A325646 Number of separable partitions of n in which the number of distinct (repeatable) parts is 2.

0, 0, 1, 2, 4, 4, 7, 8, 9, 11, 13, 14, 16, 18, 18, 22, 22, 25, 25, 29, 28, 32, 31, 38, 34, 39, 38, 44, 40, 49, 43, 52, 48, 53, 50, 63, 52, 60, 58, 69, 58, 73, 61, 74, 70, 74, 67, 90, 71, 84, 78, 89, 76, 97, 82, 100, 88, 95, 85, 119

Offset

1,4

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 4 partitions:  [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, A325647.

Sequence in context: A194118 A266188 A272881 * A325723 A353927 A262884

Adjacent sequences: A325643 A325644 A325645 * A325647 A325648 A325649

Keyword

nonn,easy

Author

Clark Kimberling, May 16 2019

Status

approved