%I #7 May 27 2023 16:44:55

%S 1,1,2,2,3,4,5,6,8,9,11,14,15,19,23,26,29,37,39,49,55,62,71,84,93,108,

%T 118,141,149,188,193,217,257,279,318,369,376,441,495,572,587,692,760,

%U 811,960,1046,1065,1307,1387,1550,1703,1796,2041,2295,2456,2753,3014

%N Number of strict integer partitions of n such that (length) * (maximum) <= 2n.

%C Also strict partitions such that (maximum) <= 2*(mean).

%C These are strict partitions whose complement (see A361851) has size <= n.

%e The partition y = (4,3,1) has length 3 and maximum 4, and 3*4 <= 2*8, so y is counted under a(8). The complement of y has size 4, which is less than or equal to n = 8.

%t Table[Length[Select[IntegerPartitions[n],UnsameQ@@#&&Max@@#<=2*Mean[#]&]],{n,30}]

%Y The equal case for median is A361850, non-strict A361849 (ranks A361856).

%Y The non-strict version is A361851, A361848 for median.

%Y The equal case is A361854, non-strict A361853 (ranks A361855).

%Y A000041 counts integer partitions, strict A000009.

%Y A008284 counts partitions by length, A058398 by mean.

%Y A051293 counts subsets with integer mean.

%Y A067538 counts partitions with integer mean.

%Y Cf. A111907, A237984, A240219, A241061, A241086, A324521, A324562, A349156, A360068, A360241, A361394, A361852, A361906.

%K nonn

%O 1,3

%A _Gus Wiseman_, May 23 2023