A206345 Number of solvable clock puzzles with n positions in Final Fantasy XIII-2.

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

Offset: 1

Author

Nathaniel Johnston, Feb 06 2012

Keywords

• nonn
• more

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.

Examples

			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.
		

Links

• N. Johnston, Counting and Solving Final Fantasy XIII-2's Clock Puzzles

Crossrefs

Cf. A206344, A206346.

Extensions

a(10) from Nathaniel Johnston, Feb 07 2012

a(11)-a(13) from Bert Dobbelaere, Apr 28 2021