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

%I A370643 #11 Mar 28 2025 14:12:52
%S A370643 0,0,0,0,0,1,7,23,46,113,287,680,1546,3374,7191,15008,30016,61013,
%T A370643 124354,252577,511229,1031064,2074281,4164716,8350912,16729473,
%U A370643 33494928,67034995,134127390,268325204,536737665,1073581062,2147162124,4294458549,8589210382,17178890873
%N A370643 Number of subsets of {2..n} such that it is not possible to choose a different binary index of each element.
%C A370643 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 A370643 The a(0) = 0 through a(7) = 23 subsets:
%e A370643   .  .  .  .  .  {2,3,4,5}  {2,4,6}      {2,4,6}
%e A370643                             {2,3,4,5}    {2,3,4,5}
%e A370643                             {2,3,4,6}    {2,3,4,6}
%e A370643                             {2,3,5,6}    {2,3,4,7}
%e A370643                             {2,4,5,6}    {2,3,5,6}
%e A370643                             {3,4,5,6}    {2,3,5,7}
%e A370643                             {2,3,4,5,6}  {2,3,6,7}
%e A370643                                          {2,4,5,6}
%e A370643                                          {2,4,5,7}
%e A370643                                          {2,4,6,7}
%e A370643                                          {2,5,6,7}
%e A370643                                          {3,4,5,6}
%e A370643                                          {3,4,5,7}
%e A370643                                          {3,4,6,7}
%e A370643                                          {3,5,6,7}
%e A370643                                          {4,5,6,7}
%e A370643                                          {2,3,4,5,6}
%e A370643                                          {2,3,4,5,7}
%e A370643                                          {2,3,4,6,7}
%e A370643                                          {2,3,5,6,7}
%e A370643                                          {2,4,5,6,7}
%e A370643                                          {3,4,5,6,7}
%e A370643                                          {2,3,4,5,6,7}
%t A370643 bpe[n_]:=Join@@Position[Reverse[IntegerDigits[n,2]],1];
%t A370643 Table[Length[Select[Subsets[Range[2,n]], Select[Tuples[bpe/@#],UnsameQ@@#&]=={}&]],{n,0,10}]
%Y A370643 The case with ones allowed is A370637, differences A370589.
%Y A370643 The minimal case is A370644, with ones A370642.
%Y A370643 A048793 lists binary indices, A000120 length, A272020 reverse, A029931 sum.
%Y A370643 A058891 counts set-systems, A003465 covering, A323818 connected.
%Y A370643 A070939 gives length of binary expansion.
%Y A370643 A096111 gives product of binary indices.
%Y A370643 Cf. A072639, A326031, A355740, A367905, A368109.
%Y A370643 Cf. A133686, A140637, A355529, A367867, A370583, A370636, A370640.
%K A370643 nonn
%O A370643 0,7
%A A370643 _Gus Wiseman_, Mar 10 2024
%E A370643 More terms from _Jinyuan Wang_, Mar 28 2025