cp's OEIS Frontend

A362049 Number of integer partitions of n such that (length) = 2*(median).

%I A362049 #11 Apr 16 2023 06:35:13
%S A362049 0,1,0,0,0,0,1,3,3,3,3,3,3,4,5,9,12,19,22,29,32,39,43,51,57,70,81,101,
%T A362049 123,153,185,230,272,328,386,454,526,617,708,824,951,1106,1277,1493,
%U A362049 1727,2020,2344,2733,3164,3684,4245,4914,5647,6502,7438,8533,9730
%N A362049 Number of integer partitions of n such that (length) = 2*(median).
%C A362049 The median of a multiset is either the middle part (for odd length), or the average of the two middle parts (for even length). All of these partitions have even length, because an odd-length multiset cannot have fractional median.
%e A362049 The a(13) = 3 through a(15) = 5 partitions:
%e A362049   (7,2,2,2)  (8,2,2,2)      (9,2,2,2)
%e A362049   (8,2,2,1)  (9,2,2,1)      (10,2,2,1)
%e A362049   (8,3,1,1)  (9,3,1,1)      (10,3,1,1)
%e A362049              (3,3,3,3,1,1)  (3,3,3,3,2,1)
%e A362049                             (4,3,3,3,1,1)
%t A362049 Table[Length[Select[IntegerPartitions[n],Length[#]==2*Median[#]&]],{n,30}]
%Y A362049 For maximum instead of median we have A237753.
%Y A362049 For minimum instead of median we have A237757.
%Y A362049 For maximum instead of length we have A361849, ranks A361856.
%Y A362049 This is the equal case of A362048.
%Y A362049 These partitions have ranks A362050.
%Y A362049 A000041 counts integer partitions, strict A000009.
%Y A362049 A000975 counts subsets with integer median.
%Y A362049 A325347 counts partitions with integer median, complement A307683.
%Y A362049 A359893 and A359901 count partitions by median.
%Y A362049 A360005 gives twice median of prime indices, distinct A360457.
%Y A362049 Cf. A008284, A013580, A027193, A079309, A237800, A240219, A361801, A361848, A361858, A361859.
%K A362049 nonn
%O A362049 1,8
%A A362049 _Gus Wiseman_, Apr 10 2023