Integer sequences related to Boolean functions/clans

These sequences are related to clans, i.e. equivalence classes created by negation and permutation of arguments.

sequences by arity

arity n		0	1	2	3	4	5
number of functions with arity ≤ n	A001146	2	4	16	256	65 536	4 294 967 296
number of functions with arity = n	A000371	2	2	10	218	64 594	4 294 642 034
number of clans with arity ≤ n	A000616	2	3	6	22	402	1 228 158
number of clans with arity = n	A000618	2	1	3	16	380	1 227 756
number of blightless clans with arity ≤ n		2	0	3	14	357
number of blightless clans with arity = n		2	0	1	11	343

triangles

clans by weight

Triangle A039754 shows the number of clans 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	A000616	row 3
0	1	1																2
1	1	1	1															3
2	1	1	2	1	1													6
3	1	1	3	3	6	3	3	1	1									22
4	1	1	4	6	19	27	50	56	74	56	50	27	19	6	4	1	1	402

This triangle shows the number of clans 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	A000618	row 3
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 clans by weight

See Studies of Euler diagrams/blightless.

This triangle shows the number of clans 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		row 3
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 clans 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

Python fragment

calculation of blightless clans by weight

This code uses the Python library discrete helpers.

from discretehelpers.boolf import Boolf
from discretehelpers.binv import Binv


n = 4

bec_indices_by_weight = []
for weight in range(2 ** n + 1):
    bec_indices_by_weight.append(set())
    
for i in range(2 ** 2 ** n):
    binv = Binv(intval=i, length=2 ** n)
    boolf = Boolf(binv)
    if boolf.sarity == n and boolf.is_blightless:
        weight = binv.weight
        bec_index = boolf.bec_index_from_fingerprint()
        bec_indices_by_weight[weight].add(bec_index)
        
[len(_) for _ in bec_indices_by_weight]  # [0, 0, 0, 0, 5, 19, 41, 54, 68, 56, 47, 27, 16, 6, 3, 1, 0]