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, 1169885964640, 200545429514697, 41101718746949920

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[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

Sage

# from Max Alekseyev, Dec 19 2024
from collections import Counter
def a239775(n): return sum( prod(k^k for k in Counter(f[t] for t in f).values()) for f in Tuples(range(n),n) )

Extensions

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

a(8)-a(10) from Max Alekseyev, Dec 19 2024