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 A361394 #10 Mar 19 2023 18:09:06
%S A361394 1,1,2,2,4,6,8,11,15,20,30,38,49,65,83,108,139,178,224,286,358,437,
%T A361394 550,684,837,1037,1269,1553,1889,2295,2770,3359,4035,4843,5808,6951,
%U A361394 8312,9902,11752,13958,16531,19541,23037,27162,31911,37488,43950,51463,60127,70229
%N A361394 Number of integer partitions of n where 2*(number of distinct parts) >= (number of parts).
%H A361394 Alois P. Heinz, <a href="/A361394/b361394.txt">Table of n, a(n) for n = 0..1000</a>
%e A361394 The a(1) = 1 through a(7) = 11 partitions:
%e A361394 (1) (2) (3) (4) (5) (6) (7)
%e A361394 (11) (21) (22) (32) (33) (43)
%e A361394 (31) (41) (42) (52)
%e A361394 (211) (221) (51) (61)
%e A361394 (311) (321) (322)
%e A361394 (2111) (411) (331)
%e A361394 (2211) (421)
%e A361394 (3111) (511)
%e A361394 (2221)
%e A361394 (3211)
%e A361394 (4111)
%p A361394 b:= proc(n, i, t) option remember; `if`(n=0, `if`(t>=0, 1, 0),
%p A361394 `if`(i<1, 0, add(b(n-i*j, i-1, t+`if`(j>0, 2, 0)-j), j=0..n/i)))
%p A361394 end:
%p A361394 a:= n-> b(n$2, 0):
%p A361394 seq(a(n), n=0..50); # _Alois P. Heinz_, Mar 19 2023
%t A361394 Table[Length[Select[IntegerPartitions[n],2*Length[Union[#]]>=Length[#]&]],{n,0,30}]
%Y A361394 The complement is counted by A360254, ranks A360558.
%Y A361394 These partitions have ranks A361395.
%Y A361394 A000041 counts integer partitions, strict A000009.
%Y A361394 A008284 counts partitions by length, reverse A058398.
%Y A361394 A067538 counts partitions with integer mean, strict A102627.
%Y A361394 A116608 counts partitions by number of distinct parts.
%Y A361394 Cf. A106529, A144300, A237363, A237832, A240219, A316413, A349156.
%K A361394 nonn
%O A361394 0,3
%A A361394 _Gus Wiseman_, Mar 17 2023