This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A363745 #6 Jul 06 2023 08:54:57
%S A363745 0,0,1,0,2,2,3,4,10,6,16,21,24,32,58,47,85,111,119,158,248,217,341,
%T A363745 442,461,596,867,792,1151,1465,1506,1916,2652,2477,3423,4298,4381,
%U A363745 5488,7334,6956,9280,11503,11663,14429,18781,17992,23383,28675,28970,35449,45203
%N A363745 Number of integer partitions of n whose rounded-down mean is 2.
%e A363745 The a(2) = 1 through a(10) = 16 partitions:
%e A363745 (2) . (22) (32) (222) (322) (332) (3222) (3322)
%e A363745 (31) (41) (321) (331) (422) (3321) (3331)
%e A363745 (411) (421) (431) (4221) (4222)
%e A363745 (511) (521) (4311) (4321)
%e A363745 (611) (5211) (4411)
%e A363745 (2222) (6111) (5221)
%e A363745 (3221) (5311)
%e A363745 (3311) (6211)
%e A363745 (4211) (7111)
%e A363745 (5111) (22222)
%e A363745 (32221)
%e A363745 (33211)
%e A363745 (42211)
%e A363745 (43111)
%e A363745 (52111)
%e A363745 (61111)
%t A363745 Table[Length[Select[IntegerPartitions[n],Floor[Mean[#]]==2&]],{n,0,30}]
%Y A363745 For 1 instead of 2 we have A025065, ranks A363949.
%Y A363745 The high version is A026905 reduplicated, ranks A363950.
%Y A363745 Column k = 2 of A363945.
%Y A363745 These partitions have ranks A363954.
%Y A363745 A008284 counts partitions by length, A058398 by mean.
%Y A363745 A051293 counts subsets with integer mean, median A000975.
%Y A363745 A067538 counts partitions with integer mean, strict A102627, ranks A316413.
%Y A363745 A349156 counts partitions with non-integer mean, ranks A348551.
%Y A363745 Cf. A000041, A002865, A027336, A237984, A241131, A327472, A327482, A363723, A363943, A363944, A363946.
%K A363745 nonn
%O A363745 0,5
%A A363745 _Gus Wiseman_, Jul 05 2023