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Number of integer partitions of n that reduce to 2, meaning their Heinz number maps to 2 under A304464.
0

%I #4 Sep 15 2018 15:46:47

%S 0,2,1,3,5,7,12,17,24,33,44,57,76,100,129,168,214,282,355,462,586,755,

%T 937,1202,1493,1900,2349,2944,3621,4520,5514,6813,8298,10150,12240,

%U 14918,17931,21654,25917,31081,37029,44256,52474,62405,73724,87378,102887

%N Number of integer partitions of n that reduce to 2, meaning their Heinz number maps to 2 under A304464.

%C 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 The a(7) = 12 partitions:

%e (43), (52), (61),

%e (322), (331), (511),

%e (2221), (3211), (4111),

%e (22111), (31111),

%e (211111).

%t Table[Length[Select[IntegerPartitions[n],NestWhile[Sort[Length/@Split[#]]&,#,Length[#]>1&]=={2}&]],{n,30}]

%Y Cf. A000837, A098859, A181819, A182850, A304464, A304465, A304634, A305563, A317245, A319149.

%K nonn

%O 1,2

%A _Gus Wiseman_, Sep 12 2018