

A206345


Number of solvable clock puzzles with n positions in Final Fantasy XIII2.


2



0, 1, 1, 13, 32, 507, 1998, 33136, 193995, 3426518, 27187715, 501668052, 5124675822
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OFFSET

1,4


COMMENTS

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.
This is the same as A206346, except clock puzzles that are rotations or reflections of each other are counted as distinct.


LINKS



EXAMPLE

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.


CROSSREFS



KEYWORD

nonn,more


AUTHOR



EXTENSIONS



STATUS

approved



