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A325534 Number of separable partitions of n; see Comments. 102
1, 1, 2, 3, 5, 6, 10, 14, 19, 26, 37, 49, 66, 87, 116, 152, 198, 254, 329, 422, 536, 678, 858, 1077, 1349, 1681, 2089, 2587, 3193, 3927, 4820, 5897, 7191, 8749, 10623, 12861, 15535, 18724, 22518, 27029, 32373, 38697, 46174, 54998, 65382, 77601, 91950, 108777 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Definition: 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..48.

FORMULA

a(n) + A325535(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

Table[Length[Select[Map[Quotient[(1 + Length[#]), Max[Map[Length, Split[#]]]] &,

IntegerPartitions[nn]], # > 1 &]], {nn, 50}]  (* Peter J. C. Moses, May 07 2019 *)

CROSSREFS

Cf. A000041, A325535.

Sequence in context: A325713 A325714 A325715 * A280013 A039840 A039845

Adjacent sequences:  A325531 A325532 A325533 * A325535 A325536 A325537

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, May 08 2019

STATUS

approved

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Last modified January 22 00:08 EST 2022. Contains 350481 sequences. (Running on oeis4.)