cp's OEIS Frontend

A361849 Number of integer partitions of n such that the maximum is twice the median.

%I A361849 #6 Apr 02 2023 09:48:00
%S A361849 0,0,0,1,1,1,4,3,4,7,9,9,15,16,20,26,34,37,50,55,68,86,103,117,145,
%T A361849 168,201,236,282,324,391,449,525,612,712,818,962,1106,1278,1470,1698,
%U A361849 1939,2238,2550,2924,3343,3824,4341,4963,5627,6399,7256,8231,9300
%N A361849 Number of integer partitions of n such that the maximum is twice the median.
%C A361849 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 A361849 The a(4) = 1 through a(11) = 9 partitions:
%e A361849   211  2111  21111  421     422      4221      631        632
%e A361849                     3211    221111   4311      4222       5321
%e A361849                     22111   2111111  2211111   42211      5411
%e A361849                     211111           21111111  322111     42221
%e A361849                                                2221111    43211
%e A361849                                                22111111   332111
%e A361849                                                211111111  22211111
%e A361849                                                           221111111
%e A361849                                                           2111111111
%e A361849 For example, the partition (3,2,1,1) has maximum 3 and median 3/2, so is counted under a(7).
%t A361849 Table[Length[Select[IntegerPartitions[n],Max@@#==2*Median[#]&]],{n,30}]
%Y A361849 For minimum instead of median we have A118096.
%Y A361849 For length instead of median we have A237753.
%Y A361849 This is the equal case of A361848.
%Y A361849 For mean instead of median we have A361853.
%Y A361849 These partitions have ranks A361856.
%Y A361849 For "greater" instead of "equal" we have A361857, allowing equality A361859.
%Y A361849 A000041 counts integer partitions, strict A000009.
%Y A361849 A008284 counts partitions by length, A058398 by mean.
%Y A361849 A325347 counts partitions with integer median, complement A307683.
%Y A361849 A359893 and A359901 count partitions by median, odd-length A359902.
%Y A361849 A360005 gives twice median of prime indices, distinct A360457.
%Y A361849 A361860 counts partitions with minimum equal to median.
%Y A361849 Cf. A013580, A027193, A053263, A061395, A067659, A111907, A116608, A237755, A240219, A361851.
%K A361849 nonn
%O A361849 1,7
%A A361849 _Gus Wiseman_, Apr 02 2023