# Studies of Euler diagrams/sequences

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Most sequences here refer to NP-equivalence classes (EC), created by input negation and permutation.
All Boolean functions in the same EC have essentially the same Euler diagram.
Each unique Euler diagram shape corresponds to a blightless EC.

## sequences by arity

arity n 0 1 2 3 4 5
number of functions with arity ≤ n 2 4 16 256 65 536 4 294 967 296
number of functions with arity = n 2 2 10 218 64 594 4 294 642 034
number of EC with arity ≤ n 2 3 6 22 402 1 228 158
number of EC with arity = n 2 1 3 16 380 1 227 756
number of blightless EC with arity ≤ n 2 0 3 14 357
number of blightless EC with arity = n 2 0 1 11 343

## triangles

### EC by weight

This triangle shows the number of EC with arity = n and weight k.
k
n
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
0 1 1 2
1 0 1 0 1
2 0 1 1 1 0 3
3 0 1 2 3 4 3 2 1 0 16
4 0 1 3 6 16 27 47 56 68 56 47 27 16 6 3 1 0 380

### blightless EC by weight

This triangle shows the number of EC with arity = n and weight k.
k
n
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
0 1 1 2
1 0 0 0 0
2 0 0 0 1 0 1
3 0 0 0 1 4 3 2 1 0 11
4 0 0 0 0 5 19 41 54 68 56 47 27 16 6 3 1 0 343

### blightless EC by number of bundles

```       0    1    2    3    4      blightless (row sums)      blighted    all (A000618)

0      2                               2                        0         2
1      0    0                          0                        1         1
2      0    0    1                     1                        2         3
3      0    6    2    3               11                        5        16
4      0  292   36   10    5         343                       37       380

298                        357                       45       402
```