A102687 Number of different squares of labeled mappings of a finite set of n elements into itself.

1, 1, 3, 12, 100, 1075, 13356, 197764, 3403576, 66159405, 1438338070

Offset

0,3

Comments

Let A be a finite set of cardinal n, F be the set of mappings from A to A and F_2 be the subset of F including all g such that there exists f in F with g = fof (composition of f with itself). Then a(n) = #F_2.

Links

Table of n, a(n) for n=0..10.

Mathematica

f[a_][b_] /; Length[a]==Length[b] := Table[b[[a[[i]]]], {i, 1, Length[a]}];
A[n_, k_] := Nest[f[#], Range[n], k]& /@ Tuples[Range[n], {n}] // Union // Length;
a[n_] := a[n] = A[n, 2];
Table[Print[n, " ", a[n]]; a[n], {n, 0, 7}] (* Jean-François Alcover, May 27 2019 *)

Crossrefs

Cf. A102709.

Column k=2 of A247026.

Sequence in context: A162055 A067300 A133359 * A202302 A350953 A366668

Adjacent sequences: A102684 A102685 A102686 * A102688 A102689 A102690

Keyword

nonn,more

Author

Eric Wegrzynowski (Eric.Wegrzynowski(AT)lifl.fr), Feb 03 2005

Extensions

a(7) from Vladeta Jovovic, Feb 05 2005

a(8) and a(9) from Joshua Zucker, May 18 2006

a(0) from Alois P. Heinz, Sep 09 2014

a(10) from Bert Dobbelaere, Jan 24 2019

Status

approved