cp's OEIS Frontend

A359894 Number of integer partitions of n whose parts do not have the same mean as median.

%I A359894 #6 Jan 20 2023 18:08:05
%S A359894 0,0,0,0,1,3,3,10,13,20,28,49,53,93,113,145,203,287,329,479,556,724,
%T A359894 955,1242,1432,1889,2370,2863,3502,4549,5237,6825,8108,9839,12188,
%U A359894 14374,16958,21617,25852,30582,36100,44561,51462,63238,73386,85990,105272,124729
%N A359894 Number of integer partitions of n whose parts do not have the same mean as median.
%e A359894 The a(4) = 1 through a(8) = 13 partitions:
%e A359894   (211)  (221)   (411)    (322)     (332)
%e A359894          (311)   (3111)   (331)     (422)
%e A359894          (2111)  (21111)  (421)     (431)
%e A359894                           (511)     (521)
%e A359894                           (2221)    (611)
%e A359894                           (3211)    (4211)
%e A359894                           (4111)    (5111)
%e A359894                           (22111)   (22211)
%e A359894                           (31111)   (32111)
%e A359894                           (211111)  (41111)
%e A359894                                     (221111)
%e A359894                                     (311111)
%e A359894                                     (2111111)
%t A359894 Table[Length[Select[IntegerPartitions[n],Mean[#]!=Median[#]&]],{n,0,30}]
%Y A359894 The complement is counted by A240219.
%Y A359894 These partitions are ranked by A359890, complement A359889.
%Y A359894 The odd-length case is ranked by A359892, complement A359891.
%Y A359894 The odd-length case is A359896, complement A359895.
%Y A359894 The strict case is A359898, complement A359897.
%Y A359894 The odd-length strict case is A359900, complement A359899.
%Y A359894 A000041 counts partitions, strict A000009.
%Y A359894 A008284 and A058398 count partitions by mean, ranked by A326567/A326568.
%Y A359894 A008289 counts strict partitions by mean.
%Y A359894 A027193 counts odd-length partitions, strict A067659, ranked by A026424.
%Y A359894 A067538 counts ptns with integer mean, strict A102627, ranked by A316413.
%Y A359894 A237984 counts ptns containing their mean, strict A240850, ranked by A327473.
%Y A359894 A325347 counts ptns with integer median, strict A359907, ranked by A359908.
%Y A359894 A326622 counts factorizations with integer mean, strict A328966.
%Y A359894 A359893 and A359901 count partitions by median, odd-length A359902.
%Y A359894 A359909 counts factorizations with the same mean as median, odd-len A359910.
%Y A359894 Cf. A066571, A316313, A327472, A327482, A349156, A359906.
%K A359894 nonn
%O A359894 0,6
%A A359894 _Gus Wiseman_, Jan 20 2023