cp's OEIS Frontend

Functions from [n] to [n] with f(i) odd for all i.

Apart from initial term first differs from A132377 at a(9).

With a(1) = 0: AGM transform of A000035. See A368366 for the definition of the AGM transform. - Alois P. Heinz, Jan 24 2024

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.

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.

Functions from [n] to [n] with f(i) even or f(i) = 1 for all i.

Functions from [n] to [n] with f(i) odd or f(i) = n for all i.