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 A325334 Number of integer partitions of n with adjusted frequency depth 3 whose parts cover an initial interval of positive integers. 10
 0, 0, 0, 1, 0, 0, 2, 0, 0, 1, 1, 0, 2, 0, 0, 2, 0, 0, 2, 0, 1, 2, 0, 0, 2, 0, 0, 1, 1, 0, 4, 0, 0, 1, 0, 0, 3, 0, 0, 1, 1, 0, 3, 0, 0, 3, 0, 0, 2, 0, 1, 1, 0, 0, 2, 1, 1, 1, 0, 0, 4, 0, 0, 2, 0, 0, 3, 0, 0, 1, 1, 0, 3, 0, 0, 2, 0, 0, 3, 0, 1, 1, 0, 0, 4, 0, 0 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,7 COMMENTS The adjusted frequency depth of an integer partition (A325280) is 0 if the partition is empty, and otherwise it is 1 plus the number of times one must take the multiset of multiplicities to reach a singleton. For example, the partition (32211) has adjusted frequency depth 5 because we have: (32211) -> (221) -> (21) -> (11) -> (2). The Heinz numbers of these partitions are given by A325374. LINKS FORMULA a(n) = A007862(n) - 1. EXAMPLE The first 30 terms count the following partitions:    3: (21)    6: (321)    6: (2211)    9: (222111)   10: (4321)   12: (332211)   12: (22221111)   15: (54321)   15: (2222211111)   18: (333222111)   18: (222222111111)   20: (44332211)   21: (654321)   21: (22222221111111)   24: (333322221111)   24: (2222222211111111)   27: (222222222111111111)   28: (7654321)   30: (5544332211)   30: (444333222111)   30: (333332222211111)   30: (22222222221111111111) MATHEMATICA normQ[m_]:=Or[m=={}, Union[m]==Range[Max[m]]]; unifQ[m_]:=SameQ@@Length/@Split[m]; Table[Length[Select[IntegerPartitions[n], normQ[#]&&!SameQ@@#&&unifQ[#]&]], {n, 0, 30}] CROSSREFS Column k = 3 of A325336. Cf. A007862, A181819, A182850, A320348, A323014, A325245, A325280, A325326, A325335, A325374. Sequence in context: A151843 A276422 A323069 * A280287 A147696 A001842 Adjacent sequences:  A325331 A325332 A325333 * A325335 A325336 A325337 KEYWORD nonn AUTHOR Gus Wiseman, May 01 2019 STATUS approved

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Last modified October 29 18:30 EDT 2020. Contains 338067 sequences. (Running on oeis4.)