A239775 Number of pairs of functions f, g from a size n set into itself satisfying f(f(g(x))) = f(f(x)).

1, 1, 10, 297, 13264, 851325, 74078496, 8325102331

Offset

0,3

Links

Table of n, a(n) for n=0..7.

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[f[g[i]]]=f[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

Crossrefs

Cf. A181162, A239769, A239773.

Sequence in context: A291658 A159960 A258794 * A059072 A000459 A125288

Adjacent sequences: A239772 A239773 A239774 * A239776 A239777 A239778

Keyword

nonn,more

Author

Chad Brewbaker, Mar 26 2014

Extensions

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

Status

approved