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A319153
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Number of integer partitions of n that reduce to 2, meaning their Heinz number maps to 2 under A304464.
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0
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0, 2, 1, 3, 5, 7, 12, 17, 24, 33, 44, 57, 76, 100, 129, 168, 214, 282, 355, 462, 586, 755, 937, 1202, 1493, 1900, 2349, 2944, 3621, 4520, 5514, 6813, 8298, 10150, 12240, 14918, 17931, 21654, 25917, 31081, 37029, 44256, 52474, 62405, 73724, 87378, 102887
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OFFSET
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1,2
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COMMENTS
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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.
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LINKS
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EXAMPLE
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The a(7) = 12 partitions:
(43), (52), (61),
(322), (331), (511),
(2221), (3211), (4111),
(22111), (31111),
(211111).
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MATHEMATICA
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Table[Length[Select[IntegerPartitions[n], NestWhile[Sort[Length/@Split[#]]&, #, Length[#]>1&]=={2}&]], {n, 30}]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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