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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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,9 LINKS 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}] CROSSREFS Cf. A000009, A108917, A275972, A299702, A301899, A301900, A316271, A316313, A316314, A316399, A316401. Sequence in context: A307985 A024164 A138805 * A061897 A047919 A272624 Adjacent sequences:  A316397 A316398 A316399 * A316401 A316402 A316403 KEYWORD nonn AUTHOR Gus Wiseman, Jul 01 2018 STATUS approved

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Last modified March 30 09:13 EDT 2020. Contains 333125 sequences. (Running on oeis4.)