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A325648
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Number of separable partitions of n in which the number of distinct (repeatable) parts is 4.
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0
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0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 5, 10, 19, 28, 48, 69, 102, 138, 190, 254, 331, 420, 534, 662, 818, 1003, 1192, 1438, 1700, 2011, 2334, 2746, 3127, 3625, 4132, 4728, 5311, 6066, 6737, 7624, 8446, 9476, 10437, 11648, 12731, 14133, 15421, 16991, 18461, 20286
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OFFSET
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1,11
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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(11) counts these 2 partitions: [4,1,3,2,1], [3,2,1,2,1,2].
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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]]==4&]]&, 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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