

A325535


Number of inseparable partitions of n; see Comments.


1



0, 1, 1, 2, 2, 5, 5, 8, 11, 16, 19, 28, 35, 48, 60, 79, 99, 131, 161, 205, 256, 324, 397, 498, 609, 755, 921, 1131, 1372, 1677, 2022, 2452, 2952, 3561, 4260, 5116, 6102, 7291, 8667, 10309, 12210, 14477, 17087, 20177, 23752, 27957, 32804, 38496, 45049, 52704
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OFFSET

1,4


COMMENTS

Definitions: a partition is separable if there is an ordering of its parts in which no consecutive parts are identical; otherwise the partition is inseparable.


LINKS

Table of n, a(n) for n=1..50.


FORMULA

a(n ) + A324534(n) = A000041(n) = number of partitions of n.


EXAMPLE

For n=5, the partition 1+2+2 is separable as 2+1+2, and 2+1+1+1 is inseparable.


MATHEMATICA

u=Table[Length[Select[Map[Quotient[(1 + Length[#]), Max[Map[Length, Split[#]]]] &,
IntegerPartitions[nn]], # > 1 &]], {nn, 50}]
Table[PartitionsP[n]  u[[n]], {n, 1, Length[u]}]
(* Peter J. C. Moses, May 07 2019 *)


CROSSREFS

Cf. A000041, A325534.
Sequence in context: A222706 A240495 A304393 * A062405 A071181 A213675
Adjacent sequences: A325532 A325533 A325534 * A325536 A325537 A325538


KEYWORD

nonn,easy


AUTHOR

Clark Kimberling, May 08 2019


STATUS

approved



