OFFSET
0,11
EXAMPLE
The two-element submultisets of y = {1,1,1,2,2,3} are {1,1}, {1,2}, {1,3}, {2,2}, {2,3}, with sums 2, 3, 4, 4, 5, which are not all different, so y is counted under a(10).
The a(8) = 1 through a(13) = 11 partitions:
(3221) (32211) (4321) (33221) (4332) (43321)
(32221) (43211) (5331) (53221)
(322111) (322211) (5421) (53311)
(3221111) (43221) (54211)
(322221) (332221)
(332211) (432211)
(432111) (3222211)
(3222111) (3322111)
(32211111) (4321111)
(32221111)
(322111111)
MATHEMATICA
Table[Length[Select[IntegerPartitions[n], !UnsameQ@@Total/@Union[Subsets[#, {2}]]&]], {n, 0, 30}]
CROSSREFS
These partitions have ranks A366740.
KEYWORD
nonn
AUTHOR
Gus Wiseman, Nov 07 2023
STATUS
approved