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

1, 1, 10, 213, 7720, 420865, 31879296, 3175850965

Offset: 0

Author

Chad Brewbaker, Mar 26 2014

Keywords

• nonn
• more

Crossrefs

Cf. A181162, A239769, A239773.

Programs

Maple

s:= proc(n, i) option remember; `if`(i=0, [[]],
       map(x-> seq([j, x[]], j=1..n), s(n, i-1)))
    end:
a:= proc(n) local l; l:= s(n$2);
       add(add(`if`([seq(evalb(f[g[f[i]]]=g[f[f[i]]]),
       i=1..n)]=[true$n], 1, 0), g=l), f=l)
    end:
seq(a(n), n=0..5);  # Alois P. Heinz, Jul 16 2014

Extensions

a(6)-a(7) from Giovanni Resta, Mar 28 2014