cp's OEIS Frontend

A239773 Number of pairs of functions f, g from a size n set into itself satisfying f(g(f(x))) = f(f(f(x))).

%I A239773 #23 Dec 19 2024 16:11:22
%S A239773 1,1,10,231,9880,644845,58790736,7077540295,1081801600384,
%T A239773 203836779804537,46268684631596800
%N A239773 Number of pairs of functions f, g from a size n set into itself satisfying f(g(f(x))) = f(f(f(x))).
%p A239773 s:= proc(n, i) option remember; `if`(i=0, [[]],
%p A239773        map(x-> seq([j, x[]], j=1..n), s(n, i-1)))
%p A239773     end:
%p A239773 a:= proc(n) (l-> add(add(`if`([true$n]=[seq(evalb(
%p A239773        f[g[f[i]]]=f[f[f[i]]]), i=1..n)], 1, 0), g=l), f=l))(s(n$2))
%p A239773     end:
%p A239773 seq(a(n), n=0..5); # _Alois P. Heinz_, Jul 16 2014
%t A239773 a[n_] := a[n] = If[n == 0, 1, Module[{f, g, T}, T = Tuples[Range[n], n]; Table[f = T[[j, #]] &; g = T[[k, #]] &; Table[True, {n}] == Table[f[g[f[i]]] == f[f[f[i]]], {i, n}], {j, n^n}, {k, n^n}] // Flatten // Count[#, True] &]];
%t A239773 Table[Print[n, " ", a[n]]; a[n], {n, 0, 5}] (* _Jean-François Alcover_, Sep 24 2022 *)
%Y A239773 Cf. A181162.
%K A239773 nonn,more
%O A239773 0,3
%A A239773 _Chad Brewbaker_, Mar 26 2014
%E A239773 a(6)-a(7) from _Giovanni Resta_, Mar 28 2014
%E A239773 a(8)-a(10) from _Max Alekseyev_, Dec 19 2024