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

0, 0, 1, 3, 9, 20, 48, 102, 219, 454, 945, 1920, 3925, 7921, 16008

Offset: 0

Author

Gus Wiseman, Jun 06 2025

Keywords

• nonn
• more

Examples

			The a(0) = 0 through a(6) = 20 subsets:
  .  .  .  {3}  {4}    {5}      {6}
                {2,4}  {1,5}    {1,6}
                {3,4}  {2,5}    {2,6}
                       {3,5}    {3,6}
                       {4,5}    {4,6}
                       {1,4,5}  {5,6}
                       {2,3,5}  {1,3,6}
                       {2,4,5}  {1,5,6}
                       {3,4,5}  {2,3,6}
                                {2,4,6}
                                {2,5,6}
                                {3,4,6}
                                {3,5,6}
                                {4,5,6}
                                {1,3,5,6}
                                {1,4,5,6}
                                {2,3,4,6}
                                {2,3,5,6}
                                {2,4,5,6}
                                {3,4,5,6}
		

Crossrefs

The complement with n is counted by A179822, first differences of A326080.

Partial sums are A384350.

A048767 is the Look-and-Say transform, fixed points A048768, counted by A217605.

A179009 counts maximally refined strict partitions, ranks A383707.

A239455 counts Look-and-Say or section-sum partitions, ranks A351294 or A381432.

A351293 counts non-Look-and-Say or non-section-sum partitions, ranks A351295 or A381433.

A383706 counts ways to choose disjoint strict partitions of prime indices, non-disjoint A357982, non-strict A299200.

Cf. A279375, A279790, A317141, A317142, A326083, A383708, A383710, A384317, A384318, A384319, A384320, A384321.

Programs

Mathematica

nonsets[y_]:=If[Length[y]==0,{},Rest[Subsets[Complement[Range[Max@@y],y]]]];
Table[Length[Select[Subsets[Range[n]],MemberQ[#,n]&&Intersection[#,Total/@nonsets[#]]!={}&]],{n,0,10}]