cp's OEIS Frontend

A359898 Number of strict integer partitions of n whose parts do not have the same mean as median.

%I A359898 #7 Jan 21 2023 16:28:27
%S A359898 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 A359898 137,165,192,241,223,324,353,405,467,518,594,741,809,911,987,1239,
%U A359898 1276,1588,1741,1823,2226,2566,2727,3138,3413,3905,4450,5093,5434,6134
%N A359898 Number of strict integer partitions of n whose parts do not have the same mean as median.
%e A359898 The a(7) = 1 through a(13) = 11 partitions:
%e A359898   (4,2,1)  (4,3,1)  (6,2,1)  (5,3,2)  (5,4,2)    (6,5,1)    (6,4,3)
%e A359898            (5,2,1)           (5,4,1)  (6,3,2)    (7,3,2)    (6,5,2)
%e A359898                              (6,3,1)  (6,4,1)    (8,3,1)    (7,4,2)
%e A359898                              (7,2,1)  (7,3,1)    (9,2,1)    (7,5,1)
%e A359898                                       (8,2,1)    (6,3,2,1)  (8,3,2)
%e A359898                                       (5,3,2,1)             (8,4,1)
%e A359898                                                             (9,3,1)
%e A359898                                                             (10,2,1)
%e A359898                                                             (5,4,3,1)
%e A359898                                                             (6,4,2,1)
%e A359898                                                             (7,3,2,1)
%t A359898 Table[Length[Select[IntegerPartitions[n], UnsameQ@@#&&Mean[#]!=Median[#]&]],{n,0,30}]
%Y A359898 The non-strict version is ranked by A359890, complement A359889.
%Y A359898 The non-strict version is A359894, complement A240219.
%Y A359898 The complement is counted by A359897.
%Y A359898 The odd-length case is A359900, complement A359899.
%Y A359898 A000041 counts partitions, strict A000009.
%Y A359898 A008284/A058398/A327482 count partitions by mean, ranked by A326567/A326568.
%Y A359898 A008289 counts strict partitions by mean.
%Y A359898 A067538 counts ptns with integer mean, strict A102627, ranked by A316413.
%Y A359898 A237984 counts ptns containing their mean, strict A240850, ranked by A327473.
%Y A359898 A325347 counts ptns with integer median, strict A359907, ranked by A359908.
%Y A359898 A359893 and A359901 count partitions by median, odd-length A359902.
%Y A359898 Cf. A000016, A065795, A066571, A082550, A135342, A240851, A327475, A327482, A328966, A359906.
%K A359898 nonn
%O A359898 0,9
%A A359898 _Gus Wiseman_, Jan 20 2023