A325714 Number of separable partitions of n in which the number of distinct (repeatable) parts <= 5.

1, 1, 2, 3, 5, 6, 10, 14, 19, 26, 37, 49, 66, 87, 116, 152, 198, 254, 329, 422, 535, 676, 853, 1067, 1329, 1645, 2025, 2486, 3027, 3673, 4432, 5329, 6361, 7580, 8978, 10591, 12439, 14563, 16962, 19717, 22801, 26295, 30212, 34612, 39531, 45006, 51100, 57839

Offset: 1

Author

Clark Kimberling, May 16 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]]<=5&]]&,separable]
(* Peter J. C. Moses, May 08 2019 *)