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
Wikipedia, Axiom of choice.
EXAMPLE
The binary indices of {1,4,5} are {{1},{3},{1,3}}, from which it is not possible to choose three different elements, so S is counted under a(3).
The binary indices of S = {1,6,8,9} are {{1},{2,3},{4},{1,4}}, from which it is not possible to choose four different elements, so S is counted under a(9).
The a(0) = 0 through a(6) = 17 subsets:
. . . {1,2,3} {1,2,3,4} {1,4,5} {2,4,6}
{1,2,3,5} {1,2,3,6}
{1,2,4,5} {1,2,4,6}
{1,3,4,5} {1,2,5,6}
{2,3,4,5} {1,3,4,6}
{1,2,3,4,5} {1,3,5,6}
{1,4,5,6}
{2,3,4,6}
{2,3,5,6}
{2,4,5,6}
{3,4,5,6}
{1,2,3,4,6}
{1,2,3,5,6}
{1,2,4,5,6}
{1,3,4,5,6}
{2,3,4,5,6}
{1,2,3,4,5,6}
MATHEMATICA
bpe[n_]:=Join@@Position[Reverse[IntegerDigits[n, 2]], 1];
Table[Length[Select[Subsets[Range[n]], MemberQ[#, n] && Select[Tuples[bpe/@#], UnsameQ@@#&]=={}&]], {n, 0, 10}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Mar 08 2024
EXTENSIONS
a(19)-a(35) from Alois P. Heinz, Mar 09 2024
STATUS
approved