A239778 - OEIS

%I #8 Jul 16 2014 19:27:14

%S 1,1,12,255,8968,452485,31456656,2899786855

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

%p s:= proc(n, i) option remember; `if`(i=0, [[]],

%p        map(x-> seq([j, x[]], j=1..n), s(n, i-1)))

%p     end:

%p a:= proc(n) (l-> add(add(`if`([true$n]=[seq(evalb(

%p        f[f[f[i]]]=f[g[g[i]]]), i=1..n)], 1, 0), g=l), f=l))(s(n$2))

%p     end:

%p seq(a(n), n=0..5);  # _Alois P. Heinz_, Jul 16 2014

%Y Cf. A181162, A239769, A239773.

%K nonn,more

%O 0,3

%A _Chad Brewbaker_, Mar 26 2014

%E a(6)-a(7) from _Giovanni Resta_, Mar 28 2014