v:Gender of Boolean functions

This triangle shows the male Boolean functions ordered by adicity (rows) and valency (columns).   (See valency ≤ adicity ≤ arity.)

• Those in the same row have adicity ${\displaystyle n}$, and thus the truth tables have period length ${\displaystyle 2^{n}}$.
  
• Those in the same column have valency ${\displaystyle k}$, i.e. ${\displaystyle k}$ of ${\displaystyle n}$ arguments are actually used.
  If ${\displaystyle k<n}$ the truth table can be described by a shorter one.

2n k n 0 1 2 3 sums 1 0 1 1 2 1 0 2 2 4 2 0 2 8 10 8 3 0 2 16 128 146

These male Boolean functions can also be seen in the following pair of 8×256 matrices.
In the matrix all truth tables are shown with length 8, but in the table they are shortened to the period length.   Only a part of the right side of the matrix is shown in the table.