1880 Census of Obion County, TN, shows him as Thomas Culp age 75, with wife Bittsy age 65, son James F. age (looks like 21, but should be about 31), and grandson Monroe age 11. Also in household is neice Jenny Hailey age 22.
1850 Census records show William C. Culp and David E. Culp living in the household of Timothy Culp as teenagers, and that they were born in Arkansas. There is no record of Timothy Culp ever having lived in Arkansas, so they were probably not his sons--perhaps orphaned brothers of a Culp relative and they had come to live with Timothy.