A325649 Number of separable partitions of n in which the number of distinct (repeatable) parts is 5.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 5, 10, 20, 35, 56, 91, 139, 207, 297, 419, 571, 789, 1036, 1369, 1760, 2269, 2843, 3599, 4437, 5470, 6657, 8101, 9697, 11660, 13801, 16357, 19181, 22481, 26147, 30372, 35015, 40305, 46167, 52722, 59979, 68043

Offset

1,16

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..52.

Example

a(16) counts these 2 partitions:  [6,4,3,2,1], [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]]==5&]]&, separable]
(* Peter J. C. Moses, May 08 2019 *)

Crossrefs

Cf. A000041, A325534.

Sequence in context: A126105 A117486 A263002 * A325719 A000710 A160461

Adjacent sequences: A325646 A325647 A325648 * A325650 A325651 A325652

Keyword

nonn,easy

Author

Clark Kimberling, May 16 2019

Status

approved