A067498 Maximum number of reflections for a ray of light which reflects at n points (reflecting more than once at most or all points).

1, 3, 7, 11, 21, 27, 43, 51, 69, 83, 111, 123, 157, 171, 199, 227, 273

Offset: 1

Author

Henry Bottomley, Feb 22 2002

Keywords

• more
• nonn

Comments

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.

Links

• M. Oskar van Deventer, Point Mirror Reflection, in The Mathemagician and the Pied Puzzler edited by E. Berlekamp and T. Rodgers, A K Peters Publishers, 1999, pp. 245-251. google books.

Crossrefs

Cf. A119959 (subsequence).

Formula

For p prime, a(p)=p^2-p+1.

a(n) <= n^2-n+1. [Deventer eq (1)]

a(n) <= n^2-2*n+3 for even n [Deventer eq. (2)]