A316401 - OEIS

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A316401

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

0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 1, 0, 3, 1, 3, 2, 4, 2, 6, 6, 11, 9, 9, 10, 20, 16, 18, 17, 27, 24, 31, 29, 43, 31, 43, 40, 59, 52, 58, 61, 83, 68, 93, 80, 124, 99, 120, 109, 145, 151, 185, 160, 232, 163, 257, 229, 314, 280, 286, 310, 427, 385, 513, 333, 596

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,10

LINKS

Table of n, a(n) for n=1..66.

EXAMPLE

The a(22) = 11 partitions:

(11,6,5), (11,7,4), (11,8,3), (11,9,2), (11,10,1),

(11,5,4,2), (11,6,3,2), (11,8,2,1), (12,5,3,2), (12,5,4,1), (14,4,3,1).

MATHEMATICA

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

CROSSREFS