A359898 - OEIS

A359898

Number of strict integer partitions of n whose parts do not have the same mean as median.

%I #7 Jan 21 2023 16:28:27

%S 0,0,0,0,0,0,0,1,2,1,4,6,5,11,12,14,21,29,26,44,44,58,68,92,92,118,

%T 137,165,192,241,223,324,353,405,467,518,594,741,809,911,987,1239,

%U 1276,1588,1741,1823,2226,2566,2727,3138,3413,3905,4450,5093,5434,6134

%N Number of strict integer partitions of n whose parts do not have the same mean as median.

%e The a(7) = 1 through a(13) = 11 partitions:

%e (4,2,1) (4,3,1) (6,2,1) (5,3,2) (5,4,2) (6,5,1) (6,4,3)

%e (5,2,1) (5,4,1) (6,3,2) (7,3,2) (6,5,2)

%e (6,3,1) (6,4,1) (8,3,1) (7,4,2)

%e (7,2,1) (7,3,1) (9,2,1) (7,5,1)

%e (8,2,1) (6,3,2,1) (8,3,2)

%e (5,3,2,1) (8,4,1)

%e (9,3,1)

%e (10,2,1)

%e (5,4,3,1)

%e (6,4,2,1)

%e (7,3,2,1)

%t Table[Length[Select[IntegerPartitions[n], UnsameQ@@#&&Mean[#]!=Median[#]&]],{n,0,30}]

%Y The non-strict version is ranked by A359890, complement A359889.

%Y The non-strict version is A359894, complement A240219.

%Y The complement is counted by A359897.

%Y The odd-length case is A359900, complement A359899.

%Y A000041 counts partitions, strict A000009.

%Y A008284/A058398/A327482 count partitions by mean, ranked by A326567/A326568.

%Y A008289 counts strict partitions by mean.

%Y A067538 counts ptns with integer mean, strict A102627, ranked by A316413.

%Y A237984 counts ptns containing their mean, strict A240850, ranked by A327473.

%Y A325347 counts ptns with integer median, strict A359907, ranked by A359908.

%Y A359893 and A359901 count partitions by median, odd-length A359902.

%Y Cf. A000016, A065795, A066571, A082550, A135342, A240851, A327475, A327482, A328966, A359906.

%K nonn

%O 0,9

%A _Gus Wiseman_, Jan 20 2023