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A325647 Number of separable partitions of n in which the number of distinct (repeatable) parts is 3. 1
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 (list; graph; refs; listen; history; text; internal format)
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 * A049753 A331809 A126326

Adjacent sequences:  A325644 A325645 A325646 * A325648 A325649 A325650

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, May 16 2019

STATUS

approved

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Last modified July 13 16:22 EDT 2020. Contains 335688 sequences. (Running on oeis4.)