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A325718
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Number of separable partitions of n in which the number of distinct (repeatable) parts is > 3.
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0
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0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 5, 10, 19, 29, 50, 74, 112, 158, 225, 311, 424, 564, 751, 979, 1273, 1638, 2082, 2640, 3323, 4159, 5171, 6419, 7895, 9707, 11872, 14481, 17573, 21319, 25709, 30997, 37205, 44619, 53304, 63646, 75698, 89998, 106664, 126306
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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 A325534 for a guide to related sequences.
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LINKS
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FORMULA
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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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