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Seth #1 Billington (m. Norris), according to my records, had the following children:
a. Abigale (b. 10JUN1804) b. Adeline (b. 04OCT1805) c. Jedidam N. (b. 13MAR1808) d. Ruth (b. 17AUG1809) e. Daniel Carey (b. 18JAN1810) f. Nathan Norris (b. 14JAN1812) g. Mary N. (01DEC1813) h. Hannah C. (05JUL1816) i. Fanny (24MAY1818) j. Philenia Celestia (01MAY1822) k. Nancy L. (11MAY 1823) l. Teri (20NOV1824)
Seth Billington #2 (m. Knowlton) had
a. Ruth Page (b. 17AUG1809) b. Aish Page (b. 17AUG1809)
The situation with Olive Ann Billington is, I believe, as follows (based on circumstantial data):
Olive Ann (b. 12MAY1812, Wayne, ME), married Dennis Sprague (m. abt 1839 at Milo, ME).Their first son was named Seth Billington Sprague (b. 12JAN1840).
Seth Billington #2 (m. Knowlton) had a sister, Olive (b. 24SEP1791), who married Nathaniel Pierce.Both Seth #1 and Seth #2 shared an aunt, Olive (b. abt MAR1780).
Based on these two facts, I would strongly suspect that Olive Ann Billington is indeed the daughter of Seth #2. The birth dates for the children of Seth #1 would seem to imply that Olive Ann could not be a daughter of his.
It is also highly probable that one, or more, of the children listed under Seth #1, could possibly belong to Seth #2.