A325718 Number of separable partitions of n in which the number of distinct (repeatable) parts is > 3.

0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 5, 10, 19, 29, 50, 74, 112, 158, 225, 311, 424, 564, 751, 979, 1273, 1638, 2082, 2640, 3323, 4159, 5171, 6419, 7895, 9707, 11872, 14481, 17573, 21319, 25709, 30997, 37205, 44619, 53304, 63646, 75698, 89998, 106664, 126306

Offset

1,11

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..49.

Formula

a(n) = A325534(n) - A325712(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]]>3&]]&, separable]
(* Peter J. C. Moses, May 08 2019 *)

Crossrefs

Cf. A000041, A325534.

Sequence in context: A127297 A018739 A325648 * A011893 A132210 A000098

Adjacent sequences: A325715 A325716 A325717 * A325719 A325720 A325721

Keyword

nonn,easy

Author

Clark Kimberling, May 17 2019

Status

approved