A325715 Number of separable partitions of n in which the number of distinct (repeatable) parts <= 6.

1, 1, 2, 3, 5, 6, 10, 14, 19, 26, 37, 49, 66, 87, 116, 152, 198, 254, 329, 422, 536, 678, 858, 1077, 1349, 1681, 2089, 2586, 3191, 3922, 4810, 5877, 7155, 8684, 10514, 12686, 15256, 18294, 21869, 26068, 30974, 36700, 43355, 51085, 59984, 70280, 82081, 95647

Offset: 1

Author

Clark Kimberling, May 17 2019

Keywords

• nonn
• easy

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.

Crossrefs

Cf. A000041, A325334.

Programs

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 *)