STATUS
proposed
approved
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Revision History for A370643
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Number of subsets of {2..n} such that it is not possible to choose a different binary index of each element.
(history; published version)
(history; published version)
STATUS
editing
proposed
NAME
allocated for Gus WisemanNumber of subsets of {2..n} such that it is not possible to choose a different binary index of each element.
DATA
0, 0, 0, 0, 0, 1, 7, 23, 46, 113, 287, 680, 1546, 3374, 7191, 15008
OFFSET
0,7
COMMENTS
A binary index of n is any position of a 1 in its reversed binary expansion. The binary indices of n are row n of A048793.
EXAMPLE
The a(0) = 0 through a(7) = 23 subsets:
. . . . . {2,3,4,5} {2,4,6} {2,4,6}
{2,3,4,5} {2,3,4,5}
{2,3,4,6} {2,3,4,6}
{2,3,5,6} {2,3,4,7}
{2,4,5,6} {2,3,5,6}
{3,4,5,6} {2,3,5,7}
{2,3,4,5,6} {2,3,6,7}
{2,4,5,6}
{2,4,5,7}
{2,4,6,7}
{2,5,6,7}
{3,4,5,6}
{3,4,5,7}
{3,4,6,7}
{3,5,6,7}
{4,5,6,7}
{2,3,4,5,6}
{2,3,4,5,7}
{2,3,4,6,7}
{2,3,5,6,7}
{2,4,5,6,7}
{3,4,5,6,7}
{2,3,4,5,6,7}
MATHEMATICA
bpe[n_]:=Join@@Position[Reverse[IntegerDigits[n, 2]], 1];
Table[Length[Select[Subsets[Range[2, n]], Select[Tuples[bpe/@#], UnsameQ@@#&]=={}&]], {n, 0, 10}]
CROSSREFS
The case with ones allowed is A370637, differences A370589.
The minimal case is A370644, with ones A370642.
A048793 lists binary indices, A000120 length, A272020 reverse, A029931 sum.
A058891 counts set-systems, A003465 covering, A323818 connected.
A070939 gives length of binary expansion.
A096111 gives product of binary indices.
A326031 gives weight of the set-system with BII-number n.
Cf. A072639, ~A355739, `A355740, `A367772, A367905, A367909, A367912, A368094, `A368095, A368109.
Cf. A133686, A140637, `A134964, A355529, A370583, `A370587, A370636, ~A370638, `A370639, `A370640, ~A370641.
KEYWORD
allocated
nonn,more
AUTHOR
Gus Wiseman, Mar 10 2024
STATUS
approved
editing
NAME
allocated for Gus Wiseman
KEYWORD
allocated
STATUS
approved