A362899 -id:A362899

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A362900

Number of nonisomorphic unordered pairs of fixed-point-free endofunctions on an n-set.

+10
3

1, 0, 1, 9, 162, 4527, 172335, 7861940, 416446379, 25076668511, 1692214417496, 126525497074469, 10384653020019554, 928348695659951013, 89797089935616345473, 9344984104905250973209, 1041167026926648579218267, 123655975822561996200923033, 15595901625395079379351443550

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

OFFSET

0,4

COMMENTS

Isomorphism is up to permutation of the elements of the n-set.

LINKS

Andrew Howroyd, Table of n, a(n) for n = 0..50

EXAMPLE

In the following example the notation 211 corresponds to the fixed-point-free mapping {1->2, 2->1, 3->1}.

The a(3) = 9 nonisomorphic pairs of endofunctions are: {211, 211}, {211, 212}, {211, 231}, {211, 232}, {211, 311}, {211, 312}, {211, 332}, {231, 231}, {231, 312}.

CROSSREFS

Column k=2 of A362899.

Cf. A054745 (allowing fixed-points).

KEYWORD

nonn

AUTHOR

Andrew Howroyd, May 10 2023

STATUS

approved

A362901

Number of nonisomorphic unordered triples of fixed-point-free endofunctions on an n-set.

+10
2

1, 0, 1, 22, 3935, 1497568, 883538845, 725601878962, 792072162839065, 1110677779035583912, 1947266694667001733208, 4175906998639267840682727, 10757238370963150080155796720, 32785728540392233760236496299048, 116709223477757580428169966318431329

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

OFFSET

0,4

COMMENTS

Isomorphism is up to permutation of the elements of the n-set.

LINKS

Andrew Howroyd, Table of n, a(n) for n = 0..50

CROSSREFS

Column k=3 of A362899.

Cf. A362900.

KEYWORD

nonn

AUTHOR

Andrew Howroyd, May 10 2023

STATUS

approved

A362902

Number of nonisomorphic multisets of fixed-point-free endofunctions on an n-set with n endofunctions.

+10
2

1, 0, 1, 22, 81015, 78954264778, 28097782272713021650, 5303746708038163087962610366540, 750301169575330570948709311656320180808090293, 107340347538849305728376873042317973326061404804760169389400111, 20170881768834535901905153264317820972982675109510814553304001503205327205300015737

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

OFFSET

0,4

COMMENTS

Isomorphism is up to permutation of the elements of the n-set.

LINKS

Andrew Howroyd, Table of n, a(n) for n = 0..25

CROSSREFS

Main diagonal of A362899.

Cf. A277839.

KEYWORD

nonn

AUTHOR

Andrew Howroyd, May 10 2023

STATUS

approved

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