OFFSET
1,7
COMMENTS
A partition is separable if there is an ordering of its parts in which no consecutive parts are identical. See A325646 for a guide to related sequences.
EXAMPLE
a(8) counts these 5 partitions: [5,2,1], [4,3,1], [1,4,1,2], [2,3,2,1], [1,3,1,2,1].
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]]==3&]]&, separable]
(* Peter J. C. Moses, May 08 2019 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, May 16 2019
STATUS
approved