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A325332
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Number of totally abnormal integer partitions of n.
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2
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0, 0, 1, 1, 2, 1, 3, 1, 4, 2, 5, 1, 8, 1, 7, 5, 10, 2, 16, 4, 21, 15, 24, 17, 49, 29, 53, 53, 84, 65, 121, 92, 148, 141, 186, 179, 280, 223, 317, 318, 428, 387, 576, 512, 700, 734, 899, 900, 1260, 1207, 1551, 1668, 2041, 2109, 2748, 2795, 3463, 3775, 4446
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OFFSET
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0,5
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COMMENTS
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A multiset is normal if its union is an initial interval of positive integers. A multiset is totally abnormal if it is not normal and either it is a singleton or its multiplicities form a totally abnormal multiset.
The Heinz numbers of these partitions are given by A325372.
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LINKS
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EXAMPLE
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The a(2) = 1 through a(12) = 8 totally abnormal partitions (A = 10, B = 11, C = 12):
(2) (3) (4) (5) (6) (7) (8) (9) (A) (B) (C)
(22) (33) (44) (333) (55) (66)
(222) (2222) (3322) (444)
(3311) (4411) (3333)
(22222) (4422)
(5511)
(222222)
(333111)
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MATHEMATICA
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normQ[m_]:=Or[m=={}, Union[m]==Range[Max[m]]];
antinrmQ[ptn_]:=!normQ[ptn]&&(Length[ptn]==1||antinrmQ[Sort[Length/@Split[ptn]]]);
Table[Length[Select[IntegerPartitions[n], antinrmQ]], {n, 0, 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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