Have you ordered Arthur's Social Security Application yet?He would have filled that out, and it *should* list the names of both of his parents and his birthplace.Here is the info from the Social Security Death Index:
Last Residence: 70634Deridder, Beauregard, Louisiana, United States of America
Born: 22 Jul 1896
Died: Feb 1973
State (Year) SSN issued: Louisiana (Before 1951 )
This is the 1930 census entry for Arthur and Rena Grethel:
1930 United States Federal Census > Louisiana > Vernon > Police Jury Ward 4 > District 13 > Page 12 A
Dwelling 209/Family 209
Arthur Maddox, head, rents home, owns a radio, white, 33, married, age 30 at first marriage, cannot read or write,b Alabama, parents b Alabama, farmer
Grethel, wife, white, 21, married, age 18 at first marriage, cannot read or write, b LA, father b Alabama, mother b LA
Eva M, daughter, white, 6, b LA, father b Al, mother b LA
James O, son, white, 3 yrs 4 months, b LA, father b Al, mother b LA
Lyles E., son, white, 4 months, b LA, father b Al, mother b LA
I'm a little curious to know if Rena and Arthur cousins of some sort, since her father was also born in Alabama.I'm not related to the family, so I don't know how common Maddox is as a name.I checked the 1930 and 1920 censuses in Vernon Parish and didn't find a Jim and Mary Maddox (or any Rena or Grethels in 1920).
I found entries in the 1900 and 1910 census for an Arthur Maddox born 1896 in Chilton County, Alabama, but the names of the siblings don't match what you have here.The mother's name is Polly.If Arthur's Social Security App or his death certificate match her name, I will get those census images for you.