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 ?

$a_n - a_{n-1} = n-2 \implies a_n = n-2 + n-3 +....+1 =  ...$
