A366317 Number of unordered pairs of strict integer partitions of n.

1, 1, 1, 3, 3, 6, 10, 15, 21, 36, 55, 78, 120, 171, 253, 378, 528, 741, 1081, 1485, 2080, 2926, 4005, 5460, 7503, 10153, 13695, 18528, 24753, 32896, 43956, 57970, 76245, 100576, 131328, 171405, 223446, 289180, 373680, 482653, 619941, 794430, 1017451, 1296855

Offset: 0

Author

Gus Wiseman, Oct 08 2023

Keywords

• nonn

Examples

			The a(1) = 1 through a(7) = 15 unordered pairs of strict partitions:
  {1,1}  {2,2}  {3,3}    {4,4}    {5,5}    {6,6}      {7,7}
                {3,21}   {4,31}   {5,32}   {6,42}     {7,43}
                {21,21}  {31,31}  {5,41}   {6,51}     {7,52}
                                  {32,32}  {42,42}    {7,61}
                                  {32,41}  {42,51}    {43,43}
                                  {41,41}  {51,51}    {43,52}
                                           {6,321}    {43,61}
                                           {42,321}   {52,52}
                                           {51,321}   {52,61}
                                           {321,321}  {61,61}
                                                      {7,421}
                                                      {43,421}
                                                      {52,421}
                                                      {61,421}
                                                      {421,421}
		

Crossrefs

For non-strict partitions we have A086737.

The disjoint case is A108796, non-strict A260669.

The ordered version is A304990, disjoint A032302.

The ordered disjoint case is A365662.

Excluding constant pairs gives A366132.

A000041 counts integer partitions, strict A000009.

A002219 and A237258 count partitions of 2n including a partition of n.

A364272 counts sum-full strict partitions, sum-free A364349.

Cf. A000712, A007582, A054440, A064914, A260664.

Programs

Mathematica

Table[Length[Select[Tuples[Select[IntegerPartitions[n], UnsameQ@@#&],2],OrderedQ]],{n,0,30}]

Formula

a(n) = A000217(A000009(n)).

Composition of A000009 and A000217.