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A316313
Number of integer partitions of n such that every distinct submultiset has a different average.
45
1, 1, 2, 2, 3, 3, 5, 6, 6, 9, 11, 10, 15, 17, 18, 22, 28, 26, 34, 37, 44, 50, 61, 53, 77, 82, 93, 89, 120, 120, 149, 138, 174, 180, 222, 193, 257, 262, 305, 281, 367, 359, 424, 398, 487, 507, 590, 526, 662, 666, 782, 729, 894, 892, 995, 987, 1154, 1188, 1370
OFFSET
1,3
COMMENTS
Note that such a partition is necessarily strict.
EXAMPLE
The a(8) = 6 integer partitions are (8), (71), (62), (53), (521), (431).
MATHEMATICA
Table[Length[Select[IntegerPartitions[n], UnsameQ@@Mean/@Union[Subsets[#]]&]], {n, 20}]
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jun 29 2018
STATUS
approved