A325720 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, 0, 0, 0, 0, 0, 0, 1, 2, 5, 10, 20, 36, 64, 101, 166, 254, 388, 568, 830, 1169, 1645, 2270, 3096, 4161, 5556, 7312, 9572, 12402, 15962, 20386, 25851, 32595, 40850, 50938, 63148, 77979, 95773, 117231, 142777, 173387

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.

Formula

a(n) = A325534(n) - A325714(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]]>5&]]&, separable]
(* Peter J. C. Moses, May 08 2019 *)

Crossrefs

Cf. A000041, A325534.

Sequence in context: A328548 A294536 A325650 * A103924 A160647 A103925

Adjacent sequences: A325717 A325718 A325719 * A325721 A325722 A325723

Keyword

nonn,easy

Author

Clark Kimberling, May 19 2019

Status

approved