OFFSET
0,11
COMMENTS
First differs from A316402 at a(16) = 11 due to (7,5,3,1).
EXAMPLE
The a(6) = 1 through a(16) = 11 partitions (A=10):
(321) . (431) . (532) (5321) (642) (5431) (743) (6432) (853)
(541) (651) (6421) (752) (6531) (862)
(4321) (5421) (7321) (761) (7431) (871)
(6321) (5432) (7521) (6532)
(6431) (9321) (6541)
(6521) (54321) (7432)
(7421) (7621)
(8321) (8431)
(8521)
(A321)
(64321)
MATHEMATICA
Table[Length[Select[IntegerPartitions[n], UnsameQ@@#&&Intersection[#, Total/@Subsets[#, {2, Length[#]}]]!={}&]], {n, 0, 30}]
CROSSREFS
The linear combination-free version is A364350.
KEYWORD
nonn
AUTHOR
Gus Wiseman, Aug 01 2023
STATUS
approved