so... $n=3$ gives $N=1$ $n=4$ gives $N=4$ $n=5$ gives $N=11$ ... etc
I (by observation) assumed the answer to be: $N=2^{n-1} - n$
However the answer is http://mathworld.wolfram.com/RegularPolygonDivisionbyDiagonals.html
$+n$.
Can anyone explain how/why please?