A316399 Number of strict integer partitions of n such that not every subset has a different average.

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, 133, 136, 176, 191, 252, 274, 332, 363, 475, 503, 602, 677, 832, 893, 1067, 1186, 1418, 1561, 1797, 2000, 2384, 2602, 2992, 3315, 3853, 4226, 4826, 5383, 6121, 6763

Offset

1,9

Links

Table of n, a(n) for n=1..57.

Formula

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

Example

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

Mathematica

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

Crossrefs

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

Sequence in context: A182930 A232187 A076241 * A139347 A288620 A263324

Adjacent sequences: A316396 A316397 A316398 * A316400 A316401 A316402

Keyword

nonn

Author

Gus Wiseman, Jul 01 2018

Status

approved