A371790 Number of non-quanimous subsets of {1..n} containing n, meaning there is only one set partition with equal block-sums.

1, 2, 3, 6, 11, 21, 40, 77, 144, 279, 517, 1004, 1882, 3635, 6912, 13223, 25163, 48927, 93770, 182765, 355226, 688259, 1333939, 2617253, 5109865, 10012410, 19624287, 38356485, 74987607, 147268359

Offset: 1

Author

Gus Wiseman, Apr 17 2024

Keywords

• nonn
• more

Examples

			The set s = {3,4,6,8,9} has set partitions {{3,4,6,8,9}} and {{3,4,8},{6,9}} with equal block-sums, so s is not counted under a(9).
The a(1) = 1 through a(5) = 11 subsets:
  {1}  {2}    {3}    {4}      {5}
       {1,2}  {1,3}  {1,4}    {1,5}
              {2,3}  {2,4}    {2,5}
                     {3,4}    {3,5}
                     {1,2,4}  {4,5}
                     {2,3,4}  {1,2,5}
                              {1,3,5}
                              {2,4,5}
                              {3,4,5}
                              {1,2,3,5}
                              {1,3,4,5}
		

Crossrefs

First differences of A371789, complement counted by A371796.

The "bi-" version is A371793, complement A232466.

The complement is counted by A371797.

A371736 counts non-quanimous strict partitions.

A371737 counts quanimous strict partitions.

A371783 counts k-quanimous partitions.

A371791 counts biquanimous subsets, complement A371792.

Cf. A002219, A035470, A038041, A275972, A316402, A321451, A321452.

Programs

Mathematica

sps[{}]:={{}};sps[set:{i_,_}]:=Join@@Function[s,Prepend[#,s]& /@ sps[Complement[set,s]]]/@Cases[Subsets[set],{i,_}];
Table[Length[Select[Subsets[Range[n]], MemberQ[#,n]&&Length[Select[sps[#],SameQ@@Total/@#&]]==1&]],{n,10}]

Extensions

a(11)-a(30) from Martin Fuller, Apr 01 2025