OFFSET
0,4
COMMENTS
EXAMPLE
The a(0) = 1 through a(6) = 17 subsets:
{} {1} {1,2} {1,2} {1,2,4} {1,2,4} {1,2,4}
{1,3} {1,3,4} {1,2,5} {1,2,5}
{2,3} {2,3,4} {1,3,4} {1,2,6}
{1,3,5} {1,3,4}
{2,3,4} {1,3,5}
{2,3,5} {1,3,6}
{2,4,5} {1,4,6}
{3,4,5} {1,5,6}
{2,3,4}
{2,3,5}
{2,3,6}
{2,4,5}
{2,5,6}
{3,4,5}
{3,4,6}
{3,5,6}
{4,5,6}
The a(0) = 1 through a(6) = 17 set-systems:
{1} {1}{2} {1}{2} {1}{2}{3} {1}{2}{3} {1}{2}{3}
{1}{12} {1}{12}{3} {1}{12}{3} {1}{12}{3}
{2}{12} {2}{12}{3} {1}{2}{13} {1}{2}{13}
{2}{12}{3} {1}{2}{23}
{2}{3}{13} {1}{3}{23}
{1}{12}{13} {2}{12}{3}
{12}{3}{13} {2}{3}{13}
{2}{12}{13} {1}{12}{13}
{1}{12}{23}
{1}{13}{23}
{12}{3}{13}
{12}{3}{23}
{2}{12}{13}
{2}{12}{23}
{2}{13}{23}
{3}{13}{23}
{12}{13}{23}
MATHEMATICA
bpe[n_]:=Join@@Position[Reverse[IntegerDigits[n, 2]], 1];
Table[Length[Select[Subsets[Range[n], {IntegerLength[n, 2]}], Select[Tuples[bpe/@#], UnsameQ@@#&]!={}&]], {n, 0, 10}]
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, Mar 10 2024
STATUS
approved