cp's OEIS Frontend

A361850 Number of strict integer partitions of n such that the maximum is twice the median.

%I A361850 #5 Apr 02 2023 09:48:32
%S A361850 0,0,0,0,0,0,1,0,0,1,2,0,2,1,3,3,4,2,5,4,7,8,10,6,11,11,15,16,21,18,
%T A361850 25,23,28,32,40,40,51,51,58,60,73,75,93,97,113,123,139,141,164,175,
%U A361850 199,217,248,263,301,320,356,383,426,450,511,551,613,664,737
%N A361850 Number of strict integer partitions of n such that the maximum is twice the median.
%C A361850 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 A361850 The a(7) = 1 through a(20) = 4 strict partitions (A..C = 10..12):
%e A361850   421  .  .  631  632   .  841   842  843   A51    A52    A53   A54   C62
%e A361850                   5321     6421       7431  7432   8531   8532  C61   9542
%e A361850                                       7521  64321  8621         9541  9632
%e A361850                                                    65321        9631  85421
%e A361850                                                                 9721
%e A361850 The partition (7,4,3,1) has maximum 7 and median 7/2, so is counted under a(15).
%e A361850 The partition (8,6,2,1) has maximum 8 and median 4, so is counted under a(17).
%t A361850 Table[Length[Select[IntegerPartitions[n],UnsameQ@@#&&Max@@#==2*Median[#]&]],{n,30}]
%Y A361850 For minimum instead of median we have A241035, non-strict A237824.
%Y A361850 For length instead of median we have A241087, non-strict A237755.
%Y A361850 The non-strict version is A361849, ranks A361856.
%Y A361850 The non-strict complement is counted by A361857, ranks A361867.
%Y A361850 A000041 counts integer partitions, strict A000009.
%Y A361850 A000975 counts subsets with integer median.
%Y A361850 A008284 counts partitions by length, A058398 by mean.
%Y A361850 A325347 counts partitions with integer median, complement A307683.
%Y A361850 A359893 and A359901 count partitions by median, odd-length A359902.
%Y A361850 A359907 counts strict partitions with integer median
%Y A361850 A360005 gives median of prime indices (times two), distinct A360457.
%Y A361850 Cf. A027193, A067659, A079309, A111907, A116608, A359897, A359908, A360952, A361851, A361858, A361859, A361860.
%K A361850 nonn
%O A361850 1,11
%A A361850 _Gus Wiseman_, Apr 02 2023