2 Timothy 2:8)); “the offspring of David” (Rev. 22:1616I Jesus have sent mine angel to testify unto you these things in the churches. I am the root and the offspring of David, and the bright and morning star. (Revelation 22:16)). And as the Lord was not really the son of Joseph, these scriptures can only be fulfilled through His mother, who must have been a lineal descendant of David and Abraham. It is better therefore to consider that Luke gives the lineal descent of the Lord through Mary. In accordance with the above it will be seen that Matthew in speaking of the birth of the Lord frequently mentions Joseph, seldom Mary; whereas Luke frequently mentions Mary, but seldom Joseph.

Strong’s Dictionary of Hebrew Words:

Transliteration:
yachas
Phonic:
yaw-khas’
Meaning:
a primitive root; to sprout; used only as denominative from 3188; to enroll by pedigree
KJV Usage:
(number after, number throughout the) genealogy (to be reckoned), be reckoned by genealogies