A206346 Number of solvable clock puzzles with n positions in Final Fantasy XIII-2, up to rotation and reflection.

0, 1, 1, 4, 8, 58, 177, 2196, 11091, 172522, 1239350, 20916154, 197149146

Offset: 1

Author

Nathaniel Johnston, Feb 06 2012

Keywords

• nonn
• more

Comments

Equals the number of Hamiltonian directed graphs on n vertices with the properties that: (1) every vertex has outdegree 1 or 2; and (2) the vertices can be arranged in a circle so that the directed edges leaving each vertex are symmetric about that vertex (e.g., if there is a directed edge that points two vertices in the clockwise direction, then the other one must point two vertices in the counterclockwise direction).

The same as A206345, except clock puzzles that are simply rotations or reflections of each other are not counted multiple times.

Links

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

Crossrefs

Cf. A206344, A206345.

Extensions

a(6)-a(9) corrected, a(10)-a(13) added by Max Alekseyev, Jul 31 2025