

A206345


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


2




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

Table of n, a(n) for n=1..10.
N. Johnston, Counting and Solving Final Fantasy XIII2's Clock Puzzles


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

Cf. A206344, A206346.
Sequence in context: A212757 A140678 A282721 * A213686 A050659 A123161
Adjacent sequences: A206342 A206343 A206344 * A206346 A206347 A206348


KEYWORD

nonn,more


AUTHOR

Nathaniel Johnston, Feb 06 2012


EXTENSIONS

a(10) from Nathaniel Johnston, Feb 07 2012


STATUS

approved



