For data from 2011 -2013, does the serial number pertain to each household that was surveyed? What are the rows without a countyicp? Are they households where it was too small to list the county? If the goal of my research is to report the average demographic for each county, how are households without countyicp codes treated?
It sounds like you are using IPUMS USA. Please correct me if I am wrong. The SERIAL variable is a household-level ID number that is unique for each household within a given IPUMS USA sample. Not all counties are identifiable in public use microdata. See this blog post for a more detailed discussion. If the goal of your research is to report summary demographic statistics for each county in the US, then you may find the aggregated tables available via IPUMS NHGIS helpful.