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A325649
Number of separable partitions of n in which the number of distinct (repeatable) parts is 5.
0
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 5, 10, 20, 35, 56, 91, 139, 207, 297, 419, 571, 789, 1036, 1369, 1760, 2269, 2843, 3599, 4437, 5470, 6657, 8101, 9697, 11660, 13801, 16357, 19181, 22481, 26147, 30372, 35015, 40305, 46167, 52722, 59979, 68043
OFFSET
1,16
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(16) counts these 2 partitions: [6,4,3,2,1], [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]]==5&]]&, separable]
(* Peter J. C. Moses, May 08 2019 *)
CROSSREFS
Sequence in context: A126105 A117486 A263002 * A325719 A000710 A160461
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, May 16 2019
STATUS
approved