Black votes were never counted as 3/5 of white votes. That's never been the case.

What you're referring to is the 3/5 Compromise... it was reached among state delegates to the 1787 Constitutional Convention to appease the South by giving them extra electoral votes. Electoral votes are based on population. The question was - should slaves be counted as part of the population? The North said no, the South said yes, so they reached a compromise.

As far as voting rights - free black males in Pennsylvania were actually able to vote until 1838. The reason being the state was founded by Quakers and they never restricted voting rights by race. (The Quakers were also some of the earliest abolitionists). However, as the demographics of the state changed, the rights of black men to vote was also taken away.

In New Jersey, both single women and black men could vote until 1807. That is when New Jersey restricted voting rights to only white men.