A325650 Number of separable partitions of n in which the number of distinct (repeatable) parts is 6.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 5, 10, 20, 36, 64, 100, 164, 249, 378, 548, 794, 1104, 1536, 2095, 2817, 3731, 4907, 6351, 8173, 10405, 13143, 16473, 20453, 25274, 30981, 37808, 45774, 55254, 66184, 79091, 93805, 111052

Offset

1,22

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..54.

Example

a(22) counts these 2 partitions:  [7,5,4,3,2,1], [6,5,4,3,1,2,1].

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]]==6&]]&, separable]
(* Peter J. C. Moses, May 08 2019 *)

Crossrefs

Cf. A000041, A325534.

Sequence in context: A263348 A328548 A294536 * A325720 A103924 A160647

Adjacent sequences: A325647 A325648 A325649 * A325651 A325652 A325653

Keyword

nonn,easy

Author

Clark Kimberling, May 16 2019

Status

approved