What is the nth term of the series? $0, 0 , 1 , 3 , 6 , 10 ....$ I am trying to find the relation between the number of nodes and the number of connections possible. So if there are $0$ nodes, that means $0$ connections possible, $1$ node still means $0$ connections possible, $2$ nodes $1$ connection possible, $3$ nodes $3$ connection and so on. How can I find the relation between $n$ nodes and the number of possible connections ?

Hint: If you have graph on $n$ nodes, an edge in the graph corresponds to a choice of $2$ of these nodes (the $2$ which the edge connects). Hence the number of possible edges in the graph is the number of ways you can choose $2$ nodes. Can you continue from here? 
