|
|
A370642
|
|
Number of minimal subsets of {1..n} such that it is not possible to choose a different binary index of each element.
|
|
9
|
|
|
0, 0, 0, 1, 1, 3, 9, 26, 26, 40, 82, 175, 338, 636, 1114
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,6
|
|
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.
|
|
LINKS
|
|
|
EXAMPLE
|
The a(0) = 0 through a(6) = 9 subsets:
. . . {1,2,3} {1,2,3} {1,2,3} {1,2,3}
{1,4,5} {1,4,5}
{2,3,4,5} {2,4,6}
{1,2,5,6}
{1,3,4,6}
{1,3,5,6}
{2,3,4,5}
{2,3,5,6}
{3,4,5,6}
|
|
MATHEMATICA
|
bpe[n_]:=Join@@Position[Reverse[IntegerDigits[n, 2]], 1];
fasmin[y_]:=Complement[y, Union@@Table[Union[s, #]& /@ Rest[Subsets[Complement[Union@@y, s]]], {s, y}]];
Table[Length[fasmin[Select[Subsets[Range[n]], Select[Tuples[bpe/@#], UnsameQ@@#&]=={}&]]], {n, 0, 10}]
|
|
CROSSREFS
|
A070939 gives length of binary expansion.
A096111 gives product of binary indices.
A326031 gives weight of the set-system with BII-number n.
A370585 counts maximal choosable sets.
|
|
KEYWORD
|
nonn,more
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|