OFFSET
0,2
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.
FORMULA
a(2^n - 1) = A370818(n).
EXAMPLE
The set {3,4} has binary indices {{1,2},{3}}, with two choices {1,3}, {2,3}, so is not counted under a(4).
The a(0) = 1 through a(5) = 19 subsets:
{} {} {} {} {} {}
{1} {1} {1} {1} {1}
{2} {2} {2} {2}
{1,2} {1,2} {4} {4}
{1,3} {1,2} {1,2}
{2,3} {1,3} {1,3}
{1,4} {1,4}
{2,3} {1,5}
{2,4} {2,3}
{1,2,4} {2,4}
{1,3,4} {4,5}
{2,3,4} {1,2,4}
{1,2,5}
{1,3,4}
{1,3,5}
{2,3,4}
{2,3,5}
{2,4,5}
{3,4,5}
MATHEMATICA
bpe[n_]:=Join@@Position[Reverse[IntegerDigits[n, 2]], 1];
Table[Length[Select[Subsets[Range[n]], Length[Union[Sort /@ Select[Tuples[bpe/@#], UnsameQ@@#&]]]==1&]], {n, 0, 10}]
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, Mar 09 2024
STATUS
approved