A102687 - OEIS

%I #19 Jan 07 2024 14:18:53

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

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

%C 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.

%t f[a_][b_] /; Length[a]==Length[b] := Table[b[[a[[i]]]], {i, 1, Length[a]}];

%t A[n_, k_] := Nest[f[#], Range[n], k]& /@ Tuples[Range[n], {n}] // Union // Length;

%t a[n_] := a[n] = A[n, 2];

%t Table[Print[n, " ", a[n]]; a[n], {n, 0, 7}] (* _Jean-François Alcover_, May 27 2019 *)

%Y Cf. A102709.

%Y Column k=2 of A247026.

%K nonn,more

%O 0,3

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

%E a(7) from _Vladeta Jovovic_, Feb 05 2005

%E a(8) and a(9) from _Joshua Zucker_, May 18 2006

%E a(0) from _Alois P. Heinz_, Sep 09 2014

%E a(10) from _Bert Dobbelaere_, Jan 24 2019