cp's OEIS Frontend

A370644 Number of minimal subsets of {2..n} such that it is not possible to choose a different binary index of each element.

%I A370644 #6 Mar 11 2024 18:06:04
%S A370644 0,0,0,0,0,1,4,13,13,26,56,126,243,471,812,1438
%N A370644 Number of minimal subsets of {2..n} such that it is not possible to choose a different binary index of each element.
%C A370644 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 A370644 The a(0) = 0 through a(7) = 13 subsets:
%e A370644   .  .  .  .  .  {2,3,4,5}  {2,4,6}    {2,4,6}
%e A370644                             {2,3,4,5}  {2,3,4,5}
%e A370644                             {2,3,5,6}  {2,3,4,7}
%e A370644                             {3,4,5,6}  {2,3,5,6}
%e A370644                                        {2,3,5,7}
%e A370644                                        {2,3,6,7}
%e A370644                                        {2,4,5,7}
%e A370644                                        {2,5,6,7}
%e A370644                                        {3,4,5,6}
%e A370644                                        {3,4,5,7}
%e A370644                                        {3,4,6,7}
%e A370644                                        {3,5,6,7}
%e A370644                                        {4,5,6,7}
%e A370644 The a(0) = 0 through a(7) = 13 set-systems:
%e A370644   .  .  .  .  .  {2}{12}{3}{13}  {2}{3}{23}       {2}{3}{23}
%e A370644                                  {2}{12}{3}{13}   {2}{12}{3}{13}
%e A370644                                  {12}{3}{13}{23}  {12}{3}{13}{23}
%e A370644                                  {2}{12}{13}{23}  {2}{12}{13}{23}
%e A370644                                                   {2}{12}{3}{123}
%e A370644                                                   {2}{3}{13}{123}
%e A370644                                                   {12}{3}{13}{123}
%e A370644                                                   {12}{3}{23}{123}
%e A370644                                                   {2}{12}{13}{123}
%e A370644                                                   {2}{12}{23}{123}
%e A370644                                                   {2}{13}{23}{123}
%e A370644                                                   {3}{13}{23}{123}
%e A370644                                                   {12}{13}{23}{123}
%t A370644 bpe[n_]:=Join@@Position[Reverse[IntegerDigits[n,2]],1];
%t A370644 fasmin[y_]:=Complement[y,Union@@Table[Union[s,#]& /@ Rest[Subsets[Complement[Union@@y,s]]],{s,y}]];
%t A370644 Table[Length[fasmin[Select[Subsets[Range[2,n]], Select[Tuples[bpe/@#],UnsameQ@@#&]=={}&]]],{n,0,10}]
%Y A370644 The version with ones allowed is A370642, minimal case of A370637.
%Y A370644 This is the minimal case of A370643.
%Y A370644 A048793 lists binary indices, A000120 length, A272020 reverse, A029931 sum.
%Y A370644 A070939 gives length of binary expansion.
%Y A370644 A096111 gives product of binary indices.
%Y A370644 A367902 counts choosable set-systems, ranks A367906, unlabeled A368095.
%Y A370644 A367903 counts non-choosable set-systems, ranks A367907, unlabeled A368094.
%Y A370644 A370585 counts maximal choosable sets.
%Y A370644 Cf. A072639, A140637, A326031, A355529, A367905, A368109, A370589, A370591, A370636, A370639, A370640.
%K A370644 nonn,more
%O A370644 0,7
%A A370644 _Gus Wiseman_, Mar 11 2024