|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
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
|
|
|
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
|
|
|
KEYWORD
|
more,nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|