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A325712
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Number of separable partitions of n in which the number of distinct (repeatable) parts <= 3.
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2
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1, 1, 2, 3, 5, 6, 10, 14, 19, 25, 35, 44, 56, 68, 87, 102, 124, 142, 171, 197, 225, 254, 294, 326, 370, 408, 451, 505, 553, 604, 661, 726, 772, 854, 916, 989, 1054, 1151, 1199, 1320, 1376, 1492, 1555, 1694, 1736, 1903, 1952, 2113, 2170, 2360, 2387, 2610
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OFFSET
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1,3
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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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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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