Sunday's do count, in fact the first "traditional" day of Lent is the First Sunday of Lent--forty days later is Holy Thursday which is still a Lenten day until sundown.
From Another View of What Lent Means:
"When does Lent begin and end?
The observation of Lent begins on the first Sunday after Ash Wednesday (the first day we are sure to gather together), and ends at sundown, Holy Thursday, although the season starts on Ash Wednesday. So strictly speaking, what we call Lent is more than 40 days. Please see the documents quoted above for more information."