This triangle shows the numbers of Boolean functions with arity and valency .
The right diagonal is = A000371. is the number of non-degenerate -ary Boolean functions. (See root.)
This is Pascal's triangle with column multiplied by .
The sum of row is . ( A001146)
k n |
0 |
1 |
2 |
3 |
4 |
5 |
sums
|
0
|
1 · 2 2
|
|
|
|
|
|
2
|
1
|
1 · 2 2
|
1 · 2 2
|
|
|
|
|
4
|
2
|
1 · 2 2
|
2 · 2 4
|
1 · 10 10
|
|
|
|
16
|
3
|
1 · 2 2
|
3 · 2 6
|
3 · 10 30
|
1 · 218 218
|
|
|
256
|
4
|
1 · 2 2
|
4 · 2 8
|
6 · 10 60
|
4 · 218 872
|
1 · 64594 64594
|
|
65536
|
5
|
1 · 2 2
|
5 · 2 10
|
10 · 10 100
|
10 · 218 2180
|
5 · 64594 322970
|
1 · 4294642034 4294642034
|
4294967296
|
|