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A325243
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Number of integer partitions of n with exactly two distinct multiplicities.
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2
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0, 0, 0, 0, 1, 3, 3, 9, 12, 19, 26, 39, 47, 70, 89, 115, 148, 189, 235, 294, 362, 450, 558, 669, 817, 980, 1197, 1421, 1709, 2012, 2429, 2836, 3380, 3961, 4699, 5433, 6457, 7433, 8770, 10109, 11818, 13547, 15912, 18109, 21105, 24121, 27959, 31736, 36840, 41670
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OFFSET
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0,6
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COMMENTS
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For example, (32211) has two distinct multiplicities (1 and 2) so is counted under a(9).
The Heinz numbers of these partitions are given by A323055.
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LINKS
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EXAMPLE
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The a(4) = 1 through a(9) = 19 partitions:
(211) (221) (411) (322) (332) (441)
(311) (3111) (331) (422) (522)
(2111) (21111) (511) (611) (711)
(2221) (3221) (3222)
(3211) (4211) (3321)
(4111) (5111) (4221)
(22111) (22211) (4311)
(31111) (32111) (5211)
(211111) (41111) (6111)
(221111) (22221)
(311111) (32211)
(2111111) (33111)
(42111)
(51111)
(321111)
(411111)
(2211111)
(3111111)
(21111111)
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MATHEMATICA
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Table[Length[Select[IntegerPartitions[n], Length[Union[Length/@Split[#]]]==2&]], {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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