%N Maximum number of reflections for a ray of light which reflects at n points (reflecting more than once at most or all points).
%C The maxima occur when the points of reflection are arranged at the vertices of a regular n-gon and the ray (except entering and leaving) follows the edges and diagonals of the polygon.
%H M.O. van Deventer in <a href="http://www.g4g4.com/paul/BOOK.pdf">The Mathemagician and the Pied Puzzler</a> edited by E. Berlekamp and T. Rodgers, AKPeters Publishers, pp. 245-251.
%F For p prime, a(p)=p^2-p+1.
%A _Henry Bottomley_, Feb 22 2002