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A325714
Number of separable partitions of n in which the number of distinct (repeatable) parts <= 5.
1
1, 1, 2, 3, 5, 6, 10, 14, 19, 26, 37, 49, 66, 87, 116, 152, 198, 254, 329, 422, 535, 676, 853, 1067, 1329, 1645, 2025, 2486, 3027, 3673, 4432, 5329, 6361, 7580, 8978, 10591, 12439, 14563, 16962, 19717, 22801, 26295, 30212, 34612, 39531, 45006, 51100, 57839
OFFSET
1,3
COMMENTS
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.
MATHEMATICA
(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]]<=5&]]&, separable]
(* Peter J. C. Moses, May 08 2019 *)
CROSSREFS
Sequence in context: A345170 A237822 A325713 * A325715 A325534 A280013
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, May 16 2019
STATUS
approved