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A325713
Number of separable partitions of n in which the number of distinct (repeatable) parts <= 4.
1
1, 1, 2, 3, 5, 6, 10, 14, 19, 26, 37, 49, 66, 87, 115, 150, 193, 244, 309, 387, 479, 585, 714, 860, 1032, 1226, 1454, 1697, 1991, 2304, 2672, 3060, 3518, 3981, 4541, 5121, 5782, 6462, 7265, 8057, 9000, 9938, 11031, 12131, 13384, 14634, 16085, 17534, 19161
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]]<=4&]]&, separable]
(* Peter J. C. Moses, May 08 2019 *)
CROSSREFS
Sequence in context: A325712 A345170 A237822 * A325714 A325715 A325534
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, May 16 2019
STATUS
approved