%I #5 Jul 01 2018 21:18:18

%S 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,

%T 36,41,56,39,47,74,71,55,101,94,110,97,145,148,189,142,214,232,280,

%U 206,362,332,414,347,504,469,658,492,726,697,867,687,1100,933

%N Number of strict integer partitions of n that are knapsack (every subset has a different sum) but not every subset has a different average.

%e The a(21) = 13 partitions:

%e (8,7,6), (9,7,5), (10,7,4), (11,7,3), (12,7,2), (13,7,1),

%e (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).

%t Table[Length[Select[IntegerPartitions[n],UnsameQ@@#&&UnsameQ@@Total/@Union[Subsets[#]]&&!UnsameQ@@Mean/@Union[Subsets[#]]&]],{n,20}]

%Y Cf. A000009, A108917, A275972, A299702, A301899, A301900, A316271, A316313, A316314, A316399, A316401.

%K nonn

%O 1,9

%A _Gus Wiseman_, Jul 01 2018