A206346 - OEIS

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A206346

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

0, 1, 1, 4, 8, 72, 236, 3665, 19037

(list; graph; refs; listen; history; text; internal format)

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..9.

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

CROSSREFS

Cf. A206344, A206345.

Sequence in context: A051226 A013112 A274461 * A240503 A221484 A338314

Adjacent sequences: A206343 A206344 A206345 * A206347 A206348 A206349

KEYWORD

nonn,more

AUTHOR

Nathaniel Johnston, Feb 06 2012

STATUS

approved