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A325724
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Number of separable partitions of n that consist of an odd number of parts.
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2
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1, 1, 1, 1, 1, 2, 3, 6, 10, 14, 22, 30, 40, 50, 70, 82, 107, 127, 166, 203, 253, 313, 402, 495, 633, 788, 984, 1251, 1551, 1929, 2388, 2963, 3603, 4465, 5412, 6570, 7936, 9617, 11477, 13852, 16482, 19708, 23384, 27830, 32923, 39066, 46078, 54416, 64114
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OFFSET
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1,6
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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, 60}]) // ColumnForm;
Map[Map[#[[1]] &, Select[Map[{#, Length[Union[#]]} &, #], #[[2]] == 2 &]] &,
separable] // ColumnForm;
Map[Length[Select[Map[{#, Length[Union[#]]} &, #], EvenQ[#[[2]]] &]] &,
Map[Length[Select[Map[{#, Length[Union[#]]} &, #], OddQ[#[[2]]] &]] &,
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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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