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A307683
Number of partitions of n having a non-integer median.
62
0, 0, 1, 0, 2, 1, 4, 1, 7, 5, 11, 8, 18, 17, 31, 28, 47, 51, 75, 81, 119, 134, 181, 206, 277, 323, 420, 488, 623, 737, 922, 1084, 1352, 1597, 1960, 2313, 2819, 3330, 4029, 4743, 5704, 6722, 8030, 9434, 11234, 13175, 15601, 18262, 21552, 25184, 29612, 34518
OFFSET
1,5
COMMENTS
This sequence and A325347 partition the partition numbers, A000041.
The median of a multiset is either the middle part (for odd length), or the average of the two middle parts (for even length). - Gus Wiseman, Mar 16 2023
LINKS
Fausto A. C. Cariboni, Table of n, a(n) for n = 1..180
EXAMPLE
a(7) counts these 4 partitions: [6,1], [5,2], [4,3], [3,2,1,1].
MATHEMATICA
Table[Count[IntegerPartitions[n], q_ /; !IntegerQ[Median[q]]], {n, 10}]
CROSSREFS
The complement is counted by A325347, strict A359907.
For mean instead of median we have A349156, strict A361391.
These partitions have ranks A359912, complement A359908.
The strict case is A360952.
A000041 counts integer partitions, strict A000009.
A008284/A058398/A327482 count partitions by mean.
A359893/A359901/A359902 count partitions by median.
Sequence in context: A097360 A360862 A325348 * A248058 A072345 A200583
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Apr 24 2019
STATUS
approved