SQL(ite) Remove (and keep some) duplicates in table

Say I have a table, called tablex, as follows:

name|year
---------
Bob | 2010
Mary| 2011
Sam | 2012
Mary| 2012
Bob | 2013

Names appear at most twice. I want to remove from the table only those names that are repeated and have a difference of one year (in which case I want to keep the newer year).

name|year
---------
Bob | 2010
Sam | 2012
Mary| 2012
Bob | 2013

I have tried:

SELECT a.Name, a.Year, b.Year
FROM tablex AS a
LEFT JOIN tablex AS b
ON a.Name=b.Name AND (a.Year=b.Year OR b.Year-a.Year=1)
ORDER BY a.Name, a.Year

results in:

  Name YearA YearB
1  Bob  2010  2010
2  Bob  2013  2013
3 Mary  2011  2011
4 Mary  2011  2012
5 Mary  2012  2012
6  Sam  2012  2012

Bob's and Sam's entries are correct, how can I restrict it further to only include Mary 2012 2012?