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A361861
Number of integer partitions of n where the median is twice the minimum.
4
0, 0, 0, 1, 1, 1, 2, 5, 5, 8, 11, 16, 20, 28, 38, 53, 67, 87, 111, 146, 183, 236, 297, 379, 471, 591, 729, 909, 1116, 1376, 1682, 2065, 2507, 3055, 3699, 4482, 5395, 6501, 7790, 9345, 11153, 13316, 15839, 18844, 22333, 26466, 31266, 36924, 43478, 51177
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) = 11 partitions:
(31) (221) (321) (421) (62) (621) (442) (542)
(2221) (521) (4221) (721) (821)
(3221) (4311) (5221) (6221)
(3311) (22221) (5311) (6311)
(22211) (32211) (32221) (33221)
(33211) (42221)
(42211) (43211)
(222211) (52211)
(222221)
(322211)
(2222111)
The partition (3,2,2,2,1,1) has median 2 and minimum 1, so is counted under a(11).
The partition (5,4,2) has median 4 and minimum 2, so is counted under a(11).
MATHEMATICA
Table[Length[Select[IntegerPartitions[n], 2*Min@@#==Median[#]&]], {n, 30}]
CROSSREFS
For maximum instead of median we have A118096.
For length instead of median we have A237757, without the coefficient A006141.
With minimum instead of twice minimum we have A361860.
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.
Sequence in context: A076520 A014249 A168071 * A330447 A145420 A336257
KEYWORD
nonn
AUTHOR
Gus Wiseman, Apr 02 2023
STATUS
approved