A325713 Number of separable partitions of n in which the number of distinct (repeatable) parts <= 4.

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

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]]<=4&]]&,separable]
(* Peter J. C. Moses, May 08 2019 *)