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

Author

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

Keywords

• nonn
• more

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.

Crossrefs

Cf. A102709.

Column k=2 of A247026.

Programs

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 *)

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