cp's OEIS Frontend

A359900 Number of strict odd-length integer partitions of n whose parts do not have the same mean as median.

%I A359900 #7 Jan 21 2023 09:33:25
%S A359900 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,
%T A359900 109,127,115,169,194,213,255,243,322,379,431,478,487,629,667,804,907,
%U A359900 902,1151,1294,1439,1530,1674,2031,2290,2559,2829,2973,3296,3939
%N A359900 Number of strict odd-length integer partitions of n whose parts do not have the same mean as median.
%e A359900 The a(7) = 1 through a(16) = 15 partitions (A=10, B=11, C=12, D=13):
%e A359900   (421)  (431)  (621)  (532)  (542)  (651)  (643)  (653)  (762)  (754)
%e A359900          (521)         (541)  (632)  (732)  (652)  (743)  (843)  (763)
%e A359900                        (631)  (641)  (831)  (742)  (752)  (861)  (853)
%e A359900                        (721)  (731)  (921)  (751)  (761)  (942)  (862)
%e A359900                               (821)         (832)  (842)  (A32)  (871)
%e A359900                                             (841)  (851)  (A41)  (943)
%e A359900                                             (931)  (932)  (B31)  (952)
%e A359900                                             (A21)  (941)  (C21)  (961)
%e A359900                                                    (A31)         (A42)
%e A359900                                                    (B21)         (A51)
%e A359900                                                                  (B32)
%e A359900                                                                  (B41)
%e A359900                                                                  (C31)
%e A359900                                                                  (D21)
%e A359900                                                                  (64321)
%t A359900 Table[Length[Select[IntegerPartitions[n], UnsameQ@@#&&OddQ[Length[#]]&&Mean[#]!=Median[#]&]],{n,0,30}]
%Y A359900 This is the strict case of A359896, complement A359895, ranked by A359892.
%Y A359900 This is the odd-length case of A359898, complement A359897.
%Y A359900 The complement is counted by A359899.
%Y A359900 A000041 counts partitions, strict A000009.
%Y A359900 A008284/A058398/A327482 count partitions by mean, ranked by A326567/A326568.
%Y A359900 A008289 counts strict partitions by mean.
%Y A359900 A027193 counts odd-length partitions, strict A067659, ranked by A026424.
%Y A359900 A359893/A359901/A359902 count partitions by median, ranked by A360005.
%Y A359900 Cf. A000016, A065795, A066571, A102627, A240850, A240851, A327475, A359894, A359906, A359907, A359910.
%K A359900 nonn
%O A359900 0,9
%A A359900 _Gus Wiseman_, Jan 21 2023