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A067498
Maximum number of reflections for a ray of light which reflects at n points (reflecting more than once at most or all points).
0
1, 3, 7, 11, 21, 27, 43, 51, 69, 83, 111, 123, 157, 171, 199, 227, 273
OFFSET
1,2
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.
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)]
CROSSREFS
Cf. A119959 (subsequence).
Sequence in context: A344483 A151923 A187264 * A018345 A082675 A201645
KEYWORD
more,nonn
AUTHOR
Henry Bottomley, Feb 22 2002
STATUS
approved