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A361849
Number of integer partitions of n such that the maximum is twice the median.
24
0, 0, 0, 1, 1, 1, 4, 3, 4, 7, 9, 9, 15, 16, 20, 26, 34, 37, 50, 55, 68, 86, 103, 117, 145, 168, 201, 236, 282, 324, 391, 449, 525, 612, 712, 818, 962, 1106, 1278, 1470, 1698, 1939, 2238, 2550, 2924, 3343, 3824, 4341, 4963, 5627, 6399, 7256, 8231, 9300
OFFSET
1,7
COMMENTS
The median of a multiset is either the middle part (for odd length), or the average of the two middle parts (for even length).
EXAMPLE
The a(4) = 1 through a(11) = 9 partitions:
211 2111 21111 421 422 4221 631 632
3211 221111 4311 4222 5321
22111 2111111 2211111 42211 5411
211111 21111111 322111 42221
2221111 43211
22111111 332111
211111111 22211111
221111111
2111111111
For example, the partition (3,2,1,1) has maximum 3 and median 3/2, so is counted under a(7).
MATHEMATICA
Table[Length[Select[IntegerPartitions[n], Max@@#==2*Median[#]&]], {n, 30}]
CROSSREFS
For minimum instead of median we have A118096.
For length instead of median we have A237753.
This is the equal case of A361848.
For mean instead of median we have A361853.
These partitions have ranks A361856.
For "greater" instead of "equal" we have A361857, allowing equality A361859.
A000041 counts integer partitions, strict A000009.
A008284 counts partitions by length, A058398 by mean.
A325347 counts partitions with integer median, complement A307683.
A359893 and A359901 count partitions by median, odd-length A359902.
A360005 gives twice median of prime indices, distinct A360457.
A361860 counts partitions with minimum equal to median.
Sequence in context: A021027 A289672 A359864 * A339409 A075246 A257840
KEYWORD
nonn
AUTHOR
Gus Wiseman, Apr 02 2023
STATUS
approved