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 A325252 Number of integer partitions of n with frequency depth floor(sqrt(n)). 1
 1, 1, 1, 1, 2, 1, 3, 1, 3, 8, 11, 11, 19, 17, 25, 29, 83, 113, 124, 171, 190, 242, 289, 368, 399, 796, 981, 1182, 1442, 1709, 2096, 2469, 2990, 3545, 4276, 5037, 8417, 10466, 12824, 15721, 19104, 23267, 27981, 33856, 40515, 48508, 57826, 68982, 81493, 446, 738 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS The adjusted frequency depth of an integer partition 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). LINKS EXAMPLE The a(2) = 1 through a(12) = 19 partitions (A = 10, B = 11):   2  3  22    11111  33      1111111  44        54      64    65    75         1111         222              2222      63      73    74    84                      111111           11111111  72      82    83    93                                                 81      91    92    A2                                                 432     532   A1    B1                                                 531     541   542   543                                                 621     631   632   642                                                 222111  721   641   651                                                         3322  731   732                                                         4321  821   741                                                         4411  5321  831                                                                     921                                                                     4422                                                                     5421                                                                     5511                                                                     6321                                                                     332211                                                                     333111                                                                     22221111 MATHEMATICA fdadj[ptn_List]:=If[ptn=={}, 0, Length[NestWhileList[Sort[Length/@Split[#1]]&, ptn, Length[#1]>1&]]]; Table[Length[Select[IntegerPartitions[n], fdadj[#]==Floor[Sqrt[n]]&]], {n, 0, 30}] CROSSREFS Cf. A117571, A181819, A225485, A323014, A323023, A325245, A325246, A325253, A325258, A325271, A325278, A325280, A325282. Sequence in context: A308673 A324287 A213594 * A243334 A234809 A135591 Adjacent sequences:  A325249 A325250 A325251 * A325253 A325254 A325255 KEYWORD nonn AUTHOR Gus Wiseman, Apr 22 2019 STATUS approved

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Last modified January 19 15:37 EST 2020. Contains 331049 sequences. (Running on oeis4.)