A325711 Number of separable partitions of n in which the number of distinct (repeatable) parts <= 2.

1, 1, 2, 3, 5, 5, 8, 9, 10, 12, 14, 15, 17, 19, 19, 23, 23, 26, 26, 30, 29, 33, 32, 39, 35, 40, 39, 45, 41, 50, 44, 53, 49, 54, 51, 64, 53, 61, 59, 70, 59, 74, 62, 75, 71, 75, 68, 91, 72, 85, 79, 90, 77, 98, 83, 101, 89, 96, 86, 120

Offset

1,3

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.

Links

Table of n, a(n) for n=1..60.

Example

a(6) counts these 5 partitions:  [6], [5,1], [4,2], [1,4,1], [2,1,2,1].

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]]<=2&]]&, separable]
(* Peter J. C. Moses, May 08 2019 *)

Crossrefs

Cf. A000041, A325334, A325712.

Sequence in context: A188201 A184165 A152771 * A306676 A363058 A341122

Adjacent sequences: A325708 A325709 A325710 * A325712 A325713 A325714

Keyword

nonn,easy

Author

Clark Kimberling, May 16 2019

Status

approved