cp's OEIS Frontend

A359897 Number of strict integer partitions of n whose parts have the same mean as median.

%I A359897 #6 Jan 21 2023 16:28:31
%S A359897 0,1,1,2,2,3,4,4,4,7,6,6,10,7,10,13,11,9,20,10,20,18,21,12,30,24,28,
%T A359897 27,30,15,73,16,37,43,45,67,74,19,55,71,126,21,150,22,75,225,78,24,
%U A359897 183,126,245,192,132,27,284,244,403,303,120,30,828
%N A359897 Number of strict integer partitions of n whose parts have the same mean as median.
%e A359897 The a(1) = 1 through a(9) = 7 partitions:
%e A359897   (1)  (2)  (3)    (4)    (5)    (6)      (7)    (8)    (9)
%e A359897             (2,1)  (3,1)  (3,2)  (4,2)    (4,3)  (5,3)  (5,4)
%e A359897                           (4,1)  (5,1)    (5,2)  (6,2)  (6,3)
%e A359897                                  (3,2,1)  (6,1)  (7,1)  (7,2)
%e A359897                                                         (8,1)
%e A359897                                                         (4,3,2)
%e A359897                                                         (5,3,1)
%t A359897 Table[Length[Select[IntegerPartitions[n],UnsameQ@@#&&Mean[#]==Median[#]&]],{n,0,30}]
%Y A359897 The non-strict version is A240219, complement A359894, ranked by A359889.
%Y A359897 The complement is counted by A359898.
%Y A359897 The odd-length case is A359899, complement A359900.
%Y A359897 A000041 counts partitions, strict A000009.
%Y A359897 A008284/A058398/A327482 count partitions by mean, ranked by A326567/A326568.
%Y A359897 A008289 counts strict partitions by mean.
%Y A359897 A237984 counts partitions containing their mean, complement A327472.
%Y A359897 A240850 counts strict partitions containing their mean, complement A240851.
%Y A359897 A325347 counts ptns with integer median, strict A359907, ranked by A359908.
%Y A359897 Cf. A065795, A066571, A067659, A082550, A102627, A135342, A316313, A327473, A327475, A328966, A359909.
%K A359897 nonn
%O A359897 0,4
%A A359897 _Gus Wiseman_, Jan 20 2023