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A317245
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Number of supernormal integer partitions of n.
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27
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1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 4, 4, 1, 3, 3, 4, 2, 4, 5, 6, 6, 10, 7, 10, 9, 9, 10, 11, 12, 12, 21, 12, 18, 17, 21, 19, 28, 23, 28, 26, 27, 24, 32, 29, 36, 34, 46, 42, 55, 48, 65, 65, 74, 70, 88, 81, 83, 103, 112, 129, 153, 157, 190, 205, 210, 242, 283, 276, 321
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OFFSET
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0,4
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COMMENTS
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An integer partition is supernormal if either (1) it is of the form 1^n for some n >= 0, or (2a) it spans an initial interval of positive integers, and (2b) its multiplicities, sorted in weakly decreasing order, are themselves a supernormal integer partition.
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LINKS
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EXAMPLE
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The a(10) = 4 supernormal integer partitions are (4321), (33211), (322111), (1111111111).
The a(21) = 10 supernormal integer partitions:
(654321),
(4443321),
(44432211), (44333211), (44332221),
(4432221111), (4333221111), (4332222111),
(433322211),
(111111111111111111111).
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MATHEMATICA
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supnrm[q_]:=Or[q=={}||Union[q]=={1}, And[Union[q]==Range[Max[q]], supnrm[Sort[Length/@Split[q], Greater]]]];
Table[Length[Select[IntegerPartitions[n], supnrm]], {n, 0, 30}]
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CROSSREFS
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Cf. A000041, A181819, A182850, A182857, A275870, A304660, A305563, A317081, A317086, A317088, A317246.
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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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