To me, not a one sounds incorrect, but not a single one sounds okay. Is there any grammar to support why my ears weep at the sound of the former phrase, but not the latter?
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."