Clearly repeats among the x_i are allowed.
(Though one could also answer with them disallowed.)

But most important, A FUNCTION OF  n  IS REQUIRED.

i.e.  what is  f(n) = card({x1, x2, ... , xn} | etc)

where the curly brackets denote unordered multisets.

So far we have  f(1) = 1,  f(2) = 1, f(3) = 3 (seemingly)
and no great effort on any higher values.

If no-one can get anywhere much theoretically,
can some computer whizz at least produce a list of
the first several values of  f  please?

-- Whacking Willy.