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 A325244 Number of integer partitions of n with one fewer distinct multiplicities than distinct parts. 10
 0, 0, 0, 1, 1, 2, 3, 4, 7, 12, 16, 21, 33, 38, 50, 75, 87, 111, 150, 185, 244, 307, 373, 461, 585, 702, 856, 1043, 1255, 1498, 1822, 2143, 2565, 3064, 3607, 4251, 5064, 5920, 6953, 8174, 9503, 11064, 12927, 14921, 17320, 19986, 23067, 26485, 30499, 34894 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,6 COMMENTS For example, (32211) has two distinct multiplicities (1, 2) and three distinct parts (1, 2, 3) so is counted under a(9). The Heinz numbers of these partitions are given by A325259. LINKS EXAMPLE The a(3) = 1 through a(10) = 16 partitions:   (21)  (31)  (32)  (42)    (43)    (53)     (54)      (64)               (41)  (51)    (52)    (62)     (63)      (73)                     (2211)  (61)    (71)     (72)      (82)                             (3211)  (3221)   (81)      (91)                                     (3311)   (3321)    (3322)                                     (4211)   (4221)    (4411)                                     (32111)  (4311)    (5221)                                              (5211)    (5311)                                              (32211)   (6211)                                              (42111)   (32221)                                              (222111)  (33211)                                              (321111)  (42211)                                                        (43111)                                                        (52111)                                                        (421111)                                                        (3211111) MATHEMATICA Table[Length[Select[IntegerPartitions[n], Length[Union[#]]==Length[Union[Length/@Split[#]]]+1&]], {n, 0, 30}] CROSSREFS Cf. A008284, A071625, A090858, A098859, A116608, A117571, A127002, A325242, A325259, A325270. Sequence in context: A223578 A073147 A249578 * A217786 A228494 A292324 Adjacent sequences:  A325241 A325242 A325243 * A325245 A325246 A325247 KEYWORD nonn AUTHOR Gus Wiseman, Apr 15 2019 STATUS approved

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Last modified October 16 18:03 EDT 2019. Contains 328102 sequences. (Running on oeis4.)