A370643 Number of subsets of {2..n} such that it is not possible to choose a different binary index of each element.

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.

Links

Table of n, a(n) for n=0..15.

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.

Cf. A072639, A326031, A355740, A367905, A368109.

Cf. A133686, A140637, A355529, A367867, A370583, A370636, A370640.

Sequence in context: A319050 A031371 A176557 * A000353 A097149 A185007

Adjacent sequences: A370640 A370641 A370642 * A370644 A370645 A370646

Keyword

nonn,more

Author

Gus Wiseman, Mar 10 2024

Status

approved