A325648 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, 1, 2, 5, 10, 19, 28, 48, 69, 102, 138, 190, 254, 331, 420, 534, 662, 818, 1003, 1192, 1438, 1700, 2011, 2334, 2746, 3127, 3625, 4132, 4728, 5311, 6066, 6737, 7624, 8446, 9476, 10437, 11648, 12731, 14133, 15421, 16991, 18461, 20286

Offset

1,11

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..51.

Example

a(11) counts these 2 partitions:  [4,1,3,2,1], [3,2,1,2,1,2].

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, A325646.

Sequence in context: A360811 A127297 A018739 * A325718 A011893 A132210

Adjacent sequences: A325645 A325646 A325647 * A325649 A325650 A325651

Keyword

nonn,easy

Author

Clark Kimberling, May 16 2019

Status

approved