Sandra, there is a family that looks very much like this one on the 1880 census in Sugar Loaf, Sebastian, Arkansas.The film number to order at any LDS Family History Center is 1254057 and the page is 641d.
The name was spelled Allun by the extractor, but it has a father named Jesse M, age 32, born TN with parents born NC and TN. The wife is Nancy J, age 21, born TN Children are David R., age 8, born TN Sarah B., age 6 born AR Thomas R. age 2 bron AR
There are two other people with the same surname. (1) Caludie L, marked as sister, age three months, born Arkansas. (2) Dora R., Niece, age 11 born TN