A239749 Number of ordered pairs of functions f,g on a set of n elements into itself satisfying f(f(x)) = g(f(g(x))).

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

Offset

0,3

Links

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

Example

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

Crossrefs

Cf. A000248, A000949.

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

Sequence in context: A113666 A365011 A123544 * A277337 A138216 A294491

Adjacent sequences: A239746 A239747 A239748 * A239750 A239751 A239752

Keyword

nonn,more

Author

Chad Brewbaker, Mar 26 2014

Extensions

a(6)-a(7) from Giovanni Resta, Mar 26 2014

Status

approved