login
A359897
Number of strict integer partitions of n whose parts have the same mean as median.
21
0, 1, 1, 2, 2, 3, 4, 4, 4, 7, 6, 6, 10, 7, 10, 13, 11, 9, 20, 10, 20, 18, 21, 12, 30, 24, 28, 27, 30, 15, 73, 16, 37, 43, 45, 67, 74, 19, 55, 71, 126, 21, 150, 22, 75, 225, 78, 24, 183, 126, 245, 192, 132, 27, 284, 244, 403, 303, 120, 30, 828
OFFSET
0,4
EXAMPLE
The a(1) = 1 through a(9) = 7 partitions:
(1) (2) (3) (4) (5) (6) (7) (8) (9)
(2,1) (3,1) (3,2) (4,2) (4,3) (5,3) (5,4)
(4,1) (5,1) (5,2) (6,2) (6,3)
(3,2,1) (6,1) (7,1) (7,2)
(8,1)
(4,3,2)
(5,3,1)
MATHEMATICA
Table[Length[Select[IntegerPartitions[n], UnsameQ@@#&&Mean[#]==Median[#]&]], {n, 0, 30}]
CROSSREFS
The non-strict version is A240219, complement A359894, ranked by A359889.
The complement is counted by A359898.
The odd-length case is A359899, complement A359900.
A000041 counts partitions, strict A000009.
A008284/A058398/A327482 count partitions by mean, ranked by A326567/A326568.
A008289 counts strict partitions by mean.
A237984 counts partitions containing their mean, complement A327472.
A240850 counts strict partitions containing their mean, complement A240851.
A325347 counts ptns with integer median, strict A359907, ranked by A359908.
Sequence in context: A210556 A208914 A049980 * A209698 A141525 A209764
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jan 20 2023
STATUS
approved