A316313 - OEIS

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A316313

Number of integer partitions of n such that every distinct submultiset has a different average.

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

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OFFSET

1,3

COMMENTS

Note that such a partition is necessarily strict.

LINKS

Table of n, a(n) for n=1..59.

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}]

CROSSREFS