%I #10 Dec 10 2015 02:33:49
%S 0,1,1,4,8,72,236,3665,19037
%N Number of solvable clock puzzles with n positions in Final Fantasy XIII-2, up to rotation and reflection.
%C Equals the number of Hamiltonian directed graphs on n vertices with the properties that: (1) every vertex has outdegree 1 or 2; and (2) the vertices can be arranged in a circle so that the directed edges leaving each vertex are symmetric about that vertex (e.g., if there is a directed edge that points two vertices in the clockwise direction, then the other one must point two vertices in the counterclockwise direction).
%C The same as A206345, except clock puzzles that are simply rotations or reflections of each other are not counted multiple times.
%H N. Johnston, <a href="http://www.njohnston.ca/2012/02/counting-and-solving-final-fantasy-xiii-2s-clock-puzzles/">Counting and Solving Final Fantasy XIII-2's Clock Puzzles</a>
%Y Cf. A206344, A206345.
%K nonn,more
%O 1,4
%A _Nathaniel Johnston_, Feb 06 2012