

A316313


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


28



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

Cf. A000009, A108917, A275972, A276024, A284640, A299702, A301899, A301900, A316271, A316314.
Sequence in context: A262365 A063988 A198453 * A325876 A325468 A320347
Adjacent sequences: A316310 A316311 A316312 * A316314 A316315 A316316


KEYWORD

nonn


AUTHOR

Gus Wiseman, Jun 29 2018


STATUS

approved



