cp's OEIS Frontend

A239770 Number of pairs of functions f, g from a size n set into itself satisfying f(g(f(x))) = g(f(f(x))).

%I A239770 #11 Dec 25 2023 17:39:40
%S A239770 1,1,10,213,7720,420865,31879296,3175850965
%N A239770 Number of pairs of functions f, g from a size n set into itself satisfying f(g(f(x))) = g(f(f(x))).
%p A239770 s:= proc(n, i) option remember; `if`(i=0, [[]],
%p A239770        map(x-> seq([j, x[]], j=1..n), s(n, i-1)))
%p A239770     end:
%p A239770 a:= proc(n) local l; l:= s(n$2);
%p A239770        add(add(`if`([seq(evalb(f[g[f[i]]]=g[f[f[i]]]),
%p A239770        i=1..n)]=[true$n], 1, 0), g=l), f=l)
%p A239770     end:
%p A239770 seq(a(n), n=0..5);  # _Alois P. Heinz_, Jul 16 2014
%Y A239770 Cf. A181162, A239769, A239773.
%K A239770 nonn,more
%O A239770 0,3
%A A239770 _Chad Brewbaker_, Mar 26 2014
%E A239770 a(6)-a(7) from _Giovanni Resta_, Mar 28 2014