Integer sequences related to Boolean functions

number of equivalence classes
See also .../clans.

by weight
number of families by weight number of clans by weight

representatives of equivalence classes
(families) and (clans) show smallest values corresponding to truth tables. Which Boolean function an integer represents, depends on the arity.

In the following the representative is always the smallest Zhegalkin index.

self-complementary
Balanced families and clans can contain their own complements.

The sequence for clans is a subsequence of the one for families. All entries are even.

misc.
$$T(n,n-k)$$ is the $$n$$-ary truth table of $$x_k$$

$$T(n,k)$$ is the number of balanced n-ary families of size $$2^k$$ $$T(n,k)$$ is the number of $$n$$-ary families of size $$2^k$$ $$a(n)$$ is the number of $$n$$-ary families of maximal size $$2^n$$

$$a(n)$$ is the number of truly $$n$$-ary functions  (number of nondegenerate Boolean functions of $$n$$ variables)