A316399 - OEIS

%I #5 Jul 01 2018 21:18:09

%S 0,0,0,0,0,1,0,0,2,1,1,5,3,5,9,10,10,20,20,27,32,39,43,69,65,83,99,

%T 133,136,176,191,252,274,332,363,475,503,602,677,832,893,1067,1186,

%U 1418,1561,1797,2000,2384,2602,2992,3315,3853,4226,4826,5383,6121,6763

%N Number of strict integer partitions of n such that not every subset has a different average.

%F a(n) = A000009(n) - A316313(n).

%e The a(12) = 5 partitions are (5,4,3), (6,4,2), (7,4,1), (5,4,2,1), (6,3,2,1).

%t Table[Length[Select[IntegerPartitions[n],UnsameQ@@#&&!UnsameQ@@Mean/@Union[Subsets[#]]&]],{n,60}]

%Y Cf. A000009, A108917, A275972, A276024, A284640, A299702, A301899, A301900, A316271, A316313, A316314, A316400, A316402.

%K nonn

%O 1,9

%A _Gus Wiseman_, Jul 01 2018