A325719 - OEIS

A325719

Number of separable partitions of n in which the number of distinct (repeatable) parts is > 4.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 5, 10, 20, 35, 57, 93, 144, 217, 317, 455, 635, 890, 1202, 1623, 2148, 2837, 3673, 4768, 6082, 7740, 9753, 12262, 15253, 18972, 23373, 28759, 35143, 42867, 51998, 62967, 75865, 91243, 109315, 130701, 155752

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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..51.

FORMULA

a(n) = A325534(n) - A325713(n) for n >= 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]]>4&]]&, separable]

(* Peter J. C. Moses, May 08 2019 *)

CROSSREFS

Cf. A000041, A325534.

Sequence in context: A117486 A263002 A325649 * A000710 A160461 A365631

Adjacent sequences: A325716 A325717 A325718 * A325720 A325721 A325722

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, May 19 2019

STATUS

approved