login
A102687
Number of different squares of labeled mappings of a finite set of n elements into itself.
15
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.
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
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