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A365662
Number of ordered pairs of disjoint strict integer partitions of n.
3
1, 0, 0, 2, 2, 6, 8, 14, 18, 32, 42, 66, 92, 136, 190, 280, 374, 532, 744, 1014, 1366, 1896, 2512, 3384, 4526, 6006, 7910, 10496, 13648, 17842, 23338, 30116, 38826, 50256, 64298, 82258, 105156, 133480, 169392, 214778, 270620, 340554, 428772, 536302, 670522
OFFSET
0,4
COMMENTS
Also the number of ways to first choose a strict partition of 2n, then a subset of it summing to n.
FORMULA
a(n) = 2*A108796(n) for n > 1.
EXAMPLE
The a(0) = 1 through a(7) = 14 pairs:
()() . . (21)(3) (31)(4) (32)(5) (42)(6) (43)(7)
(3)(21) (4)(31) (41)(5) (51)(6) (52)(7)
(5)(32) (6)(42) (61)(7)
(5)(41) (6)(51) (7)(43)
(32)(41) (321)(6) (7)(52)
(41)(32) (42)(51) (7)(61)
(51)(42) (421)(7)
(6)(321) (43)(52)
(43)(61)
(52)(43)
(52)(61)
(61)(43)
(61)(52)
(7)(421)
MATHEMATICA
Table[Length[Select[Tuples[Select[IntegerPartitions[n], UnsameQ@@#&], 2], Intersection@@#=={}&]], {n, 0, 15}]
CROSSREFS
For subsets instead of partitions we have A000244, non-disjoint A000302.
If the partitions can have different sums we get A032302.
The non-strict version is A054440, non-disjoint A001255.
The unordered version is A108796, non-strict A260669.
A000041 counts integer partitions, strict A000009.
A000124 counts distinct possible sums of subsets of {1..n}.
A000712 counts distinct submultisets of partitions.
A002219 and A237258 count partitions of 2n including a partition of n.
A304792 counts subset-sums of partitions, positive A276024, strict A284640.
A364272 counts sum-full strict partitions, sum-free A364349.
Sequence in context: A248823 A284616 A136513 * A214932 A322132 A054153
KEYWORD
nonn
AUTHOR
Gus Wiseman, Sep 19 2023
STATUS
approved