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A367905
Number of ways to choose a sequence of different binary indices, one of each binary index of n.
61
1, 1, 1, 1, 2, 1, 1, 0, 1, 1, 1, 1, 2, 1, 1, 0, 2, 1, 2, 1, 3, 1, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 2, 2, 1, 1, 3, 1, 1, 0, 1, 1, 0, 0, 1, 0, 0, 0, 3, 1, 1, 0, 2, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 3, 2, 2, 1, 4, 1, 1, 0, 2, 1, 1, 0, 2, 0, 0, 0, 4, 1, 2, 0, 3, 0, 0, 0
OFFSET
0,5
COMMENTS
A binary index of n (row n of A048793) is any position of a 1 in its reversed binary expansion. For example, 18 has reversed binary expansion (0,1,0,0,1) and binary indices {2,5}.
LINKS
Wikipedia, Axiom of choice.
EXAMPLE
352 has binary indices of binary indices {{2,3},{1,2,3},{1,4}}, and there are six possible choices (2,1,4), (2,3,1), (2,3,4), (3,1,4), (3,2,1), (3,2,4), so a(352) = 6.
MATHEMATICA
bpe[n_]:=Join@@Position[Reverse[IntegerDigits[n, 2]], 1];
Table[Length[Select[Tuples[bpe/@bpe[n]], UnsameQ@@#&]], {n, 0, 100}]
PROG
(Python)
from itertools import count, islice, product
def bin_i(n): #binary indices
return([(i+1) for i, x in enumerate(bin(n)[2:][::-1]) if x =='1'])
def a_gen(): #generator of terms
for n in count(0):
c = 0
for j in list(product(*[bin_i(k) for k in bin_i(n)])):
if len(set(j)) == len(j):
c += 1
yield c
A367905_list = list(islice(a_gen(), 90)) # John Tyler Rascoe, May 22 2024
CROSSREFS
A version for multisets is A367771, see A355529, A355740, A355744, A355745.
Positions of positive terms are A367906.
Positions of zeros are A367907.
Positions of ones are A367908.
Positions of terms > 1 are A367909.
Positions of first appearances are A367910, sorted A367911.
A048793 lists binary indices, length A000120, sum A029931.
A058891 counts set-systems, covering A003465, connected A323818.
A070939 gives length of binary expansion.
A096111 gives product of binary indices.
BII-numbers: A309314 (hyperforests), A326701 (set partitions), A326703 (chains), A326704 (antichains), A326749 (connected), A326750 (clutters), A326751 (blobs), A326752 (hypertrees), A326754 (covers), A326783 (uniform), A326784 (regular), A326788 (simple), A330217 (achiral).
Sequence in context: A104234 A355905 A368183 * A321926 A037870 A250205
KEYWORD
nonn,base
AUTHOR
Gus Wiseman, Dec 10 2023
STATUS
approved