login
A366132
Number of unordered pairs of distinct strict integer partitions of n.
2
0, 0, 0, 1, 1, 3, 6, 10, 15, 28, 45, 66, 105, 153, 231, 351, 496, 703, 1035, 1431, 2016, 2850, 3916, 5356, 7381, 10011, 13530, 18336, 24531, 32640, 43660, 57630, 75855, 100128, 130816, 170820, 222778, 288420, 372816, 481671, 618828, 793170, 1016025, 1295245
OFFSET
0,6
FORMULA
a(n) = binomial(A000009(n),2).
EXAMPLE
The a(3) = 1 through a(8) = 15 pairs of strict partitions:
{3,21} {4,31} {5,32} {6,42} {7,43} {8,53}
{5,41} {6,51} {7,52} {8,62}
{41,32} {51,42} {7,61} {8,71}
{6,321} {52,43} {62,53}
{42,321} {61,43} {71,53}
{51,321} {61,52} {71,62}
{7,421} {8,431}
{43,421} {8,521}
{52,421} {53,431}
{61,421} {53,521}
{62,431}
{62,521}
{71,431}
{71,521}
{521,431}
MATHEMATICA
Table[Length[Subsets[Select[IntegerPartitions[n], UnsameQ@@#&], {2}]], {n, 0, 30}]
CROSSREFS
For subsets instead of partitions we have A006516, non-disjoint A003462.
The disjoint case is A108796, non-strict A260669.
For non-strict partitions we have A355389.
The ordered disjoint case is A365662, non-strict A054440.
The ordered version is 2*a(n).
Including equal pairs or twins gives A366317, ordered A304990.
A000041 counts integer partitions, strict A000009.
A002219 and A237258 count partitions of 2n including a partition of n.
A161680 and A000217 count 2-subsets of {1..n}.
Sequence in context: A360893 A365696 A346734 * A230364 A214282 A130200
KEYWORD
nonn
AUTHOR
Gus Wiseman, Oct 08 2023
STATUS
approved