Geometery Formula for number of edges

HELLO, I REALLY NEED HELP TO FIND THE GEOMETERY FORMULA FOR THIS EQUATION. I FOULD OUT IT HAS TO BE AN EXPONOTIONAL FORMULA. HERE ARE THE SPEFICS...

I have a figure, if it has one vertex, it has 0 edges,so...

Vertex-----------edge

1-----------------0

2-----------------1

3-----------------3

4-----------------6

5----------------10

6----------------15

7----------------28(i think, im not sure)

8----------------(do not know, could not get)

please help to find a formula where i could find the number of edges with the number of vertexes and vice versa. I am toatally lost. this is an un directed graph. If possible please include graphs so i may undersatnd. :) :) :confused: :confused: :confused: also is a formaul and a function the same cause it says to find the function, thanxs!!!

Thanxs To Every One That Helped Me

THANXS TO EVERY ONE THAT HELPED ME!!!!!!!!!!!!!!:) :) :) :) :) :) :) :D :D :D :D :o :o :o :o