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A366317
Number of unordered pairs of strict integer partitions of n.
2
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
0,4
FORMULA
a(n) = A000217(A000009(n)).
Composition of A000009 and A000217.
EXAMPLE
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}
MATHEMATICA
Table[Length[Select[Tuples[Select[IntegerPartitions[n], UnsameQ@@#&], 2], OrderedQ]], {n, 0, 30}]
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.
Sequence in context: A374689 A266137 A265506 * A300301 A031504 A298164
KEYWORD
nonn
AUTHOR
Gus Wiseman, Oct 08 2023
STATUS
approved