cp's OEIS Frontend

A370642 Number of minimal subsets of {1..n} such that it is not possible to choose a different binary index of each element.

%I A370642 #6 Mar 10 2024 21:23:30
%S A370642 0,0,0,1,1,3,9,26,26,40,82,175,338,636,1114
%N A370642 Number of minimal subsets of {1..n} such that it is not possible to choose a different binary index of each element.
%C A370642 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 A370642 The a(0) = 0 through a(6) = 9 subsets:
%e A370642   .  .  .  {1,2,3}  {1,2,3}  {1,2,3}    {1,2,3}
%e A370642                              {1,4,5}    {1,4,5}
%e A370642                              {2,3,4,5}  {2,4,6}
%e A370642                                         {1,2,5,6}
%e A370642                                         {1,3,4,6}
%e A370642                                         {1,3,5,6}
%e A370642                                         {2,3,4,5}
%e A370642                                         {2,3,5,6}
%e A370642                                         {3,4,5,6}
%t A370642 bpe[n_]:=Join@@Position[Reverse[IntegerDigits[n,2]],1];
%t A370642 fasmin[y_]:=Complement[y,Union@@Table[Union[s,#]& /@ Rest[Subsets[Complement[Union@@y,s]]],{s,y}]];
%t A370642 Table[Length[fasmin[Select[Subsets[Range[n]], Select[Tuples[bpe/@#],UnsameQ@@#&]=={}&]]],{n,0,10}]
%Y A370642 For prime indices we have A370591, minima of A370583, complement A370582.
%Y A370642 This is the minimal case of A370637, complement A370636.
%Y A370642 The version for a unique choice is A370638, maxima A370640, diffs A370641.
%Y A370642 The case without ones is A370644.
%Y A370642 A048793 lists binary indices, A000120 length, A272020 reverse, A029931 sum.
%Y A370642 A070939 gives length of binary expansion.
%Y A370642 A096111 gives product of binary indices.
%Y A370642 A326031 gives weight of the set-system with BII-number n.
%Y A370642 A367902 counts choosable set-systems, ranks A367906, unlabeled A368095.
%Y A370642 A367903 counts non-choosable set-systems, ranks A367907, unlabeled A368094.
%Y A370642 A368100 ranks choosable multisets, complement A355529.
%Y A370642 A370585 counts maximal choosable sets.
%Y A370642 Cf. A072639, A140637, A367905, A368109, A370589, A370593, A370639.
%K A370642 nonn,more
%O A370642 0,6
%A A370642 _Gus Wiseman_, Mar 10 2024