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A239770 Number of pairs of functions f, g from a size n set into itself satisfying f(g(f(x))) = g(f(f(x)). 0

%I

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

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

%p s:= proc(n, i) option remember; `if`(i=0, [[]],

%p map(x-> seq([j, x[]], j=1..n), s(n, i-1)))

%p end:

%p a:= proc(n) local l; l:= s(n$2);

%p add(add(`if`([seq(evalb(f[g[f[i]]]=g[f[f[i]]]),

%p i=1..n)]=[true$n], 1, 0), g=l), f=l)

%p end:

%p seq(a(n), n=0..5); # _Alois P. Heinz_, Jul 16 2014

%Y Cf. A181162, A239769, A239773.

%K nonn,more

%O 0,3

%A _Chad Brewbaker_, Mar 26 2014

%E a(6)-a(7) from _Giovanni Resta_, Mar 28 2014

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Last modified September 29 17:18 EDT 2022. Contains 357090 sequences. (Running on oeis4.)