cp's OEIS Frontend

A366132 Number of unordered pairs of distinct strict integer partitions of n.

%I A366132 #7 Oct 08 2023 23:32:00
%S A366132 0,0,0,1,1,3,6,10,15,28,45,66,105,153,231,351,496,703,1035,1431,2016,
%T A366132 2850,3916,5356,7381,10011,13530,18336,24531,32640,43660,57630,75855,
%U A366132 100128,130816,170820,222778,288420,372816,481671,618828,793170,1016025,1295245
%N A366132 Number of unordered pairs of distinct strict integer partitions of n.
%F A366132 a(n) = binomial(A000009(n),2).
%e A366132 The a(3) = 1 through a(8) = 15 pairs of strict partitions:
%e A366132   {3,21}  {4,31}  {5,32}   {6,42}    {7,43}    {8,53}
%e A366132                   {5,41}   {6,51}    {7,52}    {8,62}
%e A366132                   {41,32}  {51,42}   {7,61}    {8,71}
%e A366132                            {6,321}   {52,43}   {62,53}
%e A366132                            {42,321}  {61,43}   {71,53}
%e A366132                            {51,321}  {61,52}   {71,62}
%e A366132                                      {7,421}   {8,431}
%e A366132                                      {43,421}  {8,521}
%e A366132                                      {52,421}  {53,431}
%e A366132                                      {61,421}  {53,521}
%e A366132                                                {62,431}
%e A366132                                                {62,521}
%e A366132                                                {71,431}
%e A366132                                                {71,521}
%e A366132                                                {521,431}
%t A366132 Table[Length[Subsets[Select[IntegerPartitions[n],UnsameQ@@#&],{2}]],{n,0,30}]
%Y A366132 For subsets instead of partitions we have A006516, non-disjoint A003462.
%Y A366132 The disjoint case is A108796, non-strict A260669.
%Y A366132 For non-strict partitions we have A355389.
%Y A366132 The ordered disjoint case is A365662, non-strict A054440.
%Y A366132 The ordered version is 2*a(n).
%Y A366132 Including equal pairs or twins gives A366317, ordered A304990.
%Y A366132 A000041 counts integer partitions, strict A000009.
%Y A366132 A002219 and A237258 count partitions of 2n including a partition of n.
%Y A366132 A161680 and A000217 count 2-subsets of {1..n}.
%Y A366132 Cf. A000124, A001255, A006827, A032302, A064914, A365661, A365663.
%K A366132 nonn
%O A366132 0,6
%A A366132 _Gus Wiseman_, Oct 08 2023