  We show that the problem of counting the number of $n$-variable unate
functions reduces to the problem of counting the number of $n$-variable
monotone functions. Using recently obtained results on $n$-variable monotone
functions, we obtain counts of $n$-variable unate functions up to $n=9$. We use
an enumeration strategy to obtain the number of $n$-variable balanced monotone
functions up to $n=7$. We show that the problem of counting the number of
$n$-variable balanced unate functions reduces to the problem of counting the
number of $n$-variable balanced monotone functions, and consequently, we obtain
the number of $n$-variable balanced unate functions up to $n=7$. Using
enumeration, we obtain the numbers of equivalence classes of $n$-variable
balanced monotone functions, unate functions and balanced unate functions up to
$n=6$. Further, for each of the considered sub-class of $n$-variable monotone
and unate functions, we also obtain the corresponding numbers of $n$-variable
non-degenerate functions.

Combinatorics;Discrete Mathematics