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A316400
Number of strict integer partitions of n that are knapsack (every subset has a different sum) but not every subset has a different average.
3
0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 4, 1, 2, 4, 6, 4, 13, 6, 13, 17, 15, 12, 31, 26, 27, 23, 36, 41, 56, 39, 47, 74, 71, 55, 101, 94, 110, 97, 145, 148, 189, 142, 214, 232, 280, 206, 362, 332, 414, 347, 504, 469, 658, 492, 726, 697, 867, 687, 1100, 933
OFFSET
1,9
EXAMPLE
The a(21) = 13 partitions:
(8,7,6), (9,7,5), (10,7,4), (11,7,3), (12,7,2), (13,7,1),
(7,6,5,3), (8,6,4,3), (9,7,4,1), (10,6,3,2), (11,6,3,1), (12,4,3,2), (12,5,3,1).
MATHEMATICA
Table[Length[Select[IntegerPartitions[n], UnsameQ@@#&&UnsameQ@@Total/@Union[Subsets[#]]&&!UnsameQ@@Mean/@Union[Subsets[#]]&]], {n, 20}]
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jul 01 2018
STATUS
approved