A370643 - OEIS

%I #7 Mar 10 2024 21:23:37

%S 0,0,0,0,0,1,7,23,46,113,287,680,1546,3374,7191,15008

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

%C 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.

%e The a(0) = 0 through a(7) = 23 subsets:

%e   .  .  .  .  .  {2,3,4,5}  {2,4,6}      {2,4,6}

%e                             {2,3,4,5}    {2,3,4,5}

%e                             {2,3,4,6}    {2,3,4,6}

%e                             {2,3,5,6}    {2,3,4,7}

%e                             {2,4,5,6}    {2,3,5,6}

%e                             {3,4,5,6}    {2,3,5,7}

%e                             {2,3,4,5,6}  {2,3,6,7}

%e                                          {2,4,5,6}

%e                                          {2,4,5,7}

%e                                          {2,4,6,7}

%e                                          {2,5,6,7}

%e                                          {3,4,5,6}

%e                                          {3,4,5,7}

%e                                          {3,4,6,7}

%e                                          {3,5,6,7}

%e                                          {4,5,6,7}

%e                                          {2,3,4,5,6}

%e                                          {2,3,4,5,7}

%e                                          {2,3,4,6,7}

%e                                          {2,3,5,6,7}

%e                                          {2,4,5,6,7}

%e                                          {3,4,5,6,7}

%e                                          {2,3,4,5,6,7}

%t bpe[n_]:=Join@@Position[Reverse[IntegerDigits[n,2]],1];

%t Table[Length[Select[Subsets[Range[2,n]], Select[Tuples[bpe/@#],UnsameQ@@#&]=={}&]],{n,0,10}]

%Y The case with ones allowed is A370637, differences A370589.

%Y The minimal case is A370644, with ones A370642.

%Y A048793 lists binary indices, A000120 length, A272020 reverse, A029931 sum.

%Y A058891 counts set-systems, A003465 covering, A323818 connected.

%Y A070939 gives length of binary expansion.

%Y A096111 gives product of binary indices.

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

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

%K nonn,more

%O 0,7

%A _Gus Wiseman_, Mar 10 2024