cp's OEIS Frontend

A360243 Number of integer partitions of n where the parts have the same mean as the distinct parts.

%I A360243 #5 Feb 06 2023 10:06:16
%S A360243 1,1,2,3,4,4,8,6,11,11,17,13,28,19,32,40,48,39,71,55,103,105,110,105,
%T A360243 197,170,195,237,319,257,462,341,515,543,584,784,1028,761,973,1153,
%U A360243 1606,1261,2137,1611,2368,2815,2575,2591,4393,3798,4602,4663,5777,5121
%N A360243 Number of integer partitions of n where the parts have the same mean as the distinct parts.
%e A360243 The a(1) = 1 through a(8) = 11 partitions:
%e A360243   (1)  (2)   (3)    (4)     (5)      (6)       (7)        (8)
%e A360243        (11)  (21)   (22)    (32)     (33)      (43)       (44)
%e A360243              (111)  (31)    (41)     (42)      (52)       (53)
%e A360243                     (1111)  (11111)  (51)      (61)       (62)
%e A360243                                      (222)     (421)      (71)
%e A360243                                      (321)     (1111111)  (431)
%e A360243                                      (2211)               (521)
%e A360243                                      (111111)             (2222)
%e A360243                                                           (3221)
%e A360243                                                           (3311)
%e A360243                                                           (11111111)
%t A360243 Table[Length[Select[IntegerPartitions[n],Mean[#]==Mean[Union[#]]&]],{n,0,30}]
%Y A360243 For multiplicities instead of distinct parts we have A360068.
%Y A360243 The complement is counted by A360242, ranks A360246.
%Y A360243 For median instead of mean we have A360245, complement A360244.
%Y A360243 These partitions have ranks A360247.
%Y A360243 Cf. A360250 and A360251, ranks A360252 and A360253.
%Y A360243 A000041 counts integer partitions, strict A000009.
%Y A360243 A008284 counts partitions by number of parts.
%Y A360243 A058398 counts partitions by mean, also A327482.
%Y A360243 A067538 counts partitions with integer mean, strict A102627, ranks A316413.
%Y A360243 A116608 counts partitions by number of distinct parts.
%Y A360243 A360071 counts partitions by number of parts and number of distinct parts.
%Y A360243 A360241 counts partitions whose distinct parts have integer mean.
%Y A360243 Cf. A051293, A067340, A240219, A316313, A326567/A326568, A326619/A326620, A326621, A349156, A360069.
%K A360243 nonn
%O A360243 0,3
%A A360243 _Gus Wiseman_, Feb 04 2023