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A359900
Number of strict odd-length integer partitions of n whose parts do not have the same mean as median.
12
0, 0, 0, 0, 0, 0, 0, 1, 2, 1, 4, 5, 4, 8, 10, 8, 15, 18, 17, 26, 27, 31, 43, 51, 53, 59, 81, 87, 109, 127, 115, 169, 194, 213, 255, 243, 322, 379, 431, 478, 487, 629, 667, 804, 907, 902, 1151, 1294, 1439, 1530, 1674, 2031, 2290, 2559, 2829, 2973, 3296, 3939
OFFSET
0,9
EXAMPLE
The a(7) = 1 through a(16) = 15 partitions (A=10, B=11, C=12, D=13):
(421) (431) (621) (532) (542) (651) (643) (653) (762) (754)
(521) (541) (632) (732) (652) (743) (843) (763)
(631) (641) (831) (742) (752) (861) (853)
(721) (731) (921) (751) (761) (942) (862)
(821) (832) (842) (A32) (871)
(841) (851) (A41) (943)
(931) (932) (B31) (952)
(A21) (941) (C21) (961)
(A31) (A42)
(B21) (A51)
(B32)
(B41)
(C31)
(D21)
(64321)
MATHEMATICA
Table[Length[Select[IntegerPartitions[n], UnsameQ@@#&&OddQ[Length[#]]&&Mean[#]!=Median[#]&]], {n, 0, 30}]
CROSSREFS
This is the strict case of A359896, complement A359895, ranked by A359892.
This is the odd-length case of A359898, complement A359897.
The complement is counted by A359899.
A000041 counts partitions, strict A000009.
A008284/A058398/A327482 count partitions by mean, ranked by A326567/A326568.
A008289 counts strict partitions by mean.
A027193 counts odd-length partitions, strict A067659, ranked by A026424.
A359893/A359901/A359902 count partitions by median, ranked by A360005.
Sequence in context: A047949 A222986 A222906 * A323955 A197011 A326060
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jan 21 2023
STATUS
approved