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A368830 Number of square unlabeled endofunctions from n points to themselves. 2
1, 1, 2, 4, 9, 20, 47, 105 (list; graph; refs; listen; history; text; internal format)
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
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
KEYWORD
nonn,hard,more
AUTHOR
Keith J. Bauer, Jan 07 2024
STATUS
approved

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Last modified May 18 03:12 EDT 2024. Contains 372617 sequences. (Running on oeis4.)