cp's OEIS Frontend

A361861 Number of integer partitions of n where the median is twice the minimum.

%I A361861 #6 Apr 03 2023 09:15:58
%S A361861 0,0,0,1,1,1,2,5,5,8,11,16,20,28,38,53,67,87,111,146,183,236,297,379,
%T A361861 471,591,729,909,1116,1376,1682,2065,2507,3055,3699,4482,5395,6501,
%U A361861 7790,9345,11153,13316,15839,18844,22333,26466,31266,36924,43478,51177
%N A361861 Number of integer partitions of n where the median is twice the minimum.
%C A361861 The median of a multiset is either the middle part (for odd length), or the average of the two middle parts (for even length).
%e A361861 The a(4) = 1 through a(11) = 11 partitions:
%e A361861   (31)  (221)  (321)  (421)   (62)     (621)    (442)     (542)
%e A361861                       (2221)  (521)    (4221)   (721)     (821)
%e A361861                               (3221)   (4311)   (5221)    (6221)
%e A361861                               (3311)   (22221)  (5311)    (6311)
%e A361861                               (22211)  (32211)  (32221)   (33221)
%e A361861                                                 (33211)   (42221)
%e A361861                                                 (42211)   (43211)
%e A361861                                                 (222211)  (52211)
%e A361861                                                           (222221)
%e A361861                                                           (322211)
%e A361861                                                           (2222111)
%e A361861 The partition (3,2,2,2,1,1) has median 2 and minimum 1, so is counted under a(11).
%e A361861 The partition (5,4,2) has median 4 and minimum 2, so is counted under a(11).
%t A361861 Table[Length[Select[IntegerPartitions[n],2*Min@@#==Median[#]&]],{n,30}]
%Y A361861 For maximum instead of median we have A118096.
%Y A361861 For length instead of median we have A237757, without the coefficient A006141.
%Y A361861 With minimum instead of twice minimum we have A361860.
%Y A361861 A000041 counts integer partitions, strict A000009.
%Y A361861 A008284 counts partitions by length, A058398 by mean.
%Y A361861 A325347 counts partitions with integer median, complement A307683.
%Y A361861 A359893 and A359901 count partitions by median, odd-length A359902.
%Y A361861 A360005 gives twice median of prime indices, distinct A360457.
%Y A361861 Cf. A027193, A039900, A053263, A067659, A111907, A116608, A237753, A237755, A237824, A361848, A361853.
%K A361861 nonn
%O A361861 1,7
%A A361861 _Gus Wiseman_, Apr 02 2023