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Number of ordered pairs of functions f,g on a set of n elements into itself satisfying f(f(x)) = g(f(g(x))).
4

%I #19 Jul 21 2014 13:53:01

%S 1,1,6,87,2056,69605,3201696,190933435

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

%e a(0) = a(1) = 1 since there is only one endofunction for n=0 or 1 and the equation is satisfied trivially. For n=2, each endofunction f on {1,2} is represented by [f(1),f(2)]. The list of a(2) = 6 pairs (f,g) which satisfy the equation is ([1,1], [1,1]), ([1,1], [1,2]), ([1,2], [1,2]), ([1,2], [2,1]), ([2,2], [1,2]), ([2,2], [2,2]). - _Michael Somos_, Mar 26 2014

%Y Cf. A000248, A000949.

%Y Related sequences: A053529, A181162, A239749-A239785, A239836-A239841.

%K nonn,more

%O 0,3

%A _Chad Brewbaker_, Mar 26 2014

%E a(6)-a(7) from _Giovanni Resta_, Mar 26 2014