A239774
Number of pairs of functions f, g from a size n set into itself satisfying f(f(g(x))) = f(f(f(x))).
Original entry on oeis.org
1, 1, 10, 285, 14176, 1034145, 105764256, 14367333421
Offset: 0
-
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$2);
add(add(`if`([seq(evalb(f[f[g[i]]]=f[f[f[i]]]),
i=1..n)]=[true$n], 1, 0), g=l), f=l)
end:
seq(a(n), n=0..5); # Alois P. Heinz, Jul 16 2014
A239776
Number of pairs of functions f, g from a size n set into itself satisfying f(f(g(x))) = g(g(f(x))).
Original entry on oeis.org
1, 1, 12, 189, 5200, 208945, 11517936, 828676933
Offset: 0
-
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]]]=g[g[f[i]]]), i=1..n)], 1, 0), g=l), f=l))(s(n$2))
end:
seq(a(n), n=0..5); # Alois P. Heinz, Jul 16 2014
A239780
Number of pairs of functions f, g on a size n set into itself satisfying f(f(g(x))) = f(g(g(x))).
Original entry on oeis.org
1, 1, 12, 279, 11128, 669605, 55937376, 6146973259
Offset: 0
-
s:= proc(n, i) option remember; `if`(i=0, [[]],
map(x-> seq([j, x[]], j=1..n), s(n, i-1)))
end:
a:= proc(n) (l-> add(add(`if`([true$n]=[seq(evalb(
f[f[g[i]]]=f[g[g[i]]]), i=1..n)], 1, 0), g=l), f=l))(s(n$2))
end:
seq(a(n), n=0..5); # Alois P. Heinz, Jul 17 2014