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A325650
Number of separable partitions of n in which the number of distinct (repeatable) parts is 6.
0
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 5, 10, 20, 36, 64, 100, 164, 249, 378, 548, 794, 1104, 1536, 2095, 2817, 3731, 4907, 6351, 8173, 10405, 13143, 16473, 20453, 25274, 30981, 37808, 45774, 55254, 66184, 79091, 93805, 111052
OFFSET
1,22
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.
EXAMPLE
a(22) counts these 2 partitions: [7,5,4,3,2,1], [6,5,4,3,1,2,1].
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]]==6&]]&, separable]
(* Peter J. C. Moses, May 08 2019 *)
CROSSREFS
Sequence in context: A263348 A328548 A294536 * A325720 A103924 A160647
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, May 16 2019
STATUS
approved