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 ?

the sequence is $a_0,a_1,a_2\dots$ with $a_n=\frac{n(n-1)}{2}$
