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A325647
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Number of separable partitions of n in which the number of distinct (repeatable) parts is 3.
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1
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0, 0, 0, 0, 0, 1, 2, 5, 9, 13, 21, 29, 39, 49, 68, 79, 101, 116, 145, 167, 196, 221, 262, 287, 335, 368, 412, 460, 512, 554, 617, 673, 723, 800, 865, 925, 1001, 1090, 1140, 1250, 1317, 1418, 1493, 1619, 1665, 1828, 1884, 2022, 2098, 2275, 2308, 2520, 2564
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OFFSET
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1,7
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COMMENTS
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A partition is separable if there is an ordering of its parts in which no consecutive parts are identical. See A325646 for a guide to related sequences.
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LINKS
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EXAMPLE
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a(8) counts these 5 partitions: [5,2,1], [4,3,1], [1,4,1,2], [2,3,2,1], [1,3,1,2,1].
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MATHEMATICA
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(separable=Table[Map[#[[1]]&, Select[Map[{#, Quotient[(1+Length[#]), Max[Map[Length, Split[#]]]]}&, IntegerPartitions[nn]], #[[2]]>1&]], {nn, 35}]);
Map[Length[Select[Map[{#, Length[Union[#]]}&, #], #[[2]]==3&]]&, separable]
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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