A325647 Number of separable partitions of n in which the number of distinct (repeatable) parts is 3.

0, 0, 0, 0, 0, 1, 2, 5, 9, 13, 21, 29, 39, 49, 68, 79, 101, 116, 145, 167, 196, 221, 262, 287, 335, 368, 412, 460, 512, 554, 617, 673, 723, 800, 865, 925, 1001, 1090, 1140, 1250, 1317, 1418, 1493, 1619, 1665, 1828, 1884, 2022, 2098, 2275, 2308, 2520, 2564

Offset

1,7

Comments

A partition is separable if there is an ordering of its parts in which no consecutive parts are identical. See A325646 for a guide to related sequences.

Links

Table of n, a(n) for n=1..53.

Example

a(8) counts these 5 partitions:  [5,2,1], [4,3,1], [1,4,1,2], [2,3,2,1], [1,3,1,2,1].

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]]==3&]]&, separable]
(* Peter J. C. Moses, May 08 2019 *)

Crossrefs

Cf. A000041, A325334, A325646.

Sequence in context: A190713 A288347 A109094 * A367403 A049753 A331809

Adjacent sequences: A325644 A325645 A325646 * A325648 A325649 A325650

Keyword

nonn,easy

Author

Clark Kimberling, May 16 2019

Status

approved