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A364753 Number of subsets of {1..n} containing n but not containing all first differences.

%I A364753 #10 Aug 07 2023 11:32:47
%S A364753 0,0,0,2,4,12,23,53,104,218,437,893,1785,3620,7264,14634,29382,59097,
%T A364753 118617,238291,478191,959867,1925681,3863365,7748136,15538461,
%U A364753 31154278,62458007,125194936,250924636,502855774,1007635332,2018912085,4044775367,8102759211,16230735448,32509514412,65110826347
%N A364753 Number of subsets of {1..n} containing n but not containing all first differences.
%C A364753 In other words, subsets containing both n and some element that is not the difference of two consecutive elements.
%e A364753 The a(1) = 0 through a(6) = 23 subsets:
%e A364753   .  .  {1,3}  {1,4}    {1,5}      {1,6}
%e A364753         {2,3}  {3,4}    {2,5}      {2,6}
%e A364753                {1,3,4}  {3,5}      {4,6}
%e A364753                {2,3,4}  {4,5}      {5,6}
%e A364753                         {1,2,5}    {1,2,6}
%e A364753                         {1,3,5}    {1,3,6}
%e A364753                         {1,4,5}    {1,4,6}
%e A364753                         {2,3,5}    {1,5,6}
%e A364753                         {2,4,5}    {2,3,6}
%e A364753                         {3,4,5}    {2,5,6}
%e A364753                         {1,3,4,5}  {3,4,6}
%e A364753                         {2,3,4,5}  {3,5,6}
%e A364753                                    {4,5,6}
%e A364753                                    {1,2,5,6}
%e A364753                                    {1,3,4,6}
%e A364753                                    {1,3,5,6}
%e A364753                                    {1,4,5,6}
%e A364753                                    {2,3,4,6}
%e A364753                                    {2,3,5,6}
%e A364753                                    {2,4,5,6}
%e A364753                                    {3,4,5,6}
%e A364753                                    {1,3,4,5,6}
%e A364753                                    {2,3,4,5,6}
%t A364753 Table[Length[Select[Subsets[Range[n]],MemberQ[#,n]&&!SubsetQ[#,Differences[#]]&]],{n,0,10}]
%Y A364753 Partial sums are A364672, complement A364671.
%Y A364753 The complement is counted by A364752.
%Y A364753 A054519 counts subsets containing differences, A326083 containing sums.
%Y A364753 A364463 counts subsets disjoint from differences, complement A364466.
%Y A364753 A364673, A364674, A364675 count partitions containing differences.
%Y A364753 Cf. A151897, A196723, A237668, A325325, A364345, A364464, A364537.
%K A364753 nonn
%O A364753 0,4
%A A364753 _Gus Wiseman_, Aug 06 2023
%E A364753 More terms from _Giorgos Kalogeropoulos_, Aug 07 2023