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

Offset

1,2

Links

Table of n, a(n) for n=1..10.

Example

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}

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}]

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.

Sequence in context: A079116 A109222 A191789 * A306575 A006861 A052956

Adjacent sequences: A371787 A371788 A371789 * A371791 A371792 A371793

Keyword

nonn,more

Author

Gus Wiseman, Apr 17 2024

Status

approved