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

1,4

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

Table of n, a(n) for n=1..13.

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

Crossrefs

Cf. A206344, A206345.

Sequence in context: A192200 A063083 A349859 * A270399 A269998 A335527

Adjacent sequences: A206343 A206344 A206345 * A206347 A206348 A206349

Keyword

nonn,more

Author

Nathaniel Johnston, Feb 06 2012

Extensions

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

Status

approved