$N(n,d)={\displaystyle \underset{i=1}{\overset{d}{}}}i*n^{d-i+1}-{\displaystyle \underset{j=1}{\overset{d}{}}}{n}^j$

$N(n,d)=$ # of extra nodes IDS has compared to BFS

given the same depth and # of child nodes.

$d=$ the depth of both IDS and BFS

$n=$# of child nodes per parent node