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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 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.)