cp's OEIS Frontend

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

%I A366317 #9 Oct 09 2023 12:58:23
%S A366317 1,1,1,3,3,6,10,15,21,36,55,78,120,171,253,378,528,741,1081,1485,2080,
%T A366317 2926,4005,5460,7503,10153,13695,18528,24753,32896,43956,57970,76245,
%U A366317 100576,131328,171405,223446,289180,373680,482653,619941,794430,1017451,1296855
%N A366317 Number of unordered pairs of strict integer partitions of n.
%F A366317 a(n) = A000217(A000009(n)).
%F A366317 Composition of A000009 and A000217.
%e A366317 The a(1) = 1 through a(7) = 15 unordered pairs of strict partitions:
%e A366317   {1,1}  {2,2}  {3,3}    {4,4}    {5,5}    {6,6}      {7,7}
%e A366317                 {3,21}   {4,31}   {5,32}   {6,42}     {7,43}
%e A366317                 {21,21}  {31,31}  {5,41}   {6,51}     {7,52}
%e A366317                                   {32,32}  {42,42}    {7,61}
%e A366317                                   {32,41}  {42,51}    {43,43}
%e A366317                                   {41,41}  {51,51}    {43,52}
%e A366317                                            {6,321}    {43,61}
%e A366317                                            {42,321}   {52,52}
%e A366317                                            {51,321}   {52,61}
%e A366317                                            {321,321}  {61,61}
%e A366317                                                       {7,421}
%e A366317                                                       {43,421}
%e A366317                                                       {52,421}
%e A366317                                                       {61,421}
%e A366317                                                       {421,421}
%t A366317 Table[Length[Select[Tuples[Select[IntegerPartitions[n], UnsameQ@@#&],2],OrderedQ]],{n,0,30}]
%Y A366317 For non-strict partitions we have A086737.
%Y A366317 The disjoint case is A108796, non-strict A260669.
%Y A366317 The ordered version is A304990, disjoint A032302.
%Y A366317 The ordered disjoint case is A365662.
%Y A366317 Excluding constant pairs gives A366132.
%Y A366317 A000041 counts integer partitions, strict A000009.
%Y A366317 A002219 and A237258 count partitions of 2n including a partition of n.
%Y A366317 A364272 counts sum-full strict partitions, sum-free A364349.
%Y A366317 Cf. A000712, A007582, A054440, A064914, A260664.
%K A366317 nonn
%O A366317 0,4
%A A366317 _Gus Wiseman_, Oct 08 2023