A239779 Number of pairs of functions f, g, from a size n set into itself satisfying f(g(g(x))) = g(g(f(x))).

1, 1, 12, 267, 9088, 425465, 27039096, 2261637637

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

Extensions

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