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 A319153 #4 Sep 15 2018 15:46:47
%S A319153 0,2,1,3,5,7,12,17,24,33,44,57,76,100,129,168,214,282,355,462,586,755,
%T A319153 937,1202,1493,1900,2349,2944,3621,4520,5514,6813,8298,10150,12240,
%U A319153 14918,17931,21654,25917,31081,37029,44256,52474,62405,73724,87378,102887
%N A319153 Number of integer partitions of n that reduce to 2, meaning their Heinz number maps to 2 under A304464.
%C A319153 Start with an integer partition y of n. Given a multiset, take the multiset of its multiplicities. Repeat until a multiset of size 1 is obtained. If this multiset is {2}, we say that y reduces to 2. For example, we have (3211) -> (211) -> (21) -> (11) -> (2), so (3211) reduces to 2.
%e A319153 The a(7) = 12 partitions:
%e A319153 (43), (52), (61),
%e A319153 (322), (331), (511),
%e A319153 (2221), (3211), (4111),
%e A319153 (22111), (31111),
%e A319153 (211111).
%t A319153 Table[Length[Select[IntegerPartitions[n],NestWhile[Sort[Length/@Split[#]]&,#,Length[#]>1&]=={2}&]],{n,30}]
%Y A319153 Cf. A000837, A098859, A181819, A182850, A304464, A304465, A304634, A305563, A317245, A319149.
%K A319153 nonn
%O A319153 1,2
%A A319153 _Gus Wiseman_, Sep 12 2018