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A360952 Number of strict integer partitions of n with non-integer median; a(0) = 1. 7
1, 0, 0, 1, 0, 2, 0, 3, 0, 4, 1, 6, 1, 8, 4, 11, 5, 15, 10, 20, 13, 27, 22, 36, 28, 47, 43, 63, 56, 82, 79, 107, 103, 140, 141, 180, 181, 232, 242, 299, 308, 380, 402, 483, 511, 613, 656, 772, 824, 969, 1047, 1215, 1309, 1514, 1642, 1882, 2039, 2334, 2539, 2882 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,6
COMMENTS
All of these partitions have even length.
The median of a multiset is either the middle part (for odd length), or the average of the two middle parts (for even length).
LINKS
FORMULA
a(n) = A000009(n) - A359907(n).
EXAMPLE
The a(0) = 1 through a(15) = 11 partitions (0 = {}, A..E = 10..14):
0 . . 21 . 32 . 43 . 54 4321 65 6321 76 5432 87
41 52 63 74 85 6431 96
61 72 83 94 6521 A5
81 92 A3 8321 B4
A1 B2 C3
5321 C1 D2
5431 E1
7321 6432
7431
7521
9321
MATHEMATICA
Table[Length[Select[IntegerPartitions[n], UnsameQ@@#&&!IntegerQ[Median[#]]&]], {n, 0, 30}]
CROSSREFS
The non-strict version is A307683, ranks A359912.
The non-strict complement is A325347, ranks A359908.
The strict complement is counted by A359907.
For mean instead of median we have A361391, non-strict A349156.
A000041 counts partitions, strict A000009.
A008284/A058398/A327482 count partitions by mean.
A067538 = partitions with integer mean, complement A102627, ranks A316413.
A359893/A359901/A359902 count partitions by median.
A360005(n)/2 ranks the median statistic.
Sequence in context: A239241 A263395 A240139 * A008800 A274096 A318518
KEYWORD
nonn
AUTHOR
Gus Wiseman, Mar 10 2023
STATUS
approved

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Last modified April 19 19:02 EDT 2024. Contains 371798 sequences. (Running on oeis4.)