cp's OEIS Frontend

A384391 Number of subsets of {1..n} containing n and some element that is a sum of distinct non-elements.

%I A384391 #4 Jun 06 2025 08:33:32
%S A384391 0,0,1,3,9,20,48,102,219,454,945,1920,3925,7921,16008
%N A384391 Number of subsets of {1..n} containing n and some element that is a sum of distinct non-elements.
%e A384391 The a(0) = 0 through a(6) = 20 subsets:
%e A384391   .  .  .  {3}  {4}    {5}      {6}
%e A384391                 {2,4}  {1,5}    {1,6}
%e A384391                 {3,4}  {2,5}    {2,6}
%e A384391                        {3,5}    {3,6}
%e A384391                        {4,5}    {4,6}
%e A384391                        {1,4,5}  {5,6}
%e A384391                        {2,3,5}  {1,3,6}
%e A384391                        {2,4,5}  {1,5,6}
%e A384391                        {3,4,5}  {2,3,6}
%e A384391                                 {2,4,6}
%e A384391                                 {2,5,6}
%e A384391                                 {3,4,6}
%e A384391                                 {3,5,6}
%e A384391                                 {4,5,6}
%e A384391                                 {1,3,5,6}
%e A384391                                 {1,4,5,6}
%e A384391                                 {2,3,4,6}
%e A384391                                 {2,3,5,6}
%e A384391                                 {2,4,5,6}
%e A384391                                 {3,4,5,6}
%t A384391 nonsets[y_]:=If[Length[y]==0,{},Rest[Subsets[Complement[Range[Max@@y],y]]]];
%t A384391 Table[Length[Select[Subsets[Range[n]],MemberQ[#,n]&&Intersection[#,Total/@nonsets[#]]!={}&]],{n,0,10}]
%Y A384391 The complement with n is counted by A179822, first differences of A326080.
%Y A384391 Partial sums are A384350.
%Y A384391 A048767 is the Look-and-Say transform, fixed points A048768, counted by A217605.
%Y A384391 A179009 counts maximally refined strict partitions, ranks A383707.
%Y A384391 A239455 counts Look-and-Say or section-sum partitions, ranks A351294 or A381432.
%Y A384391 A351293 counts non-Look-and-Say or non-section-sum partitions, ranks A351295 or A381433.
%Y A384391 A383706 counts ways to choose disjoint strict partitions of prime indices, non-disjoint A357982, non-strict A299200.
%Y A384391 Cf. A279375, A279790, A317141, A317142, A326083, A383708, A383710, A384317, A384318, A384319, A384320, A384321.
%K A384391 nonn,more
%O A384391 0,4
%A A384391 _Gus Wiseman_, Jun 06 2025