A368830 Number of square unlabeled endofunctions from n points to themselves.

1, 1, 2, 4, 9, 20, 47, 105

Offset

0,3

Comments

Also known as square maps or square mapping patterns.

Two endofunctions are taken to be equivalent up to labeling if one is the conjugation of the other by a permutation. (Conjugation is applying the inverse permutation, the endofunction, and then the permutation, in that order. This is equivalent to permuting the "labels" of the set.)

Links

Table of n, a(n) for n=0..7.

Example

The a(3) = 4 square endofunctions are:
  1->1, 2->2, 3->3
  1->1, 2->1, 3->1 (equivalent to any constant function)
  1->1, 2->2, 3->1 (equivalent to any function consisting of 2 1-cycles)
  1->2, 2->3, 3->1 (equivalent to any 3-cycle)
Each function listed here is its own square root, except for the 3-cycle, whose square root is its inverse.

Crossrefs

Cf. A001372, A102687 (labeled version).

Sequence in context: A218552 A110198 A104508 * A036623 A001385 A039808

Adjacent sequences: A368827 A368828 A368829 * A368831 A368832 A368833

Keyword

nonn,hard,more

Author

Keith J. Bauer, Jan 07 2024

Status

approved