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

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`%I #7 Apr 01 2022 11:39:31
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`%S 1,3,7,11,21,27,43,51,69,83,111,123,157,171,199,227,273
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`%N Maximum number of reflections for a ray of light which reflects at n points (reflecting more than once at most or all points).
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`%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.
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`%H M. Oskar van Deventer, Point Mirror Reflection, in <a href="https://web.archive.org/web/20110807034947/http://g4g4.com/paul/BOOK.pdf">The Mathemagician and the Pied Puzzler</a> edited by E. Berlekamp and T. Rodgers, A K Peters Publishers, 1999, pp. 245-251. <a href="https://books.google.de/books?id=w8O2DwAAQBAJ">google books</a>.
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`%F For p prime, a(p)=p^2-p+1.
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`%F a(n) <= n^2-n+1. [Deventer eq (1)]
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`%F a(n) <= n^2-2*n+3 for even n [Deventer eq. (2)]
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`%Y Cf. A119959 (subsequence).
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`%K more,nonn
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`%O 1,2
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`%A _Henry Bottomley_, Feb 22 2002
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