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%I #12 Apr 28 2021 14:14:19
%S 0,1,1,13,32,507,1998,33136,193995,3426518,27187715,501668052,
%T 5124675822
%N Number of solvable clock puzzles with n positions in Final Fantasy XIII-2.
%C The sequence gives the number of ways of placing the integers 1, 2, ..., floor(n/2) (with repetition) in n spaces on a circle so that you can jump to every integer exactly once, and the distance you jump is equal to the integer you are currently standing on.
%C A206344 is a trivial upper bound.
%C This is the same as A206346, except clock puzzles that are rotations or reflections of each other are counted as distinct.
%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>
%e A solvable clock puzzle in the n = 6 case arises from the following integers (placed clockwise around a circle): 1, 3, 3, 2, 1, 3. If we label the positions 0, 1, 2, 3, 4, 5, then a solution to this puzzle is the following sequence of positions: 0, 1, 4, 3, 5, 2.
%Y Cf. A206344, A206346.
%K nonn,more
%O 1,4
%A _Nathaniel Johnston_, Feb 06 2012
%E a(10) from _Nathaniel Johnston_, Feb 07 2012
%E a(11)-a(13) from _Bert Dobbelaere_, Apr 28 2021
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