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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 (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

Table of n, a(n) for n=1..10.

N. Johnston, Counting and Solving Final Fantasy XIII-2'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 * A284862 A213686 A050659

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

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Last modified June 27 13:28 EDT 2017. Contains 288788 sequences.