Why does "not a one" sound incorrect, but "not a single one" sounds okay?
The statistics at COCA are very close: around 15 for each.
However, "not a one" is seen mostly (80%) in fiction. My guess this is caused by authors wishing to be "natural" by clipping/eliding :-)
"Not a single one" is seen 40-50% in speech. Perhaps because of the stress that can be put on "single."