The Book of Mormon text often uses and to separate each member in a list of names, as in the following examples:
On the other hand, there are cases where only the last name is preceded by an and:
So here in Jacob 1:11, either reading is theoretically possible; thus the use of “second Nephi and third Nephi etc.” in the earliest extant source (the printer’s manuscript) is quite normal. The 1830 compositor, probably accidentally, omitted the and before “third Nephi”. Since either reading is possible, the critical text will accept the earliest reading, the one with the and.
Also here in Jacob 1:11, the editors for the 1920 LDS edition replaced the original etc. with the expanded English form “and so forth”. The critical text will maintain the original etc. For a brief discussion, see the 1 Nephi preface; for a complete discussion, see etc. in volume 3.
Summary: In accord with the reading of the printer’s manuscript, restore the and before “third Nephi” in Jacob 1:11; also restore the original etc. (which was edited to “and so forth” in the 1920 LDS edition).