A325712 Number of separable partitions of n in which the number of distinct (repeatable) parts <= 3.

1, 1, 2, 3, 5, 6, 10, 14, 19, 25, 35, 44, 56, 68, 87, 102, 124, 142, 171, 197, 225, 254, 294, 326, 370, 408, 451, 505, 553, 604, 661, 726, 772, 854, 916, 989, 1054, 1151, 1199, 1320, 1376, 1492, 1555, 1694, 1736, 1903, 1952, 2113, 2170, 2360, 2387, 2610

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