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A206345 Number of solvable clock puzzles with n positions in Final Fantasy XIII-2. 2
0, 1, 1, 13, 32, 507, 1998, 33136, 193995, 3426518, 27187715, 501668052, 5124675822 (list; graph; refs; listen; history; text; internal format)
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.
A206344 is a trivial upper bound.
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
Sequence in context: A212757 A140678 A282721 * A284862 A213686 A050659
KEYWORD
nonn,more
AUTHOR
Nathaniel Johnston, Feb 06 2012
EXTENSIONS
a(10) from Nathaniel Johnston, Feb 07 2012
a(11)-a(13) from Bert Dobbelaere, Apr 28 2021
STATUS
approved

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Last modified July 23 18:05 EDT 2024. Contains 374553 sequences. (Running on oeis4.)