A325647 Number of separable partitions of n in which the number of distinct (repeatable) parts is 3.

0, 0, 0, 0, 0, 1, 2, 5, 9, 13, 21, 29, 39, 49, 68, 79, 101, 116, 145, 167, 196, 221, 262, 287, 335, 368, 412, 460, 512, 554, 617, 673, 723, 800, 865, 925, 1001, 1090, 1140, 1250, 1317, 1418, 1493, 1619, 1665, 1828, 1884, 2022, 2098, 2275, 2308, 2520, 2564

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 A325646 for a guide to related sequences.

Examples

			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].
		

Crossrefs

Cf. A000041, A325334, A325646.

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]]==3&]]&,separable]
(* Peter J. C. Moses, May 08 2019 *)