cp's OEIS Frontend

A359896 Number of odd-length integer partitions of n whose parts do not have the same mean as median.

%I A359896 #7 Jan 21 2023 16:28:35
%S A359896 0,0,0,0,1,2,2,6,9,11,15,27,32,50,58,72,112,149,171,246,286,359,477,
%T A359896 630,773,941,1181,1418,1749,2289,2668,3429,4162,4878,6074,7091,8590,
%U A359896 10834,12891,15180,18491,22314,25845,31657,36394,42269,52547,62414,73576,85701
%N A359896 Number of odd-length integer partitions of n whose parts do not have the same mean as median.
%e A359896 The a(4) = 1 through a(9) = 11 partitions:
%e A359896   (211)  (221)  (411)    (322)    (332)      (441)
%e A359896          (311)  (21111)  (331)    (422)      (522)
%e A359896                          (421)    (431)      (621)
%e A359896                          (511)    (521)      (711)
%e A359896                          (22111)  (611)      (22221)
%e A359896                          (31111)  (22211)    (32211)
%e A359896                                   (32111)    (33111)
%e A359896                                   (41111)    (42111)
%e A359896                                   (2111111)  (51111)
%e A359896                                              (2211111)
%e A359896                                              (3111111)
%t A359896 Table[Length[Select[IntegerPartitions[n], OddQ[Length[#]]&&Mean[#]!=Median[#]&]],{n,0,30}]
%Y A359896 These partitions are ranked by A359892.
%Y A359896 The any-length version is A359894, complement A240219, strict A359898.
%Y A359896 The complement is counted by A359895, ranked by A359891.
%Y A359896 The strict case is A359900, complement A359899.
%Y A359896 A000041 counts partitions, strict A000009.
%Y A359896 A008284/A058398/A327482 count partitions by mean, ranked by A326567/A326568.
%Y A359896 A027193 counts odd-length partitions, strict A067659, ranked by A026424.
%Y A359896 A067538 counts ptns with integer mean, strict A102627, ranked by A316413.
%Y A359896 A237984 counts ptns containing their mean, strict A240850, ranked by A327473.
%Y A359896 A325347 counts ptns with integer median, strict A359907, ranked by A359908.
%Y A359896 A359893 and A359901 count partitions by median, odd-length A359902.
%Y A359896 Cf. A008289, A066571, A316313, A327472, A327482, A359890, A359906, A359910.
%K A359896 nonn
%O A359896 0,6
%A A359896 _Gus Wiseman_, Jan 20 2023