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%I #12 Jun 30 2021 12:40:52
%S 6,8,17,10,20,22,27,23,34,33,51,44,52
%N Number of segments of the longest possible zigzag paths fitting into a circle of diameter 3 if the path with index n is constructed according to the rules of the "Snakes on a Plane" problem of Al Zimmermann's programming contest.
%C The problems corresponding to n=3,4,6 had been excluded from the contest.
%C a(16) >= 52. - _Hugo Pfoertner_, Jun 30 2021
%H Contest Organizers, <a href="http://www.enginemonitoring.net/azpc/zz/descript.htm">Snakes on a plane.</a>. Rules for the Fall 2006 round of Al Zimmermann's Programming Contests.
%H Contest Organizers, <a href="http://www.recmath.org/contest/Snakes/index.php">Al Zimmermann's Programming Contests - Snakes on a Plane</a>
%H Hugo Pfoertner, <a href="http://www.enginemonitoring.net/azpc/zz/azpczzresults.htm">Submitted Zigzag Paths Sorted by Problem Class.</a> Contest results.
%H Hugo Pfoertner, <a href="http://www.antiton.de/snake/index.html?s=13+fFfFfFfFDACACADFfFfFfFfafFfFfFfFfdFdfFfFfFfafFfFfF">Longest snake for n=13</a>
%H Hugo Pfoertner, <a href="http://www.antiton.de/snake/index.html?s=14+FfFfF0fFfbabcfFfFfF0fFCABFfF0e0fFfFfFfcdFfF">Longest snake for n=14</a>
%H Hugo Pfoertner, <a href="http://www.antiton.de/snake/index.html?s=15+GagGgGgGgAGAGgGgGgGgdbcacbddgEFfGaGgGgGagagGgGgGgAG">Longest snake for n=15</a>, first possible configuration.
%H Hugo Pfoertner, <a href="http://www.antiton.de/snake/index.html?s=15+GgGgGagbGgcacbgAGgGgGgGAGAgGgGgagaGgGDgGfcdAgGgGgGg">Longest snake for n=15</a>, second possible configuration.
%H Hugo Pfoertner, <a href="http://www.antiton.de/snake/index.html?s=16+gGgGgGgGgGgGCEgGgGgdbGBBBACADGgGgGgGgGgacgCGgGgGgGg">Longest known snake for n=16</a>, conjectured unique solution.
%Y Cf. A127399 [solutions for container diameter 2], A127401 [solutions for container diameter 4], A122223, A122224, A122226 [solutions for hinge angles excluded from contest].
%K hard,more,nonn
%O 3,1
%A _Hugo Pfoertner_, Jan 12 2007
%E a(13)-a(15) and update of links from _Hugo Pfoertner_, Jul 02 2011
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