
:grumbling I've been asking all day...Now it looks like I'm begging.....And I am!!!

Can someone please help me to find the nth term for this quadratic sequence:
0,1,3,6,10......
Also:
Lines Crossovers Open regions Closed regions Total regions
1 0 2 0 2
2 1 4 0 4
3 3 6 1 7
4 6 8 3 11
5 10 10 6 16
Can someone help me to get the equation for 'crossovers'...?
This will mean A LOT to me.....JAZAKALLAH KHAIR to everyone who replies.