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A325279
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Number of integer partitions of n whose maximum multiplicity is one greater than their minimum multiplicity.
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1
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0, 0, 0, 0, 1, 2, 1, 5, 6, 9, 10, 18, 18, 31, 34, 48, 57, 80, 86, 122, 138, 183, 211, 275, 311, 402, 461, 576, 663, 825, 942, 1163, 1334, 1621, 1865, 2248, 2566, 3084, 3532, 4193, 4794, 5674, 6472, 7617, 8685, 10153, 11576, 13483, 15320, 17790, 20200, 23342
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OFFSET
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0,6
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COMMENTS
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The Heinz numbers of these partitions are given by A325241.
For example, the partition (44111) has two multiplicities (2 and 3) which differ by 1, so is counted under a(11).
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LINKS
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Table of n, a(n) for n=0..51.
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EXAMPLE
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The a(4) = 1 through a(11) = 18 partitions:
(211) (221) (411) (322) (332) (441) (433) (443)
(311) (331) (422) (522) (442) (533)
(511) (611) (711) (622) (551)
(3211) (3221) (3321) (811) (722)
(22111) (4211) (4221) (5221) (911)
(22211) (4311) (5311) (4322)
(5211) (6211) (4331)
(32211) (33211) (4421)
(33111) (42211) (5411)
(2221111) (6221)
(6311)
(7211)
(33221)
(33311)
(43211)
(44111)
(52211)
(2222111)
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MATHEMATICA
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Table[Length[Select[IntegerPartitions[n], Max@@Length/@Split[#]-Min@@Length/@Split[#]==1&]], {n, 0, 30}]
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CROSSREFS
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Cf. A047966, A062770, A071625, A098859, A117571, A127002, A325242, A325244, A325245, A325280.
Sequence in context: A026214 A026221 A030740 * A095242 A357179 A125080
Adjacent sequences: A325276 A325277 A325278 * A325280 A325281 A325282
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KEYWORD
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nonn
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AUTHOR
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Gus Wiseman, Apr 18 2019
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STATUS
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approved
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